repo
string | commit
string | message
string | diff
string |
|---|---|---|---|
jquery/sizzle
|
11767a18f778c8a237d4b055dc1c33db4e0e22de
|
Selector: Detect incorrect escape handling by old Firefox
|
diff --git a/dist/sizzle.js b/dist/sizzle.js
index f411ff8..db5ac77 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -1,1360 +1,1366 @@
/*!
* Sizzle CSS Selector Engine v2.3.5-pre
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
- * Date: 2019-07-02
+ * Date: 2019-08-20
*/
( function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ( {} ).hasOwnProperty,
arr = [],
pop = arr.pop,
pushNative = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[ i ] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
"ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5]
// or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
whitespace + "*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
"*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace +
"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
funescape = function( escape, nonHex ) {
var high = "0x" + escape.slice( 1 ) - 0x10000;
return nonHex ?
// Strip the backslash prefix from a non-hex escape sequence
nonHex :
// Replace a hexadecimal escape sequence with the encoded Unicode code point
// Support: IE <=11+
// For values outside the Basic Multilingual Plane (BMP), manually construct a
// surrogate pair
high < 0 ?
String.fromCharCode( high + 0x10000 ) :
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" +
ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
( arr = slice.call( preferredDoc.childNodes ) ),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
// eslint-disable-next-line no-unused-expressions
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
pushNative.apply( target, slice.call( els ) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( ( target[ j++ ] = els[ i++ ] ) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
// ID selector
if ( ( m = match[ 1 ] ) ) {
// Document context
if ( nodeType === 9 ) {
if ( ( elem = context.getElementById( m ) ) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && ( elem = newContext.getElementById( m ) ) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[ 2 ] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
// Support: IE 8 only
// Exclude object elements
( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( ( nid = context.getAttribute( "id" ) ) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", ( nid = expando ) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[ i ] = "#" + nid + " " + toSelector( groups[ i ] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return ( cache[ key + " " ] = value );
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement( "fieldset" );
try {
return !!fn( el );
} catch ( e ) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split( "|" ),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[ i ] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( ( cur = cur.nextSibling ) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return ( name === "input" || name === "button" ) && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction( function( argument ) {
argument = +argument;
return markFunction( function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
seed[ j ] = !( matches[ j ] = seed[ j ] );
}
}
} );
} );
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
var namespace = elem.namespaceURI,
docElem = ( elem.ownerDocument || elem ).documentElement;
// Support: IE <=8
// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
// https://bugs.jquery.com/ticket/4833
return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert( function( el ) {
el.className = "i";
return !el.getAttribute( "className" );
} );
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert( function( el ) {
el.appendChild( document.createComment( "" ) );
return !el.getElementsByTagName( "*" ).length;
} );
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert( function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
} );
// ID filter and find
if ( support.getById ) {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute( "id" ) === attrId;
};
};
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
var node = typeof elem.getAttributeNode !== "undefined" &&
elem.getAttributeNode( "id" );
return node && node.value === attrId;
};
};
// Support: IE 6 - 7 only
// getElementById is not reliable as a find shortcut
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var node, i, elems,
elem = context.getElementById( id );
if ( elem ) {
// Verify the id attribute
node = elem.getAttributeNode( "id" );
if ( node && node.value === id ) {
return [ elem ];
}
// Fall back on getElementsByName
elems = context.getElementsByName( id );
i = 0;
while ( ( elem = elems[ i++ ] ) ) {
node = elem.getAttributeNode( "id" );
if ( node && node.value === id ) {
return [ elem ];
}
}
}
return [];
}
};
}
// Tag
Expr.find[ "TAG" ] = support.getElementsByTagName ?
function( tag, context ) {
if ( typeof context.getElementsByTagName !== "undefined" ) {
return context.getElementsByTagName( tag );
// DocumentFragment nodes don't have gEBTN
} else if ( support.qsa ) {
return context.querySelectorAll( tag );
}
} :
function( tag, context ) {
var elem,
tmp = [],
i = 0,
// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
results = context.getElementsByTagName( tag );
// Filter out possible comments
if ( tag === "*" ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem.nodeType === 1 ) {
tmp.push( elem );
}
}
return tmp;
}
return results;
};
// Class
Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
return context.getElementsByClassName( className );
}
};
/* QSA/matchesSelector
---------------------------------------------------------------------- */
// QSA and matchesSelector support
// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
rbuggyMatches = [];
// qSa(:focus) reports false when true (Chrome 21)
// We allow this because of a bug in IE8/9 that throws an error
// whenever `document.activeElement` is accessed on an iframe
// So, we allow :focus to pass through QSA all the time to avoid the IE error
// See https://bugs.jquery.com/ticket/13378
rbuggyQSA = [];
if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
// Build QSA regex
// Regex strategy adopted from Diego Perini
assert( function( el ) {
// Select is set to empty string on purpose
// This is to test IE's treatment of not explicitly
// setting a boolean content attribute,
// since its presence should be enough
// https://bugs.jquery.com/ticket/12359
docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
"<select id='" + expando + "-\r\\' msallowcapture=''>" +
"<option selected=''></option></select>";
// Support: IE8, Opera 11-12.16
// Nothing should be selected when empty strings follow ^= or $= or *=
// The test attribute must be unknown in Opera but "safe" for WinRT
// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
}
// Support: IE8
// Boolean attributes and "value" are not treated correctly
if ( !el.querySelectorAll( "[selected]" ).length ) {
rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
}
// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
rbuggyQSA.push( "~=" );
}
// Webkit/Opera - :checked should return selected option elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
// IE8 throws error here and will not see later tests
if ( !el.querySelectorAll( ":checked" ).length ) {
rbuggyQSA.push( ":checked" );
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push( ".#.+[+~]" );
}
} );
assert( function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement( "input" );
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll( "[name=d]" ).length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
+ // Support: Firefox <=3.6 - 5 only
+ // Old Firefox doesn't throw on a badly-escaped identifier.
+ el.querySelectorAll( "\\\f" );
+ rbuggyQSA.push( "[\\r\\n\\f]" );
+
+ // Support: Opera 10 - 11 only
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll( "*,:x" );
rbuggyQSA.push( ",.*:" );
} );
}
if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector ) ) ) ) {
assert( function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
} );
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
) );
} :
function( a, b ) {
if ( b ) {
while ( ( b = b.parentNode ) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
// Choose the first element that is related to our preferred document
if ( a === document ||
a.ownerDocument === preferredDoc &&
contains( preferredDoc, a ) ) {
return -1;
}
if ( b === document ||
b.ownerDocument === preferredDoc &&
contains( preferredDoc, b ) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( ( cur = cur.parentNode ) ) {
ap.unshift( cur );
}
cur = b;
while ( ( cur = cur.parentNode ) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[ i ] === bp[ i ] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[ i ], bp[ i ] ) :
// Otherwise nodes in our document sort first
ap[ i ] === preferredDoc ? -1 :
bp[ i ] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch ( e ) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return ( sel + "" ).replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( ( node = elem[ i++ ] ) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[ 1 ] = match[ 1 ].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
match[ 5 ] || "" ).replace( runescape, funescape );
if ( match[ 2 ] === "~=" ) {
match[ 3 ] = " " + match[ 3 ] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[ 1 ] = match[ 1 ].toLowerCase();
if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[ 4 ] = +( match[ 4 ] ?
match[ 5 ] + ( match[ 6 ] || 1 ) :
2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
// other types prohibit arguments
} else if ( match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[ 6 ] && match[ 2 ];
if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[ 3 ] ) {
match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
( excess = tokenize( unquoted, true ) ) &&
// advance to the next closing parenthesis
( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
// excess is a negative index
match[ 0 ] = match[ 0 ].slice( 0, excess );
match[ 2 ] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() {
return true;
} :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
( pattern = new RegExp( "(^|" + whitespace +
")" + className + "(" + whitespace + "|$)" ) ) && classCache(
className, function( elem ) {
return pattern.test(
typeof elem.className === "string" && elem.className ||
typeof elem.getAttribute !== "undefined" &&
elem.getAttribute( "class" ) ||
""
);
} );
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
/* eslint-disable max-len */
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
/* eslint-enable max-len */
};
},
"CHILD": function( type, what, _argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
function( elem, _context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( ( node = node[ dir ] ) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
diff --git a/dist/sizzle.min.js b/dist/sizzle.min.js
index db8e8bb..dd8d4dd 100644
--- a/dist/sizzle.min.js
+++ b/dist/sizzle.min.js
@@ -1,3 +1,3 @@
/*! Sizzle v2.3.5-pre | (c) JS Foundation and other contributors | js.foundation */
-!function(e){var t,n,r,i,o,u,l,a,c,s,f,d,p,h,g,m,y,w,v,b="sizzle"+1*new Date,N=e.document,x=0,C=0,E=ae(),D=ae(),A=ae(),S=ae(),T=function(e,t){return e===t&&(f=!0),0},L={}.hasOwnProperty,I=[],q=I.pop,B=I.push,R=I.push,$=I.slice,k=function(e,t){for(var n=0,r=e.length;n<r;n++)if(e[n]===t)return n;return-1},H="checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",M="[\\x20\\t\\r\\n\\f]",P="(?:\\\\[\\da-fA-F]{1,6}"+M+"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",z="\\["+M+"*("+P+")(?:"+M+"*([*^$|!~]?=)"+M+"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|("+P+"))|)"+M+"*\\]",F=":("+P+")(?:\\((('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|((?:\\\\.|[^\\\\()[\\]]|"+z+")*)|.*)\\)|)",O=new RegExp(M+"+","g"),j=new RegExp("^"+M+"+|((?:^|[^\\\\])(?:\\\\.)*)"+M+"+$","g"),G=new RegExp("^"+M+"*,"+M+"*"),U=new RegExp("^"+M+"*([>+~]|"+M+")"+M+"*"),V=new RegExp(M+"|>"),X=new RegExp(F),J=new RegExp("^"+P+"$"),K={ID:new RegExp("^#("+P+")"),CLASS:new RegExp("^\\.("+P+")"),TAG:new RegExp("^("+P+"|[*])"),ATTR:new RegExp("^"+z),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\("+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\\)|)","i"),bool:new RegExp("^(?:"+H+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\("+M+"*((?:-\\d)?\\d*)"+M+"*\\)|)(?=[^-]|$)","i")},Q=/HTML$/i,W=/^(?:input|select|textarea|button)$/i,Y=/^h\d$/i,Z=/^[^{]+\{\s*\[native \w/,_=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\[\\da-fA-F]{1,6}"+M+"?|\\\\([^\\r\\n\\f])","g"),ne=function(e,t){var n="0x"+e.slice(1)-65536;return t||(n<0?String.fromCharCode(n+65536):String.fromCharCode(n>>10|55296,1023&n|56320))},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" 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\ No newline at end of file
diff --git a/src/sizzle.js b/src/sizzle.js
index 7841b98..b6c2837 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -337,1024 +337,1030 @@ function Sizzle( selector, context, results, seed ) {
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[ i ] = "#" + nid + " " + toSelector( groups[ i ] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return ( cache[ key + " " ] = value );
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement( "fieldset" );
try {
return !!fn( el );
} catch ( e ) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split( "|" ),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[ i ] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( ( cur = cur.nextSibling ) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return ( name === "input" || name === "button" ) && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction( function( argument ) {
argument = +argument;
return markFunction( function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
seed[ j ] = !( matches[ j ] = seed[ j ] );
}
}
} );
} );
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
var namespace = elem.namespaceURI,
docElem = ( elem.ownerDocument || elem ).documentElement;
// Support: IE <=8
// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
// https://bugs.jquery.com/ticket/4833
return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert( function( el ) {
el.className = "i";
return !el.getAttribute( "className" );
} );
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert( function( el ) {
el.appendChild( document.createComment( "" ) );
return !el.getElementsByTagName( "*" ).length;
} );
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert( function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
} );
// ID filter and find
if ( support.getById ) {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute( "id" ) === attrId;
};
};
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
var node = typeof elem.getAttributeNode !== "undefined" &&
elem.getAttributeNode( "id" );
return node && node.value === attrId;
};
};
// Support: IE 6 - 7 only
// getElementById is not reliable as a find shortcut
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var node, i, elems,
elem = context.getElementById( id );
if ( elem ) {
// Verify the id attribute
node = elem.getAttributeNode( "id" );
if ( node && node.value === id ) {
return [ elem ];
}
// Fall back on getElementsByName
elems = context.getElementsByName( id );
i = 0;
while ( ( elem = elems[ i++ ] ) ) {
node = elem.getAttributeNode( "id" );
if ( node && node.value === id ) {
return [ elem ];
}
}
}
return [];
}
};
}
// Tag
Expr.find[ "TAG" ] = support.getElementsByTagName ?
function( tag, context ) {
if ( typeof context.getElementsByTagName !== "undefined" ) {
return context.getElementsByTagName( tag );
// DocumentFragment nodes don't have gEBTN
} else if ( support.qsa ) {
return context.querySelectorAll( tag );
}
} :
function( tag, context ) {
var elem,
tmp = [],
i = 0,
// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
results = context.getElementsByTagName( tag );
// Filter out possible comments
if ( tag === "*" ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem.nodeType === 1 ) {
tmp.push( elem );
}
}
return tmp;
}
return results;
};
// Class
Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
return context.getElementsByClassName( className );
}
};
/* QSA/matchesSelector
---------------------------------------------------------------------- */
// QSA and matchesSelector support
// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
rbuggyMatches = [];
// qSa(:focus) reports false when true (Chrome 21)
// We allow this because of a bug in IE8/9 that throws an error
// whenever `document.activeElement` is accessed on an iframe
// So, we allow :focus to pass through QSA all the time to avoid the IE error
// See https://bugs.jquery.com/ticket/13378
rbuggyQSA = [];
if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
// Build QSA regex
// Regex strategy adopted from Diego Perini
assert( function( el ) {
// Select is set to empty string on purpose
// This is to test IE's treatment of not explicitly
// setting a boolean content attribute,
// since its presence should be enough
// https://bugs.jquery.com/ticket/12359
docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
"<select id='" + expando + "-\r\\' msallowcapture=''>" +
"<option selected=''></option></select>";
// Support: IE8, Opera 11-12.16
// Nothing should be selected when empty strings follow ^= or $= or *=
// The test attribute must be unknown in Opera but "safe" for WinRT
// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
}
// Support: IE8
// Boolean attributes and "value" are not treated correctly
if ( !el.querySelectorAll( "[selected]" ).length ) {
rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
}
// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
rbuggyQSA.push( "~=" );
}
// Webkit/Opera - :checked should return selected option elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
// IE8 throws error here and will not see later tests
if ( !el.querySelectorAll( ":checked" ).length ) {
rbuggyQSA.push( ":checked" );
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push( ".#.+[+~]" );
}
} );
assert( function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement( "input" );
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll( "[name=d]" ).length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
+ // Support: Firefox <=3.6 - 5 only
+ // Old Firefox doesn't throw on a badly-escaped identifier.
+ el.querySelectorAll( "\\\f" );
+ rbuggyQSA.push( "[\\r\\n\\f]" );
+
+ // Support: Opera 10 - 11 only
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll( "*,:x" );
rbuggyQSA.push( ",.*:" );
} );
}
if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector ) ) ) ) {
assert( function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
} );
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
) );
} :
function( a, b ) {
if ( b ) {
while ( ( b = b.parentNode ) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
// Choose the first element that is related to our preferred document
if ( a === document ||
a.ownerDocument === preferredDoc &&
contains( preferredDoc, a ) ) {
return -1;
}
if ( b === document ||
b.ownerDocument === preferredDoc &&
contains( preferredDoc, b ) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( ( cur = cur.parentNode ) ) {
ap.unshift( cur );
}
cur = b;
while ( ( cur = cur.parentNode ) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[ i ] === bp[ i ] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[ i ], bp[ i ] ) :
// Otherwise nodes in our document sort first
ap[ i ] === preferredDoc ? -1 :
bp[ i ] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch ( e ) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return ( sel + "" ).replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( ( node = elem[ i++ ] ) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[ 1 ] = match[ 1 ].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
match[ 5 ] || "" ).replace( runescape, funescape );
if ( match[ 2 ] === "~=" ) {
match[ 3 ] = " " + match[ 3 ] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[ 1 ] = match[ 1 ].toLowerCase();
if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[ 4 ] = +( match[ 4 ] ?
match[ 5 ] + ( match[ 6 ] || 1 ) :
2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
// other types prohibit arguments
} else if ( match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[ 6 ] && match[ 2 ];
if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[ 3 ] ) {
match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
( excess = tokenize( unquoted, true ) ) &&
// advance to the next closing parenthesis
( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
// excess is a negative index
match[ 0 ] = match[ 0 ].slice( 0, excess );
match[ 2 ] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() {
return true;
} :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
( pattern = new RegExp( "(^|" + whitespace +
")" + className + "(" + whitespace + "|$)" ) ) && classCache(
className, function( elem ) {
return pattern.test(
typeof elem.className === "string" && elem.className ||
typeof elem.getAttribute !== "undefined" &&
elem.getAttribute( "class" ) ||
""
);
} );
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
/* eslint-disable max-len */
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
/* eslint-enable max-len */
};
},
"CHILD": function( type, what, _argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
function( elem, _context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( ( node = node[ dir ] ) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
|
jquery/sizzle
|
b2b650b629192beaf419098c459411a65121f5a1
|
Selector: Allow whitespace after hex escapes in CSS identifiers
|
diff --git a/dist/sizzle.js b/dist/sizzle.js
index 5bd623a..f411ff8 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -1,677 +1,677 @@
/*!
* Sizzle CSS Selector Engine v2.3.5-pre
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
- * Date: 2019-05-29
+ * Date: 2019-07-02
*/
( function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ( {} ).hasOwnProperty,
arr = [],
pop = arr.pop,
pushNative = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[ i ] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
"ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
- // http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
- identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
+ // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+ identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+ "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5]
// or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
whitespace + "*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
"*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace +
"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
- runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace +
- ")|.)", "ig" ),
- funescape = function( _, escaped, escapedWhitespace ) {
- var high = "0x" + escaped - 0x10000;
-
- // NaN means non-codepoint
- // Support: Firefox<24
- // Workaround erroneous numeric interpretation of +"0x"
- return high !== high || escapedWhitespace ?
- escaped :
- high < 0 ?
+ runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+ funescape = function( escape, nonHex ) {
+ var high = "0x" + escape.slice( 1 ) - 0x10000;
- // BMP codepoint
- String.fromCharCode( high + 0x10000 ) :
+ return nonHex ?
+
+ // Strip the backslash prefix from a non-hex escape sequence
+ nonHex :
- // Supplemental Plane codepoint (surrogate pair)
+ // Replace a hexadecimal escape sequence with the encoded Unicode code point
+ // Support: IE <=11+
+ // For values outside the Basic Multilingual Plane (BMP), manually construct a
+ // surrogate pair
+ high < 0 ?
+ String.fromCharCode( high + 0x10000 ) :
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" +
ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
( arr = slice.call( preferredDoc.childNodes ) ),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
// eslint-disable-next-line no-unused-expressions
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
pushNative.apply( target, slice.call( els ) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( ( target[ j++ ] = els[ i++ ] ) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
// ID selector
if ( ( m = match[ 1 ] ) ) {
// Document context
if ( nodeType === 9 ) {
if ( ( elem = context.getElementById( m ) ) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && ( elem = newContext.getElementById( m ) ) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[ 2 ] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
// Support: IE 8 only
// Exclude object elements
( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( ( nid = context.getAttribute( "id" ) ) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", ( nid = expando ) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[ i ] = "#" + nid + " " + toSelector( groups[ i ] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return ( cache[ key + " " ] = value );
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement( "fieldset" );
try {
return !!fn( el );
} catch ( e ) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split( "|" ),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[ i ] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( ( cur = cur.nextSibling ) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return ( name === "input" || name === "button" ) && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction( function( argument ) {
argument = +argument;
return markFunction( function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
seed[ j ] = !( matches[ j ] = seed[ j ] );
}
}
} );
} );
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
var namespace = elem.namespaceURI,
docElem = ( elem.ownerDocument || elem ).documentElement;
// Support: IE <=8
// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
// https://bugs.jquery.com/ticket/4833
return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert( function( el ) {
el.className = "i";
return !el.getAttribute( "className" );
} );
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert( function( el ) {
el.appendChild( document.createComment( "" ) );
return !el.getElementsByTagName( "*" ).length;
} );
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert( function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
} );
// ID filter and find
if ( support.getById ) {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute( "id" ) === attrId;
};
};
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
diff --git a/dist/sizzle.min.js b/dist/sizzle.min.js
index 981dc1e..db8e8bb 100644
--- a/dist/sizzle.min.js
+++ b/dist/sizzle.min.js
@@ -1,3 +1,3 @@
/*! Sizzle v2.3.5-pre | (c) JS Foundation and other contributors | js.foundation */
-!function(e){var t,n,r,i,o,u,l,a,c,s,f,d,p,h,g,m,y,w,v,b="sizzle"+1*new Date,N=e.document,x=0,C=0,E=ae(),D=ae(),S=ae(),A=ae(),T=function(e,t){return e===t&&(f=!0),0},L={}.hasOwnProperty,I=[],q=I.pop,B=I.push,R=I.push,$=I.slice,k=function(e,t){for(var n=0,r=e.length;n<r;n++)if(e[n]===t)return n;return-1},H="checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",M="[\\x20\\t\\r\\n\\f]",P="(?:\\\\.|[\\w-]|[^\0-\\xa0])+",z="\\["+M+"*("+P+")(?:"+M+"*([*^$|!~]?=)"+M+"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|("+P+"))|)"+M+"*\\]",F=":("+P+")(?:\\((('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|((?:\\\\.|[^\\\\()[\\]]|"+z+")*)|.*)\\)|)",O=new RegExp(M+"+","g"),j=new RegExp("^"+M+"+|((?:^|[^\\\\])(?:\\\\.)*)"+M+"+$","g"),G=new RegExp("^"+M+"*,"+M+"*"),U=new RegExp("^"+M+"*([>+~]|"+M+")"+M+"*"),V=new RegExp(M+"|>"),X=new RegExp(F),J=new RegExp("^"+P+"$"),K={ID:new RegExp("^#("+P+")"),CLASS:new RegExp("^\\.("+P+")"),TAG:new RegExp("^("+P+"|[*])"),ATTR:new RegExp("^"+z),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\("+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\\)|)","i"),bool:new RegExp("^(?:"+H+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\("+M+"*((?:-\\d)?\\d*)"+M+"*\\)|)(?=[^-]|$)","i")},Q=/HTML$/i,W=/^(?:input|select|textarea|button)$/i,Y=/^h\d$/i,Z=/^[^{]+\{\s*\[native \w/,_=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\([\\da-f]{1,6}"+M+"?|("+M+")|.)","ig"),ne=function(e,t,n){var r="0x"+t-65536;return r!==r||n?t:r<0?String.fromCharCode(r+65536):String.fromCharCode(r>>10|55296,1023&r|56320)},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" 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\ No newline at end of file
diff --git a/src/sizzle.js b/src/sizzle.js
index 2bb9065..7841b98 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -1,677 +1,677 @@
/*!
* Sizzle CSS Selector Engine v@VERSION
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
* Date: @DATE
*/
( function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ( {} ).hasOwnProperty,
arr = [],
pop = arr.pop,
pushNative = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[ i ] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
"ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
- // http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
- identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
+ // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+ identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+ "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5]
// or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
whitespace + "*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
"*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace +
"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
- runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace +
- ")|.)", "ig" ),
- funescape = function( _, escaped, escapedWhitespace ) {
- var high = "0x" + escaped - 0x10000;
-
- // NaN means non-codepoint
- // Support: Firefox<24
- // Workaround erroneous numeric interpretation of +"0x"
- return high !== high || escapedWhitespace ?
- escaped :
- high < 0 ?
+ runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+ funescape = function( escape, nonHex ) {
+ var high = "0x" + escape.slice( 1 ) - 0x10000;
- // BMP codepoint
- String.fromCharCode( high + 0x10000 ) :
+ return nonHex ?
+
+ // Strip the backslash prefix from a non-hex escape sequence
+ nonHex :
- // Supplemental Plane codepoint (surrogate pair)
+ // Replace a hexadecimal escape sequence with the encoded Unicode code point
+ // Support: IE <=11+
+ // For values outside the Basic Multilingual Plane (BMP), manually construct a
+ // surrogate pair
+ high < 0 ?
+ String.fromCharCode( high + 0x10000 ) :
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" +
ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
( arr = slice.call( preferredDoc.childNodes ) ),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
// eslint-disable-next-line no-unused-expressions
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
pushNative.apply( target, slice.call( els ) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( ( target[ j++ ] = els[ i++ ] ) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
// ID selector
if ( ( m = match[ 1 ] ) ) {
// Document context
if ( nodeType === 9 ) {
if ( ( elem = context.getElementById( m ) ) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && ( elem = newContext.getElementById( m ) ) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[ 2 ] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
// Support: IE 8 only
// Exclude object elements
( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( ( nid = context.getAttribute( "id" ) ) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", ( nid = expando ) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[ i ] = "#" + nid + " " + toSelector( groups[ i ] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return ( cache[ key + " " ] = value );
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement( "fieldset" );
try {
return !!fn( el );
} catch ( e ) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split( "|" ),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[ i ] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( ( cur = cur.nextSibling ) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return ( name === "input" || name === "button" ) && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction( function( argument ) {
argument = +argument;
return markFunction( function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
seed[ j ] = !( matches[ j ] = seed[ j ] );
}
}
} );
} );
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
var namespace = elem.namespaceURI,
docElem = ( elem.ownerDocument || elem ).documentElement;
// Support: IE <=8
// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
// https://bugs.jquery.com/ticket/4833
return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert( function( el ) {
el.className = "i";
return !el.getAttribute( "className" );
} );
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert( function( el ) {
el.appendChild( document.createComment( "" ) );
return !el.getElementsByTagName( "*" ).length;
} );
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert( function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
} );
// ID filter and find
if ( support.getById ) {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute( "id" ) === attrId;
};
};
Expr.find[ "ID" ] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter[ "ID" ] = function( id ) {
var attrId = id.replace( runescape, funescape );
diff --git a/test/unit/selector.js b/test/unit/selector.js
index 0e80f2f..729ea8c 100644
--- a/test/unit/selector.js
+++ b/test/unit/selector.js
@@ -1,1122 +1,1130 @@
QUnit.module( "selector", { beforeEach: setup } );
/*
======== testinit.js reference ========
See data/testinit.js
q(...);
Returns an array of elements with the given IDs
@example q("main", "foo", "bar") => [<div id="main">, <span id="foo">, <input id="bar">]
t( testName, selector, [ "array", "of", "ids" ] );
Asserts that a select matches the given IDs
@example t("Check for something", "//[a]", ["foo", "baar"]);
url( "some/url.php" );
Add random number to url to stop caching
@example url("data/test.html") => "data/test.html?10538358428943"
@example url("data/test.php?foo=bar") => "data/test.php?foo=bar&10538358345554"
*/
QUnit.test( "element", function( assert ) {
assert.expect( 35 );
var form, all, good, i, lengthtest, siblingTest, html;
assert.equal( Sizzle( "" ).length, 0, "Empty selector returns an empty array" );
assert.deepEqual( Sizzle( "div", document.createTextNode( "" ) ), [],
"Text element as context fails silently" );
form = document.getElementById( "form" );
assert.ok( !Sizzle.matchesSelector( form, "" ),
"Empty string passed to matchesSelector does not match" );
assert.equal( Sizzle( " " ).length, 0, "Empty selector returns an empty array" );
assert.equal( Sizzle( "\t" ).length, 0, "Empty selector returns an empty array" );
all = Sizzle( "*" );
assert.ok( all.length >= 30, "Select all" );
good = true;
for ( i = 0; i < all.length; i++ ) {
if ( all[ i ].nodeType === 8 ) {
good = false;
}
}
assert.ok( good, "Select all elements, no comment nodes" );
t( "Element Selector", "html", [ "html" ] );
t( "Element Selector", "body", [ "body" ] );
t( "Element Selector", "#qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Leading space", " #qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Leading tab", "\t#qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Leading carriage return", "\r#qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Leading line feed", "\n#qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Leading form feed", "\f#qunit-fixture p", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Trailing space", "#qunit-fixture p ", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Trailing tab", "#qunit-fixture p\t", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Trailing carriage return", "#qunit-fixture p\r",
[ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Trailing line feed", "#qunit-fixture p\n", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Trailing form feed", "#qunit-fixture p\f", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
assert.deepEqual(
jQuery( Sizzle( "div ol" ) ).filter( "#qunit-fixture *" ).get(),
q( "empty", "listWithTabIndex" ),
"Parent Element"
);
assert.deepEqual(
jQuery( Sizzle( "div\tol" ) ).filter( "#qunit-fixture *" ).get(),
q( "empty", "listWithTabIndex" ),
"Parent Element (non-space descendant combinator)"
);
// Check for unique-ness and sort order
assert.deepEqual( Sizzle( "p, div p" ), Sizzle( "p" ), "Check for duplicates: p, div p" );
jQuery( "<h1 id='h1'/><h2 id='h2'/><h2 id='h2-2'/>" ).prependTo( "#qunit-fixture" );
t( "Checking sort order", "#qunit-fixture h2, #qunit-fixture h1", [ "h1", "h2", "h2-2" ] );
t( "Checking sort order", "#qunit-fixture h2:first, #qunit-fixture h1:first", [ "h1", "h2" ] );
t( "Checking sort order", "#qunit-fixture p, #qunit-fixture p a",
[ "firstp", "simon1", "ap", "google", "groups", "anchor1", "mark", "sndp", "en", "yahoo",
"sap", "anchor2", "simon", "first" ] );
// Test Conflict ID
lengthtest = document.getElementById( "lengthtest" );
assert.deepEqual( Sizzle( "#idTest", lengthtest ), q( "idTest" ),
"Finding element with id of ID." );
assert.deepEqual( Sizzle( "[name='id']", lengthtest ), q( "idTest" ),
"Finding element with id of ID." );
assert.deepEqual( Sizzle( "input[id='idTest']", lengthtest ), q( "idTest" ),
"Finding elements with id of ID." );
siblingTest = document.getElementById( "siblingTest" );
assert.deepEqual( Sizzle( "div em", siblingTest ), [],
"Element-rooted QSA does not select based on document context" );
assert.deepEqual( Sizzle( "div em, div em, div em:not(div em)", siblingTest ), [],
"Element-rooted QSA does not select based on document context" );
assert.deepEqual( Sizzle( "div em, em\\,", siblingTest ), [],
"Escaped commas do not get treated with an id in element-rooted QSA" );
html = "";
for ( i = 0; i < 100; i++ ) {
html = "<div>" + html + "</div>";
}
html = jQuery( html ).appendTo( document.body );
assert.ok( !!Sizzle( "body div div div" ).length,
"No stack or performance problems with large amounts of descendants" );
assert.ok( !!Sizzle( "body>div div div" ).length,
"No stack or performance problems with large amounts of descendants" );
html.remove();
// Real use case would be using .watch in browsers with window.watch (see Issue #157)
q( "qunit-fixture" )[ 0 ].appendChild( document.createElement( "toString" ) ).id = "toString";
t( "Element name matches Object.prototype property", "toString#toString", [ "toString" ] );
} );
QUnit.test( "XML Document Selectors", function( assert ) {
var xml = createWithFriesXML();
assert.expect( 11 );
assert.equal( Sizzle( "foo_bar", xml ).length, 1, "Element Selector with underscore" );
assert.equal( Sizzle( ".component", xml ).length, 1, "Class selector" );
assert.equal( Sizzle( "[class*=component]", xml ).length, 1, "Attribute selector for class" );
assert.equal( Sizzle( "property[name=prop2]", xml ).length, 1, "Attribute selector with name" );
assert.equal( Sizzle( "[name=prop2]", xml ).length, 1, "Attribute selector with name" );
assert.equal( Sizzle( "#seite1", xml ).length, 1, "Attribute selector with ID" );
assert.equal( Sizzle( "component#seite1", xml ).length, 1, "Attribute selector with ID" );
assert.equal( Sizzle.matches( "#seite1", Sizzle( "component", xml ) ).length, 1,
"Attribute selector filter with ID" );
assert.equal( Sizzle( "meta property thing", xml ).length, 2,
"Descendent selector and dir caching" );
assert.ok( Sizzle.matchesSelector( xml.lastChild, "soap\\:Envelope" ),
"Check for namespaced element" );
xml = jQuery.parseXML( "<?xml version='1.0' encoding='UTF-8'?><root><elem id='1'/></root>" );
assert.equal( Sizzle( "elem:not(:has(*))", xml ).length, 1,
"Non-qSA path correctly handles numeric ids (jQuery #14142)" );
} );
QUnit.test( "broken", function( assert ) {
- assert.expect( 29 );
+ assert.expect( 30 );
var attrbad,
broken = function( name, selector ) {
assert.throws( function() {
// Setting context to null here somehow avoids QUnit's window.error handling
// making the e & e.message correct
// For whatever reason, without this,
// Sizzle.error will be called but no error will be seen in oldIE
Sizzle.call( null, selector );
}, function( e ) {
return e.message.indexOf( "Syntax error" ) >= 0;
}, name + ": " + selector );
};
broken( "Broken Selector", "[" );
broken( "Broken Selector", "(" );
broken( "Broken Selector", "{" );
broken( "Broken Selector", "<" );
broken( "Broken Selector", "()" );
broken( "Broken Selector", "<>" );
broken( "Broken Selector", "{}" );
broken( "Broken Selector", "," );
broken( "Broken Selector", ",a" );
broken( "Broken Selector", "a," );
+ broken( "Identifier with bad escape", "foo\\\fbaz" );
// Hangs on IE 9 if regular expression is inefficient
broken( "Broken Selector", "[id=012345678901234567890123456789" );
broken( "Doesn't exist", ":visble" );
broken( "Nth-child", ":nth-child" );
// Sigh again. IE 9 thinks this is also a real selector
// not super critical that we fix this case
//broken( "Nth-child", ":nth-child(-)" );
// Sigh. WebKit thinks this is a real selector in qSA
// They've already fixed this and it'll be coming into
// current browsers soon. Currently, Safari 5.0 still has this problem
// broken( "Nth-child", ":nth-child(asdf)", [] );
broken( "Nth-child", ":nth-child(2n+-0)" );
broken( "Nth-child", ":nth-child(2+0)" );
broken( "Nth-child", ":nth-child(- 1n)" );
broken( "Nth-child", ":nth-child(-1 n)" );
broken( "First-child", ":first-child(n)" );
broken( "Last-child", ":last-child(n)" );
broken( "Only-child", ":only-child(n)" );
broken( "Nth-last-last-child", ":nth-last-last-child(1)" );
broken( "First-last-child", ":first-last-child" );
broken( "Last-last-child", ":last-last-child" );
broken( "Only-last-child", ":only-last-child" );
// Make sure attribute value quoting works correctly. See: #6093
attrbad = jQuery( "<input type='hidden' value='2' name='foo.baz' id='attrbad1'/><input type='hidden' value='2' name='foo[baz]' id='attrbad2'/>" ).appendTo( "#qunit-fixture" );
broken( "Attribute equals non-value", "input[name=]" );
- broken( "Attribute equals unquoted non-identifer", "input[name=foo.baz]" );
- broken( "Attribute equals unquoted non-identifer", "input[name=foo[baz]]" );
+ broken( "Attribute equals unquoted non-identifier", "input[name=foo.baz]" );
+ broken( "Attribute equals unquoted non-identifier", "input[name=foo[baz]]" );
broken( "Attribute equals bad string", "input[name=''double-quoted'']" );
broken( "Attribute equals bad string", "input[name='apostrophe'd']" );
} );
QUnit.test( "id", function( assert ) {
assert.expect( 34 );
var fiddle, a;
t( "ID Selector", "#body", [ "body" ] );
t( "ID Selector w/ Element", "body#body", [ "body" ] );
t( "ID Selector w/ Element", "ul#first", [] );
t( "ID selector with existing ID descendant", "#firstp #simon1", [ "simon1" ] );
t( "ID selector with non-existant descendant", "#firstp #foobar", [] );
t( "ID selector using UTF8", "#å°åTaÌibeÌi", [ "å°åTaÌibeÌi" ] );
t( "Multiple ID selectors using UTF8", "#å°åTaÌibeÌi, #å°å", [ "å°åTaÌibeÌi", "å°å" ] );
t( "Descendant ID selector using UTF8", "div #å°å", [ "å°å" ] );
t( "Child ID selector using UTF8", "form > #å°å", [ "å°å" ] );
t( "Escaped ID", "#foo\\:bar", [ "foo:bar" ] );
t( "Escaped ID with descendant", "#foo\\:bar span:not(:input)", [ "foo_descendant" ] );
t( "Escaped ID", "#test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
t( "Descendant escaped ID", "div #foo\\:bar", [ "foo:bar" ] );
t( "Descendant escaped ID", "div #test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
t( "Child escaped ID", "form > #foo\\:bar", [ "foo:bar" ] );
t( "Child escaped ID", "form > #test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
fiddle = jQuery( "<div id='fiddle\\Foo'><span id='fiddleSpan'></span></div>" )
.appendTo( "#qunit-fixture" );
assert.deepEqual( Sizzle( "> span", Sizzle( "#fiddle\\\\Foo" )[ 0 ] ), q( [ "fiddleSpan" ] ),
"Escaped ID as context" );
fiddle.remove();
t( "ID Selector, child ID present", "#form > #radio1", [ "radio1" ] ); // bug #267
t( "ID Selector, not an ancestor ID", "#form #first", [] );
t( "ID Selector, not a child ID", "#form > #option1a", [] );
t( "All Children of ID", "#foo > *", [ "sndp", "en", "sap" ] );
t( "All Children of ID with no children", "#firstUL > *", [] );
assert.equal( Sizzle( "#tName1" )[ 0 ].id, "tName1",
"ID selector with same value for a name attribute" );
t( "ID selector non-existing but name attribute on an A tag", "#tName2", [] );
t( "Leading ID selector non-existing but name attribute on an A tag", "#tName2 span", [] );
t( "Leading ID selector existing, retrieving the child", "#tName1 span", [ "tName1-span" ] );
assert.equal( Sizzle( "div > div #tName1" )[ 0 ].id, Sizzle( "#tName1-span" )[ 0 ].parentNode.id,
"Ending with ID" );
a = jQuery( "<a id='backslash\\foo'></a>" ).appendTo( "#qunit-fixture" );
t( "ID Selector contains backslash", "#backslash\\\\foo", [ "backslash\\foo" ] );
t( "ID Selector on Form with an input that has a name of 'id'", "#lengthtest", [ "lengthtest" ] );
t( "ID selector with non-existant ancestor", "#asdfasdf #foobar", [] ); // bug #986
assert.deepEqual( Sizzle( "div#form", document.body ), [],
"ID selector within the context of another element" );
t( "Underscore ID", "#types_all", [ "types_all" ] );
t( "Dash ID", "#qunit-fixture", [ "qunit-fixture" ] );
t( "ID with weird characters in it", "#name\\+value", [ "name+value" ] );
} );
QUnit.test( "class", function( assert ) {
assert.expect( 27 );
t( "Class Selector", ".blog", [ "mark", "simon" ] );
t( "Class Selector", ".GROUPS", [ "groups" ] );
t( "Class Selector", ".blog.link", [ "simon" ] );
t( "Class Selector w/ Element", "a.blog", [ "mark", "simon" ] );
t( "Parent Class Selector", "p .blog", [ "mark", "simon" ] );
t( "Class selector using UTF8", ".å°åTaÌibeÌi", [ "utf8class1" ] );
//t( "Class selector using UTF8", ".å°å", ["utf8class1","utf8class2"] );
t( "Class selector using UTF8", ".å°åTaÌibeÌi.å°å", [ "utf8class1" ] );
t( "Class selector using UTF8", ".å°åTaÌibeÌi, .å°å", [ "utf8class1", "utf8class2" ] );
t( "Descendant class selector using UTF8", "div .å°åTaÌibeÌi", [ "utf8class1" ] );
t( "Child class selector using UTF8", "form > .å°åTaÌibeÌi", [ "utf8class1" ] );
t( "Escaped Class", ".foo\\:bar", [ "foo:bar" ] );
t( "Escaped Class", ".test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
t( "Descendant escaped Class", "div .foo\\:bar", [ "foo:bar" ] );
t( "Descendant escaped Class", "div .test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
t( "Child escaped Class", "form > .foo\\:bar", [ "foo:bar" ] );
t( "Child escaped Class", "form > .test\\.foo\\[5\\]bar", [ "test.foo[5]bar" ] );
var div = document.createElement( "div" );
div.innerHTML = "<div class='test e'></div><div class='test'></div>";
assert.deepEqual( Sizzle( ".e", div ), [ div.firstChild ], "Finding a second class." );
div.lastChild.className = "e";
assert.deepEqual( Sizzle( ".e", div ), [ div.firstChild, div.lastChild ],
"Finding a modified class." );
assert.ok( !Sizzle.matchesSelector( div, ".null" ),
".null does not match an element with no class" );
assert.ok( !Sizzle.matchesSelector( div.firstChild, ".null div" ),
".null does not match an element with no class" );
div.className = "null";
assert.ok( Sizzle.matchesSelector( div, ".null" ), ".null matches element with class 'null'" );
assert.ok( Sizzle.matchesSelector( div.firstChild, ".null div" ),
"caching system respects DOM changes" );
assert.ok( !Sizzle.matchesSelector( document, ".foo" ),
"testing class on document doesn't error" );
assert.ok( !Sizzle.matchesSelector( window, ".foo" ), "testing class on window doesn't error" );
div.lastChild.className += " hasOwnProperty toString";
assert.deepEqual( Sizzle( ".e.hasOwnProperty.toString", div ), [ div.lastChild ],
"Classes match Object.prototype properties" );
div = jQuery( "<div><svg width='200' height='250' version='1.1'" +
" xmlns='http://www.w3.org/2000/svg'><rect x='10' y='10' width='30' height='30'" +
"class='foo'></rect></svg></div>" )[ 0 ];
assert.equal( Sizzle( ".foo", div ).length, 1, "Class selector against SVG container" );
// Support: IE <=7
// Test SVG selection only if SVG works
if ( div.firstChild.firstChild ) {
assert.equal( Sizzle( ".foo", div.firstChild ).length, 1,
"Class selector directly against SVG" );
} else {
assert.ok( true, "SVG not supported" );
}
} );
QUnit.test( "name", function( assert ) {
assert.expect( 14 );
var form;
t( "Name selector", "input[name=action]", [ "text1" ] );
t( "Name selector with single quotes", "input[name='action']", [ "text1" ] );
t( "Name selector with double quotes", "input[name=\"action\"]", [ "text1" ] );
t( "Name selector non-input", "[name=example]", [ "name-is-example" ] );
t( "Name selector non-input", "[name=div]", [ "name-is-div" ] );
t( "Name selector non-input", "*[name=iframe]", [ "iframe" ] );
t( "Name selector for grouped input", "input[name='types[]']", [ "types_all", "types_anime", "types_movie" ] );
form = document.getElementById( "form" );
assert.deepEqual( Sizzle( "input[name=action]", form ), q( "text1" ),
"Name selector within the context of another element" );
assert.deepEqual( Sizzle( "input[name='foo[bar]']", form ), q( "hidden2" ),
"Name selector for grouped form element within the context of another element" );
form = jQuery( "<form><input name='id'/></form>" ).appendTo( "body" );
assert.equal( Sizzle( "input", form[ 0 ] ).length, 1,
"Make sure that rooted queries on forms (with possible expandos) work." );
form.remove();
t( "Find elements that have similar IDs", "[name=tName1]", [ "tName1ID" ] );
t( "Find elements that have similar IDs", "[name=tName2]", [ "tName2ID" ] );
t( "Find elements that have similar IDs", "#tName2ID", [ "tName2ID" ] );
t( "Case-sensitivity", "[name=tname1]", [] );
} );
QUnit.test( "multiple", function( assert ) {
assert.expect( 6 );
jQuery( "#qunit-fixture" ).prepend( "<h2 id='h2'/>" );
t( "Comma Support", "#qunit-fixture h2, #qunit-fixture p",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Comma Support", "#qunit-fixture h2 , #qunit-fixture p",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Comma Support", "#qunit-fixture h2 , #qunit-fixture p",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Comma Support", "#qunit-fixture h2,#qunit-fixture p",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Comma Support", "#qunit-fixture h2,#qunit-fixture p ",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Comma Support", "#qunit-fixture h2\t,\r#qunit-fixture p\n",
[ "h2", "firstp", "ap", "sndp", "en", "sap", "first" ] );
} );
QUnit.test( "child and adjacent", function( assert ) {
assert.expect( 43 );
var siblingFirst, en, nothiddendiv;
t( "Child", "p > a", [ "simon1", "google", "groups", "mark", "yahoo", "simon" ] );
t( "Child minus whitespace", "p>a", [ "simon1", "google", "groups", "mark", "yahoo", "simon" ] );
t( "Child minus trailing whitespace", "p> a",
[ "simon1", "google", "groups", "mark", "yahoo", "simon" ] );
t( "Child minus leading whitespace", "p >a",
[ "simon1", "google", "groups", "mark", "yahoo", "simon" ] );
t( "Child w/ Class", "p > a.blog", [ "mark", "simon" ] );
t( "All Children", "code > *", [ "anchor1", "anchor2" ] );
t( "All Grandchildren", "p > * > *", [ "anchor1", "anchor2" ] );
t( "Rooted tag adjacent", "#qunit-fixture a + a", [ "groups", "tName2ID" ] );
t( "Rooted tag adjacent minus whitespace", "#qunit-fixture a+a", [ "groups", "tName2ID" ] );
t( "Rooted tag adjacent minus leading whitespace", "#qunit-fixture a +a",
[ "groups", "tName2ID" ] );
t( "Rooted tag adjacent minus trailing whitespace", "#qunit-fixture a+ a",
[ "groups", "tName2ID" ] );
t( "Tag adjacent", "p + p", [ "ap", "en", "sap" ] );
t( "#id adjacent", "#firstp + p", [ "ap" ] );
t( "Tag#id adjacent", "p#firstp + p", [ "ap" ] );
t( "Tag[attr] adjacent", "p[lang=en] + p", [ "sap" ] );
t( "Tag.class adjacent", "a.GROUPS + code + a", [ "mark" ] );
t( "Comma, Child, and Adjacent", "#qunit-fixture a + a, code > a",
[ "groups", "anchor1", "anchor2", "tName2ID" ] );
t( "Element Preceded By", "#qunit-fixture p ~ div",
[ "foo", "nothiddendiv", "moretests", "tabindex-tests", "liveHandlerOrder", "siblingTest" ] );
t( "Element Preceded By", "#first ~ div",
[ "moretests", "tabindex-tests", "liveHandlerOrder", "siblingTest" ] );
t( "Element Preceded By", "#groups ~ a", [ "mark" ] );
t( "Element Preceded By", "#length ~ input", [ "idTest" ] );
t( "Element Preceded By", "#siblingfirst ~ em", [ "siblingnext", "siblingthird" ] );
t( "Element Preceded By (multiple)", "#siblingTest em ~ em ~ em ~ span", [ "siblingspan" ] );
t( "Element Preceded By, Containing", "#liveHandlerOrder ~ div em:contains('1')",
[ "siblingfirst" ] );
siblingFirst = document.getElementById( "siblingfirst" );
assert.deepEqual( Sizzle( "~ em", siblingFirst ), q( "siblingnext", "siblingthird" ),
"Element Preceded By with a context." );
assert.deepEqual( Sizzle( "+ em", siblingFirst ), q( "siblingnext" ),
"Element Directly Preceded By with a context." );
assert.deepEqual( Sizzle( "~ em:first", siblingFirst ), q( "siblingnext" ),
"Element Preceded By positional with a context." );
en = document.getElementById( "en" );
assert.deepEqual( Sizzle( "+ p, a", en ), q( "yahoo", "sap" ),
"Compound selector with context, beginning with sibling test." );
assert.deepEqual( Sizzle( "a, + p", en ), q( "yahoo", "sap" ),
"Compound selector with context, containing sibling test." );
t( "Multiple combinators selects all levels", "#siblingTest em *",
[ "siblingchild", "siblinggrandchild", "siblinggreatgrandchild" ] );
t( "Multiple combinators selects all levels", "#siblingTest > em *",
[ "siblingchild", "siblinggrandchild", "siblinggreatgrandchild" ] );
t( "Multiple sibling combinators doesn't miss general siblings",
"#siblingTest > em:first-child + em ~ span",
[ "siblingspan" ] );
t( "Combinators are not skipped when mixing general and specific",
"#siblingTest > em:contains('x') + em ~ span",
[] );
assert.equal( Sizzle( "#listWithTabIndex" ).length, 1,
"Parent div for next test is found via ID (#8310)" );
assert.equal( Sizzle( "#listWithTabIndex li:eq(2) ~ li" ).length, 1,
"Find by general sibling combinator (#8310)" );
assert.equal( Sizzle( "#__sizzle__" ).length, 0,
"Make sure the temporary id assigned by sizzle is cleared out (#8310)" );
assert.equal( Sizzle( "#listWithTabIndex" ).length, 1,
"Parent div for previous test is still found via ID (#8310)" );
t( "Verify deep class selector", "div.blah > p > a", [] );
t( "No element deep selector", "div.foo > span > a", [] );
nothiddendiv = document.getElementById( "nothiddendiv" );
assert.deepEqual( Sizzle( "> :first", nothiddendiv ), q( "nothiddendivchild" ),
"Verify child context positional selector" );
assert.deepEqual( Sizzle( "> :eq(0)", nothiddendiv ), q( "nothiddendivchild" ),
"Verify child context positional selector" );
assert.deepEqual( Sizzle( "> *:first", nothiddendiv ), q( "nothiddendivchild" ),
"Verify child context positional selector" );
t( "Non-existant ancestors", ".fototab > .thumbnails > a", [] );
} );
QUnit.test( "attributes - existence", function( assert ) {
assert.expect( 7 );
t( "on element", "#qunit-fixture a[title]", [ "google" ] );
t( "on element (whitespace ignored)", "#qunit-fixture a[ title ]", [ "google" ] );
t( "on element (case-insensitive)", "#qunit-fixture a[TITLE]", [ "google" ] );
t( "on any element", "#qunit-fixture *[title]", [ "google" ] );
t( "on implicit element", "#qunit-fixture [title]", [ "google" ] );
t( "boolean", "#select2 option[selected]", [ "option2d" ] );
t( "for attribute on label", "form label[for]", [ "label-for" ] );
} );
QUnit.test( "attributes - equals", function( assert ) {
assert.expect( 20 );
t( "identifier", "#qunit-fixture a[rel=bookmark]", [ "simon1" ] );
t( "identifier containing underscore", "input[id=types_all]", [ "types_all" ] );
t( "string", "#qunit-fixture a[rel='bookmark']", [ "simon1" ] );
t( "string (whitespace ignored)", "#qunit-fixture a[ rel = 'bookmark' ]", [ "simon1" ] );
t( "non-identifier string", "#qunit-fixture a[href='http://www.google.com/']", [ "google" ] );
t( "empty string", "#select1 option[value='']", [ "option1a" ] );
t( "number",
"#qunit-fixture option[value=1]",
[ "option1b", "option2b", "option3b", "option4b", "option5c" ] );
t( "negative number", "#qunit-fixture li[tabIndex=-1]", [ "foodWithNegativeTabIndex" ] );
t( "non-ASCII identifier", "span[lang=ä¸æ]", [ "å°å" ] );
t( "input[type=text]", "#form input[type=text]", [ "text1", "text2", "hidden2", "name" ] );
t( "input[type=search]", "#form input[type=search]", [ "search" ] );
t( "script[src] (jQuery #13777)", "#moretests script[src]", [ "script-src" ] );
t( "boolean attribute equals name", "#select2 option[selected='selected']", [ "option2d" ] );
t( "for attribute in form", "#form [for=action]", [ "label-for" ] );
t( "name attribute", "input[name='foo[bar]']", [ "hidden2" ] );
t( "value attribute", "input[value=Test]", [ "text1", "text2" ] );
assert.deepEqual(
Sizzle( "input[data-comma='0,1']" ),
q( "el12087" ),
"Without context, single-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma=\"0,1\"]" ),
q( "el12087" ),
"Without context, double-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma='0,1']", document.getElementById( "t12087" ) ),
q( "el12087" ),
"With context, single-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma=\"0,1\"]", document.getElementById( "t12087" ) ),
q( "el12087" ),
"With context, double-quoted attribute containing ','" );
} );
QUnit.test( "attributes - does not equal", function( assert ) {
assert.expect( 2 );
t( "string", "#ap a[hreflang!='en']", [ "google", "groups", "anchor1" ] );
t( "empty string", "#select1 option[value!='']", [ "option1b", "option1c", "option1d" ] );
} );
QUnit.test( "attributes - starts with", function( assert ) {
assert.expect( 4 );
// Support: IE<8
// There is apparently no way to bypass interpolation of the *originally-defined* href attribute
document.getElementById( "anchor2" ).href = "#2";
t( "string (whitespace ignored)", "a[href ^= 'http://www']", [ "google", "yahoo" ] );
t( "href starts with hash", "p a[href^='#']", [ "anchor2" ] );
t( "string containing '['", "input[name^='foo[']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name^='foo[bar]']", [ "hidden2" ] );
} );
QUnit.test( "attributes - contains", function( assert ) {
assert.expect( 4 );
t( "string (whitespace ignored)", "a[href *= 'google']", [ "google", "groups" ] );
t( "string starting with '[' ... ']'", "input[name*='[bar]']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name*='foo[bar]']", [ "hidden2" ] );
t( "href contains hash", "p a[href*='#']", [ "simon1", "anchor2" ] );
} );
QUnit.test( "attributes - ends with", function( assert ) {
assert.expect( 4 );
t( "string (whitespace ignored)", "a[href $= 'org/']", [ "mark" ] );
t( "string ending with ']'", "input[name$='bar]']", [ "hidden2" ] );
t( "string like '[' ... ']'", "input[name$='[bar]']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name$='foo[bar]']", [ "hidden2" ] );
} );
QUnit.test( "attributes - whitespace list includes", function( assert ) {
assert.expect( 3 );
t( "string found at the beginning",
"input[data-15233~='foo']",
[ "t15233-single", "t15233-double", "t15233-double-tab", "t15233-double-nl", "t15233-triple" ] );
t( "string found in the middle",
"input[data-15233~='bar']",
[ "t15233-double", "t15233-double-tab", "t15233-double-nl", "t15233-triple" ] );
t( "string found at the end", "input[data-15233~='baz']", [ "t15233-triple" ] );
} );
QUnit.test( "attributes - hyphen-prefix matches", function( assert ) {
assert.expect( 3 );
t( "string", "#names-group span[id|='name']", [ "name-is-example", "name-is-div" ] );
t( "string containing hyphen",
"#names-group span[id|='name-is']",
[ "name-is-example", "name-is-div" ] );
t( "string ending with hyphen", "#names-group span[id|='name-is-']", [] );
} );
QUnit.test( "attributes - special characters", function( assert ) {
- assert.expect( 13 );
+ assert.expect( 15 );
var attrbad,
div = document.createElement( "div" );
// #3279
div.innerHTML = "<div id='foo' xml:test='something'></div>";
assert.deepEqual( Sizzle( "[xml\\:test]", div ),
[ div.firstChild ],
"attribute name containing colon" );
// Make sure attribute value quoting works correctly. See jQuery #6093; #6428; #13894
// Use seeded results to bypass querySelectorAll optimizations
attrbad = jQuery(
"<input type='hidden' id='attrbad_space' name='foo bar'/>" +
"<input type='hidden' id='attrbad_dot' value='2' name='foo.baz'/>" +
"<input type='hidden' id='attrbad_brackets' value='2' name='foo[baz]'/>" +
+ "<input type='hidden' id='attrbad_leading_digits' name='agent' value='007'/>" +
"<input type='hidden' id='attrbad_injection' data-attr='foo_baz']'/>" +
"<input type='hidden' id='attrbad_quote' data-attr='''/>" +
"<input type='hidden' id='attrbad_backslash' data-attr='\'/>" +
"<input type='hidden' id='attrbad_backslash_quote' data-attr='\''/>" +
"<input type='hidden' id='attrbad_backslash_backslash' data-attr='\\'/>" +
"<input type='hidden' id='attrbad_unicode' data-attr='一'/>"
).appendTo( "#qunit-fixture" ).get();
assert.deepEqual( Sizzle( "input[name=foo\\ bar]", null, null, attrbad ),
q( "attrbad_space" ),
"identifier containing space" );
assert.deepEqual( Sizzle( "input[name=foo\\.baz]", null, null, attrbad ),
q( "attrbad_dot" ),
"identifier containing dot" );
assert.deepEqual( Sizzle( "input[name=foo\\[baz\\]]", null, null, attrbad ),
q( "attrbad_brackets" ),
"identifier containing brackets" );
assert.deepEqual( Sizzle( "input[data-attr='foo_baz\\']']", null, null, attrbad ),
q( "attrbad_injection" ),
"string containing quote and right bracket" );
+ assert.deepEqual( Sizzle( "input[value=\\30 \\30\\37 ]", null, null, attrbad ),
+ q( "attrbad_leading_digits" ),
+ "identifier containing escaped leading digits with whitespace termination" );
+ assert.deepEqual( Sizzle( "input[value=\\00003007]", null, null, attrbad ),
+ q( "attrbad_leading_digits" ),
+ "identifier containing escaped leading digits without whitespace termination" );
assert.deepEqual( Sizzle( "input[data-attr='\\'']", null, null, attrbad ),
q( "attrbad_quote" ),
"string containing quote" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\']", null, null, attrbad ),
q( "attrbad_backslash" ),
"string containing backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\\\'']", null, null, attrbad ),
q( "attrbad_backslash_quote" ),
"string containing backslash and quote" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing adjacent backslashes" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C \\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape-with-trailing-space backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C\t\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape-with-trailing-tab backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\04e00']", null, null, attrbad ),
q( "attrbad_unicode" ),
"Long numeric escape (BMP)" );
document.getElementById( "attrbad_unicode" ).setAttribute( "data-attr", "\uD834\uDF06A" );
// It was too much code to fix Safari 5.x Supplemental Plane crashes (see ba5f09fa404379a87370ec905ffa47f8ac40aaa3)
// assert.deepEqual( Sizzle( "input[data-attr='\\01D306A']", null, null, attrbad ),
// q( "attrbad_unicode" ),
// "Long numeric escape (non-BMP)" );
} );
QUnit.test( "attributes - other", function( assert ) {
assert.expect( 7 );
var div = document.getElementById( "foo" );
t( "Selector list with multiple quoted attribute-equals",
"#form input[type='radio'], #form input[type='hidden']",
[ "radio1", "radio2", "hidden1" ] );
t( "Selector list with differently-quoted attribute-equals",
"#form input[type='radio'], #form input[type=\"hidden\"]",
[ "radio1", "radio2", "hidden1" ] );
t( "Selector list with quoted and unquoted attribute-equals",
"#form input[type='radio'], #form input[type=hidden]",
[ "radio1", "radio2", "hidden1" ] );
t( "attribute name is Object.prototype property \"constructor\" (negative)",
"[constructor]",
[] );
t( "attribute name is Gecko Object.prototype property \"watch\" (negative)",
"[watch]",
[] );
div.setAttribute( "constructor", "foo" );
div.setAttribute( "watch", "bar" );
t( "attribute name is Object.prototype property \"constructor\"",
"[constructor='foo']",
[ "foo" ] );
t( "attribute name is Gecko Object.prototype property \"watch\"",
"[watch='bar']",
[ "foo" ] );
} );
QUnit.test( "pseudo - (parent|empty)", function( assert ) {
assert.expect( 3 );
t( "Empty", "#qunit-fixture ul:empty", [ "firstUL" ] );
t( "Empty with comment node", "#qunit-fixture ol:empty", [ "empty" ] );
t( "Is A Parent", "#qunit-fixture p:parent", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
} );
QUnit.test( "pseudo - (first|last|only)-(child|of-type)", function( assert ) {
assert.expect( 12 );
t( "First Child", "#qunit-fixture p:first-child", [ "firstp", "sndp" ] );
t( "First Child (leading id)", "#qunit-fixture p:first-child", [ "firstp", "sndp" ] );
t( "First Child (leading class)", ".nothiddendiv div:first-child", [ "nothiddendivchild" ] );
t( "First Child (case-insensitive)", "#qunit-fixture p:FIRST-CHILD", [ "firstp", "sndp" ] );
t( "Last Child", "#qunit-fixture p:last-child", [ "sap" ] );
t( "Last Child (leading id)", "#qunit-fixture a:last-child", [ "simon1", "anchor1", "mark", "yahoo", "anchor2", "simon", "liveLink1", "liveLink2" ] );
t( "Only Child", "#qunit-fixture a:only-child", [ "simon1", "anchor1", "yahoo", "anchor2", "liveLink1", "liveLink2" ] );
t( "First-of-type", "#qunit-fixture > p:first-of-type", [ "firstp" ] );
t( "Last-of-type", "#qunit-fixture > p:last-of-type", [ "first" ] );
t( "Only-of-type", "#qunit-fixture > :only-of-type", [ "name+value", "firstUL", "empty", "floatTest", "iframe", "table", "last" ] );
// Verify that the child position isn't being cached improperly
var secondChildren = jQuery( "p:nth-child(2)" ).before( "<div></div>" );
t( "No longer second child", "p:nth-child(2)", [] );
secondChildren.prev().remove();
t( "Restored second child", "p:nth-child(2)", [ "ap", "en" ] );
} );
QUnit.test( "pseudo - nth-child", function( assert ) {
assert.expect( 30 );
t( "Nth-child", "p:nth-child(1)", [ "firstp", "sndp" ] );
t( "Nth-child (with whitespace)", "p:nth-child( 1 )", [ "firstp", "sndp" ] );
t( "Nth-child (case-insensitive)", "#form select:first option:NTH-child(3)", [ "option1c" ] );
t( "Not nth-child", "#qunit-fixture p:not(:nth-child(1))", [ "ap", "en", "sap", "first" ] );
t( "Nth-child(2)", "#qunit-fixture form#form > *:nth-child(2)", [ "text1" ] );
t( "Nth-child(2)", "#qunit-fixture form#form > :nth-child(2)", [ "text1" ] );
t( "Nth-child(-1)", "#form select:first option:nth-child(-1)", [] );
t( "Nth-child(3)", "#form select:first option:nth-child(3)", [ "option1c" ] );
t( "Nth-child(0n+3)", "#form select:first option:nth-child(0n+3)", [ "option1c" ] );
t( "Nth-child(1n+0)", "#form select:first option:nth-child(1n+0)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-child(1n)", "#form select:first option:nth-child(1n)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-child(n)", "#form select:first option:nth-child(n)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-child(even)", "#form select:first option:nth-child(even)", [ "option1b", "option1d" ] );
t( "Nth-child(odd)", "#form select:first option:nth-child(odd)", [ "option1a", "option1c" ] );
t( "Nth-child(2n)", "#form select:first option:nth-child(2n)", [ "option1b", "option1d" ] );
t( "Nth-child(2n+1)", "#form select:first option:nth-child(2n+1)", [ "option1a", "option1c" ] );
t( "Nth-child(2n + 1)", "#form select:first option:nth-child(2n + 1)", [ "option1a", "option1c" ] );
t( "Nth-child(+2n + 1)", "#form select:first option:nth-child(+2n + 1)", [ "option1a", "option1c" ] );
t( "Nth-child(3n)", "#form select:first option:nth-child(3n)", [ "option1c" ] );
t( "Nth-child(3n+1)", "#form select:first option:nth-child(3n+1)", [ "option1a", "option1d" ] );
t( "Nth-child(3n+2)", "#form select:first option:nth-child(3n+2)", [ "option1b" ] );
t( "Nth-child(3n+3)", "#form select:first option:nth-child(3n+3)", [ "option1c" ] );
t( "Nth-child(3n-1)", "#form select:first option:nth-child(3n-1)", [ "option1b" ] );
t( "Nth-child(3n-2)", "#form select:first option:nth-child(3n-2)", [ "option1a", "option1d" ] );
t( "Nth-child(3n-3)", "#form select:first option:nth-child(3n-3)", [ "option1c" ] );
t( "Nth-child(3n+0)", "#form select:first option:nth-child(3n+0)", [ "option1c" ] );
t( "Nth-child(-1n+3)", "#form select:first option:nth-child(-1n+3)", [ "option1a", "option1b", "option1c" ] );
t( "Nth-child(-n+3)", "#form select:first option:nth-child(-n+3)", [ "option1a", "option1b", "option1c" ] );
t( "Nth-child(-1n + 3)", "#form select:first option:nth-child(-1n + 3)", [ "option1a", "option1b", "option1c" ] );
assert.deepEqual(
Sizzle( ":nth-child(n)", null, null, [ document.createElement( "a" ) ].concat( q( "ap" ) ) ),
q( "ap" ),
"Seeded nth-child"
);
} );
QUnit.test( "pseudo - nth-last-child", function( assert ) {
assert.expect( 30 );
jQuery( "#qunit-fixture" ).append( "<form id='nth-last-child-form'/><i/><i/><i/><i/>" );
t( "Nth-last-child", "form:nth-last-child(5)", [ "nth-last-child-form" ] );
t( "Nth-last-child (with whitespace)", "form:nth-last-child( 5 )", [ "nth-last-child-form" ] );
t( "Nth-last-child (case-insensitive)", "#form select:first option:NTH-last-child(3)", [ "option1b" ] );
t( "Not nth-last-child", "#qunit-fixture p:not(:nth-last-child(1))", [ "firstp", "ap", "sndp", "en", "first" ] );
t( "Nth-last-child(-1)", "#form select:first option:nth-last-child(-1)", [] );
t( "Nth-last-child(3)", "#form select:first :nth-last-child(3)", [ "option1b" ] );
t( "Nth-last-child(3)", "#form select:first *:nth-last-child(3)", [ "option1b" ] );
t( "Nth-last-child(3)", "#form select:first option:nth-last-child(3)", [ "option1b" ] );
t( "Nth-last-child(0n+3)", "#form select:first option:nth-last-child(0n+3)", [ "option1b" ] );
t( "Nth-last-child(1n+0)", "#form select:first option:nth-last-child(1n+0)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-last-child(1n)", "#form select:first option:nth-last-child(1n)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-last-child(n)", "#form select:first option:nth-last-child(n)", [ "option1a", "option1b", "option1c", "option1d" ] );
t( "Nth-last-child(even)", "#form select:first option:nth-last-child(even)", [ "option1a", "option1c" ] );
t( "Nth-last-child(odd)", "#form select:first option:nth-last-child(odd)", [ "option1b", "option1d" ] );
t( "Nth-last-child(2n)", "#form select:first option:nth-last-child(2n)", [ "option1a", "option1c" ] );
t( "Nth-last-child(2n+1)", "#form select:first option:nth-last-child(2n+1)", [ "option1b", "option1d" ] );
t( "Nth-last-child(2n + 1)", "#form select:first option:nth-last-child(2n + 1)", [ "option1b", "option1d" ] );
t( "Nth-last-child(+2n + 1)", "#form select:first option:nth-last-child(+2n + 1)", [ "option1b", "option1d" ] );
t( "Nth-last-child(3n)", "#form select:first option:nth-last-child(3n)", [ "option1b" ] );
t( "Nth-last-child(3n+1)", "#form select:first option:nth-last-child(3n+1)", [ "option1a", "option1d" ] );
t( "Nth-last-child(3n+2)", "#form select:first option:nth-last-child(3n+2)", [ "option1c" ] );
t( "Nth-last-child(3n+3)", "#form select:first option:nth-last-child(3n+3)", [ "option1b" ] );
t( "Nth-last-child(3n-1)", "#form select:first option:nth-last-child(3n-1)", [ "option1c" ] );
t( "Nth-last-child(3n-2)", "#form select:first option:nth-last-child(3n-2)", [ "option1a", "option1d" ] );
t( "Nth-last-child(3n-3)", "#form select:first option:nth-last-child(3n-3)", [ "option1b" ] );
t( "Nth-last-child(3n+0)", "#form select:first option:nth-last-child(3n+0)", [ "option1b" ] );
t( "Nth-last-child(-1n+3)", "#form select:first option:nth-last-child(-1n+3)", [ "option1b", "option1c", "option1d" ] );
t( "Nth-last-child(-n+3)", "#form select:first option:nth-last-child(-n+3)", [ "option1b", "option1c", "option1d" ] );
t( "Nth-last-child(-1n + 3)", "#form select:first option:nth-last-child(-1n + 3)", [ "option1b", "option1c", "option1d" ] );
QUnit.deepEqual(
Sizzle(
":nth-last-child(n)",
null,
null,
[ document.createElement( "a" ) ].concat( q( "ap" ) )
),
q( "ap" ),
"Seeded nth-last-child"
);
} );
QUnit.test( "pseudo - nth-of-type", function( assert ) {
assert.expect( 9 );
t( "Nth-of-type(-1)", ":nth-of-type(-1)", [] );
t( "Nth-of-type(3)", "#ap :nth-of-type(3)", [ "mark" ] );
t( "Nth-of-type(n)", "#ap :nth-of-type(n)", [ "google", "groups", "code1", "anchor1", "mark" ] );
t( "Nth-of-type(0n+3)", "#ap :nth-of-type(0n+3)", [ "mark" ] );
t( "Nth-of-type(2n)", "#ap :nth-of-type(2n)", [ "groups" ] );
t( "Nth-of-type(even)", "#ap :nth-of-type(even)", [ "groups" ] );
t( "Nth-of-type(2n+1)", "#ap :nth-of-type(2n+1)", [ "google", "code1", "anchor1", "mark" ] );
t( "Nth-of-type(odd)", "#ap :nth-of-type(odd)", [ "google", "code1", "anchor1", "mark" ] );
t( "Nth-of-type(-n+2)", "#qunit-fixture > :nth-of-type(-n+2)", [ "firstp", "ap", "foo", "nothiddendiv", "name+value", "firstUL", "empty", "form", "floatTest", "iframe", "lengthtest", "table", "last" ] );
} );
QUnit.test( "pseudo - nth-last-of-type", function( assert ) {
assert.expect( 9 );
t( "Nth-last-of-type(-1)", ":nth-last-of-type(-1)", [] );
t( "Nth-last-of-type(3)", "#ap :nth-last-of-type(3)", [ "google" ] );
t( "Nth-last-of-type(n)", "#ap :nth-last-of-type(n)", [ "google", "groups", "code1", "anchor1", "mark" ] );
t( "Nth-last-of-type(0n+3)", "#ap :nth-last-of-type(0n+3)", [ "google" ] );
t( "Nth-last-of-type(2n)", "#ap :nth-last-of-type(2n)", [ "groups" ] );
t( "Nth-last-of-type(even)", "#ap :nth-last-of-type(even)", [ "groups" ] );
t( "Nth-last-of-type(2n+1)", "#ap :nth-last-of-type(2n+1)", [ "google", "code1", "anchor1", "mark" ] );
t( "Nth-last-of-type(odd)", "#ap :nth-last-of-type(odd)", [ "google", "code1", "anchor1", "mark" ] );
t( "Nth-last-of-type(-n+2)", "#qunit-fixture > :nth-last-of-type(-n+2)", [ "ap", "name+value", "first", "firstUL", "empty", "floatTest", "iframe", "table", "testForm", "liveHandlerOrder", "disabled-tests", "siblingTest", "last" ] );
} );
QUnit.test( "pseudo - has", function( assert ) {
assert.expect( 3 );
t( "Basic test", "p:has(a)", [ "firstp", "ap", "en", "sap" ] );
t( "Basic test (irrelevant whitespace)", "p:has( a )", [ "firstp", "ap", "en", "sap" ] );
t( "Nested with overlapping candidates", "#qunit-fixture div:has(div:has(div:not([id])))", [ "moretests", "t2037" ] );
} );
QUnit.test( "pseudo - contains", function( assert ) {
assert.expect( 9 );
var gh335 = document.getElementById( "qunit-fixture" ).appendChild(
document.createElement( "mark" ) );
gh335.id = "gh-335";
gh335.appendChild( document.createTextNode( "raw line 1\nline 2" ) );
assert.ok( Sizzle( "a:contains('')" ).length, "empty string" );
t( "unquoted argument", "a:contains(Google)", [ "google", "groups" ] );
t( "unquoted argument with whitespace", "a:contains(Google Groups)", [ "groups" ] );
t( "quoted argument with whitespace and parentheses",
"a:contains('Google Groups (Link)')", [ "groups" ] );
t( "quoted argument with double quotes and parentheses",
"a:contains(\"(Link)\")", [ "groups" ] );
t( "unquoted argument with whitespace and paired parentheses",
"a:contains(Google Groups (Link))", [ "groups" ] );
t( "unquoted argument with paired parentheses", "a:contains((Link))", [ "groups" ] );
t( "quoted argument with CSS escapes",
"span:contains(\"\\\"'\\53F0 \\5317 Ta\\301 ibe\\30C i\")",
[ "utf8class1" ] );
t( "collapsed whitespace", "mark:contains('line 1\\A line')", [ "gh-335" ] );
} );
QUnit.test( "pseudo - misc", function( assert ) {
assert.expect( 32 );
var select, tmp, input;
jQuery( "<h1 id='h1'/><h2 id='h2'/><h2 id='h2-2'/>" ).prependTo( "#qunit-fixture" );
t( "Headers", "#qunit-fixture :header", [ "h1", "h2", "h2-2" ] );
t( "Headers(case-insensitive)", "#qunit-fixture :Header", [ "h1", "h2", "h2-2" ] );
t( "Multiple matches with the same context (cache check)", "#form select:has(option:first-child:contains('o'))", [ "select1", "select2", "select3", "select4" ] );
assert.ok( Sizzle( "#qunit-fixture :not(:has(:has(*)))" ).length, "All not grandparents" );
select = document.getElementById( "select1" );
assert.ok( Sizzle.matchesSelector( select, ":has(option)" ), "Has Option Matches" );
tmp = document.createElement( "div" );
tmp.id = "tmp_input";
document.body.appendChild( tmp );
jQuery.each( [ "button", "submit", "reset" ], function( i, type ) {
var els = jQuery(
"<input id='input_%' type='%'/><button id='button_%' type='%'>test</button>"
.replace( /%/g, type )
).appendTo( tmp );
t( "Input Buttons :" + type, "#tmp_input :" + type, [ "input_" + type, "button_" + type ] );
assert.ok( Sizzle.matchesSelector( els[ 0 ], ":" + type ), "Input Matches :" + type );
assert.ok( Sizzle.matchesSelector( els[ 1 ], ":" + type ), "Button Matches :" + type );
} );
document.body.removeChild( tmp );
// Recreate tmp
tmp = document.createElement( "div" );
tmp.id = "tmp_input";
tmp.innerHTML = "<span>Hello I am focusable.</span>";
// Setting tabIndex should make the element focusable
// http://dev.w3.org/html5/spec/single-page.html#focus-management
document.body.appendChild( tmp );
tmp.tabIndex = 0;
tmp.focus();
if ( document.activeElement !== tmp || ( document.hasFocus && !document.hasFocus() ) ||
( document.querySelectorAll && !document.querySelectorAll( "div:focus" ).length ) ) {
assert.ok( true, "The div was not focused. Skip checking the :focus match." );
assert.ok( true, "The div was not focused. Skip checking the :focus match." );
} else {
t( "tabIndex element focused", ":focus", [ "tmp_input" ] );
assert.ok( Sizzle.matchesSelector( tmp, ":focus" ), ":focus matches tabIndex div" );
}
// Blur tmp
tmp.blur();
document.body.focus();
assert.ok( !Sizzle.matchesSelector( tmp, ":focus" ), ":focus doesn't match tabIndex div" );
document.body.removeChild( tmp );
// Input focus/active
input = document.createElement( "input" );
input.type = "text";
input.id = "focus-input";
document.body.appendChild( input );
input.focus();
// Inputs can't be focused unless the document has focus
if ( document.activeElement !== input || ( document.hasFocus && !document.hasFocus() ) ||
( document.querySelectorAll && !document.querySelectorAll( "input:focus" ).length ) ) {
assert.ok( true, "The input was not focused. Skip checking the :focus match." );
assert.ok( true, "The input was not focused. Skip checking the :focus match." );
} else {
t( "Element focused", "input:focus", [ "focus-input" ] );
assert.ok( Sizzle.matchesSelector( input, ":focus" ), ":focus matches" );
}
input.blur();
// When IE is out of focus, blur does not work. Force it here.
if ( document.activeElement === input ) {
document.body.focus();
}
assert.ok( !Sizzle.matchesSelector( input, ":focus" ), ":focus doesn't match" );
document.body.removeChild( input );
assert.deepEqual(
Sizzle( "[id='select1'] *:not(:last-child), [id='select2'] *:not(:last-child)", q( "qunit-fixture" )[ 0 ] ),
q( "option1a", "option1b", "option1c", "option2a", "option2b", "option2c" ),
"caching system tolerates recursive selection"
);
// Tokenization edge cases
t( "Sequential pseudos", "#qunit-fixture p:has(:contains(mark)):has(code)", [ "ap" ] );
t( "Sequential pseudos", "#qunit-fixture p:has(:contains(mark)):has(code):contains(This link)", [ "ap" ] );
t( "Pseudo argument containing ')'", "p:has(>a.GROUPS[src!=')'])", [ "ap" ] );
t( "Pseudo argument containing ')'", "p:has(>a.GROUPS[src!=')'])", [ "ap" ] );
t( "Pseudo followed by token containing ')'", "p:contains(id=\"foo\")[id!=\\)]", [ "sndp" ] );
t( "Pseudo followed by token containing ')'", "p:contains(id=\"foo\")[id!=')']", [ "sndp" ] );
t( "Multi-pseudo", "#ap:has(*), #ap:has(*)", [ "ap" ] );
t( "Multi-positional", "#ap:gt(0), #ap:lt(1)", [ "ap" ] );
t( "Multi-pseudo with leading nonexistent id", "#nonexistent:has(*), #ap:has(*)", [ "ap" ] );
t( "Multi-positional with leading nonexistent id", "#nonexistent:gt(0), #ap:lt(1)", [ "ap" ] );
t( "Tokenization stressor", "a[class*=blog]:not(:has(*, :contains(!)), :contains(!)), br:contains(]), p:contains(]), :not(:empty):not(:parent)", [ "ap", "mark", "yahoo", "simon" ] );
} );
QUnit.test( "pseudo - :not", function( assert ) {
assert.expect( 43 );
t( "Not", "a.blog:not(.link)", [ "mark" ] );
t( ":not() with :first", "#foo p:not(:first) .link", [ "simon" ] );
t( "Not - multiple", "#form option:not(:contains(Nothing),#option1b,:selected)", [ "option1c", "option1d", "option2b", "option2c", "option3d", "option3e", "option4e", "option5b", "option5c" ] );
t( "Not - recursive", "#form option:not(:not(:selected))[id^='option3']", [ "option3b", "option3c" ] );
t( ":not() failing interior", "#qunit-fixture p:not(.foo)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not() failing interior", "#qunit-fixture p:not(div.foo)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not() failing interior", "#qunit-fixture p:not(p.foo)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not() failing interior", "#qunit-fixture p:not(#blargh)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not() failing interior", "#qunit-fixture p:not(div#blargh)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not() failing interior", "#qunit-fixture p:not(p#blargh)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not Multiple", "#qunit-fixture p:not(a)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not Multiple", "#qunit-fixture p:not( a )", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not Multiple", "#qunit-fixture p:not( p )", [] );
t( ":not Multiple", "#qunit-fixture p:not(a, b)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not Multiple", "#qunit-fixture p:not(a, b, div)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( ":not Multiple", "p:not(p)", [] );
t( ":not Multiple", "p:not(a,p)", [] );
t( ":not Multiple", "p:not(p,a)", [] );
t( ":not Multiple", "p:not(a,p,b)", [] );
t( ":not Multiple", ":input:not(:image,:input,:submit)", [] );
t( ":not Multiple", "#qunit-fixture p:not(:has(a), :nth-child(1))", [ "first" ] );
t( "No element not selector", ".container div:not(.excluded) div", [] );
t( ":not() Existing attribute", "#form select:not([multiple])", [ "select1", "select2", "select5" ] );
t( ":not() Equals attribute", "#form select:not([name=select1])", [ "select2", "select3", "select4", "select5" ] );
t( ":not() Equals quoted attribute", "#form select:not([name='select1'])", [ "select2", "select3", "select4", "select5" ] );
t( ":not() Multiple Class", "#foo a:not(.blog)", [ "yahoo", "anchor2" ] );
t( ":not() Multiple Class", "#foo a:not(.link)", [ "yahoo", "anchor2" ] );
t( ":not() Multiple Class", "#foo a:not(.blog.link)", [ "yahoo", "anchor2" ] );
t( ":not chaining (compound)", "#qunit-fixture div[id]:not(:has(div, span)):not(:has(*))", [ "nothiddendivchild", "divWithNoTabIndex" ] );
t( ":not chaining (with attribute)", "#qunit-fixture form[id]:not([action$='formaction']):not(:button)", [ "lengthtest", "name-tests", "testForm", "disabled-tests" ] );
t( ":not chaining (colon in attribute)", "#qunit-fixture form[id]:not([action='form:action']):not(:button)", [ "form", "lengthtest", "name-tests", "testForm", "disabled-tests" ] );
t( ":not chaining (colon in attribute and nested chaining)", "#qunit-fixture form[id]:not([action='form:action']:button):not(:input)", [ "form", "lengthtest", "name-tests", "testForm", "disabled-tests" ] );
t( ":not chaining", "#form select:not(.select1):contains(Nothing) > option:not(option)", [] );
t( "positional :not()", "#foo p:not(:last)", [ "sndp", "en" ] );
t( "positional :not() prefix", "#foo p:not(:last) a", [ "yahoo" ] );
t( "compound positional :not()", "#foo p:not(:first, :last)", [ "en" ] );
t( "compound positional :not()", "#foo p:not(:first, :even)", [ "en" ] );
t( "compound positional :not()", "#foo p:not(:first, :odd)", [ "sap" ] );
t( "reordered compound positional :not()", "#foo p:not(:odd, :first)", [ "sap" ] );
t( "positional :not() with pre-filter", "#foo p:not([id]:first)", [ "en", "sap" ] );
t( "positional :not() with post-filter", "#foo p:not(:first[id])", [ "en", "sap" ] );
t( "positional :not() with pre-filter", "#foo p:not([lang]:first)", [ "sndp", "sap" ] );
t( "positional :not() with post-filter", "#foo p:not(:first[lang])", [ "sndp", "en", "sap" ] );
} );
QUnit.test( "pseudo - position", function( assert ) {
assert.expect( 34 );
t( "First element", "#qunit-fixture p:first", [ "firstp" ] );
t( "First element(case-insensitive)", "#qunit-fixture p:fiRst", [ "firstp" ] );
t( "nth Element", "#qunit-fixture p:nth(1)", [ "ap" ] );
t( "First Element", "#qunit-fixture p:first", [ "firstp" ] );
t( "Last Element", "p:last", [ "first" ] );
t( "Even Elements", "#qunit-fixture p:even", [ "firstp", "sndp", "sap" ] );
t( "Odd Elements", "#qunit-fixture p:odd", [ "ap", "en", "first" ] );
t( "Position Equals", "#qunit-fixture p:eq(1)", [ "ap" ] );
t( "Position Equals (negative)", "#qunit-fixture p:eq(-1)", [ "first" ] );
t( "Position Greater Than", "#qunit-fixture p:gt(0)", [ "ap", "sndp", "en", "sap", "first" ] );
t( "Position Less Than", "#qunit-fixture p:lt(3)", [ "firstp", "ap", "sndp" ] );
t( "Position Less Than Big Number", "#qunit-fixture p:lt(9007199254740991)", [ "firstp", "ap", "sndp", "en", "sap", "first" ] );
t( "Check position filtering", "div#nothiddendiv:eq(0)", [ "nothiddendiv" ] );
t( "Check position filtering", "div#nothiddendiv:last", [ "nothiddendiv" ] );
t( "Check position filtering", "div#nothiddendiv:not(:gt(0))", [ "nothiddendiv" ] );
t( "Check position filtering", "#foo > :not(:first)", [ "en", "sap" ] );
t( "Check position filtering", "#qunit-fixture select > :not(:gt(2))", [ "option1a", "option1b", "option1c" ] );
t( "Check position filtering", "#qunit-fixture select:lt(2) :not(:first)", [ "option1b", "option1c", "option1d", "option2a", "option2b", "option2c", "option2d" ] );
t( "Check position filtering", "div.nothiddendiv:eq(0)", [ "nothiddendiv" ] );
t( "Check position filtering", "div.nothiddendiv:last", [ "nothiddendiv" ] );
t( "Check position filtering", "div.nothiddendiv:not(:lt(0))", [ "nothiddendiv" ] );
t( "Check element position", "#qunit-fixture div div:eq(0)", [ "nothiddendivchild" ] );
t( "Check element position", "#select1 option:eq(3)", [ "option1d" ] );
t( "Check element position", "#qunit-fixture div div:eq(10)", [ "names-group" ] );
t( "Check element position", "#qunit-fixture div div:first", [ "nothiddendivchild" ] );
t( "Check element position", "#qunit-fixture div > div:first", [ "nothiddendivchild" ] );
t( "Check element position", "#qunit-fixture div:first a:first", [ "yahoo" ] );
t( "Check element position", "#qunit-fixture div:first > p:first", [ "sndp" ] );
t( "Check element position", "div#nothiddendiv:first > div:first", [ "nothiddendivchild" ] );
t( "Chained pseudo after a pos pseudo", "#listWithTabIndex li:eq(0):contains(Rice)", [ "foodWithNegativeTabIndex" ] );
t( "Check sort order with POS and comma", "#qunit-fixture em>em>em>em:first-child,div>em:first", [ "siblingfirst", "siblinggreatgrandchild" ] );
t( "Isolated position", "#qunit-fixture :last", [ "last" ] );
assert.deepEqual( Sizzle( "*:lt(2) + *", null, [], Sizzle( "#qunit-fixture > p" ) ), q( "ap" ),
"Seeded pos with trailing relative" );
// jQuery #12526
var context = jQuery( "#qunit-fixture" ).append( "<div id='jquery12526'></div>" )[ 0 ];
assert.deepEqual( Sizzle( ":last", context ), q( "jquery12526" ),
"Post-manipulation positional" );
} );
QUnit.test( "pseudo - form", function( assert ) {
assert.expect( 10 );
var extraTexts = jQuery( "<input id=\"impliedText\"/><input id=\"capitalText\" type=\"TEXT\">" ).appendTo( "#form" );
t( "Form element :input", "#form :input", [ "text1", "text2", "radio1", "radio2", "check1", "check2", "hidden1", "hidden2", "name", "search", "button", "area1", "select1", "select2", "select3", "select4", "select5", "impliedText", "capitalText" ] );
t( "Form element :radio", "#form :radio", [ "radio1", "radio2" ] );
t( "Form element :checkbox", "#form :checkbox", [ "check1", "check2" ] );
t( "Form element :text", "#form :text", [ "text1", "text2", "hidden2", "name", "impliedText", "capitalText" ] );
t( "Form element :radio:checked", "#form :radio:checked", [ "radio2" ] );
t( "Form element :checkbox:checked", "#form :checkbox:checked", [ "check1" ] );
t( "Form element :radio:checked, :checkbox:checked", "#form :radio:checked, #form :checkbox:checked", [ "radio2", "check1" ] );
t( "Selected option element",
"#form option:selected",
[ "option1a", "option2d", "option3b", "option3c", "option4b", "option4c", "option4d",
"option5a" ] );
t( "Selected option elements are also :checked", "#form option:checked",
[ "option1a", "option2d", "option3b", "option3c", "option4b", "option4c", "option4d",
"option5a" ] );
t( "Hidden inputs are still :enabled",
"#hidden1:enabled",
[ "hidden1" ] );
extraTexts.remove();
} );
QUnit.test( "pseudo - :(dis|en)abled, explicitly disabled", function( assert ) {
assert.expect( 2 );
// Set a meaningless disabled property on a common ancestor
var container = document.getElementById( "disabled-tests" );
container.disabled = true;
// Support: IE 6 - 11
// Unset the property where it is not meaningless
if ( document.getElementById( "enabled-input" ).isDisabled ) {
container.disabled = undefined;
}
t(
"Explicitly disabled elements",
"#enabled-fieldset :disabled",
[ "disabled-input", "disabled-textarea", "disabled-button",
"disabled-select", "disabled-optgroup", "disabled-option" ]
);
t(
"Enabled elements",
|
jquery/sizzle
|
9ffbb8b6e18d79bdc8cc9ee94d7b923de0661b32
|
Build: Update eslint-config-jquery, fix violations, fix the build task
|
diff --git a/Gruntfile.js b/Gruntfile.js
index 076578f..45fd75b 100644
--- a/Gruntfile.js
+++ b/Gruntfile.js
@@ -1,285 +1,292 @@
module.exports = function( grunt ) {
"use strict";
var gzip = require( "gzip-js" ),
isBrowserStack = process.env.BROWSER_STACK_USERNAME && process.env.BROWSER_STACK_ACCESS_KEY,
browsers = {
phantom: [ "PhantomJS" ],
desktop: [],
android: [],
ios: [],
old: {
firefox: [],
chrome: [],
safari: [],
ie: [],
opera: [],
android: []
}
},
files = {
source: "src/sizzle.js",
speed: "speed/speed.js",
tests: "test/{data,unit}/*.js",
karma: "test/karma/*.js",
grunt: [ "Gruntfile.js", "tasks/*" ]
};
// if Browserstack is set up, assume we can use it
if ( isBrowserStack ) {
// See https://github.com/jquery/sizzle/wiki/Sizzle-Documentation#browsers
browsers.desktop = [
"bs_chrome-45", // shares V8 with Node.js 4 LTS
"bs_chrome-70", "bs_chrome-71",
"bs_firefox-52", "bs_firefox-60", // Firefox ESR
"bs_firefox-63", "bs_firefox-64",
"bs_edge-17", "bs_edge-18",
"bs_ie-9", "bs_ie-10", "bs_ie-11",
"bs_opera-56", "bs_opera-57",
// Real Safari 6.1 and 7.0 are not available
"bs_safari-6.0", "bs_safari-8.0", "bs_safari-9.1", "bs_safari-10.1",
"bs_safari-11.1", "bs_safari-12.0"
];
browsers.ios = [
"bs_ios-5.1", "bs_ios-6.0", "bs_ios-7.0", "bs_ios-8.3", "bs_ios-9.3", "bs_ios-10.3",
"bs_ios-11.4", "bs_ios-12.1"
];
browsers.android = [
"bs_android-4.0", "bs_android-4.1", "bs_android-4.2",
"bs_android-4.3", "bs_android-4.4"
];
browsers.old = {
firefox: [ "bs_firefox-3.6" ],
chrome: [ "bs_chrome-16" ],
safari: [ "bs_safari-4.0", "bs_safari-5.0", "bs_safari-5.1" ],
ie: [ "bs_ie-7", "bs_ie-8" ],
opera: [ "bs_opera-11.6", "bs_opera-12.16" ],
android: [ "bs_android-2.3" ]
};
}
// Project configuration
grunt.initConfig( {
pkg: grunt.file.readJSON( "package.json" ),
dateString: new Date().toISOString().replace( /\..*Z/, "" ),
compile: {
all: {
dest: "dist/sizzle.js",
src: "src/sizzle.js"
}
},
version: {
files: [ "package.json", "bower.json" ]
},
uglify: {
all: {
files: {
"dist/sizzle.min.js": [ "dist/sizzle.js" ]
},
options: {
compress: {
"hoist_funs": false,
loops: false
},
output: {
ascii_only: true
},
banner: "/*! Sizzle v<%= pkg.version %> | (c) " +
"JS Foundation and other contributors | js.foundation */",
sourceMap: true,
sourceMapName: "dist/sizzle.min.map"
}
}
},
"ensure_ascii": {
files: [ "dist/*.js" ]
},
"compare_size": {
files: [ "dist/sizzle.js", "dist/sizzle.min.js" ],
options: {
compress: {
gz: function( contents ) {
return gzip.zip( contents, {} ).length;
}
},
cache: "dist/.sizecache.json"
}
},
npmcopy: {
all: {
options: {
destPrefix: "external"
},
files: {
"benchmark/benchmark.js": "benchmark/benchmark.js",
"benchmark/LICENSE.txt": "benchmark/LICENSE.txt",
"jquery/jquery.js": "jquery/jquery.js",
"jquery/MIT-LICENSE.txt": "jquery/MIT-LICENSE.txt",
"qunit/qunit.js": "qunitjs/qunit/qunit.js",
"qunit/qunit.css": "qunitjs/qunit/qunit.css",
"qunit/LICENSE.txt": "qunitjs/LICENSE.txt",
"requirejs/require.js": "requirejs/require.js",
"requirejs-domready/domReady.js": "requirejs-domready/domReady.js",
"requirejs-text/text.js": "requirejs-text/text.js"
}
}
},
eslint: {
options: {
// See https://github.com/sindresorhus/grunt-eslint/issues/119
quiet: true
},
dist: {
src: "dist/sizzle.js"
},
dev: {
src: [ files.source, files.grunt, files.karma, files.speed, files.tests ]
},
grunt: {
src: files.grunt
},
speed: {
src: [ files.speed ]
},
tests: {
src: [ files.tests ]
},
karma: {
src: [ files.karma ]
}
},
jsonlint: {
pkg: {
src: [ "package.json" ]
},
bower: {
src: [ "bower.json" ]
}
},
karma: {
options: {
configFile: "test/karma/karma.conf.js",
singleRun: true
},
watch: {
background: true,
singleRun: false,
browsers: browsers.phantom
},
phantom: {
browsers: browsers.phantom
},
desktop: {
browsers: browsers.desktop
},
android: {
browsers: browsers.android
},
ios: {
browsers: browsers.ios
},
oldIe: {
browsers: browsers.old.ie,
// Support: IE <=8 only
// Force use of JSONP polling
transports: [ "polling" ],
forceJSONP: true
},
oldOpera: {
browsers: browsers.old.opera
},
oldFirefox: {
browsers: browsers.old.firefox
},
oldChrome: {
browsers: browsers.old.chrome
},
oldSafari: {
browsers: browsers.old.safari
},
oldAndroid: {
browsers: browsers.old.android
},
all: {
browsers: browsers.phantom.concat(
browsers.desktop,
browsers.ios,
browsers.android,
browsers.old.firefox,
browsers.old.chrome,
browsers.old.safari,
browsers.old.ie,
browsers.old.opera,
browsers.old.android
)
}
},
watch: {
options: {
livereload: true
},
files: [
files.source,
files.grunt,
files.karma,
files.speed,
"test/**/*",
"test/*.html",
"{package,bower}.json"
],
tasks: [ "build", "karma:watch:run" ]
}
} );
// Integrate Sizzle specific tasks
grunt.loadTasks( "tasks" );
// Load dev dependencies
require( "load-grunt-tasks" )( grunt );
grunt.registerTask( "lint", [ "jsonlint", "eslint:dev", "eslint:dist" ] );
grunt.registerTask( "start", [ "karma:watch:start", "watch" ] );
// Execute tests all browsers in sequential way,
// so slow connections would not affect other runs
grunt.registerTask( "tests", isBrowserStack ? [
"karma:phantom", "karma:desktop",
"karma:ios",
"karma:oldIe", "karma:oldFirefox", "karma:oldChrome",
"karma:oldSafari", "karma:oldOpera"
// See #314 :-(
// "karma:android", "karma:oldAndroid"
] : "karma:phantom" );
- grunt.registerTask( "build", [ "lint", "compile", "uglify", "dist", "ensure_ascii" ] );
- grunt.registerTask( "default", [
+ grunt.registerTask( "build", [
+ "jsonlint",
"eslint:dev",
+ "compile",
+ "uglify",
+ "dist",
+ "eslint:dist",
+ "ensure_ascii"
+ ] );
+ grunt.registerTask( "default", [
"build",
"tests",
"compare_size",
"eslint:dist"
] );
grunt.registerTask( "bower", "bowercopy" );
};
diff --git a/dist/sizzle.js b/dist/sizzle.js
index 604ae2b..5bd623a 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -809,1588 +809,1588 @@ setDocument = Sizzle.setDocument = function( node ) {
rbuggyQSA.push( ":checked" );
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push( ".#.+[+~]" );
}
} );
assert( function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement( "input" );
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll( "[name=d]" ).length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll( "*,:x" );
rbuggyQSA.push( ",.*:" );
} );
}
if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector ) ) ) ) {
assert( function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
} );
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
) );
} :
function( a, b ) {
if ( b ) {
while ( ( b = b.parentNode ) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
// Choose the first element that is related to our preferred document
if ( a === document ||
a.ownerDocument === preferredDoc &&
contains( preferredDoc, a ) ) {
return -1;
}
if ( b === document ||
b.ownerDocument === preferredDoc &&
contains( preferredDoc, b ) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( ( cur = cur.parentNode ) ) {
ap.unshift( cur );
}
cur = b;
while ( ( cur = cur.parentNode ) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[ i ] === bp[ i ] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[ i ], bp[ i ] ) :
// Otherwise nodes in our document sort first
ap[ i ] === preferredDoc ? -1 :
bp[ i ] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch ( e ) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return ( sel + "" ).replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( ( node = elem[ i++ ] ) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[ 1 ] = match[ 1 ].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
match[ 5 ] || "" ).replace( runescape, funescape );
if ( match[ 2 ] === "~=" ) {
match[ 3 ] = " " + match[ 3 ] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[ 1 ] = match[ 1 ].toLowerCase();
if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[ 4 ] = +( match[ 4 ] ?
match[ 5 ] + ( match[ 6 ] || 1 ) :
2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
// other types prohibit arguments
} else if ( match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[ 6 ] && match[ 2 ];
if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[ 3 ] ) {
match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
( excess = tokenize( unquoted, true ) ) &&
// advance to the next closing parenthesis
( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
// excess is a negative index
match[ 0 ] = match[ 0 ].slice( 0, excess );
match[ 2 ] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() {
return true;
} :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
( pattern = new RegExp( "(^|" + whitespace +
")" + className + "(" + whitespace + "|$)" ) ) && classCache(
className, function( elem ) {
return pattern.test(
typeof elem.className === "string" && elem.className ||
typeof elem.getAttribute !== "undefined" &&
elem.getAttribute( "class" ) ||
""
);
} );
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
/* eslint-disable max-len */
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
/* eslint-enable max-len */
};
},
- "CHILD": function( type, what, argument, first, last ) {
+ "CHILD": function( type, what, _argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
- function( elem, context, xml ) {
+ function( elem, _context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( ( node = node[ dir ] ) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
start = [ forward ? parent.firstChild : parent.lastChild ];
// non-xml :nth-child(...) stores cache data on `parent`
if ( forward && useCache ) {
// Seek `elem` from a previously-cached index
// ...in a gzip-friendly way
node = parent;
outerCache = node[ expando ] || ( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex && cache[ 2 ];
node = nodeIndex && parent.childNodes[ nodeIndex ];
while ( ( node = ++nodeIndex && node && node[ dir ] ||
// Fallback to seeking `elem` from the start
( diff = nodeIndex = 0 ) || start.pop() ) ) {
// When found, cache indexes on `parent` and break
if ( node.nodeType === 1 && ++diff && node === elem ) {
uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
break;
}
}
} else {
// Use previously-cached element index if available
if ( useCache ) {
// ...in a gzip-friendly way
node = elem;
outerCache = node[ expando ] || ( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex;
}
// xml :nth-child(...)
// or :nth-last-child(...) or :nth(-last)?-of-type(...)
if ( diff === false ) {
// Use the same loop as above to seek `elem` from the start
while ( ( node = ++nodeIndex && node && node[ dir ] ||
( diff = nodeIndex = 0 ) || start.pop() ) ) {
if ( ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) &&
++diff ) {
// Cache the index of each encountered element
if ( useCache ) {
outerCache = node[ expando ] ||
( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
uniqueCache[ type ] = [ dirruns, diff ];
}
if ( node === elem ) {
break;
}
}
}
}
}
// Incorporate the offset, then check against cycle size
diff -= last;
return diff === first || ( diff % first === 0 && diff / first >= 0 );
}
};
},
"PSEUDO": function( pseudo, argument ) {
// pseudo-class names are case-insensitive
// http://www.w3.org/TR/selectors/#pseudo-classes
// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
// Remember that setFilters inherits from pseudos
var args,
fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
Sizzle.error( "unsupported pseudo: " + pseudo );
// The user may use createPseudo to indicate that
// arguments are needed to create the filter function
// just as Sizzle does
if ( fn[ expando ] ) {
return fn( argument );
}
// But maintain support for old signatures
if ( fn.length > 1 ) {
args = [ pseudo, pseudo, "", argument ];
return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
markFunction( function( seed, matches ) {
var idx,
matched = fn( seed, argument ),
i = matched.length;
while ( i-- ) {
idx = indexOf( seed, matched[ i ] );
seed[ idx ] = !( matches[ idx ] = matched[ i ] );
}
} ) :
function( elem ) {
return fn( elem, 0, args );
};
}
return fn;
}
},
pseudos: {
// Potentially complex pseudos
"not": markFunction( function( selector ) {
// Trim the selector passed to compile
// to avoid treating leading and trailing
// spaces as combinators
var input = [],
results = [],
matcher = compile( selector.replace( rtrim, "$1" ) );
return matcher[ expando ] ?
- markFunction( function( seed, matches, context, xml ) {
+ markFunction( function( seed, matches, _context, xml ) {
var elem,
unmatched = matcher( seed, null, xml, [] ),
i = seed.length;
// Match elements unmatched by `matcher`
while ( i-- ) {
if ( ( elem = unmatched[ i ] ) ) {
seed[ i ] = !( matches[ i ] = elem );
}
}
} ) :
- function( elem, context, xml ) {
+ function( elem, _context, xml ) {
input[ 0 ] = elem;
matcher( input, null, xml, results );
// Don't keep the element (issue #299)
input[ 0 ] = null;
return !results.pop();
};
} ),
"has": markFunction( function( selector ) {
return function( elem ) {
return Sizzle( selector, elem ).length > 0;
};
} ),
"contains": markFunction( function( text ) {
text = text.replace( runescape, funescape );
return function( elem ) {
return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
};
} ),
// "Whether an element is represented by a :lang() selector
// is based solely on the element's language value
// being equal to the identifier C,
// or beginning with the identifier C immediately followed by "-".
// The matching of C against the element's language value is performed case-insensitively.
// The identifier C does not have to be a valid language name."
// http://www.w3.org/TR/selectors/#lang-pseudo
"lang": markFunction( function( lang ) {
// lang value must be a valid identifier
if ( !ridentifier.test( lang || "" ) ) {
Sizzle.error( "unsupported lang: " + lang );
}
lang = lang.replace( runescape, funescape ).toLowerCase();
return function( elem ) {
var elemLang;
do {
if ( ( elemLang = documentIsHTML ?
elem.lang :
elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
elemLang = elemLang.toLowerCase();
return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
}
} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
return false;
};
} ),
// Miscellaneous
"target": function( elem ) {
var hash = window.location && window.location.hash;
return hash && hash.slice( 1 ) === elem.id;
},
"root": function( elem ) {
return elem === docElem;
},
"focus": function( elem ) {
return elem === document.activeElement &&
( !document.hasFocus || document.hasFocus() ) &&
!!( elem.type || elem.href || ~elem.tabIndex );
},
// Boolean properties
"enabled": createDisabledPseudo( false ),
"disabled": createDisabledPseudo( true ),
"checked": function( elem ) {
// In CSS3, :checked should return both checked and selected elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
var nodeName = elem.nodeName.toLowerCase();
return ( nodeName === "input" && !!elem.checked ) ||
( nodeName === "option" && !!elem.selected );
},
"selected": function( elem ) {
// Accessing this property makes selected-by-default
// options in Safari work properly
if ( elem.parentNode ) {
// eslint-disable-next-line no-unused-expressions
elem.parentNode.selectedIndex;
}
return elem.selected === true;
},
// Contents
"empty": function( elem ) {
// http://www.w3.org/TR/selectors/#empty-pseudo
// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
// but not by others (comment: 8; processing instruction: 7; etc.)
// nodeType < 6 works because attributes (2) do not appear as children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
if ( elem.nodeType < 6 ) {
return false;
}
}
return true;
},
"parent": function( elem ) {
return !Expr.pseudos[ "empty" ]( elem );
},
// Element/input types
"header": function( elem ) {
return rheader.test( elem.nodeName );
},
"input": function( elem ) {
return rinputs.test( elem.nodeName );
},
"button": function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === "button" || name === "button";
},
"text": function( elem ) {
var attr;
return elem.nodeName.toLowerCase() === "input" &&
elem.type === "text" &&
// Support: IE<8
// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
( ( attr = elem.getAttribute( "type" ) ) == null ||
attr.toLowerCase() === "text" );
},
// Position-in-collection
"first": createPositionalPseudo( function() {
return [ 0 ];
} ),
- "last": createPositionalPseudo( function( matchIndexes, length ) {
+ "last": createPositionalPseudo( function( _matchIndexes, length ) {
return [ length - 1 ];
} ),
- "eq": createPositionalPseudo( function( matchIndexes, length, argument ) {
+ "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
return [ argument < 0 ? argument + length : argument ];
} ),
"even": createPositionalPseudo( function( matchIndexes, length ) {
var i = 0;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"odd": createPositionalPseudo( function( matchIndexes, length ) {
var i = 1;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
var i = argument < 0 ?
argument + length :
argument > length ?
length :
argument;
for ( ; --i >= 0; ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
var i = argument < 0 ? argument + length : argument;
for ( ; ++i < length; ) {
matchIndexes.push( i );
}
return matchIndexes;
} )
}
};
Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
// Add button/input type pseudos
for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
Expr.pseudos[ i ] = createInputPseudo( i );
}
for ( i in { submit: true, reset: true } ) {
Expr.pseudos[ i ] = createButtonPseudo( i );
}
// Easy API for creating new setFilters
function setFilters() {}
setFilters.prototype = Expr.filters = Expr.pseudos;
Expr.setFilters = new setFilters();
tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
var matched, match, tokens, type,
soFar, groups, preFilters,
cached = tokenCache[ selector + " " ];
if ( cached ) {
return parseOnly ? 0 : cached.slice( 0 );
}
soFar = selector;
groups = [];
preFilters = Expr.preFilter;
while ( soFar ) {
// Comma and first run
if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
if ( match ) {
// Don't consume trailing commas as valid
soFar = soFar.slice( match[ 0 ].length ) || soFar;
}
groups.push( ( tokens = [] ) );
}
matched = false;
// Combinators
if ( ( match = rcombinators.exec( soFar ) ) ) {
matched = match.shift();
tokens.push( {
value: matched,
// Cast descendant combinators to space
type: match[ 0 ].replace( rtrim, " " )
} );
soFar = soFar.slice( matched.length );
}
// Filters
for ( type in Expr.filter ) {
if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
( match = preFilters[ type ]( match ) ) ) ) {
matched = match.shift();
tokens.push( {
value: matched,
type: type,
matches: match
} );
soFar = soFar.slice( matched.length );
}
}
if ( !matched ) {
break;
}
}
// Return the length of the invalid excess
// if we're just parsing
// Otherwise, throw an error or return tokens
return parseOnly ?
soFar.length :
soFar ?
Sizzle.error( selector ) :
// Cache the tokens
tokenCache( selector, groups ).slice( 0 );
};
function toSelector( tokens ) {
var i = 0,
len = tokens.length,
selector = "";
for ( ; i < len; i++ ) {
selector += tokens[ i ].value;
}
return selector;
}
function addCombinator( matcher, combinator, base ) {
var dir = combinator.dir,
skip = combinator.next,
key = skip || dir,
checkNonElements = base && key === "parentNode",
doneName = done++;
return combinator.first ?
// Check against closest ancestor/preceding element
function( elem, context, xml ) {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
return matcher( elem, context, xml );
}
}
return false;
} :
// Check against all ancestor/preceding elements
function( elem, context, xml ) {
var oldCache, uniqueCache, outerCache,
newCache = [ dirruns, doneName ];
// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
if ( xml ) {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
if ( matcher( elem, context, xml ) ) {
return true;
}
}
}
} else {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
outerCache = elem[ expando ] || ( elem[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ elem.uniqueID ] ||
( outerCache[ elem.uniqueID ] = {} );
if ( skip && skip === elem.nodeName.toLowerCase() ) {
elem = elem[ dir ] || elem;
} else if ( ( oldCache = uniqueCache[ key ] ) &&
oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
// Assign to newCache so results back-propagate to previous elements
return ( newCache[ 2 ] = oldCache[ 2 ] );
} else {
// Reuse newcache so results back-propagate to previous elements
uniqueCache[ key ] = newCache;
// A match means we're done; a fail means we have to keep checking
if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
return true;
}
}
}
}
}
return false;
};
}
function elementMatcher( matchers ) {
return matchers.length > 1 ?
function( elem, context, xml ) {
var i = matchers.length;
while ( i-- ) {
if ( !matchers[ i ]( elem, context, xml ) ) {
return false;
}
}
return true;
} :
matchers[ 0 ];
}
function multipleContexts( selector, contexts, results ) {
var i = 0,
len = contexts.length;
for ( ; i < len; i++ ) {
Sizzle( selector, contexts[ i ], results );
}
return results;
}
function condense( unmatched, map, filter, context, xml ) {
var elem,
newUnmatched = [],
i = 0,
len = unmatched.length,
mapped = map != null;
for ( ; i < len; i++ ) {
if ( ( elem = unmatched[ i ] ) ) {
if ( !filter || filter( elem, context, xml ) ) {
newUnmatched.push( elem );
if ( mapped ) {
map.push( i );
}
}
}
}
return newUnmatched;
}
function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
if ( postFilter && !postFilter[ expando ] ) {
postFilter = setMatcher( postFilter );
}
if ( postFinder && !postFinder[ expando ] ) {
postFinder = setMatcher( postFinder, postSelector );
}
return markFunction( function( seed, results, context, xml ) {
var temp, i, elem,
preMap = [],
postMap = [],
preexisting = results.length,
// Get initial elements from seed or context
elems = seed || multipleContexts(
selector || "*",
context.nodeType ? [ context ] : context,
[]
),
// Prefilter to get matcher input, preserving a map for seed-results synchronization
matcherIn = preFilter && ( seed || !selector ) ?
condense( elems, preMap, preFilter, context, xml ) :
elems,
matcherOut = matcher ?
// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
// ...intermediate processing is necessary
[] :
// ...otherwise use results directly
results :
matcherIn;
// Find primary matches
if ( matcher ) {
matcher( matcherIn, matcherOut, context, xml );
}
// Apply postFilter
if ( postFilter ) {
temp = condense( matcherOut, postMap );
postFilter( temp, [], context, xml );
// Un-match failing elements by moving them back to matcherIn
i = temp.length;
while ( i-- ) {
if ( ( elem = temp[ i ] ) ) {
matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
}
}
}
if ( seed ) {
if ( postFinder || preFilter ) {
if ( postFinder ) {
// Get the final matcherOut by condensing this intermediate into postFinder contexts
temp = [];
i = matcherOut.length;
while ( i-- ) {
if ( ( elem = matcherOut[ i ] ) ) {
// Restore matcherIn since elem is not yet a final match
temp.push( ( matcherIn[ i ] = elem ) );
}
}
postFinder( null, ( matcherOut = [] ), temp, xml );
}
// Move matched elements from seed to results to keep them synchronized
i = matcherOut.length;
while ( i-- ) {
if ( ( elem = matcherOut[ i ] ) &&
( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
seed[ temp ] = !( results[ temp ] = elem );
}
}
}
// Add elements to results, through postFinder if defined
} else {
matcherOut = condense(
matcherOut === results ?
matcherOut.splice( preexisting, matcherOut.length ) :
matcherOut
);
if ( postFinder ) {
postFinder( null, results, matcherOut, xml );
} else {
push.apply( results, matcherOut );
}
}
} );
}
function matcherFromTokens( tokens ) {
var checkContext, matcher, j,
len = tokens.length,
leadingRelative = Expr.relative[ tokens[ 0 ].type ],
implicitRelative = leadingRelative || Expr.relative[ " " ],
i = leadingRelative ? 1 : 0,
// The foundational matcher ensures that elements are reachable from top-level context(s)
matchContext = addCombinator( function( elem ) {
return elem === checkContext;
}, implicitRelative, true ),
matchAnyContext = addCombinator( function( elem ) {
return indexOf( checkContext, elem ) > -1;
}, implicitRelative, true ),
matchers = [ function( elem, context, xml ) {
var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
( checkContext = context ).nodeType ?
matchContext( elem, context, xml ) :
matchAnyContext( elem, context, xml ) );
// Avoid hanging onto element (issue #299)
checkContext = null;
return ret;
} ];
for ( ; i < len; i++ ) {
if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
} else {
matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
// Return special upon seeing a positional matcher
if ( matcher[ expando ] ) {
// Find the next relative operator (if any) for proper handling
j = ++i;
for ( ; j < len; j++ ) {
if ( Expr.relative[ tokens[ j ].type ] ) {
break;
}
}
return setMatcher(
i > 1 && elementMatcher( matchers ),
i > 1 && toSelector(
// If the preceding token was a descendant combinator, insert an implicit any-element `*`
tokens
.slice( 0, i - 1 )
.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
).replace( rtrim, "$1" ),
matcher,
i < j && matcherFromTokens( tokens.slice( i, j ) ),
j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
j < len && toSelector( tokens )
);
}
matchers.push( matcher );
}
}
return elementMatcher( matchers );
}
function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
var bySet = setMatchers.length > 0,
byElement = elementMatchers.length > 0,
superMatcher = function( seed, context, xml, results, outermost ) {
var elem, j, matcher,
matchedCount = 0,
i = "0",
unmatched = seed && [],
setMatched = [],
contextBackup = outermostContext,
// We must always have either seed elements or outermost context
elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
// Use integer dirruns iff this is the outermost matcher
dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
len = elems.length;
if ( outermost ) {
outermostContext = context === document || context || outermost;
}
// Add elements passing elementMatchers directly to results
// Support: IE<9, Safari
// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
if ( byElement && elem ) {
j = 0;
if ( !context && elem.ownerDocument !== document ) {
setDocument( elem );
xml = !documentIsHTML;
}
while ( ( matcher = elementMatchers[ j++ ] ) ) {
if ( matcher( elem, context || document, xml ) ) {
results.push( elem );
break;
}
}
if ( outermost ) {
dirruns = dirrunsUnique;
}
}
// Track unmatched elements for set filters
if ( bySet ) {
// They will have gone through all possible matchers
if ( ( elem = !matcher && elem ) ) {
matchedCount--;
}
// Lengthen the array for every element, matched or not
if ( seed ) {
unmatched.push( elem );
}
}
}
// `i` is now the count of elements visited above, and adding it to `matchedCount`
// makes the latter nonnegative.
matchedCount += i;
// Apply set filters to unmatched elements
// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
// no element matchers and no seed.
// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
// case, which will result in a "00" `matchedCount` that differs from `i` but is also
// numerically zero.
if ( bySet && i !== matchedCount ) {
j = 0;
while ( ( matcher = setMatchers[ j++ ] ) ) {
matcher( unmatched, setMatched, context, xml );
}
if ( seed ) {
// Reintegrate element matches to eliminate the need for sorting
if ( matchedCount > 0 ) {
while ( i-- ) {
if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
setMatched[ i ] = pop.call( results );
}
}
}
// Discard index placeholder values to get only actual matches
setMatched = condense( setMatched );
}
// Add matches to results
push.apply( results, setMatched );
// Seedless set matches succeeding multiple successful matchers stipulate sorting
if ( outermost && !seed && setMatched.length > 0 &&
( matchedCount + setMatchers.length ) > 1 ) {
Sizzle.uniqueSort( results );
}
}
// Override manipulation of globals by nested matchers
if ( outermost ) {
dirruns = dirrunsUnique;
outermostContext = contextBackup;
}
return unmatched;
};
return bySet ?
markFunction( superMatcher ) :
superMatcher;
}
compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
var i,
setMatchers = [],
elementMatchers = [],
cached = compilerCache[ selector + " " ];
if ( !cached ) {
// Generate a function of recursive functions that can be used to check each element
if ( !match ) {
match = tokenize( selector );
}
i = match.length;
while ( i-- ) {
cached = matcherFromTokens( match[ i ] );
if ( cached[ expando ] ) {
setMatchers.push( cached );
} else {
elementMatchers.push( cached );
}
}
// Cache the compiled function
cached = compilerCache(
selector,
matcherFromGroupMatchers( elementMatchers, setMatchers )
);
// Save selector and tokenization
cached.selector = selector;
}
return cached;
};
/**
* A low-level selection function that works with Sizzle's compiled
* selector functions
* @param {String|Function} selector A selector or a pre-compiled
* selector function built with Sizzle.compile
* @param {Element} context
* @param {Array} [results]
* @param {Array} [seed] A set of elements to match against
*/
select = Sizzle.select = function( selector, context, results, seed ) {
var i, tokens, token, type, find,
compiled = typeof selector === "function" && selector,
match = !seed && tokenize( ( selector = compiled.selector || selector ) );
results = results || [];
// Try to minimize operations if there is only one selector in the list and no seed
// (the latter of which guarantees us context)
if ( match.length === 1 ) {
// Reduce context if the leading compound selector is an ID
tokens = match[ 0 ] = match[ 0 ].slice( 0 );
if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
.replace( runescape, funescape ), context ) || [] )[ 0 ];
if ( !context ) {
return results;
// Precompiled matchers will still verify ancestry, so step up a level
} else if ( compiled ) {
context = context.parentNode;
}
selector = selector.slice( tokens.shift().value.length );
}
// Fetch a seed set for right-to-left matching
i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
while ( i-- ) {
token = tokens[ i ];
// Abort if we hit a combinator
if ( Expr.relative[ ( type = token.type ) ] ) {
break;
}
if ( ( find = Expr.find[ type ] ) ) {
// Search, expanding context for leading sibling combinators
if ( ( seed = find(
token.matches[ 0 ].replace( runescape, funescape ),
rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
context
) ) ) {
// If seed is empty or no tokens remain, we can return early
tokens.splice( i, 1 );
selector = seed.length && toSelector( tokens );
if ( !selector ) {
push.apply( results, seed );
return results;
}
break;
}
}
}
}
// Compile and execute a filtering function if one is not provided
// Provide `match` to avoid retokenization if we modified the selector above
( compiled || compile( selector, match ) )(
seed,
context,
!documentIsHTML,
results,
!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
);
return results;
};
// One-time assignments
// Sort stability
support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
// Support: Chrome 14-35+
// Always assume duplicates if they aren't passed to the comparison function
support.detectDuplicates = !!hasDuplicate;
// Initialize against the default document
setDocument();
// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
// Detached nodes confoundingly follow *each other*
support.sortDetached = assert( function( el ) {
// Should return 1, but returns 4 (following)
return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
} );
// Support: IE<8
// Prevent attribute/property "interpolation"
// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
if ( !assert( function( el ) {
el.innerHTML = "<a href='#'></a>";
return el.firstChild.getAttribute( "href" ) === "#";
} ) ) {
addHandle( "type|href|height|width", function( elem, name, isXML ) {
if ( !isXML ) {
return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
}
} );
}
// Support: IE<9
// Use defaultValue in place of getAttribute("value")
if ( !support.attributes || !assert( function( el ) {
el.innerHTML = "<input/>";
el.firstChild.setAttribute( "value", "" );
return el.firstChild.getAttribute( "value" ) === "";
} ) ) {
- addHandle( "value", function( elem, name, isXML ) {
+ addHandle( "value", function( elem, _name, isXML ) {
if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
return elem.defaultValue;
}
} );
}
// Support: IE<9
// Use getAttributeNode to fetch booleans when getAttribute lies
if ( !assert( function( el ) {
return el.getAttribute( "disabled" ) == null;
} ) ) {
addHandle( booleans, function( elem, name, isXML ) {
var val;
if ( !isXML ) {
return elem[ name ] === true ? name.toLowerCase() :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
}
} );
}
// EXPOSE
var _sizzle = window.Sizzle;
Sizzle.noConflict = function() {
if ( window.Sizzle === Sizzle ) {
window.Sizzle = _sizzle;
}
return Sizzle;
};
if ( typeof define === "function" && define.amd ) {
define( function() {
return Sizzle;
} );
// Sizzle requires that there be a global window in Common-JS like environments
} else if ( typeof module !== "undefined" && module.exports ) {
module.exports = Sizzle;
} else {
window.Sizzle = Sizzle;
}
// EXPOSE
} )( window );
diff --git a/dist/sizzle.min.map b/dist/sizzle.min.map
index 037121a..2003de8 100644
--- a/dist/sizzle.min.map
+++ b/dist/sizzle.min.map
@@ -1 +1 @@
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diff --git a/package.json b/package.json
index 1c51bc5..4a83d14 100644
--- a/package.json
+++ b/package.json
@@ -1,85 +1,85 @@
{
"title": "Sizzle",
"name": "sizzle",
"version": "2.3.5-pre",
"description": "A pure-JavaScript, bottom-up CSS selector engine designed to be easily dropped in to a host library.",
"keywords": [
"sizzle",
"javascript",
"CSS",
"selector",
"jquery"
],
"homepage": "https://sizzlejs.com",
"author": {
"name": "JS Foundation and other contributors",
"url": "https://github.com/jquery/sizzle/blob/2.3.4/AUTHORS.txt"
},
"repository": {
"type": "git",
"url": "https://github.com/jquery/sizzle.git"
},
"bugs": {
"url": "https://github.com/jquery/sizzle/issues"
},
"license": "MIT",
"files": [
"AUTHORS.txt",
"LICENSE.txt",
"dist/sizzle.js",
"dist/sizzle.min.js",
"dist/sizzle.min.map"
],
"main": "dist/sizzle.js",
"dependencies": {},
"devDependencies": {
"benchmark": "2.1.4",
"commitplease": "2.7.10",
- "eslint-config-jquery": "1.0.1",
+ "eslint-config-jquery": "2.0.0",
"grunt": "0.4.5",
"grunt-cli": "0.1.13",
"grunt-compare-size": "0.4.2",
"grunt-contrib-qunit": "2.0.0",
"grunt-contrib-uglify": "3.0.1",
"grunt-contrib-watch": "1.0.0",
"grunt-eslint": "21.0.0",
"grunt-git-authors": "3.2.0",
"grunt-jsonlint": "1.1.0",
"grunt-karma": "2.0.0",
"grunt-npmcopy": "0.1.0",
"gzip-js": "0.3.2",
"jquery": "1.9.1",
"karma": "1.3.0",
"karma-browserstack-launcher": "1.3.0",
"karma-chrome-launcher": "2.2.0",
"karma-firefox-launcher": "1.0.1",
"karma-html2js-preprocessor": "1.1.0",
"karma-phantomjs-launcher": "1.0.4",
"karma-qunit": "1.2.1",
"load-grunt-tasks": "3.5.2",
"phantomjs-prebuilt": "2.1.15",
"qunitjs": "1.23.1",
"requirejs": "2.3.5",
"requirejs-domready": "2.0.3",
"requirejs-text": "2.0.15"
},
"scripts": {
"build": "npm install && grunt",
"start": "grunt start",
"test": "grunt test"
},
"commitplease": {
"components": [
"Misc",
"Docs",
"Tests",
"Build",
"Release",
"Core",
"Tokenize",
"Compile",
"Selector",
"SetDocument"
]
}
}
diff --git a/src/sizzle.js b/src/sizzle.js
index 8dfbdd6..2bb9065 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -809,1588 +809,1588 @@ setDocument = Sizzle.setDocument = function( node ) {
rbuggyQSA.push( ":checked" );
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push( ".#.+[+~]" );
}
} );
assert( function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement( "input" );
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll( "[name=d]" ).length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll( "*,:x" );
rbuggyQSA.push( ",.*:" );
} );
}
if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector ) ) ) ) {
assert( function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
} );
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
) );
} :
function( a, b ) {
if ( b ) {
while ( ( b = b.parentNode ) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
// Choose the first element that is related to our preferred document
if ( a === document ||
a.ownerDocument === preferredDoc &&
contains( preferredDoc, a ) ) {
return -1;
}
if ( b === document ||
b.ownerDocument === preferredDoc &&
contains( preferredDoc, b ) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( ( cur = cur.parentNode ) ) {
ap.unshift( cur );
}
cur = b;
while ( ( cur = cur.parentNode ) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[ i ] === bp[ i ] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[ i ], bp[ i ] ) :
// Otherwise nodes in our document sort first
ap[ i ] === preferredDoc ? -1 :
bp[ i ] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch ( e ) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return ( sel + "" ).replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( ( elem = results[ i++ ] ) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( ( node = elem[ i++ ] ) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[ 1 ] = match[ 1 ].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
match[ 5 ] || "" ).replace( runescape, funescape );
if ( match[ 2 ] === "~=" ) {
match[ 3 ] = " " + match[ 3 ] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[ 1 ] = match[ 1 ].toLowerCase();
if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[ 4 ] = +( match[ 4 ] ?
match[ 5 ] + ( match[ 6 ] || 1 ) :
2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
// other types prohibit arguments
} else if ( match[ 3 ] ) {
Sizzle.error( match[ 0 ] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[ 6 ] && match[ 2 ];
if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[ 3 ] ) {
match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
( excess = tokenize( unquoted, true ) ) &&
// advance to the next closing parenthesis
( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
// excess is a negative index
match[ 0 ] = match[ 0 ].slice( 0, excess );
match[ 2 ] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() {
return true;
} :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
( pattern = new RegExp( "(^|" + whitespace +
")" + className + "(" + whitespace + "|$)" ) ) && classCache(
className, function( elem ) {
return pattern.test(
typeof elem.className === "string" && elem.className ||
typeof elem.getAttribute !== "undefined" &&
elem.getAttribute( "class" ) ||
""
);
} );
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
/* eslint-disable max-len */
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
/* eslint-enable max-len */
};
},
- "CHILD": function( type, what, argument, first, last ) {
+ "CHILD": function( type, what, _argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
- function( elem, context, xml ) {
+ function( elem, _context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( ( node = node[ dir ] ) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
start = [ forward ? parent.firstChild : parent.lastChild ];
// non-xml :nth-child(...) stores cache data on `parent`
if ( forward && useCache ) {
// Seek `elem` from a previously-cached index
// ...in a gzip-friendly way
node = parent;
outerCache = node[ expando ] || ( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex && cache[ 2 ];
node = nodeIndex && parent.childNodes[ nodeIndex ];
while ( ( node = ++nodeIndex && node && node[ dir ] ||
// Fallback to seeking `elem` from the start
( diff = nodeIndex = 0 ) || start.pop() ) ) {
// When found, cache indexes on `parent` and break
if ( node.nodeType === 1 && ++diff && node === elem ) {
uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
break;
}
}
} else {
// Use previously-cached element index if available
if ( useCache ) {
// ...in a gzip-friendly way
node = elem;
outerCache = node[ expando ] || ( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex;
}
// xml :nth-child(...)
// or :nth-last-child(...) or :nth(-last)?-of-type(...)
if ( diff === false ) {
// Use the same loop as above to seek `elem` from the start
while ( ( node = ++nodeIndex && node && node[ dir ] ||
( diff = nodeIndex = 0 ) || start.pop() ) ) {
if ( ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) &&
++diff ) {
// Cache the index of each encountered element
if ( useCache ) {
outerCache = node[ expando ] ||
( node[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
( outerCache[ node.uniqueID ] = {} );
uniqueCache[ type ] = [ dirruns, diff ];
}
if ( node === elem ) {
break;
}
}
}
}
}
// Incorporate the offset, then check against cycle size
diff -= last;
return diff === first || ( diff % first === 0 && diff / first >= 0 );
}
};
},
"PSEUDO": function( pseudo, argument ) {
// pseudo-class names are case-insensitive
// http://www.w3.org/TR/selectors/#pseudo-classes
// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
// Remember that setFilters inherits from pseudos
var args,
fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
Sizzle.error( "unsupported pseudo: " + pseudo );
// The user may use createPseudo to indicate that
// arguments are needed to create the filter function
// just as Sizzle does
if ( fn[ expando ] ) {
return fn( argument );
}
// But maintain support for old signatures
if ( fn.length > 1 ) {
args = [ pseudo, pseudo, "", argument ];
return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
markFunction( function( seed, matches ) {
var idx,
matched = fn( seed, argument ),
i = matched.length;
while ( i-- ) {
idx = indexOf( seed, matched[ i ] );
seed[ idx ] = !( matches[ idx ] = matched[ i ] );
}
} ) :
function( elem ) {
return fn( elem, 0, args );
};
}
return fn;
}
},
pseudos: {
// Potentially complex pseudos
"not": markFunction( function( selector ) {
// Trim the selector passed to compile
// to avoid treating leading and trailing
// spaces as combinators
var input = [],
results = [],
matcher = compile( selector.replace( rtrim, "$1" ) );
return matcher[ expando ] ?
- markFunction( function( seed, matches, context, xml ) {
+ markFunction( function( seed, matches, _context, xml ) {
var elem,
unmatched = matcher( seed, null, xml, [] ),
i = seed.length;
// Match elements unmatched by `matcher`
while ( i-- ) {
if ( ( elem = unmatched[ i ] ) ) {
seed[ i ] = !( matches[ i ] = elem );
}
}
} ) :
- function( elem, context, xml ) {
+ function( elem, _context, xml ) {
input[ 0 ] = elem;
matcher( input, null, xml, results );
// Don't keep the element (issue #299)
input[ 0 ] = null;
return !results.pop();
};
} ),
"has": markFunction( function( selector ) {
return function( elem ) {
return Sizzle( selector, elem ).length > 0;
};
} ),
"contains": markFunction( function( text ) {
text = text.replace( runescape, funescape );
return function( elem ) {
return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
};
} ),
// "Whether an element is represented by a :lang() selector
// is based solely on the element's language value
// being equal to the identifier C,
// or beginning with the identifier C immediately followed by "-".
// The matching of C against the element's language value is performed case-insensitively.
// The identifier C does not have to be a valid language name."
// http://www.w3.org/TR/selectors/#lang-pseudo
"lang": markFunction( function( lang ) {
// lang value must be a valid identifier
if ( !ridentifier.test( lang || "" ) ) {
Sizzle.error( "unsupported lang: " + lang );
}
lang = lang.replace( runescape, funescape ).toLowerCase();
return function( elem ) {
var elemLang;
do {
if ( ( elemLang = documentIsHTML ?
elem.lang :
elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
elemLang = elemLang.toLowerCase();
return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
}
} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
return false;
};
} ),
// Miscellaneous
"target": function( elem ) {
var hash = window.location && window.location.hash;
return hash && hash.slice( 1 ) === elem.id;
},
"root": function( elem ) {
return elem === docElem;
},
"focus": function( elem ) {
return elem === document.activeElement &&
( !document.hasFocus || document.hasFocus() ) &&
!!( elem.type || elem.href || ~elem.tabIndex );
},
// Boolean properties
"enabled": createDisabledPseudo( false ),
"disabled": createDisabledPseudo( true ),
"checked": function( elem ) {
// In CSS3, :checked should return both checked and selected elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
var nodeName = elem.nodeName.toLowerCase();
return ( nodeName === "input" && !!elem.checked ) ||
( nodeName === "option" && !!elem.selected );
},
"selected": function( elem ) {
// Accessing this property makes selected-by-default
// options in Safari work properly
if ( elem.parentNode ) {
// eslint-disable-next-line no-unused-expressions
elem.parentNode.selectedIndex;
}
return elem.selected === true;
},
// Contents
"empty": function( elem ) {
// http://www.w3.org/TR/selectors/#empty-pseudo
// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
// but not by others (comment: 8; processing instruction: 7; etc.)
// nodeType < 6 works because attributes (2) do not appear as children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
if ( elem.nodeType < 6 ) {
return false;
}
}
return true;
},
"parent": function( elem ) {
return !Expr.pseudos[ "empty" ]( elem );
},
// Element/input types
"header": function( elem ) {
return rheader.test( elem.nodeName );
},
"input": function( elem ) {
return rinputs.test( elem.nodeName );
},
"button": function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === "button" || name === "button";
},
"text": function( elem ) {
var attr;
return elem.nodeName.toLowerCase() === "input" &&
elem.type === "text" &&
// Support: IE<8
// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
( ( attr = elem.getAttribute( "type" ) ) == null ||
attr.toLowerCase() === "text" );
},
// Position-in-collection
"first": createPositionalPseudo( function() {
return [ 0 ];
} ),
- "last": createPositionalPseudo( function( matchIndexes, length ) {
+ "last": createPositionalPseudo( function( _matchIndexes, length ) {
return [ length - 1 ];
} ),
- "eq": createPositionalPseudo( function( matchIndexes, length, argument ) {
+ "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
return [ argument < 0 ? argument + length : argument ];
} ),
"even": createPositionalPseudo( function( matchIndexes, length ) {
var i = 0;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"odd": createPositionalPseudo( function( matchIndexes, length ) {
var i = 1;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
var i = argument < 0 ?
argument + length :
argument > length ?
length :
argument;
for ( ; --i >= 0; ) {
matchIndexes.push( i );
}
return matchIndexes;
} ),
"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
var i = argument < 0 ? argument + length : argument;
for ( ; ++i < length; ) {
matchIndexes.push( i );
}
return matchIndexes;
} )
}
};
Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
// Add button/input type pseudos
for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
Expr.pseudos[ i ] = createInputPseudo( i );
}
for ( i in { submit: true, reset: true } ) {
Expr.pseudos[ i ] = createButtonPseudo( i );
}
// Easy API for creating new setFilters
function setFilters() {}
setFilters.prototype = Expr.filters = Expr.pseudos;
Expr.setFilters = new setFilters();
tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
var matched, match, tokens, type,
soFar, groups, preFilters,
cached = tokenCache[ selector + " " ];
if ( cached ) {
return parseOnly ? 0 : cached.slice( 0 );
}
soFar = selector;
groups = [];
preFilters = Expr.preFilter;
while ( soFar ) {
// Comma and first run
if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
if ( match ) {
// Don't consume trailing commas as valid
soFar = soFar.slice( match[ 0 ].length ) || soFar;
}
groups.push( ( tokens = [] ) );
}
matched = false;
// Combinators
if ( ( match = rcombinators.exec( soFar ) ) ) {
matched = match.shift();
tokens.push( {
value: matched,
// Cast descendant combinators to space
type: match[ 0 ].replace( rtrim, " " )
} );
soFar = soFar.slice( matched.length );
}
// Filters
for ( type in Expr.filter ) {
if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
( match = preFilters[ type ]( match ) ) ) ) {
matched = match.shift();
tokens.push( {
value: matched,
type: type,
matches: match
} );
soFar = soFar.slice( matched.length );
}
}
if ( !matched ) {
break;
}
}
// Return the length of the invalid excess
// if we're just parsing
// Otherwise, throw an error or return tokens
return parseOnly ?
soFar.length :
soFar ?
Sizzle.error( selector ) :
// Cache the tokens
tokenCache( selector, groups ).slice( 0 );
};
function toSelector( tokens ) {
var i = 0,
len = tokens.length,
selector = "";
for ( ; i < len; i++ ) {
selector += tokens[ i ].value;
}
return selector;
}
function addCombinator( matcher, combinator, base ) {
var dir = combinator.dir,
skip = combinator.next,
key = skip || dir,
checkNonElements = base && key === "parentNode",
doneName = done++;
return combinator.first ?
// Check against closest ancestor/preceding element
function( elem, context, xml ) {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
return matcher( elem, context, xml );
}
}
return false;
} :
// Check against all ancestor/preceding elements
function( elem, context, xml ) {
var oldCache, uniqueCache, outerCache,
newCache = [ dirruns, doneName ];
// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
if ( xml ) {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
if ( matcher( elem, context, xml ) ) {
return true;
}
}
}
} else {
while ( ( elem = elem[ dir ] ) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
outerCache = elem[ expando ] || ( elem[ expando ] = {} );
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ elem.uniqueID ] ||
( outerCache[ elem.uniqueID ] = {} );
if ( skip && skip === elem.nodeName.toLowerCase() ) {
elem = elem[ dir ] || elem;
} else if ( ( oldCache = uniqueCache[ key ] ) &&
oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
// Assign to newCache so results back-propagate to previous elements
return ( newCache[ 2 ] = oldCache[ 2 ] );
} else {
// Reuse newcache so results back-propagate to previous elements
uniqueCache[ key ] = newCache;
// A match means we're done; a fail means we have to keep checking
if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
return true;
}
}
}
}
}
return false;
};
}
function elementMatcher( matchers ) {
return matchers.length > 1 ?
function( elem, context, xml ) {
var i = matchers.length;
while ( i-- ) {
if ( !matchers[ i ]( elem, context, xml ) ) {
return false;
}
}
return true;
} :
matchers[ 0 ];
}
function multipleContexts( selector, contexts, results ) {
var i = 0,
len = contexts.length;
for ( ; i < len; i++ ) {
Sizzle( selector, contexts[ i ], results );
}
return results;
}
function condense( unmatched, map, filter, context, xml ) {
var elem,
newUnmatched = [],
i = 0,
len = unmatched.length,
mapped = map != null;
for ( ; i < len; i++ ) {
if ( ( elem = unmatched[ i ] ) ) {
if ( !filter || filter( elem, context, xml ) ) {
newUnmatched.push( elem );
if ( mapped ) {
map.push( i );
}
}
}
}
return newUnmatched;
}
function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
if ( postFilter && !postFilter[ expando ] ) {
postFilter = setMatcher( postFilter );
}
if ( postFinder && !postFinder[ expando ] ) {
postFinder = setMatcher( postFinder, postSelector );
}
return markFunction( function( seed, results, context, xml ) {
var temp, i, elem,
preMap = [],
postMap = [],
preexisting = results.length,
// Get initial elements from seed or context
elems = seed || multipleContexts(
selector || "*",
context.nodeType ? [ context ] : context,
[]
),
// Prefilter to get matcher input, preserving a map for seed-results synchronization
matcherIn = preFilter && ( seed || !selector ) ?
condense( elems, preMap, preFilter, context, xml ) :
elems,
matcherOut = matcher ?
// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
// ...intermediate processing is necessary
[] :
// ...otherwise use results directly
results :
matcherIn;
// Find primary matches
if ( matcher ) {
matcher( matcherIn, matcherOut, context, xml );
}
// Apply postFilter
if ( postFilter ) {
temp = condense( matcherOut, postMap );
postFilter( temp, [], context, xml );
// Un-match failing elements by moving them back to matcherIn
i = temp.length;
while ( i-- ) {
if ( ( elem = temp[ i ] ) ) {
matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
}
}
}
if ( seed ) {
if ( postFinder || preFilter ) {
if ( postFinder ) {
// Get the final matcherOut by condensing this intermediate into postFinder contexts
temp = [];
i = matcherOut.length;
while ( i-- ) {
if ( ( elem = matcherOut[ i ] ) ) {
// Restore matcherIn since elem is not yet a final match
temp.push( ( matcherIn[ i ] = elem ) );
}
}
postFinder( null, ( matcherOut = [] ), temp, xml );
}
// Move matched elements from seed to results to keep them synchronized
i = matcherOut.length;
while ( i-- ) {
if ( ( elem = matcherOut[ i ] ) &&
( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
seed[ temp ] = !( results[ temp ] = elem );
}
}
}
// Add elements to results, through postFinder if defined
} else {
matcherOut = condense(
matcherOut === results ?
matcherOut.splice( preexisting, matcherOut.length ) :
matcherOut
);
if ( postFinder ) {
postFinder( null, results, matcherOut, xml );
} else {
push.apply( results, matcherOut );
}
}
} );
}
function matcherFromTokens( tokens ) {
var checkContext, matcher, j,
len = tokens.length,
leadingRelative = Expr.relative[ tokens[ 0 ].type ],
implicitRelative = leadingRelative || Expr.relative[ " " ],
i = leadingRelative ? 1 : 0,
// The foundational matcher ensures that elements are reachable from top-level context(s)
matchContext = addCombinator( function( elem ) {
return elem === checkContext;
}, implicitRelative, true ),
matchAnyContext = addCombinator( function( elem ) {
return indexOf( checkContext, elem ) > -1;
}, implicitRelative, true ),
matchers = [ function( elem, context, xml ) {
var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
( checkContext = context ).nodeType ?
matchContext( elem, context, xml ) :
matchAnyContext( elem, context, xml ) );
// Avoid hanging onto element (issue #299)
checkContext = null;
return ret;
} ];
for ( ; i < len; i++ ) {
if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
} else {
matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
// Return special upon seeing a positional matcher
if ( matcher[ expando ] ) {
// Find the next relative operator (if any) for proper handling
j = ++i;
for ( ; j < len; j++ ) {
if ( Expr.relative[ tokens[ j ].type ] ) {
break;
}
}
return setMatcher(
i > 1 && elementMatcher( matchers ),
i > 1 && toSelector(
// If the preceding token was a descendant combinator, insert an implicit any-element `*`
tokens
.slice( 0, i - 1 )
.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
).replace( rtrim, "$1" ),
matcher,
i < j && matcherFromTokens( tokens.slice( i, j ) ),
j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
j < len && toSelector( tokens )
);
}
matchers.push( matcher );
}
}
return elementMatcher( matchers );
}
function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
var bySet = setMatchers.length > 0,
byElement = elementMatchers.length > 0,
superMatcher = function( seed, context, xml, results, outermost ) {
var elem, j, matcher,
matchedCount = 0,
i = "0",
unmatched = seed && [],
setMatched = [],
contextBackup = outermostContext,
// We must always have either seed elements or outermost context
elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
// Use integer dirruns iff this is the outermost matcher
dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
len = elems.length;
if ( outermost ) {
outermostContext = context === document || context || outermost;
}
// Add elements passing elementMatchers directly to results
// Support: IE<9, Safari
// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
if ( byElement && elem ) {
j = 0;
if ( !context && elem.ownerDocument !== document ) {
setDocument( elem );
xml = !documentIsHTML;
}
while ( ( matcher = elementMatchers[ j++ ] ) ) {
if ( matcher( elem, context || document, xml ) ) {
results.push( elem );
break;
}
}
if ( outermost ) {
dirruns = dirrunsUnique;
}
}
// Track unmatched elements for set filters
if ( bySet ) {
// They will have gone through all possible matchers
if ( ( elem = !matcher && elem ) ) {
matchedCount--;
}
// Lengthen the array for every element, matched or not
if ( seed ) {
unmatched.push( elem );
}
}
}
// `i` is now the count of elements visited above, and adding it to `matchedCount`
// makes the latter nonnegative.
matchedCount += i;
// Apply set filters to unmatched elements
// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
// no element matchers and no seed.
// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
// case, which will result in a "00" `matchedCount` that differs from `i` but is also
// numerically zero.
if ( bySet && i !== matchedCount ) {
j = 0;
while ( ( matcher = setMatchers[ j++ ] ) ) {
matcher( unmatched, setMatched, context, xml );
}
if ( seed ) {
// Reintegrate element matches to eliminate the need for sorting
if ( matchedCount > 0 ) {
while ( i-- ) {
if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
setMatched[ i ] = pop.call( results );
}
}
}
// Discard index placeholder values to get only actual matches
setMatched = condense( setMatched );
}
// Add matches to results
push.apply( results, setMatched );
// Seedless set matches succeeding multiple successful matchers stipulate sorting
if ( outermost && !seed && setMatched.length > 0 &&
( matchedCount + setMatchers.length ) > 1 ) {
Sizzle.uniqueSort( results );
}
}
// Override manipulation of globals by nested matchers
if ( outermost ) {
dirruns = dirrunsUnique;
outermostContext = contextBackup;
}
return unmatched;
};
return bySet ?
markFunction( superMatcher ) :
superMatcher;
}
compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
var i,
setMatchers = [],
elementMatchers = [],
cached = compilerCache[ selector + " " ];
if ( !cached ) {
// Generate a function of recursive functions that can be used to check each element
if ( !match ) {
match = tokenize( selector );
}
i = match.length;
while ( i-- ) {
cached = matcherFromTokens( match[ i ] );
if ( cached[ expando ] ) {
setMatchers.push( cached );
} else {
elementMatchers.push( cached );
}
}
// Cache the compiled function
cached = compilerCache(
selector,
matcherFromGroupMatchers( elementMatchers, setMatchers )
);
// Save selector and tokenization
cached.selector = selector;
}
return cached;
};
/**
* A low-level selection function that works with Sizzle's compiled
* selector functions
* @param {String|Function} selector A selector or a pre-compiled
* selector function built with Sizzle.compile
* @param {Element} context
* @param {Array} [results]
* @param {Array} [seed] A set of elements to match against
*/
select = Sizzle.select = function( selector, context, results, seed ) {
var i, tokens, token, type, find,
compiled = typeof selector === "function" && selector,
match = !seed && tokenize( ( selector = compiled.selector || selector ) );
results = results || [];
// Try to minimize operations if there is only one selector in the list and no seed
// (the latter of which guarantees us context)
if ( match.length === 1 ) {
// Reduce context if the leading compound selector is an ID
tokens = match[ 0 ] = match[ 0 ].slice( 0 );
if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
.replace( runescape, funescape ), context ) || [] )[ 0 ];
if ( !context ) {
return results;
// Precompiled matchers will still verify ancestry, so step up a level
} else if ( compiled ) {
context = context.parentNode;
}
selector = selector.slice( tokens.shift().value.length );
}
// Fetch a seed set for right-to-left matching
i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
while ( i-- ) {
token = tokens[ i ];
// Abort if we hit a combinator
if ( Expr.relative[ ( type = token.type ) ] ) {
break;
}
if ( ( find = Expr.find[ type ] ) ) {
// Search, expanding context for leading sibling combinators
if ( ( seed = find(
token.matches[ 0 ].replace( runescape, funescape ),
rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
context
) ) ) {
// If seed is empty or no tokens remain, we can return early
tokens.splice( i, 1 );
selector = seed.length && toSelector( tokens );
if ( !selector ) {
push.apply( results, seed );
return results;
}
break;
}
}
}
}
// Compile and execute a filtering function if one is not provided
// Provide `match` to avoid retokenization if we modified the selector above
( compiled || compile( selector, match ) )(
seed,
context,
!documentIsHTML,
results,
!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
);
return results;
};
// One-time assignments
// Sort stability
support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
// Support: Chrome 14-35+
// Always assume duplicates if they aren't passed to the comparison function
support.detectDuplicates = !!hasDuplicate;
// Initialize against the default document
setDocument();
// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
// Detached nodes confoundingly follow *each other*
support.sortDetached = assert( function( el ) {
// Should return 1, but returns 4 (following)
return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
} );
// Support: IE<8
// Prevent attribute/property "interpolation"
// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
if ( !assert( function( el ) {
el.innerHTML = "<a href='#'></a>";
return el.firstChild.getAttribute( "href" ) === "#";
} ) ) {
addHandle( "type|href|height|width", function( elem, name, isXML ) {
if ( !isXML ) {
return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
}
} );
}
// Support: IE<9
// Use defaultValue in place of getAttribute("value")
if ( !support.attributes || !assert( function( el ) {
el.innerHTML = "<input/>";
el.firstChild.setAttribute( "value", "" );
return el.firstChild.getAttribute( "value" ) === "";
} ) ) {
- addHandle( "value", function( elem, name, isXML ) {
+ addHandle( "value", function( elem, _name, isXML ) {
if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
return elem.defaultValue;
}
} );
}
// Support: IE<9
// Use getAttributeNode to fetch booleans when getAttribute lies
if ( !assert( function( el ) {
return el.getAttribute( "disabled" ) == null;
} ) ) {
addHandle( booleans, function( elem, name, isXML ) {
var val;
if ( !isXML ) {
return elem[ name ] === true ? name.toLowerCase() :
( val = elem.getAttributeNode( name ) ) && val.specified ?
val.value :
null;
}
} );
}
// EXPOSE
var _sizzle = window.Sizzle;
Sizzle.noConflict = function() {
if ( window.Sizzle === Sizzle ) {
window.Sizzle = _sizzle;
}
return Sizzle;
};
if ( typeof define === "function" && define.amd ) {
define( function() {
return Sizzle;
} );
// Sizzle requires that there be a global window in Common-JS like environments
} else if ( typeof module !== "undefined" && module.exports ) {
module.exports = Sizzle;
} else {
window.Sizzle = Sizzle;
}
// EXPOSE
} )( window );
|
jquery/sizzle
|
7d92424c1a65a367a45034803e9de97462ea42e5
|
Core: Throw a better error when documentElement is missing
|
diff --git a/src/sizzle.js b/src/sizzle.js
index 66b8577..648136a 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -70,1025 +70,1025 @@ var i,
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
"*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
funescape = function( _, escaped, escapedWhitespace ) {
var high = "0x" + escaped - 0x10000;
// NaN means non-codepoint
// Support: Firefox<24
// Workaround erroneous numeric interpretation of +"0x"
return high !== high || escapedWhitespace ?
escaped :
high < 0 ?
// BMP codepoint
String.fromCharCode( high + 0x10000 ) :
// Supplemental Plane codepoint (surrogate pair)
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
(arr = slice.call( preferredDoc.childNodes )),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
push_native.apply( target, slice.call(els) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( (target[j++] = els[i++]) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
// ID selector
if ( (m = match[1]) ) {
// Document context
if ( nodeType === 9 ) {
if ( (elem = context.getElementById( m )) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && (elem = newContext.getElementById( m )) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[2] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( (m = match[3]) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
// Support: IE 8 only
// Exclude object elements
(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( (nid = context.getAttribute( "id" )) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", (nid = expando) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[i] = "#" + nid + " " + toSelector( groups[i] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return (cache[ key + " " ] = value);
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement("fieldset");
try {
return !!fn( el );
} catch (e) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split("|"),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[i] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( (cur = cur.nextSibling) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return (name === "input" || name === "button") && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction(function( argument ) {
argument = +argument;
return markFunction(function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ (j = matchIndexes[i]) ] ) {
seed[j] = !(matches[j] = seed[j]);
}
}
});
});
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
var namespace = elem.namespaceURI,
docElem = (elem.ownerDocument || elem).documentElement;
// Support: IE <=8
// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
// https://bugs.jquery.com/ticket/4833
return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
- if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
+ if ( doc === document || doc.nodeType !== 9 ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
(subWindow = document.defaultView) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert(function( el ) {
el.className = "i";
return !el.getAttribute("className");
});
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert(function( el ) {
el.appendChild( document.createComment("") );
return !el.getElementsByTagName("*").length;
});
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert(function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
});
// ID filter and find
if ( support.getById ) {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute("id") === attrId;
};
};
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
var node = typeof elem.getAttributeNode !== "undefined" &&
elem.getAttributeNode("id");
return node && node.value === attrId;
};
};
// Support: IE 6 - 7 only
// getElementById is not reliable as a find shortcut
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var node, i, elems,
elem = context.getElementById( id );
if ( elem ) {
// Verify the id attribute
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
// Fall back on getElementsByName
elems = context.getElementsByName( id );
i = 0;
while ( (elem = elems[i++]) ) {
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
}
}
return [];
}
};
}
// Tag
Expr.find["TAG"] = support.getElementsByTagName ?
function( tag, context ) {
if ( typeof context.getElementsByTagName !== "undefined" ) {
return context.getElementsByTagName( tag );
// DocumentFragment nodes don't have gEBTN
} else if ( support.qsa ) {
return context.querySelectorAll( tag );
}
} :
function( tag, context ) {
var elem,
tmp = [],
i = 0,
// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
results = context.getElementsByTagName( tag );
// Filter out possible comments
if ( tag === "*" ) {
while ( (elem = results[i++]) ) {
if ( elem.nodeType === 1 ) {
tmp.push( elem );
}
}
return tmp;
}
return results;
};
// Class
Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) {
if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
return context.getElementsByClassName( className );
}
};
/* QSA/matchesSelector
---------------------------------------------------------------------- */
// QSA and matchesSelector support
// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
rbuggyMatches = [];
// qSa(:focus) reports false when true (Chrome 21)
// We allow this because of a bug in IE8/9 that throws an error
// whenever `document.activeElement` is accessed on an iframe
// So, we allow :focus to pass through QSA all the time to avoid the IE error
// See https://bugs.jquery.com/ticket/13378
rbuggyQSA = [];
if ( (support.qsa = rnative.test( document.querySelectorAll )) ) {
// Build QSA regex
// Regex strategy adopted from Diego Perini
assert(function( el ) {
// Select is set to empty string on purpose
// This is to test IE's treatment of not explicitly
// setting a boolean content attribute,
// since its presence should be enough
// https://bugs.jquery.com/ticket/12359
docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
"<select id='" + expando + "-\r\\' msallowcapture=''>" +
"<option selected=''></option></select>";
// Support: IE8, Opera 11-12.16
// Nothing should be selected when empty strings follow ^= or $= or *=
// The test attribute must be unknown in Opera but "safe" for WinRT
// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
if ( el.querySelectorAll("[msallowcapture^='']").length ) {
rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
}
// Support: IE8
// Boolean attributes and "value" are not treated correctly
if ( !el.querySelectorAll("[selected]").length ) {
rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
}
// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
rbuggyQSA.push("~=");
}
// Webkit/Opera - :checked should return selected option elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
// IE8 throws error here and will not see later tests
if ( !el.querySelectorAll(":checked").length ) {
rbuggyQSA.push(":checked");
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push(".#.+[+~]");
}
});
assert(function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement("input");
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll("[name=d]").length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll(":enabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll(":disabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll("*,:x");
rbuggyQSA.push(",.*:");
});
}
if ( (support.matchesSelector = rnative.test( (matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector) )) ) {
assert(function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
});
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
));
} :
function( a, b ) {
if ( b ) {
while ( (b = b.parentNode) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
(!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) {
// Choose the first element that is related to our preferred document
if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) {
return -1;
}
if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( (cur = cur.parentNode) ) {
ap.unshift( cur );
}
cur = b;
while ( (cur = cur.parentNode) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[i] === bp[i] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[i], bp[i] ) :
// Otherwise nodes in our document sort first
ap[i] === preferredDoc ? -1 :
bp[i] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch (e) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
(val = elem.getAttributeNode(name)) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return (sel + "").replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( (elem = results[i++]) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
|
jquery/sizzle
|
f27f9ffc9f8288cbb8cfed4d7735bdf42f2945ce
|
Release: Fix AUTHORS.txt
|
diff --git a/AUTHORS.txt b/AUTHORS.txt
index ad68a50..7f52a5e 100644
--- a/AUTHORS.txt
+++ b/AUTHORS.txt
@@ -1,64 +1,65 @@
-[4mRunning "authors" task[24m
+Authors ordered by first contribution
+
John Resig <jeresig@gmail.com>
Cheah Chu Yeow <chuyeow@gmail.com>
Andrew Chalkley <andrew@chalkley.org>
Fabio Buffoni <fabio.buffoni@bitmaster.it>
Stefan Bauckmeier <stefan@bauckmeier.de>
Brandon Aaron <brandon.aaron@gmail.com>
Anton Kovalyov <anton@kovalyov.net>
Dušan B. Jovanovic <dbjdbj@gmail.com>
Riccardo De Agostini <rdeago@gmail.com>
Fabian Jakobs <fabian.jakobs@web.de>
Karl Swedberg <kswedberg@gmail.com>
Jake Archibald <jake.archibald@bbc.co.uk>
Colin Snover <github.com@zetafleet.com>
Anton Matzneller <obhvsbypqghgc@gmail.com>
Dave Methvin <dave.methvin@gmail.com>
Corey Frang <gnarf@gnarf.net>
Mathias Bynens <mathias@qiwi.be>
John Firebaugh <john_firebaugh@us.ibm.com>
Timmy Willison <timmywillisn@gmail.com>
Mike Sherov <mike.sherov@gmail.com>
Rock Hymas <rock@fogcreek.com>
Yehuda Katz <wycats@gmail.com>
Jörn Zaefferer <joern.zaefferer@gmail.com>
Richard Gibson <richard.gibson@gmail.com>
Vitya Muhachev <vic99999@yandex.ru>
Henri Wiechers <hwiechers@gmail.com>
Alan Plum <github@ap.apsq.de>
Chad Killingsworth <chadkillingsworth@missouristate.edu>
Markus Staab <markus.staab@redaxo.de>
Timo Tijhof <krinklemail@gmail.com>
Diego Tres <diegotres@gmail.com>
Jonathan Sampson <jjdsampson@gmail.com>
Pascal Borreli <pascal@borreli.com>
Daniel Herman <daniel.c.herman@gmail.com>
Frederic Junod <frederic.junod@camptocamp.com>
Mitch Foley <mitch@thefoley.net>
Scott González <scott.gonzalez@gmail.com>
Oleg Gaidarenko <markelog@gmail.com>
Dan Burzo <danburzo@gmail.com>
Goare Mao <mygoare@gmail.com>
Dongseok Paeng <dongseok83.paeng@lge.com>
MichaÅ GoÅÄbiowski-Owczarek <m.goleb@gmail.com>
Philip Jägenstedt <philip@foolip.org>
Chris Antaki <ChrisAntaki@gmail.com>
Benjamin Tan <demoneaux@gmail.com>
T.J. Crowder <tj.crowder@farsightsoftware.com>
Anne-Gaelle Colom <coloma@westminster.ac.uk>
Neftaly Hernandez <neftaly.hernandez@gmail.com>
Jörn Wagner <joern.wagner@explicatis.com>
Chris Rebert <code@rebertia.com>
Colin Frick <colin@bash.li>
John-David Dalton <john.david.dalton@gmail.com>
Kevin Kirsche <Kev.Kirsche+GitHub@gmail.com>
Steve Mao <maochenyan@gmail.com>
Tom von Clef <thomas.vonclef@gmail.com>
Josh Soref <apache@soref.com>
Saptak Sengupta <saptak013@gmail.com>
Jon Dufresne <jon.dufresne@gmail.com>
Andrey Meshkov <ay.meshkov@gmail.com>
Sébastien Règne <regseb@users.noreply.github.com>
Andrey Meshkov <am@adguard.com>
Siddharth Dungarwal <sd5869@gmail.com>
wartmanm <3869625+wartmanm@users.noreply.github.com>
|
jquery/sizzle
|
66f59e690521bdc38c79b33d94900bca9d7b87aa
|
Build: Updating the master version to 2.3.5-pre.
|
diff --git a/package.json b/package.json
index 2f5da0d..35ee503 100644
--- a/package.json
+++ b/package.json
@@ -1,85 +1,85 @@
{
"title": "Sizzle",
"name": "sizzle",
- "version": "2.3.4",
+ "version": "2.3.5-pre",
"description": "A pure-JavaScript, bottom-up CSS selector engine designed to be easily dropped in to a host library.",
"keywords": [
"sizzle",
"javascript",
"CSS",
"selector",
"jquery"
],
"homepage": "https://sizzlejs.com",
"author": {
"name": "JS Foundation and other contributors",
"url": "https://github.com/jquery/sizzle/blob/2.3.4/AUTHORS.txt"
},
"repository": {
"type": "git",
"url": "https://github.com/jquery/sizzle.git"
},
"bugs": {
"url": "https://github.com/jquery/sizzle/issues"
},
"license": "MIT",
"files": [
"AUTHORS.txt",
"LICENSE.txt",
"dist/sizzle.js",
"dist/sizzle.min.js",
"dist/sizzle.min.map"
],
"main": "dist/sizzle.js",
"dependencies": {},
"devDependencies": {
"benchmark": "2.1.4",
"commitplease": "2.7.10",
"grunt": "0.4.5",
"grunt-cli": "0.1.13",
"grunt-compare-size": "0.4.2",
"grunt-contrib-jshint": "1.1.0",
"grunt-contrib-qunit": "2.0.0",
"grunt-contrib-uglify": "3.0.1",
"grunt-contrib-watch": "1.0.0",
"grunt-git-authors": "3.2.0",
"grunt-jscs": "0.6.2",
"grunt-jsonlint": "1.1.0",
"grunt-karma": "2.0.0",
"grunt-npmcopy": "0.1.0",
"gzip-js": "0.3.2",
"jquery": "1.9.1",
"karma": "1.3.0",
"karma-browserstack-launcher": "1.3.0",
"karma-chrome-launcher": "2.2.0",
"karma-firefox-launcher": "1.0.1",
"karma-html2js-preprocessor": "1.1.0",
"karma-phantomjs-launcher": "1.0.4",
"karma-qunit": "1.2.1",
"load-grunt-tasks": "3.5.2",
"phantomjs-prebuilt": "2.1.15",
"qunitjs": "1.23.1",
"requirejs": "2.3.5",
"requirejs-domready": "2.0.3",
"requirejs-text": "2.0.15"
},
"scripts": {
"build": "npm install && grunt",
"start": "grunt start",
"test": "grunt test"
},
"commitplease": {
"components": [
"Misc",
"Docs",
"Tests",
"Build",
"Release",
"Core",
"Tokenize",
"Compile",
"Selector",
"SetDocument"
]
}
}
|
jquery/sizzle
|
1734d4b26e6170bbcb6ab26cfcf209ed40f6e24e
|
Release: Update version to 2.3.4
|
diff --git a/bower.json b/bower.json
index 68b0659..c908c13 100644
--- a/bower.json
+++ b/bower.json
@@ -1,25 +1,26 @@
{
"name": "sizzle",
"main": "./dist/sizzle.js",
"license": "MIT",
"ignore": [
"**/.*",
"package.json",
"bower.json",
"speed",
"Makefile",
"*.md",
"*.txt",
"!LICENSE.txt",
"src",
"test",
"Gruntfile.js"
],
"keywords": [
"sizzle",
"javascript",
"CSS",
"selector",
"jquery"
- ]
+ ],
+ "version": "2.3.4"
}
diff --git a/changelog b/changelog
new file mode 100644
index 0000000..a50ab2f
--- /dev/null
+++ b/changelog
@@ -0,0 +1,27 @@
+* 2.3.4 ([a04b7c5](https://github.com/jquery/sizzle/commit/a04b7c5db3b1d3c5a17265127d50e9ea9c5be5f0))
+* Build: Restore ASCII-only output ([5dfff27](https://github.com/jquery/sizzle/commit/5dfff27be7b3f398e2bad246e83cfa3582c119a7))
+* Core: Avoid unnecessary pre-qSA DOM manipulation ([#430](https://github.com/jquery/sizzle/issues/430), [71fe25c](https://github.com/jquery/sizzle/commit/71fe25c4c9a10d8827b845d398ca8fb7da163749))
+* Core: Stop changing matchesSelector input ([#408](https://github.com/jquery/sizzle/issues/408), [#406](https://github.com/jquery/sizzle/issues/406), [8bda6c9](https://github.com/jquery/sizzle/commit/8bda6c95617777ea596bf54636b27548af69d086))
+* Misc: Update isXML to recognize HTML-embedded elements ([#378](https://github.com/jquery/sizzle/issues/378), [26a1f3f](https://github.com/jquery/sizzle/commit/26a1f3f6f156cb687d0d7adc7bf79f0e5454811a))
+* Release: Add jquery-release script ([686f08d](https://github.com/jquery/sizzle/commit/686f08dc3493e2e1ed3d97e4e3f80f158b1c94c8))
+* Selector: Fix nonnativeSelectorCache ([#418](https://github.com/jquery/sizzle/issues/418), [3116795](https://github.com/jquery/sizzle/commit/3116795bba9a0c3d624e0718006b25aa5568d4cb))
+* Selector: Prevent seeded invocations from cutting off the qSA path ([#393](https://github.com/jquery/sizzle/issues/393), [eabce51](https://github.com/jquery/sizzle/commit/eabce51ea7360c4507da2eeaec2633378de4ec8d))
+* Selector: Stop using innerText in :contains ([#335](https://github.com/jquery/sizzle/issues/335), [67e9691](https://github.com/jquery/sizzle/commit/67e9691e8689b824387affb9da06dc663da63598))
+* Selector: Only fieldset ancestors can :disable form elements ([abde99f](https://github.com/jquery/sizzle/commit/abde99f6dc2ed3d489a6d7a52f3df9774be16a32))
+* Selector: Optimize ":lt(bigNumber)" ([1c0c330](https://github.com/jquery/sizzle/commit/1c0c33066f053e62ac268658f65e7d912f3bdb0d))
+
+
+
+--- Issue List ---
+#430 querySelectorAll workaround is not always needed
+#418 Selector: fix nonnativeSelectorCache
+#408 Selectors with escaped = characters gaining extra single-quotes through filter().
+#406 Edge 15 fails the matchesSelector "attribute-equals non-value" test
+#393 Performance impact: sizzle don't use querySelectorAll for specific selector after using $('...').filter('selector')
+#378 Sizzle.isXML misidentifies embedded SVG
+#377 Travis has been broken for a long time
+#362 Error when testing on oldIE
+#335 pseudo contains uses innerText
+#333 ID selectors provide no filtering benefit at all in oldIE
+#314 Browserstack and android devices
+#305 Mobile devices are often not getting captured on Travis
diff --git a/dist/sizzle.js b/dist/sizzle.js
index 1065e13..414d172 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -1,521 +1,521 @@
/*!
- * Sizzle CSS Selector Engine v2.3.4-pre
+ * Sizzle CSS Selector Engine v2.3.4
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
- * Date: 2019-01-14
+ * Date: 2019-04-08
*/
(function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ({}).hasOwnProperty,
arr = [],
pop = arr.pop,
push_native = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[i] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
"*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
funescape = function( _, escaped, escapedWhitespace ) {
var high = "0x" + escaped - 0x10000;
// NaN means non-codepoint
// Support: Firefox<24
// Workaround erroneous numeric interpretation of +"0x"
return high !== high || escapedWhitespace ?
escaped :
high < 0 ?
// BMP codepoint
String.fromCharCode( high + 0x10000 ) :
// Supplemental Plane codepoint (surrogate pair)
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
(arr = slice.call( preferredDoc.childNodes )),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
push_native.apply( target, slice.call(els) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( (target[j++] = els[i++]) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
// ID selector
if ( (m = match[1]) ) {
// Document context
if ( nodeType === 9 ) {
if ( (elem = context.getElementById( m )) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && (elem = newContext.getElementById( m )) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[2] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( (m = match[3]) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
// Support: IE 8 only
// Exclude object elements
(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( (nid = context.getAttribute( "id" )) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", (nid = expando) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[i] = "#" + nid + " " + toSelector( groups[i] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return (cache[ key + " " ] = value);
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement("fieldset");
try {
return !!fn( el );
} catch (e) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split("|"),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[i] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( (cur = cur.nextSibling) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return (name === "input" || name === "button") && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
diff --git a/dist/sizzle.min.js b/dist/sizzle.min.js
index 0e403e4..fdbef69 100644
--- a/dist/sizzle.min.js
+++ b/dist/sizzle.min.js
@@ -1,3 +1,3 @@
-/*! Sizzle v2.3.4-pre | (c) JS Foundation and other contributors | js.foundation */
+/*! Sizzle v2.3.4 | (c) JS Foundation and other contributors | js.foundation */
!function(e){var t,n,r,i,o,u,l,a,c,s,f,d,p,h,g,m,y,w,v,b="sizzle"+1*new Date,N=e.document,x=0,C=0,E=ae(),D=ae(),S=ae(),A=ae(),T=function(e,t){return e===t&&(f=!0),0},L={}.hasOwnProperty,I=[],q=I.pop,B=I.push,R=I.push,$=I.slice,k=function(e,t){for(var n=0,r=e.length;n<r;n++)if(e[n]===t)return n;return-1},H="checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",M="[\\x20\\t\\r\\n\\f]",P="(?:\\\\.|[\\w-]|[^\0-\\xa0])+",z="\\["+M+"*("+P+")(?:"+M+"*([*^$|!~]?=)"+M+"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|("+P+"))|)"+M+"*\\]",F=":("+P+")(?:\\((('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|((?:\\\\.|[^\\\\()[\\]]|"+z+")*)|.*)\\)|)",O=new RegExp(M+"+","g"),j=new RegExp("^"+M+"+|((?:^|[^\\\\])(?:\\\\.)*)"+M+"+$","g"),G=new RegExp("^"+M+"*,"+M+"*"),U=new RegExp("^"+M+"*([>+~]|"+M+")"+M+"*"),V=new RegExp(M+"|>"),X=new RegExp(F),J=new RegExp("^"+P+"$"),K={ID:new RegExp("^#("+P+")"),CLASS:new 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diff --git a/package.json b/package.json
index 5505e16..2f5da0d 100644
--- a/package.json
+++ b/package.json
@@ -1,85 +1,85 @@
{
"title": "Sizzle",
"name": "sizzle",
- "version": "2.3.4-pre",
+ "version": "2.3.4",
"description": "A pure-JavaScript, bottom-up CSS selector engine designed to be easily dropped in to a host library.",
"keywords": [
"sizzle",
"javascript",
"CSS",
"selector",
"jquery"
],
"homepage": "https://sizzlejs.com",
"author": {
"name": "JS Foundation and other contributors",
- "url": "https://github.com/jquery/sizzle/blob/master/AUTHORS.txt"
+ "url": "https://github.com/jquery/sizzle/blob/2.3.4/AUTHORS.txt"
},
"repository": {
"type": "git",
"url": "https://github.com/jquery/sizzle.git"
},
"bugs": {
"url": "https://github.com/jquery/sizzle/issues"
},
"license": "MIT",
"files": [
"AUTHORS.txt",
"LICENSE.txt",
"dist/sizzle.js",
"dist/sizzle.min.js",
"dist/sizzle.min.map"
],
"main": "dist/sizzle.js",
"dependencies": {},
"devDependencies": {
"benchmark": "2.1.4",
"commitplease": "2.7.10",
"grunt": "0.4.5",
"grunt-cli": "0.1.13",
"grunt-compare-size": "0.4.2",
"grunt-contrib-jshint": "1.1.0",
"grunt-contrib-qunit": "2.0.0",
"grunt-contrib-uglify": "3.0.1",
"grunt-contrib-watch": "1.0.0",
"grunt-git-authors": "3.2.0",
"grunt-jscs": "0.6.2",
"grunt-jsonlint": "1.1.0",
"grunt-karma": "2.0.0",
"grunt-npmcopy": "0.1.0",
"gzip-js": "0.3.2",
"jquery": "1.9.1",
"karma": "1.3.0",
"karma-browserstack-launcher": "1.3.0",
"karma-chrome-launcher": "2.2.0",
"karma-firefox-launcher": "1.0.1",
"karma-html2js-preprocessor": "1.1.0",
"karma-phantomjs-launcher": "1.0.4",
"karma-qunit": "1.2.1",
"load-grunt-tasks": "3.5.2",
"phantomjs-prebuilt": "2.1.15",
"qunitjs": "1.23.1",
"requirejs": "2.3.5",
"requirejs-domready": "2.0.3",
"requirejs-text": "2.0.15"
},
"scripts": {
"build": "npm install && grunt",
"start": "grunt start",
"test": "grunt test"
},
"commitplease": {
"components": [
"Misc",
"Docs",
"Tests",
"Build",
"Release",
"Core",
"Tokenize",
"Compile",
"Selector",
"SetDocument"
]
}
}
|
jquery/sizzle
|
3ec907866c44720e77ea23a12be6e5ff88bf86b6
|
Release: Update AUTHORS.txt
|
diff --git a/AUTHORS.txt b/AUTHORS.txt
index a26aa85..ad68a50 100644
--- a/AUTHORS.txt
+++ b/AUTHORS.txt
@@ -1,60 +1,64 @@
-Authors ordered by first contribution
-
+[4mRunning "authors" task[24m
John Resig <jeresig@gmail.com>
Cheah Chu Yeow <chuyeow@gmail.com>
Andrew Chalkley <andrew@chalkley.org>
Fabio Buffoni <fabio.buffoni@bitmaster.it>
Stefan Bauckmeier <stefan@bauckmeier.de>
Brandon Aaron <brandon.aaron@gmail.com>
Anton Kovalyov <anton@kovalyov.net>
Dušan B. Jovanovic <dbjdbj@gmail.com>
Riccardo De Agostini <rdeago@gmail.com>
Fabian Jakobs <fabian.jakobs@web.de>
Karl Swedberg <kswedberg@gmail.com>
Jake Archibald <jake.archibald@bbc.co.uk>
Colin Snover <github.com@zetafleet.com>
Anton Matzneller <obhvsbypqghgc@gmail.com>
Dave Methvin <dave.methvin@gmail.com>
Corey Frang <gnarf@gnarf.net>
Mathias Bynens <mathias@qiwi.be>
John Firebaugh <john_firebaugh@us.ibm.com>
Timmy Willison <timmywillisn@gmail.com>
Mike Sherov <mike.sherov@gmail.com>
Rock Hymas <rock@fogcreek.com>
Yehuda Katz <wycats@gmail.com>
Jörn Zaefferer <joern.zaefferer@gmail.com>
Richard Gibson <richard.gibson@gmail.com>
Vitya Muhachev <vic99999@yandex.ru>
Henri Wiechers <hwiechers@gmail.com>
Alan Plum <github@ap.apsq.de>
Chad Killingsworth <chadkillingsworth@missouristate.edu>
Markus Staab <markus.staab@redaxo.de>
Timo Tijhof <krinklemail@gmail.com>
Diego Tres <diegotres@gmail.com>
Jonathan Sampson <jjdsampson@gmail.com>
Pascal Borreli <pascal@borreli.com>
Daniel Herman <daniel.c.herman@gmail.com>
Frederic Junod <frederic.junod@camptocamp.com>
Mitch Foley <mitch@thefoley.net>
Scott González <scott.gonzalez@gmail.com>
Oleg Gaidarenko <markelog@gmail.com>
Dan Burzo <danburzo@gmail.com>
Goare Mao <mygoare@gmail.com>
Dongseok Paeng <dongseok83.paeng@lge.com>
MichaÅ GoÅÄbiowski-Owczarek <m.goleb@gmail.com>
Philip Jägenstedt <philip@foolip.org>
Chris Antaki <ChrisAntaki@gmail.com>
Benjamin Tan <demoneaux@gmail.com>
T.J. Crowder <tj.crowder@farsightsoftware.com>
Anne-Gaelle Colom <coloma@westminster.ac.uk>
Neftaly Hernandez <neftaly.hernandez@gmail.com>
Jörn Wagner <joern.wagner@explicatis.com>
Chris Rebert <code@rebertia.com>
Colin Frick <colin@bash.li>
John-David Dalton <john.david.dalton@gmail.com>
Kevin Kirsche <Kev.Kirsche+GitHub@gmail.com>
Steve Mao <maochenyan@gmail.com>
Tom von Clef <thomas.vonclef@gmail.com>
Josh Soref <apache@soref.com>
Saptak Sengupta <saptak013@gmail.com>
Jon Dufresne <jon.dufresne@gmail.com>
+Andrey Meshkov <ay.meshkov@gmail.com>
+Sébastien Règne <regseb@users.noreply.github.com>
+Andrey Meshkov <am@adguard.com>
+Siddharth Dungarwal <sd5869@gmail.com>
+wartmanm <3869625+wartmanm@users.noreply.github.com>
|
jquery/sizzle
|
30eae9b4c758254597ea33f32a90834f062a4f83
|
Build: Update dependencies
|
diff --git a/package-lock.json b/package-lock.json
index 46c230f..5a7ca61 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,5321 +1,6320 @@
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"name": "sizzle",
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"lockfileVersion": 1,
"requires": true,
"dependencies": {
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"integrity": "sha1-0Hf2glVx+CEy+d/67Vh7QCn+/1c=",
"dev": true
},
"abbrev": {
- "version": "1.1.0",
- "resolved": "https://registry.npmjs.org/abbrev/-/abbrev-1.1.0.tgz",
- "integrity": "sha1-0FVMIlZjbi9W58LlrRg/hZQo2B8=",
+ "version": "1.1.1",
+ "resolved": "https://registry.npmjs.org/abbrev/-/abbrev-1.1.1.tgz",
+ "integrity": "sha512-nne9/IiQ/hzIhY6pdDnbBtz7DjPTKrY00P/zvPSm5pOFkl6xuGrGnXn/VtTNNfNtAfZ9/1RtehkszU9qcTii0Q==",
"dev": true
},
"accepts": {
"version": "1.1.4",
"resolved": "https://registry.npmjs.org/accepts/-/accepts-1.1.4.tgz",
"integrity": "sha1-1xyW99QdD+2iw4zRToonwEFY30o=",
"dev": true,
"requires": {
"mime-types": "~2.0.4",
"negotiator": "0.4.9"
},
"dependencies": {
"mime-db": {
"version": "1.12.0",
"resolved": "https://registry.npmjs.org/mime-db/-/mime-db-1.12.0.tgz",
"integrity": "sha1-PQxjGA9FjrENMlqqN9fFiuMS6dc=",
"dev": true
},
"mime-types": {
"version": "2.0.14",
"resolved": "https://registry.npmjs.org/mime-types/-/mime-types-2.0.14.tgz",
"integrity": "sha1-MQ4VnbI+B3+Lsit0jav6SVcUCqY=",
"dev": true,
"requires": {
"mime-db": "~1.12.0"
}
}
}
},
"after": {
"version": "0.8.1",
"resolved": "https://registry.npmjs.org/after/-/after-0.8.1.tgz",
"integrity": "sha1-q11PuIP1loFtNRX495HAr0ht1ic=",
"dev": true
},
"agent-base": {
"version": "2.1.1",
"resolved": "https://registry.npmjs.org/agent-base/-/agent-base-2.1.1.tgz",
"integrity": "sha1-1t4Q1a9hMtW9aSQn1G/FOFOQlMc=",
"dev": true,
"requires": {
"extend": "~3.0.0",
"semver": "~5.0.1"
},
"dependencies": {
"semver": {
"version": "5.0.3",
"resolved": "https://registry.npmjs.org/semver/-/semver-5.0.3.tgz",
"integrity": "sha1-d0Zt5YnNXTyV8TiqeLxWmjy10no=",
"dev": true
}
}
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"ajv": {
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"resolved": "https://registry.npmjs.org/ajv/-/ajv-4.11.8.tgz",
"integrity": "sha1-gv+wKynmYq5TvcIK8VlHcGc5xTY=",
"dev": true,
"requires": {
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"integrity": "sha1-w7M6te42DYbg5ijwRorn7yfWVN8=",
"dev": true
},
"ansi-styles": {
"version": "2.2.1",
"resolved": "https://registry.npmjs.org/ansi-styles/-/ansi-styles-2.2.1.tgz",
"integrity": "sha1-tDLdM1i2NM914eRmQ2gkBTPB3b4=",
"dev": true
},
"anymatch": {
"version": "1.3.2",
"resolved": "https://registry.npmjs.org/anymatch/-/anymatch-1.3.2.tgz",
"integrity": "sha512-0XNayC8lTHQ2OI8aljNCN3sSx6hsr/1+rlcDAotXJR7C1oZZHCNsfpbKwMjRA3Uqb5tF1Rae2oloTr4xpq+WjA==",
"dev": true,
"requires": {
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"argparse": {
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+ "arr-union": {
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+ "resolved": "https://registry.npmjs.org/arr-union/-/arr-union-3.1.0.tgz",
+ "integrity": "sha1-45sJrqne+Gao8gbiiK9jkZuuOcQ=",
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}
}
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- "integrity": "sha1-KAS6vnEq0zeUWaz74kdGqywwP7w=",
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+ "integrity": "sha512-DpKm2Ui/xN7/HQKCtpZxoRWBhZ9Z0kqtygG8XCgNQ8ZlDnxuQmWhj566j8fN4Cu3/JmbhsDo7fcAJq4s9h27Ew==",
"dev": true,
"requires": {
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+ "spdx-correct": "^3.0.0",
+ "spdx-expression-parse": "^3.0.0"
}
},
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},
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}
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- "resolved": "https://registry.npmjs.org/vow/-/vow-0.4.16.tgz",
- "integrity": "sha1-u51U2TjV+AUg1linQOeoleMP7us=",
+ "version": "0.4.19",
+ "resolved": "https://registry.npmjs.org/vow/-/vow-0.4.19.tgz",
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- "integrity": "sha1-5/4XFg4Vx8QYTRtmapvGThjjAYQ=",
+ "version": "0.4.3",
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+ "integrity": "sha512-/poAKDTFL3zYbeQg7cl4BGcfP4sGgXKrHnRFSKj97dteUFu8oyXMwIcdwu8NSx/RmPGIuYx1Bik/y5vU4H/VKw==",
"dev": true,
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}
},
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- "integrity": "sha1-XLJVbOuF9Dc8bYI4qmkchFThOjY=",
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+ "integrity": "sha1-DK+dLXVdk67gSdS90NP+LMoqJOs=",
"dev": true,
"requires": {
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"websocket-extensions": ">=0.1.1"
}
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- "version": "0.1.1",
- "resolved": "https://registry.npmjs.org/websocket-extensions/-/websocket-extensions-0.1.1.tgz",
- "integrity": "sha1-domUmcGEtu91Q3fC27DNbLVdKec=",
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"integrity": "sha1-fQsqLljN3YGQOcKcneZQReGzEOk=",
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"integrity": "sha1-O3dB/qSoZnWXbpCNKW1ERZYfqmc=",
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+ "resolved": "https://registry.npmjs.org/yallist/-/yallist-2.1.2.tgz",
+ "integrity": "sha1-HBH5IY8HYImkfdUS+TxmmaaoHVI=",
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"yeast": {
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"integrity": "sha1-AI4G2AlDIMNy28L47XagymyKxBk=",
"dev": true
}
}
}
|
jquery/sizzle
|
67e9691e8689b824387affb9da06dc663da63598
|
Selector: Stop using innerText in :contains
|
diff --git a/dist/sizzle.js b/dist/sizzle.js
index 150d90c..1065e13 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -1,521 +1,521 @@
/*!
* Sizzle CSS Selector Engine v2.3.4-pre
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
- * Date: 2018-12-03
+ * Date: 2019-01-14
*/
(function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ({}).hasOwnProperty,
arr = [],
pop = arr.pop,
push_native = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[i] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
"*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
funescape = function( _, escaped, escapedWhitespace ) {
var high = "0x" + escaped - 0x10000;
// NaN means non-codepoint
// Support: Firefox<24
// Workaround erroneous numeric interpretation of +"0x"
return high !== high || escapedWhitespace ?
escaped :
high < 0 ?
// BMP codepoint
String.fromCharCode( high + 0x10000 ) :
// Supplemental Plane codepoint (surrogate pair)
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
(arr = slice.call( preferredDoc.childNodes )),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
push_native.apply( target, slice.call(els) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( (target[j++] = els[i++]) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
// ID selector
if ( (m = match[1]) ) {
// Document context
if ( nodeType === 9 ) {
if ( (elem = context.getElementById( m )) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && (elem = newContext.getElementById( m )) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[2] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( (m = match[3]) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
// Support: IE 8 only
// Exclude object elements
(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( (nid = context.getAttribute( "id" )) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", (nid = expando) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[i] = "#" + nid + " " + toSelector( groups[i] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return (cache[ key + " " ] = value);
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement("fieldset");
try {
return !!fn( el );
} catch (e) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split("|"),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[i] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( (cur = cur.nextSibling) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return (name === "input" || name === "button") && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
@@ -955,1025 +955,1025 @@ setDocument = Sizzle.setDocument = function( node ) {
while ( (cur = cur.parentNode) ) {
ap.unshift( cur );
}
cur = b;
while ( (cur = cur.parentNode) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[i] === bp[i] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[i], bp[i] ) :
// Otherwise nodes in our document sort first
ap[i] === preferredDoc ? -1 :
bp[i] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch (e) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
(val = elem.getAttributeNode(name)) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return (sel + "").replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( (elem = results[i++]) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( (node = elem[i++]) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[1] = match[1].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape );
if ( match[2] === "~=" ) {
match[3] = " " + match[3] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[1] = match[1].toLowerCase();
if ( match[1].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[3] ) {
Sizzle.error( match[0] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) );
match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" );
// other types prohibit arguments
} else if ( match[3] ) {
Sizzle.error( match[0] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[6] && match[2];
if ( matchExpr["CHILD"].test( match[0] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[3] ) {
match[2] = match[4] || match[5] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
(excess = tokenize( unquoted, true )) &&
// advance to the next closing parenthesis
(excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) {
// excess is a negative index
match[0] = match[0].slice( 0, excess );
match[2] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() { return true; } :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
(pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) &&
classCache( className, function( elem ) {
return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" );
});
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
};
},
"CHILD": function( type, what, argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
function( elem, context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( (node = node[ dir ]) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
start = [ forward ? parent.firstChild : parent.lastChild ];
// non-xml :nth-child(...) stores cache data on `parent`
if ( forward && useCache ) {
// Seek `elem` from a previously-cached index
// ...in a gzip-friendly way
node = parent;
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex && cache[ 2 ];
node = nodeIndex && parent.childNodes[ nodeIndex ];
while ( (node = ++nodeIndex && node && node[ dir ] ||
// Fallback to seeking `elem` from the start
(diff = nodeIndex = 0) || start.pop()) ) {
// When found, cache indexes on `parent` and break
if ( node.nodeType === 1 && ++diff && node === elem ) {
uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
break;
}
}
} else {
// Use previously-cached element index if available
if ( useCache ) {
// ...in a gzip-friendly way
node = elem;
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex;
}
// xml :nth-child(...)
// or :nth-last-child(...) or :nth(-last)?-of-type(...)
if ( diff === false ) {
// Use the same loop as above to seek `elem` from the start
while ( (node = ++nodeIndex && node && node[ dir ] ||
(diff = nodeIndex = 0) || start.pop()) ) {
if ( ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) &&
++diff ) {
// Cache the index of each encountered element
if ( useCache ) {
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
uniqueCache[ type ] = [ dirruns, diff ];
}
if ( node === elem ) {
break;
}
}
}
}
}
// Incorporate the offset, then check against cycle size
diff -= last;
return diff === first || ( diff % first === 0 && diff / first >= 0 );
}
};
},
"PSEUDO": function( pseudo, argument ) {
// pseudo-class names are case-insensitive
// http://www.w3.org/TR/selectors/#pseudo-classes
// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
// Remember that setFilters inherits from pseudos
var args,
fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
Sizzle.error( "unsupported pseudo: " + pseudo );
// The user may use createPseudo to indicate that
// arguments are needed to create the filter function
// just as Sizzle does
if ( fn[ expando ] ) {
return fn( argument );
}
// But maintain support for old signatures
if ( fn.length > 1 ) {
args = [ pseudo, pseudo, "", argument ];
return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
markFunction(function( seed, matches ) {
var idx,
matched = fn( seed, argument ),
i = matched.length;
while ( i-- ) {
idx = indexOf( seed, matched[i] );
seed[ idx ] = !( matches[ idx ] = matched[i] );
}
}) :
function( elem ) {
return fn( elem, 0, args );
};
}
return fn;
}
},
pseudos: {
// Potentially complex pseudos
"not": markFunction(function( selector ) {
// Trim the selector passed to compile
// to avoid treating leading and trailing
// spaces as combinators
var input = [],
results = [],
matcher = compile( selector.replace( rtrim, "$1" ) );
return matcher[ expando ] ?
markFunction(function( seed, matches, context, xml ) {
var elem,
unmatched = matcher( seed, null, xml, [] ),
i = seed.length;
// Match elements unmatched by `matcher`
while ( i-- ) {
if ( (elem = unmatched[i]) ) {
seed[i] = !(matches[i] = elem);
}
}
}) :
function( elem, context, xml ) {
input[0] = elem;
matcher( input, null, xml, results );
// Don't keep the element (issue #299)
input[0] = null;
return !results.pop();
};
}),
"has": markFunction(function( selector ) {
return function( elem ) {
return Sizzle( selector, elem ).length > 0;
};
}),
"contains": markFunction(function( text ) {
text = text.replace( runescape, funescape );
return function( elem ) {
- return ( elem.textContent || elem.innerText || getText( elem ) ).indexOf( text ) > -1;
+ return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
};
}),
// "Whether an element is represented by a :lang() selector
// is based solely on the element's language value
// being equal to the identifier C,
// or beginning with the identifier C immediately followed by "-".
// The matching of C against the element's language value is performed case-insensitively.
// The identifier C does not have to be a valid language name."
// http://www.w3.org/TR/selectors/#lang-pseudo
"lang": markFunction( function( lang ) {
// lang value must be a valid identifier
if ( !ridentifier.test(lang || "") ) {
Sizzle.error( "unsupported lang: " + lang );
}
lang = lang.replace( runescape, funescape ).toLowerCase();
return function( elem ) {
var elemLang;
do {
if ( (elemLang = documentIsHTML ?
elem.lang :
elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) {
elemLang = elemLang.toLowerCase();
return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
}
} while ( (elem = elem.parentNode) && elem.nodeType === 1 );
return false;
};
}),
// Miscellaneous
"target": function( elem ) {
var hash = window.location && window.location.hash;
return hash && hash.slice( 1 ) === elem.id;
},
"root": function( elem ) {
return elem === docElem;
},
"focus": function( elem ) {
return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex);
},
// Boolean properties
"enabled": createDisabledPseudo( false ),
"disabled": createDisabledPseudo( true ),
"checked": function( elem ) {
// In CSS3, :checked should return both checked and selected elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
var nodeName = elem.nodeName.toLowerCase();
return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected);
},
"selected": function( elem ) {
// Accessing this property makes selected-by-default
// options in Safari work properly
if ( elem.parentNode ) {
elem.parentNode.selectedIndex;
}
return elem.selected === true;
},
// Contents
"empty": function( elem ) {
// http://www.w3.org/TR/selectors/#empty-pseudo
// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
// but not by others (comment: 8; processing instruction: 7; etc.)
// nodeType < 6 works because attributes (2) do not appear as children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
if ( elem.nodeType < 6 ) {
return false;
}
}
return true;
},
"parent": function( elem ) {
return !Expr.pseudos["empty"]( elem );
},
// Element/input types
"header": function( elem ) {
return rheader.test( elem.nodeName );
},
"input": function( elem ) {
return rinputs.test( elem.nodeName );
},
"button": function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === "button" || name === "button";
},
"text": function( elem ) {
var attr;
return elem.nodeName.toLowerCase() === "input" &&
elem.type === "text" &&
// Support: IE<8
// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" );
},
// Position-in-collection
"first": createPositionalPseudo(function() {
return [ 0 ];
}),
"last": createPositionalPseudo(function( matchIndexes, length ) {
return [ length - 1 ];
}),
"eq": createPositionalPseudo(function( matchIndexes, length, argument ) {
return [ argument < 0 ? argument + length : argument ];
}),
"even": createPositionalPseudo(function( matchIndexes, length ) {
var i = 0;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"odd": createPositionalPseudo(function( matchIndexes, length ) {
var i = 1;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"lt": createPositionalPseudo(function( matchIndexes, length, argument ) {
var i = argument < 0 ?
argument + length :
argument > length ?
length :
argument;
for ( ; --i >= 0; ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"gt": createPositionalPseudo(function( matchIndexes, length, argument ) {
var i = argument < 0 ? argument + length : argument;
for ( ; ++i < length; ) {
matchIndexes.push( i );
}
return matchIndexes;
})
}
};
Expr.pseudos["nth"] = Expr.pseudos["eq"];
// Add button/input type pseudos
for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
Expr.pseudos[ i ] = createInputPseudo( i );
}
for ( i in { submit: true, reset: true } ) {
Expr.pseudos[ i ] = createButtonPseudo( i );
}
// Easy API for creating new setFilters
function setFilters() {}
setFilters.prototype = Expr.filters = Expr.pseudos;
Expr.setFilters = new setFilters();
tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
var matched, match, tokens, type,
soFar, groups, preFilters,
cached = tokenCache[ selector + " " ];
if ( cached ) {
return parseOnly ? 0 : cached.slice( 0 );
}
soFar = selector;
groups = [];
preFilters = Expr.preFilter;
while ( soFar ) {
// Comma and first run
if ( !matched || (match = rcomma.exec( soFar )) ) {
if ( match ) {
// Don't consume trailing commas as valid
soFar = soFar.slice( match[0].length ) || soFar;
}
groups.push( (tokens = []) );
}
matched = false;
// Combinators
if ( (match = rcombinators.exec( soFar )) ) {
matched = match.shift();
tokens.push({
value: matched,
// Cast descendant combinators to space
type: match[0].replace( rtrim, " " )
});
soFar = soFar.slice( matched.length );
}
// Filters
for ( type in Expr.filter ) {
if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] ||
(match = preFilters[ type ]( match ))) ) {
matched = match.shift();
tokens.push({
value: matched,
type: type,
matches: match
});
soFar = soFar.slice( matched.length );
}
}
if ( !matched ) {
break;
}
}
// Return the length of the invalid excess
// if we're just parsing
// Otherwise, throw an error or return tokens
return parseOnly ?
soFar.length :
soFar ?
Sizzle.error( selector ) :
// Cache the tokens
tokenCache( selector, groups ).slice( 0 );
};
function toSelector( tokens ) {
var i = 0,
len = tokens.length,
selector = "";
for ( ; i < len; i++ ) {
selector += tokens[i].value;
}
return selector;
}
function addCombinator( matcher, combinator, base ) {
var dir = combinator.dir,
skip = combinator.next,
key = skip || dir,
checkNonElements = base && key === "parentNode",
doneName = done++;
return combinator.first ?
// Check against closest ancestor/preceding element
function( elem, context, xml ) {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
return matcher( elem, context, xml );
}
}
return false;
} :
// Check against all ancestor/preceding elements
function( elem, context, xml ) {
var oldCache, uniqueCache, outerCache,
newCache = [ dirruns, doneName ];
// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
if ( xml ) {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
if ( matcher( elem, context, xml ) ) {
return true;
}
}
}
} else {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
outerCache = elem[ expando ] || (elem[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {});
if ( skip && skip === elem.nodeName.toLowerCase() ) {
elem = elem[ dir ] || elem;
} else if ( (oldCache = uniqueCache[ key ]) &&
oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
// Assign to newCache so results back-propagate to previous elements
return (newCache[ 2 ] = oldCache[ 2 ]);
} else {
// Reuse newcache so results back-propagate to previous elements
uniqueCache[ key ] = newCache;
// A match means we're done; a fail means we have to keep checking
if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) {
return true;
}
}
}
}
}
return false;
};
}
function elementMatcher( matchers ) {
return matchers.length > 1 ?
function( elem, context, xml ) {
var i = matchers.length;
while ( i-- ) {
if ( !matchers[i]( elem, context, xml ) ) {
return false;
}
}
return true;
} :
matchers[0];
}
function multipleContexts( selector, contexts, results ) {
var i = 0,
len = contexts.length;
for ( ; i < len; i++ ) {
Sizzle( selector, contexts[i], results );
}
return results;
}
function condense( unmatched, map, filter, context, xml ) {
var elem,
newUnmatched = [],
i = 0,
len = unmatched.length,
mapped = map != null;
for ( ; i < len; i++ ) {
if ( (elem = unmatched[i]) ) {
if ( !filter || filter( elem, context, xml ) ) {
newUnmatched.push( elem );
if ( mapped ) {
map.push( i );
}
}
}
}
return newUnmatched;
}
function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
if ( postFilter && !postFilter[ expando ] ) {
postFilter = setMatcher( postFilter );
}
if ( postFinder && !postFinder[ expando ] ) {
postFinder = setMatcher( postFinder, postSelector );
}
return markFunction(function( seed, results, context, xml ) {
var temp, i, elem,
preMap = [],
postMap = [],
preexisting = results.length,
// Get initial elements from seed or context
elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ),
// Prefilter to get matcher input, preserving a map for seed-results synchronization
matcherIn = preFilter && ( seed || !selector ) ?
condense( elems, preMap, preFilter, context, xml ) :
elems,
matcherOut = matcher ?
// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
// ...intermediate processing is necessary
[] :
// ...otherwise use results directly
results :
matcherIn;
// Find primary matches
if ( matcher ) {
matcher( matcherIn, matcherOut, context, xml );
}
// Apply postFilter
if ( postFilter ) {
temp = condense( matcherOut, postMap );
postFilter( temp, [], context, xml );
// Un-match failing elements by moving them back to matcherIn
i = temp.length;
while ( i-- ) {
if ( (elem = temp[i]) ) {
matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem);
}
}
}
if ( seed ) {
if ( postFinder || preFilter ) {
if ( postFinder ) {
// Get the final matcherOut by condensing this intermediate into postFinder contexts
temp = [];
i = matcherOut.length;
while ( i-- ) {
if ( (elem = matcherOut[i]) ) {
// Restore matcherIn since elem is not yet a final match
temp.push( (matcherIn[i] = elem) );
}
}
postFinder( null, (matcherOut = []), temp, xml );
}
// Move matched elements from seed to results to keep them synchronized
i = matcherOut.length;
while ( i-- ) {
if ( (elem = matcherOut[i]) &&
(temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) {
seed[temp] = !(results[temp] = elem);
}
}
}
// Add elements to results, through postFinder if defined
} else {
matcherOut = condense(
matcherOut === results ?
matcherOut.splice( preexisting, matcherOut.length ) :
matcherOut
);
if ( postFinder ) {
postFinder( null, results, matcherOut, xml );
} else {
push.apply( results, matcherOut );
}
}
});
}
function matcherFromTokens( tokens ) {
var checkContext, matcher, j,
len = tokens.length,
leadingRelative = Expr.relative[ tokens[0].type ],
implicitRelative = leadingRelative || Expr.relative[" "],
i = leadingRelative ? 1 : 0,
// The foundational matcher ensures that elements are reachable from top-level context(s)
matchContext = addCombinator( function( elem ) {
return elem === checkContext;
}, implicitRelative, true ),
matchAnyContext = addCombinator( function( elem ) {
return indexOf( checkContext, elem ) > -1;
}, implicitRelative, true ),
matchers = [ function( elem, context, xml ) {
var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
(checkContext = context).nodeType ?
matchContext( elem, context, xml ) :
matchAnyContext( elem, context, xml ) );
// Avoid hanging onto element (issue #299)
checkContext = null;
return ret;
} ];
for ( ; i < len; i++ ) {
if ( (matcher = Expr.relative[ tokens[i].type ]) ) {
matchers = [ addCombinator(elementMatcher( matchers ), matcher) ];
} else {
matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches );
// Return special upon seeing a positional matcher
if ( matcher[ expando ] ) {
// Find the next relative operator (if any) for proper handling
j = ++i;
for ( ; j < len; j++ ) {
if ( Expr.relative[ tokens[j].type ] ) {
break;
}
}
return setMatcher(
i > 1 && elementMatcher( matchers ),
i > 1 && toSelector(
// If the preceding token was a descendant combinator, insert an implicit any-element `*`
tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" })
).replace( rtrim, "$1" ),
matcher,
i < j && matcherFromTokens( tokens.slice( i, j ) ),
j < len && matcherFromTokens( (tokens = tokens.slice( j )) ),
j < len && toSelector( tokens )
);
}
matchers.push( matcher );
}
}
return elementMatcher( matchers );
}
function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
var bySet = setMatchers.length > 0,
diff --git a/dist/sizzle.min.js b/dist/sizzle.min.js
index d4ea5ac..0e403e4 100644
--- a/dist/sizzle.min.js
+++ b/dist/sizzle.min.js
@@ -1,3 +1,3 @@
/*! Sizzle v2.3.4-pre | (c) JS Foundation and other contributors | js.foundation */
-!function(e){var t,n,r,i,o,u,l,a,c,s,f,d,p,h,g,m,y,w,v,b="sizzle"+1*new Date,N=e.document,x=0,C=0,E=ae(),D=ae(),S=ae(),A=ae(),T=function(e,t){return e===t&&(f=!0),0},L={}.hasOwnProperty,I=[],q=I.pop,B=I.push,R=I.push,$=I.slice,k=function(e,t){for(var n=0,r=e.length;n<r;n++)if(e[n]===t)return n;return-1},H="checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",M="[\\x20\\t\\r\\n\\f]",P="(?:\\\\.|[\\w-]|[^\0-\\xa0])+",z="\\["+M+"*("+P+")(?:"+M+"*([*^$|!~]?=)"+M+"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|("+P+"))|)"+M+"*\\]",F=":("+P+")(?:\\((('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|((?:\\\\.|[^\\\\()[\\]]|"+z+")*)|.*)\\)|)",O=new RegExp(M+"+","g"),j=new RegExp("^"+M+"+|((?:^|[^\\\\])(?:\\\\.)*)"+M+"+$","g"),G=new RegExp("^"+M+"*,"+M+"*"),U=new RegExp("^"+M+"*([>+~]|"+M+")"+M+"*"),V=new RegExp(M+"|>"),X=new RegExp(F),J=new RegExp("^"+P+"$"),K={ID:new RegExp("^#("+P+")"),CLASS:new RegExp("^\\.("+P+")"),TAG:new RegExp("^("+P+"|[*])"),ATTR:new RegExp("^"+z),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\("+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\\)|)","i"),bool:new RegExp("^(?:"+H+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\("+M+"*((?:-\\d)?\\d*)"+M+"*\\)|)(?=[^-]|$)","i")},Q=/HTML$/i,W=/^(?:input|select|textarea|button)$/i,Y=/^h\d$/i,Z=/^[^{]+\{\s*\[native \w/,_=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\([\\da-f]{1,6}"+M+"?|("+M+")|.)","ig"),ne=function(e,t,n){var r="0x"+t-65536;return r!==r||n?t:r<0?String.fromCharCode(r+65536):String.fromCharCode(r>>10|55296,1023&r|56320)},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" 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\ No newline at end of file
diff --git a/src/sizzle.js b/src/sizzle.js
index 868342d..66b8577 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -955,1025 +955,1025 @@ setDocument = Sizzle.setDocument = function( node ) {
while ( (cur = cur.parentNode) ) {
ap.unshift( cur );
}
cur = b;
while ( (cur = cur.parentNode) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[i] === bp[i] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[i], bp[i] ) :
// Otherwise nodes in our document sort first
ap[i] === preferredDoc ? -1 :
bp[i] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch (e) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
(val = elem.getAttributeNode(name)) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return (sel + "").replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( (elem = results[i++]) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
};
/**
* Utility function for retrieving the text value of an array of DOM nodes
* @param {Array|Element} elem
*/
getText = Sizzle.getText = function( elem ) {
var node,
ret = "",
i = 0,
nodeType = elem.nodeType;
if ( !nodeType ) {
// If no nodeType, this is expected to be an array
while ( (node = elem[i++]) ) {
// Do not traverse comment nodes
ret += getText( node );
}
} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
// Use textContent for elements
// innerText usage removed for consistency of new lines (jQuery #11153)
if ( typeof elem.textContent === "string" ) {
return elem.textContent;
} else {
// Traverse its children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
ret += getText( elem );
}
}
} else if ( nodeType === 3 || nodeType === 4 ) {
return elem.nodeValue;
}
// Do not include comment or processing instruction nodes
return ret;
};
Expr = Sizzle.selectors = {
// Can be adjusted by the user
cacheLength: 50,
createPseudo: markFunction,
match: matchExpr,
attrHandle: {},
find: {},
relative: {
">": { dir: "parentNode", first: true },
" ": { dir: "parentNode" },
"+": { dir: "previousSibling", first: true },
"~": { dir: "previousSibling" }
},
preFilter: {
"ATTR": function( match ) {
match[1] = match[1].replace( runescape, funescape );
// Move the given value to match[3] whether quoted or unquoted
match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape );
if ( match[2] === "~=" ) {
match[3] = " " + match[3] + " ";
}
return match.slice( 0, 4 );
},
"CHILD": function( match ) {
/* matches from matchExpr["CHILD"]
1 type (only|nth|...)
2 what (child|of-type)
3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
4 xn-component of xn+y argument ([+-]?\d*n|)
5 sign of xn-component
6 x of xn-component
7 sign of y-component
8 y of y-component
*/
match[1] = match[1].toLowerCase();
if ( match[1].slice( 0, 3 ) === "nth" ) {
// nth-* requires argument
if ( !match[3] ) {
Sizzle.error( match[0] );
}
// numeric x and y parameters for Expr.filter.CHILD
// remember that false/true cast respectively to 0/1
match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) );
match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" );
// other types prohibit arguments
} else if ( match[3] ) {
Sizzle.error( match[0] );
}
return match;
},
"PSEUDO": function( match ) {
var excess,
unquoted = !match[6] && match[2];
if ( matchExpr["CHILD"].test( match[0] ) ) {
return null;
}
// Accept quoted arguments as-is
if ( match[3] ) {
match[2] = match[4] || match[5] || "";
// Strip excess characters from unquoted arguments
} else if ( unquoted && rpseudo.test( unquoted ) &&
// Get excess from tokenize (recursively)
(excess = tokenize( unquoted, true )) &&
// advance to the next closing parenthesis
(excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) {
// excess is a negative index
match[0] = match[0].slice( 0, excess );
match[2] = unquoted.slice( 0, excess );
}
// Return only captures needed by the pseudo filter method (type and argument)
return match.slice( 0, 3 );
}
},
filter: {
"TAG": function( nodeNameSelector ) {
var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
return nodeNameSelector === "*" ?
function() { return true; } :
function( elem ) {
return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
};
},
"CLASS": function( className ) {
var pattern = classCache[ className + " " ];
return pattern ||
(pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) &&
classCache( className, function( elem ) {
return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" );
});
},
"ATTR": function( name, operator, check ) {
return function( elem ) {
var result = Sizzle.attr( elem, name );
if ( result == null ) {
return operator === "!=";
}
if ( !operator ) {
return true;
}
result += "";
return operator === "=" ? result === check :
operator === "!=" ? result !== check :
operator === "^=" ? check && result.indexOf( check ) === 0 :
operator === "*=" ? check && result.indexOf( check ) > -1 :
operator === "$=" ? check && result.slice( -check.length ) === check :
operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
false;
};
},
"CHILD": function( type, what, argument, first, last ) {
var simple = type.slice( 0, 3 ) !== "nth",
forward = type.slice( -4 ) !== "last",
ofType = what === "of-type";
return first === 1 && last === 0 ?
// Shortcut for :nth-*(n)
function( elem ) {
return !!elem.parentNode;
} :
function( elem, context, xml ) {
var cache, uniqueCache, outerCache, node, nodeIndex, start,
dir = simple !== forward ? "nextSibling" : "previousSibling",
parent = elem.parentNode,
name = ofType && elem.nodeName.toLowerCase(),
useCache = !xml && !ofType,
diff = false;
if ( parent ) {
// :(first|last|only)-(child|of-type)
if ( simple ) {
while ( dir ) {
node = elem;
while ( (node = node[ dir ]) ) {
if ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) {
return false;
}
}
// Reverse direction for :only-* (if we haven't yet done so)
start = dir = type === "only" && !start && "nextSibling";
}
return true;
}
start = [ forward ? parent.firstChild : parent.lastChild ];
// non-xml :nth-child(...) stores cache data on `parent`
if ( forward && useCache ) {
// Seek `elem` from a previously-cached index
// ...in a gzip-friendly way
node = parent;
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex && cache[ 2 ];
node = nodeIndex && parent.childNodes[ nodeIndex ];
while ( (node = ++nodeIndex && node && node[ dir ] ||
// Fallback to seeking `elem` from the start
(diff = nodeIndex = 0) || start.pop()) ) {
// When found, cache indexes on `parent` and break
if ( node.nodeType === 1 && ++diff && node === elem ) {
uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
break;
}
}
} else {
// Use previously-cached element index if available
if ( useCache ) {
// ...in a gzip-friendly way
node = elem;
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
cache = uniqueCache[ type ] || [];
nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
diff = nodeIndex;
}
// xml :nth-child(...)
// or :nth-last-child(...) or :nth(-last)?-of-type(...)
if ( diff === false ) {
// Use the same loop as above to seek `elem` from the start
while ( (node = ++nodeIndex && node && node[ dir ] ||
(diff = nodeIndex = 0) || start.pop()) ) {
if ( ( ofType ?
node.nodeName.toLowerCase() === name :
node.nodeType === 1 ) &&
++diff ) {
// Cache the index of each encountered element
if ( useCache ) {
outerCache = node[ expando ] || (node[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ node.uniqueID ] ||
(outerCache[ node.uniqueID ] = {});
uniqueCache[ type ] = [ dirruns, diff ];
}
if ( node === elem ) {
break;
}
}
}
}
}
// Incorporate the offset, then check against cycle size
diff -= last;
return diff === first || ( diff % first === 0 && diff / first >= 0 );
}
};
},
"PSEUDO": function( pseudo, argument ) {
// pseudo-class names are case-insensitive
// http://www.w3.org/TR/selectors/#pseudo-classes
// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
// Remember that setFilters inherits from pseudos
var args,
fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
Sizzle.error( "unsupported pseudo: " + pseudo );
// The user may use createPseudo to indicate that
// arguments are needed to create the filter function
// just as Sizzle does
if ( fn[ expando ] ) {
return fn( argument );
}
// But maintain support for old signatures
if ( fn.length > 1 ) {
args = [ pseudo, pseudo, "", argument ];
return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
markFunction(function( seed, matches ) {
var idx,
matched = fn( seed, argument ),
i = matched.length;
while ( i-- ) {
idx = indexOf( seed, matched[i] );
seed[ idx ] = !( matches[ idx ] = matched[i] );
}
}) :
function( elem ) {
return fn( elem, 0, args );
};
}
return fn;
}
},
pseudos: {
// Potentially complex pseudos
"not": markFunction(function( selector ) {
// Trim the selector passed to compile
// to avoid treating leading and trailing
// spaces as combinators
var input = [],
results = [],
matcher = compile( selector.replace( rtrim, "$1" ) );
return matcher[ expando ] ?
markFunction(function( seed, matches, context, xml ) {
var elem,
unmatched = matcher( seed, null, xml, [] ),
i = seed.length;
// Match elements unmatched by `matcher`
while ( i-- ) {
if ( (elem = unmatched[i]) ) {
seed[i] = !(matches[i] = elem);
}
}
}) :
function( elem, context, xml ) {
input[0] = elem;
matcher( input, null, xml, results );
// Don't keep the element (issue #299)
input[0] = null;
return !results.pop();
};
}),
"has": markFunction(function( selector ) {
return function( elem ) {
return Sizzle( selector, elem ).length > 0;
};
}),
"contains": markFunction(function( text ) {
text = text.replace( runescape, funescape );
return function( elem ) {
- return ( elem.textContent || elem.innerText || getText( elem ) ).indexOf( text ) > -1;
+ return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
};
}),
// "Whether an element is represented by a :lang() selector
// is based solely on the element's language value
// being equal to the identifier C,
// or beginning with the identifier C immediately followed by "-".
// The matching of C against the element's language value is performed case-insensitively.
// The identifier C does not have to be a valid language name."
// http://www.w3.org/TR/selectors/#lang-pseudo
"lang": markFunction( function( lang ) {
// lang value must be a valid identifier
if ( !ridentifier.test(lang || "") ) {
Sizzle.error( "unsupported lang: " + lang );
}
lang = lang.replace( runescape, funescape ).toLowerCase();
return function( elem ) {
var elemLang;
do {
if ( (elemLang = documentIsHTML ?
elem.lang :
elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) {
elemLang = elemLang.toLowerCase();
return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
}
} while ( (elem = elem.parentNode) && elem.nodeType === 1 );
return false;
};
}),
// Miscellaneous
"target": function( elem ) {
var hash = window.location && window.location.hash;
return hash && hash.slice( 1 ) === elem.id;
},
"root": function( elem ) {
return elem === docElem;
},
"focus": function( elem ) {
return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex);
},
// Boolean properties
"enabled": createDisabledPseudo( false ),
"disabled": createDisabledPseudo( true ),
"checked": function( elem ) {
// In CSS3, :checked should return both checked and selected elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
var nodeName = elem.nodeName.toLowerCase();
return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected);
},
"selected": function( elem ) {
// Accessing this property makes selected-by-default
// options in Safari work properly
if ( elem.parentNode ) {
elem.parentNode.selectedIndex;
}
return elem.selected === true;
},
// Contents
"empty": function( elem ) {
// http://www.w3.org/TR/selectors/#empty-pseudo
// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
// but not by others (comment: 8; processing instruction: 7; etc.)
// nodeType < 6 works because attributes (2) do not appear as children
for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
if ( elem.nodeType < 6 ) {
return false;
}
}
return true;
},
"parent": function( elem ) {
return !Expr.pseudos["empty"]( elem );
},
// Element/input types
"header": function( elem ) {
return rheader.test( elem.nodeName );
},
"input": function( elem ) {
return rinputs.test( elem.nodeName );
},
"button": function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === "button" || name === "button";
},
"text": function( elem ) {
var attr;
return elem.nodeName.toLowerCase() === "input" &&
elem.type === "text" &&
// Support: IE<8
// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" );
},
// Position-in-collection
"first": createPositionalPseudo(function() {
return [ 0 ];
}),
"last": createPositionalPseudo(function( matchIndexes, length ) {
return [ length - 1 ];
}),
"eq": createPositionalPseudo(function( matchIndexes, length, argument ) {
return [ argument < 0 ? argument + length : argument ];
}),
"even": createPositionalPseudo(function( matchIndexes, length ) {
var i = 0;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"odd": createPositionalPseudo(function( matchIndexes, length ) {
var i = 1;
for ( ; i < length; i += 2 ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"lt": createPositionalPseudo(function( matchIndexes, length, argument ) {
var i = argument < 0 ?
argument + length :
argument > length ?
length :
argument;
for ( ; --i >= 0; ) {
matchIndexes.push( i );
}
return matchIndexes;
}),
"gt": createPositionalPseudo(function( matchIndexes, length, argument ) {
var i = argument < 0 ? argument + length : argument;
for ( ; ++i < length; ) {
matchIndexes.push( i );
}
return matchIndexes;
})
}
};
Expr.pseudos["nth"] = Expr.pseudos["eq"];
// Add button/input type pseudos
for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
Expr.pseudos[ i ] = createInputPseudo( i );
}
for ( i in { submit: true, reset: true } ) {
Expr.pseudos[ i ] = createButtonPseudo( i );
}
// Easy API for creating new setFilters
function setFilters() {}
setFilters.prototype = Expr.filters = Expr.pseudos;
Expr.setFilters = new setFilters();
tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
var matched, match, tokens, type,
soFar, groups, preFilters,
cached = tokenCache[ selector + " " ];
if ( cached ) {
return parseOnly ? 0 : cached.slice( 0 );
}
soFar = selector;
groups = [];
preFilters = Expr.preFilter;
while ( soFar ) {
// Comma and first run
if ( !matched || (match = rcomma.exec( soFar )) ) {
if ( match ) {
// Don't consume trailing commas as valid
soFar = soFar.slice( match[0].length ) || soFar;
}
groups.push( (tokens = []) );
}
matched = false;
// Combinators
if ( (match = rcombinators.exec( soFar )) ) {
matched = match.shift();
tokens.push({
value: matched,
// Cast descendant combinators to space
type: match[0].replace( rtrim, " " )
});
soFar = soFar.slice( matched.length );
}
// Filters
for ( type in Expr.filter ) {
if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] ||
(match = preFilters[ type ]( match ))) ) {
matched = match.shift();
tokens.push({
value: matched,
type: type,
matches: match
});
soFar = soFar.slice( matched.length );
}
}
if ( !matched ) {
break;
}
}
// Return the length of the invalid excess
// if we're just parsing
// Otherwise, throw an error or return tokens
return parseOnly ?
soFar.length :
soFar ?
Sizzle.error( selector ) :
// Cache the tokens
tokenCache( selector, groups ).slice( 0 );
};
function toSelector( tokens ) {
var i = 0,
len = tokens.length,
selector = "";
for ( ; i < len; i++ ) {
selector += tokens[i].value;
}
return selector;
}
function addCombinator( matcher, combinator, base ) {
var dir = combinator.dir,
skip = combinator.next,
key = skip || dir,
checkNonElements = base && key === "parentNode",
doneName = done++;
return combinator.first ?
// Check against closest ancestor/preceding element
function( elem, context, xml ) {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
return matcher( elem, context, xml );
}
}
return false;
} :
// Check against all ancestor/preceding elements
function( elem, context, xml ) {
var oldCache, uniqueCache, outerCache,
newCache = [ dirruns, doneName ];
// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
if ( xml ) {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
if ( matcher( elem, context, xml ) ) {
return true;
}
}
}
} else {
while ( (elem = elem[ dir ]) ) {
if ( elem.nodeType === 1 || checkNonElements ) {
outerCache = elem[ expando ] || (elem[ expando ] = {});
// Support: IE <9 only
// Defend against cloned attroperties (jQuery gh-1709)
uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {});
if ( skip && skip === elem.nodeName.toLowerCase() ) {
elem = elem[ dir ] || elem;
} else if ( (oldCache = uniqueCache[ key ]) &&
oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
// Assign to newCache so results back-propagate to previous elements
return (newCache[ 2 ] = oldCache[ 2 ]);
} else {
// Reuse newcache so results back-propagate to previous elements
uniqueCache[ key ] = newCache;
// A match means we're done; a fail means we have to keep checking
if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) {
return true;
}
}
}
}
}
return false;
};
}
function elementMatcher( matchers ) {
return matchers.length > 1 ?
function( elem, context, xml ) {
var i = matchers.length;
while ( i-- ) {
if ( !matchers[i]( elem, context, xml ) ) {
return false;
}
}
return true;
} :
matchers[0];
}
function multipleContexts( selector, contexts, results ) {
var i = 0,
len = contexts.length;
for ( ; i < len; i++ ) {
Sizzle( selector, contexts[i], results );
}
return results;
}
function condense( unmatched, map, filter, context, xml ) {
var elem,
newUnmatched = [],
i = 0,
len = unmatched.length,
mapped = map != null;
for ( ; i < len; i++ ) {
if ( (elem = unmatched[i]) ) {
if ( !filter || filter( elem, context, xml ) ) {
newUnmatched.push( elem );
if ( mapped ) {
map.push( i );
}
}
}
}
return newUnmatched;
}
function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
if ( postFilter && !postFilter[ expando ] ) {
postFilter = setMatcher( postFilter );
}
if ( postFinder && !postFinder[ expando ] ) {
postFinder = setMatcher( postFinder, postSelector );
}
return markFunction(function( seed, results, context, xml ) {
var temp, i, elem,
preMap = [],
postMap = [],
preexisting = results.length,
// Get initial elements from seed or context
elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ),
// Prefilter to get matcher input, preserving a map for seed-results synchronization
matcherIn = preFilter && ( seed || !selector ) ?
condense( elems, preMap, preFilter, context, xml ) :
elems,
matcherOut = matcher ?
// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
// ...intermediate processing is necessary
[] :
// ...otherwise use results directly
results :
matcherIn;
// Find primary matches
if ( matcher ) {
matcher( matcherIn, matcherOut, context, xml );
}
// Apply postFilter
if ( postFilter ) {
temp = condense( matcherOut, postMap );
postFilter( temp, [], context, xml );
// Un-match failing elements by moving them back to matcherIn
i = temp.length;
while ( i-- ) {
if ( (elem = temp[i]) ) {
matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem);
}
}
}
if ( seed ) {
if ( postFinder || preFilter ) {
if ( postFinder ) {
// Get the final matcherOut by condensing this intermediate into postFinder contexts
temp = [];
i = matcherOut.length;
while ( i-- ) {
if ( (elem = matcherOut[i]) ) {
// Restore matcherIn since elem is not yet a final match
temp.push( (matcherIn[i] = elem) );
}
}
postFinder( null, (matcherOut = []), temp, xml );
}
// Move matched elements from seed to results to keep them synchronized
i = matcherOut.length;
while ( i-- ) {
if ( (elem = matcherOut[i]) &&
(temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) {
seed[temp] = !(results[temp] = elem);
}
}
}
// Add elements to results, through postFinder if defined
} else {
matcherOut = condense(
matcherOut === results ?
matcherOut.splice( preexisting, matcherOut.length ) :
matcherOut
);
if ( postFinder ) {
postFinder( null, results, matcherOut, xml );
} else {
push.apply( results, matcherOut );
}
}
});
}
function matcherFromTokens( tokens ) {
var checkContext, matcher, j,
len = tokens.length,
leadingRelative = Expr.relative[ tokens[0].type ],
implicitRelative = leadingRelative || Expr.relative[" "],
i = leadingRelative ? 1 : 0,
// The foundational matcher ensures that elements are reachable from top-level context(s)
matchContext = addCombinator( function( elem ) {
return elem === checkContext;
}, implicitRelative, true ),
matchAnyContext = addCombinator( function( elem ) {
return indexOf( checkContext, elem ) > -1;
}, implicitRelative, true ),
matchers = [ function( elem, context, xml ) {
var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
(checkContext = context).nodeType ?
matchContext( elem, context, xml ) :
matchAnyContext( elem, context, xml ) );
// Avoid hanging onto element (issue #299)
checkContext = null;
return ret;
} ];
for ( ; i < len; i++ ) {
if ( (matcher = Expr.relative[ tokens[i].type ]) ) {
matchers = [ addCombinator(elementMatcher( matchers ), matcher) ];
} else {
matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches );
// Return special upon seeing a positional matcher
if ( matcher[ expando ] ) {
// Find the next relative operator (if any) for proper handling
j = ++i;
for ( ; j < len; j++ ) {
if ( Expr.relative[ tokens[j].type ] ) {
break;
}
}
return setMatcher(
i > 1 && elementMatcher( matchers ),
i > 1 && toSelector(
// If the preceding token was a descendant combinator, insert an implicit any-element `*`
tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" })
).replace( rtrim, "$1" ),
matcher,
i < j && matcherFromTokens( tokens.slice( i, j ) ),
j < len && matcherFromTokens( (tokens = tokens.slice( j )) ),
j < len && toSelector( tokens )
);
}
matchers.push( matcher );
}
}
return elementMatcher( matchers );
}
function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
var bySet = setMatchers.length > 0,
diff --git a/test/unit/selector.js b/test/unit/selector.js
index 6c04b15..3117daa 100644
--- a/test/unit/selector.js
+++ b/test/unit/selector.js
@@ -321,1051 +321,1064 @@ QUnit.test("name", function( assert ) {
var form;
t( "Name selector", "input[name=action]", ["text1"] );
t( "Name selector with single quotes", "input[name='action']", ["text1"] );
t( "Name selector with double quotes", "input[name=\"action\"]", ["text1"] );
t( "Name selector non-input", "[name=example]", ["name-is-example"] );
t( "Name selector non-input", "[name=div]", ["name-is-div"] );
t( "Name selector non-input", "*[name=iframe]", ["iframe"] );
t( "Name selector for grouped input", "input[name='types[]']", ["types_all", "types_anime", "types_movie"] );
form = document.getElementById("form");
assert.deepEqual( Sizzle("input[name=action]", form), q("text1"),
"Name selector within the context of another element" );
assert.deepEqual( Sizzle("input[name='foo[bar]']", form), q("hidden2"),
"Name selector for grouped form element within the context of another element" );
form = jQuery("<form><input name='id'/></form>").appendTo("body");
assert.equal( Sizzle("input", form[0]).length, 1,
"Make sure that rooted queries on forms (with possible expandos) work." );
form.remove();
t( "Find elements that have similar IDs", "[name=tName1]", ["tName1ID"] );
t( "Find elements that have similar IDs", "[name=tName2]", ["tName2ID"] );
t( "Find elements that have similar IDs", "#tName2ID", ["tName2ID"] );
t( "Case-sensitivity", "[name=tname1]", [] );
});
QUnit.test( "multiple", function( assert ) {
assert.expect( 6 );
jQuery( "#qunit-fixture" ).prepend( "<h2 id='h2'/>" );
t( "Comma Support", "#qunit-fixture h2, #qunit-fixture p",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
t( "Comma Support", "#qunit-fixture h2 , #qunit-fixture p",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
t( "Comma Support", "#qunit-fixture h2 , #qunit-fixture p",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
t( "Comma Support", "#qunit-fixture h2,#qunit-fixture p",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
t( "Comma Support", "#qunit-fixture h2,#qunit-fixture p ",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
t( "Comma Support", "#qunit-fixture h2\t,\r#qunit-fixture p\n",
[ "h2","firstp","ap","sndp","en","sap","first" ] );
});
QUnit.test("child and adjacent", function( assert ) {
assert.expect( 43 );
var siblingFirst, en, nothiddendiv;
t( "Child", "p > a", ["simon1","google","groups","mark","yahoo","simon"] );
t( "Child minus whitespace", "p>a", ["simon1","google","groups","mark","yahoo","simon"] );
t( "Child minus trailing whitespace", "p> a",
["simon1","google","groups","mark","yahoo","simon"] );
t( "Child minus leading whitespace", "p >a",
["simon1","google","groups","mark","yahoo","simon"] );
t( "Child w/ Class", "p > a.blog", ["mark","simon"] );
t( "All Children", "code > *", ["anchor1","anchor2"] );
t( "All Grandchildren", "p > * > *", ["anchor1","anchor2"] );
t( "Rooted tag adjacent", "#qunit-fixture a + a", ["groups", "tName2ID"] );
t( "Rooted tag adjacent minus whitespace", "#qunit-fixture a+a", ["groups", "tName2ID"] );
t( "Rooted tag adjacent minus leading whitespace", "#qunit-fixture a +a",
["groups", "tName2ID"] );
t( "Rooted tag adjacent minus trailing whitespace", "#qunit-fixture a+ a",
["groups", "tName2ID"] );
t( "Tag adjacent", "p + p", ["ap","en","sap"] );
t( "#id adjacent", "#firstp + p", ["ap"] );
t( "Tag#id adjacent", "p#firstp + p", ["ap"] );
t( "Tag[attr] adjacent", "p[lang=en] + p", ["sap"] );
t( "Tag.class adjacent", "a.GROUPS + code + a", ["mark"] );
t( "Comma, Child, and Adjacent", "#qunit-fixture a + a, code > a",
["groups","anchor1","anchor2","tName2ID"] );
t( "Element Preceded By", "#qunit-fixture p ~ div",
["foo", "nothiddendiv", "moretests","tabindex-tests", "liveHandlerOrder", "siblingTest"] );
t( "Element Preceded By", "#first ~ div",
["moretests","tabindex-tests", "liveHandlerOrder", "siblingTest"] );
t( "Element Preceded By", "#groups ~ a", ["mark"] );
t( "Element Preceded By", "#length ~ input", ["idTest"] );
t( "Element Preceded By", "#siblingfirst ~ em", ["siblingnext", "siblingthird"] );
t( "Element Preceded By (multiple)", "#siblingTest em ~ em ~ em ~ span", ["siblingspan"] );
t( "Element Preceded By, Containing", "#liveHandlerOrder ~ div em:contains('1')",
["siblingfirst"] );
siblingFirst = document.getElementById("siblingfirst");
assert.deepEqual( Sizzle("~ em", siblingFirst), q("siblingnext", "siblingthird"),
"Element Preceded By with a context." );
assert.deepEqual( Sizzle("+ em", siblingFirst), q("siblingnext"),
"Element Directly Preceded By with a context." );
assert.deepEqual( Sizzle("~ em:first", siblingFirst), q("siblingnext"),
"Element Preceded By positional with a context." );
en = document.getElementById("en");
assert.deepEqual( Sizzle("+ p, a", en), q("yahoo", "sap"),
"Compound selector with context, beginning with sibling test." );
assert.deepEqual( Sizzle("a, + p", en), q("yahoo", "sap"),
"Compound selector with context, containing sibling test." );
t( "Multiple combinators selects all levels", "#siblingTest em *",
["siblingchild", "siblinggrandchild", "siblinggreatgrandchild"] );
t( "Multiple combinators selects all levels", "#siblingTest > em *",
["siblingchild", "siblinggrandchild", "siblinggreatgrandchild"] );
t( "Multiple sibling combinators doesn't miss general siblings",
"#siblingTest > em:first-child + em ~ span",
["siblingspan"] );
t( "Combinators are not skipped when mixing general and specific",
"#siblingTest > em:contains('x') + em ~ span",
[] );
assert.equal( Sizzle("#listWithTabIndex").length, 1,
"Parent div for next test is found via ID (#8310)" );
assert.equal( Sizzle("#listWithTabIndex li:eq(2) ~ li").length, 1,
"Find by general sibling combinator (#8310)" );
assert.equal( Sizzle("#__sizzle__").length, 0,
"Make sure the temporary id assigned by sizzle is cleared out (#8310)" );
assert.equal( Sizzle("#listWithTabIndex").length, 1,
"Parent div for previous test is still found via ID (#8310)" );
t( "Verify deep class selector", "div.blah > p > a", [] );
t( "No element deep selector", "div.foo > span > a", [] );
nothiddendiv = document.getElementById("nothiddendiv");
assert.deepEqual( Sizzle("> :first", nothiddendiv), q("nothiddendivchild"),
"Verify child context positional selector" );
assert.deepEqual( Sizzle("> :eq(0)", nothiddendiv), q("nothiddendivchild"),
"Verify child context positional selector" );
assert.deepEqual( Sizzle("> *:first", nothiddendiv), q("nothiddendivchild"),
"Verify child context positional selector" );
t( "Non-existant ancestors", ".fototab > .thumbnails > a", [] );
});
QUnit.test("attributes - existence", function( assert ) {
assert.expect( 7 );
t( "on element", "#qunit-fixture a[title]", [ "google" ] );
t( "on element (whitespace ignored)", "#qunit-fixture a[ title ]", [ "google" ] );
t( "on element (case-insensitive)", "#qunit-fixture a[TITLE]", [ "google" ] );
t( "on any element", "#qunit-fixture *[title]", [ "google" ] );
t( "on implicit element", "#qunit-fixture [title]", [ "google" ] );
t( "boolean", "#select2 option[selected]", [ "option2d" ]);
t( "for attribute on label", "form label[for]", [ "label-for" ] );
});
QUnit.test("attributes - equals", function( assert ) {
assert.expect( 20 );
t( "identifier", "#qunit-fixture a[rel=bookmark]", [ "simon1" ] );
t( "identifier containing underscore", "input[id=types_all]", ["types_all"] );
t( "string", "#qunit-fixture a[rel='bookmark']", [ "simon1" ] );
t( "string (whitespace ignored)", "#qunit-fixture a[ rel = 'bookmark' ]", [ "simon1" ] );
t( "non-identifier string", "#qunit-fixture a[href='http://www.google.com/']", [ "google" ] );
t( "empty string", "#select1 option[value='']", [ "option1a" ] );
t( "number",
"#qunit-fixture option[value=1]",
[ "option1b", "option2b", "option3b", "option4b", "option5c" ] );
t( "negative number", "#qunit-fixture li[tabIndex=-1]", [ "foodWithNegativeTabIndex" ] );
t( "non-ASCII identifier", "span[lang=ä¸æ]", ["å°å"] );
t( "input[type=text]", "#form input[type=text]", [ "text1", "text2", "hidden2", "name" ] );
t( "input[type=search]", "#form input[type=search]", [ "search" ] );
t( "script[src] (jQuery #13777)", "#moretests script[src]", [ "script-src" ] );
t( "boolean attribute equals name", "#select2 option[selected='selected']", [ "option2d" ]);
t( "for attribute in form", "#form [for=action]", [ "label-for" ] );
t( "name attribute", "input[name='foo[bar]']", [ "hidden2" ] );
t( "value attribute", "input[value=Test]", [ "text1", "text2" ] );
assert.deepEqual(
Sizzle( "input[data-comma='0,1']" ),
q( "el12087" ),
"Without context, single-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma=\"0,1\"]" ),
q( "el12087" ),
"Without context, double-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma='0,1']", document.getElementById( "t12087" ) ),
q( "el12087" ),
"With context, single-quoted attribute containing ','" );
assert.deepEqual(
Sizzle( "input[data-comma=\"0,1\"]", document.getElementById( "t12087" ) ),
q( "el12087" ),
"With context, double-quoted attribute containing ','" );
});
QUnit.test("attributes - does not equal", function( assert ) {
assert.expect( 2 );
t( "string", "#ap a[hreflang!='en']", [ "google", "groups", "anchor1" ] );
t( "empty string", "#select1 option[value!='']", [ "option1b", "option1c", "option1d" ] );
});
QUnit.test("attributes - starts with", function( assert ) {
assert.expect( 4 );
// Support: IE<8
// There is apparently no way to bypass interpolation of the *originally-defined* href attribute
document.getElementById("anchor2").href = "#2";
t( "string (whitespace ignored)", "a[href ^= 'http://www']", [ "google", "yahoo" ] );
t( "href starts with hash", "p a[href^='#']", [ "anchor2" ] );
t( "string containing '['", "input[name^='foo[']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name^='foo[bar]']", [ "hidden2" ] );
});
QUnit.test("attributes - contains", function( assert ) {
assert.expect( 4 );
t( "string (whitespace ignored)", "a[href *= 'google']", [ "google", "groups" ] );
t( "string starting with '[' ... ']'", "input[name*='[bar]']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name*='foo[bar]']", [ "hidden2" ] );
t( "href contains hash", "p a[href*='#']", [ "simon1", "anchor2" ] );
});
QUnit.test("attributes - ends with", function( assert ) {
assert.expect( 4 );
t( "string (whitespace ignored)", "a[href $= 'org/']", [ "mark" ] );
t( "string ending with ']'", "input[name$='bar]']", [ "hidden2" ] );
t( "string like '[' ... ']'", "input[name$='[bar]']", [ "hidden2" ] );
t( "string containing '[' ... ']'", "input[name$='foo[bar]']", [ "hidden2" ] );
});
QUnit.test("attributes - whitespace list includes", function( assert ) {
assert.expect( 3 );
t( "string found at the beginning",
"input[data-15233~='foo']",
[ "t15233-single", "t15233-double", "t15233-double-tab", "t15233-double-nl", "t15233-triple" ] );
t( "string found in the middle",
"input[data-15233~='bar']",
[ "t15233-double", "t15233-double-tab", "t15233-double-nl", "t15233-triple" ] );
t( "string found at the end", "input[data-15233~='baz']", [ "t15233-triple" ] );
});
QUnit.test("attributes - hyphen-prefix matches", function( assert ) {
assert.expect( 3 );
t( "string", "#names-group span[id|='name']", [ "name-is-example", "name-is-div" ] );
t( "string containing hyphen",
"#names-group span[id|='name-is']",
[ "name-is-example", "name-is-div" ] );
t( "string ending with hyphen", "#names-group span[id|='name-is-']", [] );
});
QUnit.test("attributes - special characters", function( assert ) {
assert.expect( 13 );
var attrbad,
div = document.createElement( "div" );
// #3279
div.innerHTML = "<div id='foo' xml:test='something'></div>";
assert.deepEqual( Sizzle( "[xml\\:test]", div ),
[ div.firstChild ],
"attribute name containing colon" );
// Make sure attribute value quoting works correctly. See jQuery #6093; #6428; #13894
// Use seeded results to bypass querySelectorAll optimizations
attrbad = jQuery(
"<input type='hidden' id='attrbad_space' name='foo bar'/>" +
"<input type='hidden' id='attrbad_dot' value='2' name='foo.baz'/>" +
"<input type='hidden' id='attrbad_brackets' value='2' name='foo[baz]'/>" +
"<input type='hidden' id='attrbad_injection' data-attr='foo_baz']'/>" +
"<input type='hidden' id='attrbad_quote' data-attr='''/>" +
"<input type='hidden' id='attrbad_backslash' data-attr='\'/>" +
"<input type='hidden' id='attrbad_backslash_quote' data-attr='\''/>" +
"<input type='hidden' id='attrbad_backslash_backslash' data-attr='\\'/>" +
"<input type='hidden' id='attrbad_unicode' data-attr='一'/>"
).appendTo("#qunit-fixture").get();
assert.deepEqual( Sizzle( "input[name=foo\\ bar]", null, null, attrbad ),
q( "attrbad_space" ),
"identifier containing space" );
assert.deepEqual( Sizzle( "input[name=foo\\.baz]", null, null, attrbad ),
q( "attrbad_dot" ),
"identifier containing dot" );
assert.deepEqual( Sizzle( "input[name=foo\\[baz\\]]", null, null, attrbad ),
q( "attrbad_brackets" ),
"identifier containing brackets" );
assert.deepEqual( Sizzle( "input[data-attr='foo_baz\\']']", null, null, attrbad ),
q( "attrbad_injection" ),
"string containing quote and right bracket" );
assert.deepEqual( Sizzle( "input[data-attr='\\'']", null, null, attrbad ),
q( "attrbad_quote" ),
"string containing quote" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\']", null, null, attrbad ),
q( "attrbad_backslash" ),
"string containing backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\\\'']", null, null, attrbad ),
q( "attrbad_backslash_quote" ),
"string containing backslash and quote" );
assert.deepEqual( Sizzle( "input[data-attr='\\\\\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing adjacent backslashes" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C \\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape-with-trailing-space backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\5C\t\\\\']", null, null, attrbad ),
q( "attrbad_backslash_backslash" ),
"string containing numeric-escape-with-trailing-tab backslash and backslash" );
assert.deepEqual( Sizzle( "input[data-attr='\\04e00']", null, null, attrbad ),
q( "attrbad_unicode" ),
"Long numeric escape (BMP)" );
document.getElementById( "attrbad_unicode" ).setAttribute( "data-attr", "\uD834\uDF06A" );
// It was too much code to fix Safari 5.x Supplemental Plane crashes (see ba5f09fa404379a87370ec905ffa47f8ac40aaa3)
// assert.deepEqual( Sizzle( "input[data-attr='\\01D306A']", null, null, attrbad ),
// q( "attrbad_unicode" ),
// "Long numeric escape (non-BMP)" );
});
QUnit.test("attributes - other", function( assert ) {
assert.expect( 7 );
var div = document.getElementById( "foo" );
t( "Selector list with multiple quoted attribute-equals",
"#form input[type='radio'], #form input[type='hidden']",
[ "radio1", "radio2", "hidden1" ] );
t( "Selector list with differently-quoted attribute-equals",
"#form input[type='radio'], #form input[type=\"hidden\"]",
[ "radio1", "radio2", "hidden1" ] );
t( "Selector list with quoted and unquoted attribute-equals",
"#form input[type='radio'], #form input[type=hidden]",
[ "radio1", "radio2", "hidden1" ] );
t( "attribute name is Object.prototype property \"constructor\" (negative)",
"[constructor]",
[] );
t( "attribute name is Gecko Object.prototype property \"watch\" (negative)",
"[watch]",
[] );
div.setAttribute( "constructor", "foo" );
div.setAttribute( "watch", "bar" );
t( "attribute name is Object.prototype property \"constructor\"",
"[constructor='foo']",
[ "foo" ] );
t( "attribute name is Gecko Object.prototype property \"watch\"",
"[watch='bar']",
[ "foo" ] );
});
QUnit.test("pseudo - (parent|empty)", function( assert ) {
assert.expect( 3 );
t( "Empty", "#qunit-fixture ul:empty", ["firstUL"] );
t( "Empty with comment node", "#qunit-fixture ol:empty", ["empty"] );
t( "Is A Parent", "#qunit-fixture p:parent", ["firstp","ap","sndp","en","sap","first"] );
});
QUnit.test("pseudo - (first|last|only)-(child|of-type)", function( assert ) {
assert.expect( 12 );
t( "First Child", "#qunit-fixture p:first-child", ["firstp","sndp"] );
t( "First Child (leading id)", "#qunit-fixture p:first-child", ["firstp","sndp"] );
t( "First Child (leading class)", ".nothiddendiv div:first-child", ["nothiddendivchild"] );
t( "First Child (case-insensitive)", "#qunit-fixture p:FIRST-CHILD", ["firstp","sndp"] );
t( "Last Child", "#qunit-fixture p:last-child", ["sap"] );
t( "Last Child (leading id)", "#qunit-fixture a:last-child", ["simon1","anchor1","mark","yahoo","anchor2","simon","liveLink1","liveLink2"] );
t( "Only Child", "#qunit-fixture a:only-child", ["simon1","anchor1","yahoo","anchor2","liveLink1","liveLink2"] );
t( "First-of-type", "#qunit-fixture > p:first-of-type", ["firstp"] );
t( "Last-of-type", "#qunit-fixture > p:last-of-type", ["first"] );
t( "Only-of-type", "#qunit-fixture > :only-of-type", ["name+value", "firstUL", "empty", "floatTest", "iframe", "table", "last"] );
// Verify that the child position isn't being cached improperly
var secondChildren = jQuery("p:nth-child(2)").before("<div></div>");
t( "No longer second child", "p:nth-child(2)", [] );
secondChildren.prev().remove();
t( "Restored second child", "p:nth-child(2)", ["ap","en"] );
});
QUnit.test("pseudo - nth-child", function( assert ) {
assert.expect( 30 );
t( "Nth-child", "p:nth-child(1)", ["firstp","sndp"] );
t( "Nth-child (with whitespace)", "p:nth-child( 1 )", ["firstp","sndp"] );
t( "Nth-child (case-insensitive)", "#form select:first option:NTH-child(3)", ["option1c"] );
t( "Not nth-child", "#qunit-fixture p:not(:nth-child(1))", ["ap","en","sap","first"] );
t( "Nth-child(2)", "#qunit-fixture form#form > *:nth-child(2)", ["text1"] );
t( "Nth-child(2)", "#qunit-fixture form#form > :nth-child(2)", ["text1"] );
t( "Nth-child(-1)", "#form select:first option:nth-child(-1)", [] );
t( "Nth-child(3)", "#form select:first option:nth-child(3)", ["option1c"] );
t( "Nth-child(0n+3)", "#form select:first option:nth-child(0n+3)", ["option1c"] );
t( "Nth-child(1n+0)", "#form select:first option:nth-child(1n+0)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-child(1n)", "#form select:first option:nth-child(1n)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-child(n)", "#form select:first option:nth-child(n)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-child(even)", "#form select:first option:nth-child(even)", ["option1b", "option1d"] );
t( "Nth-child(odd)", "#form select:first option:nth-child(odd)", ["option1a", "option1c"] );
t( "Nth-child(2n)", "#form select:first option:nth-child(2n)", ["option1b", "option1d"] );
t( "Nth-child(2n+1)", "#form select:first option:nth-child(2n+1)", ["option1a", "option1c"] );
t( "Nth-child(2n + 1)", "#form select:first option:nth-child(2n + 1)", ["option1a", "option1c"] );
t( "Nth-child(+2n + 1)", "#form select:first option:nth-child(+2n + 1)", ["option1a", "option1c"] );
t( "Nth-child(3n)", "#form select:first option:nth-child(3n)", ["option1c"] );
t( "Nth-child(3n+1)", "#form select:first option:nth-child(3n+1)", ["option1a", "option1d"] );
t( "Nth-child(3n+2)", "#form select:first option:nth-child(3n+2)", ["option1b"] );
t( "Nth-child(3n+3)", "#form select:first option:nth-child(3n+3)", ["option1c"] );
t( "Nth-child(3n-1)", "#form select:first option:nth-child(3n-1)", ["option1b"] );
t( "Nth-child(3n-2)", "#form select:first option:nth-child(3n-2)", ["option1a", "option1d"] );
t( "Nth-child(3n-3)", "#form select:first option:nth-child(3n-3)", ["option1c"] );
t( "Nth-child(3n+0)", "#form select:first option:nth-child(3n+0)", ["option1c"] );
t( "Nth-child(-1n+3)", "#form select:first option:nth-child(-1n+3)", ["option1a", "option1b", "option1c"] );
t( "Nth-child(-n+3)", "#form select:first option:nth-child(-n+3)", ["option1a", "option1b", "option1c"] );
t( "Nth-child(-1n + 3)", "#form select:first option:nth-child(-1n + 3)", ["option1a", "option1b", "option1c"] );
assert.deepEqual(
Sizzle( ":nth-child(n)", null, null, [ document.createElement("a") ].concat( q("ap") ) ),
q("ap"),
"Seeded nth-child"
);
});
QUnit.test("pseudo - nth-last-child", function( assert ) {
assert.expect( 30 );
jQuery( "#qunit-fixture" ).append( "<form id='nth-last-child-form'/><i/><i/><i/><i/>" );
t( "Nth-last-child", "form:nth-last-child(5)", ["nth-last-child-form"] );
t( "Nth-last-child (with whitespace)", "form:nth-last-child( 5 )", ["nth-last-child-form"] );
t( "Nth-last-child (case-insensitive)", "#form select:first option:NTH-last-child(3)", ["option1b"] );
t( "Not nth-last-child", "#qunit-fixture p:not(:nth-last-child(1))", ["firstp", "ap", "sndp", "en", "first"] );
t( "Nth-last-child(-1)", "#form select:first option:nth-last-child(-1)", [] );
t( "Nth-last-child(3)", "#form select:first :nth-last-child(3)", ["option1b"] );
t( "Nth-last-child(3)", "#form select:first *:nth-last-child(3)", ["option1b"] );
t( "Nth-last-child(3)", "#form select:first option:nth-last-child(3)", ["option1b"] );
t( "Nth-last-child(0n+3)", "#form select:first option:nth-last-child(0n+3)", ["option1b"] );
t( "Nth-last-child(1n+0)", "#form select:first option:nth-last-child(1n+0)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-last-child(1n)", "#form select:first option:nth-last-child(1n)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-last-child(n)", "#form select:first option:nth-last-child(n)", ["option1a", "option1b", "option1c", "option1d"] );
t( "Nth-last-child(even)", "#form select:first option:nth-last-child(even)", ["option1a", "option1c"] );
t( "Nth-last-child(odd)", "#form select:first option:nth-last-child(odd)", ["option1b", "option1d"] );
t( "Nth-last-child(2n)", "#form select:first option:nth-last-child(2n)", ["option1a", "option1c"] );
t( "Nth-last-child(2n+1)", "#form select:first option:nth-last-child(2n+1)", ["option1b", "option1d"] );
t( "Nth-last-child(2n + 1)", "#form select:first option:nth-last-child(2n + 1)", ["option1b", "option1d"] );
t( "Nth-last-child(+2n + 1)", "#form select:first option:nth-last-child(+2n + 1)", ["option1b", "option1d"] );
t( "Nth-last-child(3n)", "#form select:first option:nth-last-child(3n)", ["option1b"] );
t( "Nth-last-child(3n+1)", "#form select:first option:nth-last-child(3n+1)", ["option1a", "option1d"] );
t( "Nth-last-child(3n+2)", "#form select:first option:nth-last-child(3n+2)", ["option1c"] );
t( "Nth-last-child(3n+3)", "#form select:first option:nth-last-child(3n+3)", ["option1b"] );
t( "Nth-last-child(3n-1)", "#form select:first option:nth-last-child(3n-1)", ["option1c"] );
t( "Nth-last-child(3n-2)", "#form select:first option:nth-last-child(3n-2)", ["option1a", "option1d"] );
t( "Nth-last-child(3n-3)", "#form select:first option:nth-last-child(3n-3)", ["option1b"] );
t( "Nth-last-child(3n+0)", "#form select:first option:nth-last-child(3n+0)", ["option1b"] );
t( "Nth-last-child(-1n+3)", "#form select:first option:nth-last-child(-1n+3)", ["option1b", "option1c", "option1d"] );
t( "Nth-last-child(-n+3)", "#form select:first option:nth-last-child(-n+3)", ["option1b", "option1c", "option1d"] );
t( "Nth-last-child(-1n + 3)", "#form select:first option:nth-last-child(-1n + 3)", ["option1b", "option1c", "option1d"] );
QUnit.deepEqual(
Sizzle(
":nth-last-child(n)",
null,
null,
[ document.createElement("a") ].concat( q("ap") )
),
q("ap"),
"Seeded nth-last-child"
);
});
QUnit.test("pseudo - nth-of-type", function( assert ) {
assert.expect( 9 );
t( "Nth-of-type(-1)", ":nth-of-type(-1)", [] );
t( "Nth-of-type(3)", "#ap :nth-of-type(3)", ["mark"] );
t( "Nth-of-type(n)", "#ap :nth-of-type(n)", ["google", "groups", "code1", "anchor1", "mark"] );
t( "Nth-of-type(0n+3)", "#ap :nth-of-type(0n+3)", ["mark"] );
t( "Nth-of-type(2n)", "#ap :nth-of-type(2n)", ["groups"] );
t( "Nth-of-type(even)", "#ap :nth-of-type(even)", ["groups"] );
t( "Nth-of-type(2n+1)", "#ap :nth-of-type(2n+1)", ["google", "code1", "anchor1", "mark"] );
t( "Nth-of-type(odd)", "#ap :nth-of-type(odd)", ["google", "code1", "anchor1", "mark"] );
t( "Nth-of-type(-n+2)", "#qunit-fixture > :nth-of-type(-n+2)", ["firstp", "ap", "foo", "nothiddendiv", "name+value", "firstUL", "empty", "form", "floatTest", "iframe", "lengthtest", "table", "last"] );
});
QUnit.test("pseudo - nth-last-of-type", function( assert ) {
assert.expect( 9 );
t( "Nth-last-of-type(-1)", ":nth-last-of-type(-1)", [] );
t( "Nth-last-of-type(3)", "#ap :nth-last-of-type(3)", ["google"] );
t( "Nth-last-of-type(n)", "#ap :nth-last-of-type(n)", ["google", "groups", "code1", "anchor1", "mark"] );
t( "Nth-last-of-type(0n+3)", "#ap :nth-last-of-type(0n+3)", ["google"] );
t( "Nth-last-of-type(2n)", "#ap :nth-last-of-type(2n)", ["groups"] );
t( "Nth-last-of-type(even)", "#ap :nth-last-of-type(even)", ["groups"] );
t( "Nth-last-of-type(2n+1)", "#ap :nth-last-of-type(2n+1)", ["google", "code1", "anchor1", "mark"] );
t( "Nth-last-of-type(odd)", "#ap :nth-last-of-type(odd)", ["google", "code1", "anchor1", "mark"] );
t( "Nth-last-of-type(-n+2)", "#qunit-fixture > :nth-last-of-type(-n+2)", ["ap", "name+value", "first", "firstUL", "empty", "floatTest", "iframe", "table", "testForm", "liveHandlerOrder", "disabled-tests", "siblingTest", "last"] );
});
QUnit.test("pseudo - has", function( assert ) {
assert.expect( 3 );
t( "Basic test", "p:has(a)", ["firstp","ap","en","sap"] );
t( "Basic test (irrelevant whitespace)", "p:has( a )", ["firstp","ap","en","sap"] );
t( "Nested with overlapping candidates", "#qunit-fixture div:has(div:has(div:not([id])))", [ "moretests", "t2037" ] );
});
+QUnit.test("pseudo - contains", function( assert ) {
+ assert.expect( 9 );
+
+ var gh335 = document.getElementById( "qunit-fixture" ).appendChild(
+ document.createElement( "mark" ) );
+ gh335.id = "gh-335";
+ gh335.appendChild( document.createTextNode( "raw line 1\nline 2" ) );
+
+ assert.ok( Sizzle("a:contains('')").length, "empty string" );
+ t( "unquoted argument", "a:contains(Google)", ["google","groups"] );
+ t( "unquoted argument with whitespace", "a:contains(Google Groups)", ["groups"] );
+ t( "quoted argument with whitespace and parentheses",
+ "a:contains('Google Groups (Link)')", ["groups"] );
+ t( "quoted argument with double quotes and parentheses",
+ "a:contains(\"(Link)\")", ["groups"] );
+ t( "unquoted argument with whitespace and paired parentheses",
+ "a:contains(Google Groups (Link))", ["groups"] );
+ t( "unquoted argument with paired parentheses", "a:contains((Link))", ["groups"] );
+ t( "quoted argument with CSS escapes",
+ "span:contains(\"\\\"'\\53F0 \\5317 Ta\\301 ibe\\30C i\")",
+ ["utf8class1"] );
+
+ t( "collapsed whitespace", "mark:contains('line 1\\A line')", ["gh-335"] );
+});
+
QUnit.test("pseudo - misc", function( assert ) {
- assert.expect( 40 );
+ assert.expect( 32 );
var select, tmp, input;
jQuery( "<h1 id='h1'/><h2 id='h2'/><h2 id='h2-2'/>" ).prependTo( "#qunit-fixture" );
t( "Headers", "#qunit-fixture :header", ["h1", "h2", "h2-2"] );
t( "Headers(case-insensitive)", "#qunit-fixture :Header", ["h1", "h2", "h2-2"] );
t( "Multiple matches with the same context (cache check)", "#form select:has(option:first-child:contains('o'))", ["select1", "select2", "select3", "select4"] );
assert.ok( Sizzle("#qunit-fixture :not(:has(:has(*)))").length, "All not grandparents" );
select = document.getElementById("select1");
assert.ok( Sizzle.matchesSelector( select, ":has(option)" ), "Has Option Matches" );
- assert.ok( Sizzle("a:contains('')").length, "Empty string contains" );
- t( "Text Contains", "a:contains(Google)", ["google","groups"] );
- t( "Text Contains", "a:contains(Google Groups)", ["groups"] );
-
- t( "Text Contains", "a:contains('Google Groups (Link)')", ["groups"] );
- t( "Text Contains", "a:contains(\"(Link)\")", ["groups"] );
- t( "Text Contains", "a:contains(Google Groups (Link))", ["groups"] );
- t( "Text Contains", "a:contains((Link))", ["groups"] );
-
- t( "Contains with CSS escapes", "span:contains(\"\\\"'\\53F0 \\5317 Ta\\301 ibe\\30C i\")",
- ["utf8class1"] );
-
tmp = document.createElement("div");
tmp.id = "tmp_input";
document.body.appendChild( tmp );
jQuery.each( [ "button", "submit", "reset" ], function( i, type ) {
var els = jQuery(
"<input id='input_%' type='%'/><button id='button_%' type='%'>test</button>"
.replace( /%/g, type )
).appendTo( tmp );
t( "Input Buttons :" + type, "#tmp_input :" + type, [ "input_" + type, "button_" + type ] );
assert.ok( Sizzle.matchesSelector( els[0], ":" + type ), "Input Matches :" + type );
assert.ok( Sizzle.matchesSelector( els[1], ":" + type ), "Button Matches :" + type );
});
document.body.removeChild( tmp );
// Recreate tmp
tmp = document.createElement("div");
tmp.id = "tmp_input";
tmp.innerHTML = "<span>Hello I am focusable.</span>";
// Setting tabIndex should make the element focusable
// http://dev.w3.org/html5/spec/single-page.html#focus-management
document.body.appendChild( tmp );
tmp.tabIndex = 0;
tmp.focus();
if ( document.activeElement !== tmp || (document.hasFocus && !document.hasFocus()) ||
(document.querySelectorAll && !document.querySelectorAll("div:focus").length) ) {
assert.ok( true, "The div was not focused. Skip checking the :focus match." );
assert.ok( true, "The div was not focused. Skip checking the :focus match." );
} else {
t( "tabIndex element focused", ":focus", [ "tmp_input" ] );
assert.ok( Sizzle.matchesSelector( tmp, ":focus" ), ":focus matches tabIndex div" );
}
// Blur tmp
tmp.blur();
document.body.focus();
assert.ok( !Sizzle.matchesSelector( tmp, ":focus" ), ":focus doesn't match tabIndex div" );
document.body.removeChild( tmp );
// Input focus/active
input = document.createElement("input");
input.type = "text";
input.id = "focus-input";
document.body.appendChild( input );
input.focus();
// Inputs can't be focused unless the document has focus
if ( document.activeElement !== input || (document.hasFocus && !document.hasFocus()) ||
(document.querySelectorAll && !document.querySelectorAll("input:focus").length) ) {
assert.ok( true, "The input was not focused. Skip checking the :focus match." );
assert.ok( true, "The input was not focused. Skip checking the :focus match." );
} else {
t( "Element focused", "input:focus", [ "focus-input" ] );
assert.ok( Sizzle.matchesSelector( input, ":focus" ), ":focus matches" );
}
input.blur();
// When IE is out of focus, blur does not work. Force it here.
if ( document.activeElement === input ) {
document.body.focus();
}
assert.ok( !Sizzle.matchesSelector( input, ":focus" ), ":focus doesn't match" );
document.body.removeChild( input );
assert.deepEqual(
Sizzle( "[id='select1'] *:not(:last-child), [id='select2'] *:not(:last-child)", q("qunit-fixture")[0] ),
q( "option1a", "option1b", "option1c", "option2a", "option2b", "option2c" ),
"caching system tolerates recursive selection"
);
// Tokenization edge cases
t( "Sequential pseudos", "#qunit-fixture p:has(:contains(mark)):has(code)", ["ap"] );
t( "Sequential pseudos", "#qunit-fixture p:has(:contains(mark)):has(code):contains(This link)", ["ap"] );
t( "Pseudo argument containing ')'", "p:has(>a.GROUPS[src!=')'])", ["ap"] );
t( "Pseudo argument containing ')'", "p:has(>a.GROUPS[src!=')'])", ["ap"] );
t( "Pseudo followed by token containing ')'", "p:contains(id=\"foo\")[id!=\\)]", ["sndp"] );
t( "Pseudo followed by token containing ')'", "p:contains(id=\"foo\")[id!=')']", ["sndp"] );
t( "Multi-pseudo", "#ap:has(*), #ap:has(*)", ["ap"] );
t( "Multi-positional", "#ap:gt(0), #ap:lt(1)", ["ap"] );
t( "Multi-pseudo with leading nonexistent id", "#nonexistent:has(*), #ap:has(*)", ["ap"] );
t( "Multi-positional with leading nonexistent id", "#nonexistent:gt(0), #ap:lt(1)", ["ap"] );
t( "Tokenization stressor", "a[class*=blog]:not(:has(*, :contains(!)), :contains(!)), br:contains(]), p:contains(]), :not(:empty):not(:parent)", ["ap", "mark","yahoo","simon"] );
});
QUnit.test("pseudo - :not", function( assert ) {
assert.expect( 43 );
t( "Not", "a.blog:not(.link)", ["mark"] );
t( ":not() with :first", "#foo p:not(:first) .link", ["simon"] );
t( "Not - multiple", "#form option:not(:contains(Nothing),#option1b,:selected)", ["option1c", "option1d", "option2b", "option2c", "option3d", "option3e", "option4e", "option5b", "option5c"] );
t( "Not - recursive", "#form option:not(:not(:selected))[id^='option3']", [ "option3b", "option3c"] );
t( ":not() failing interior", "#qunit-fixture p:not(.foo)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not() failing interior", "#qunit-fixture p:not(div.foo)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not() failing interior", "#qunit-fixture p:not(p.foo)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not() failing interior", "#qunit-fixture p:not(#blargh)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not() failing interior", "#qunit-fixture p:not(div#blargh)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not() failing interior", "#qunit-fixture p:not(p#blargh)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not Multiple", "#qunit-fixture p:not(a)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not Multiple", "#qunit-fixture p:not( a )", ["firstp","ap","sndp","en","sap","first"] );
t( ":not Multiple", "#qunit-fixture p:not( p )", [] );
t( ":not Multiple", "#qunit-fixture p:not(a, b)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not Multiple", "#qunit-fixture p:not(a, b, div)", ["firstp","ap","sndp","en","sap","first"] );
t( ":not Multiple", "p:not(p)", [] );
t( ":not Multiple", "p:not(a,p)", [] );
t( ":not Multiple", "p:not(p,a)", [] );
t( ":not Multiple", "p:not(a,p,b)", [] );
t( ":not Multiple", ":input:not(:image,:input,:submit)", [] );
t( ":not Multiple", "#qunit-fixture p:not(:has(a), :nth-child(1))", ["first"] );
t( "No element not selector", ".container div:not(.excluded) div", [] );
t( ":not() Existing attribute", "#form select:not([multiple])", ["select1", "select2", "select5"]);
t( ":not() Equals attribute", "#form select:not([name=select1])", ["select2", "select3", "select4","select5"]);
t( ":not() Equals quoted attribute", "#form select:not([name='select1'])", ["select2", "select3", "select4", "select5"]);
t( ":not() Multiple Class", "#foo a:not(.blog)", ["yahoo", "anchor2"] );
t( ":not() Multiple Class", "#foo a:not(.link)", ["yahoo", "anchor2"] );
t( ":not() Multiple Class", "#foo a:not(.blog.link)", ["yahoo", "anchor2"] );
t( ":not chaining (compound)", "#qunit-fixture div[id]:not(:has(div, span)):not(:has(*))", ["nothiddendivchild", "divWithNoTabIndex"] );
t( ":not chaining (with attribute)", "#qunit-fixture form[id]:not([action$='formaction']):not(:button)", ["lengthtest", "name-tests", "testForm", "disabled-tests"] );
t( ":not chaining (colon in attribute)", "#qunit-fixture form[id]:not([action='form:action']):not(:button)", ["form", "lengthtest", "name-tests", "testForm", "disabled-tests"] );
t( ":not chaining (colon in attribute and nested chaining)", "#qunit-fixture form[id]:not([action='form:action']:button):not(:input)", ["form", "lengthtest", "name-tests", "testForm", "disabled-tests"] );
t( ":not chaining", "#form select:not(.select1):contains(Nothing) > option:not(option)", [] );
t( "positional :not()", "#foo p:not(:last)", ["sndp", "en"] );
t( "positional :not() prefix", "#foo p:not(:last) a", ["yahoo"] );
t( "compound positional :not()", "#foo p:not(:first, :last)", ["en"] );
t( "compound positional :not()", "#foo p:not(:first, :even)", ["en"] );
t( "compound positional :not()", "#foo p:not(:first, :odd)", ["sap"] );
t( "reordered compound positional :not()", "#foo p:not(:odd, :first)", ["sap"] );
t( "positional :not() with pre-filter", "#foo p:not([id]:first)", ["en", "sap"] );
t( "positional :not() with post-filter", "#foo p:not(:first[id])", ["en", "sap"] );
t( "positional :not() with pre-filter", "#foo p:not([lang]:first)", ["sndp", "sap"] );
t( "positional :not() with post-filter", "#foo p:not(:first[lang])", ["sndp", "en", "sap"] );
});
QUnit.test("pseudo - position", function( assert ) {
assert.expect( 34 );
t( "First element", "#qunit-fixture p:first", ["firstp"] );
t( "First element(case-insensitive)", "#qunit-fixture p:fiRst", ["firstp"] );
t( "nth Element", "#qunit-fixture p:nth(1)", ["ap"] );
t( "First Element", "#qunit-fixture p:first", ["firstp"] );
t( "Last Element", "p:last", ["first"] );
t( "Even Elements", "#qunit-fixture p:even", ["firstp","sndp","sap"] );
t( "Odd Elements", "#qunit-fixture p:odd", ["ap","en","first"] );
t( "Position Equals", "#qunit-fixture p:eq(1)", ["ap"] );
t( "Position Equals (negative)", "#qunit-fixture p:eq(-1)", ["first"] );
t( "Position Greater Than", "#qunit-fixture p:gt(0)", ["ap","sndp","en","sap","first"] );
t( "Position Less Than", "#qunit-fixture p:lt(3)", ["firstp","ap","sndp"] );
t( "Position Less Than Big Number", "#qunit-fixture p:lt(9007199254740991)", ["firstp","ap","sndp","en","sap","first"] );
t( "Check position filtering", "div#nothiddendiv:eq(0)", ["nothiddendiv"] );
t( "Check position filtering", "div#nothiddendiv:last", ["nothiddendiv"] );
t( "Check position filtering", "div#nothiddendiv:not(:gt(0))", ["nothiddendiv"] );
t( "Check position filtering", "#foo > :not(:first)", ["en", "sap"] );
t( "Check position filtering", "#qunit-fixture select > :not(:gt(2))", ["option1a", "option1b", "option1c"] );
t( "Check position filtering", "#qunit-fixture select:lt(2) :not(:first)", ["option1b", "option1c", "option1d", "option2a", "option2b", "option2c", "option2d"] );
t( "Check position filtering", "div.nothiddendiv:eq(0)", ["nothiddendiv"] );
t( "Check position filtering", "div.nothiddendiv:last", ["nothiddendiv"] );
t( "Check position filtering", "div.nothiddendiv:not(:lt(0))", ["nothiddendiv"] );
t( "Check element position", "#qunit-fixture div div:eq(0)", ["nothiddendivchild"] );
t( "Check element position", "#select1 option:eq(3)", ["option1d"] );
t( "Check element position", "#qunit-fixture div div:eq(10)", ["names-group"] );
t( "Check element position", "#qunit-fixture div div:first", ["nothiddendivchild"] );
t( "Check element position", "#qunit-fixture div > div:first", ["nothiddendivchild"] );
t( "Check element position", "#qunit-fixture div:first a:first", ["yahoo"] );
t( "Check element position", "#qunit-fixture div:first > p:first", ["sndp"] );
t( "Check element position", "div#nothiddendiv:first > div:first", ["nothiddendivchild"] );
t( "Chained pseudo after a pos pseudo", "#listWithTabIndex li:eq(0):contains(Rice)", ["foodWithNegativeTabIndex"] );
t( "Check sort order with POS and comma", "#qunit-fixture em>em>em>em:first-child,div>em:first", ["siblingfirst", "siblinggreatgrandchild"] );
t( "Isolated position", "#qunit-fixture :last", ["last"] );
assert.deepEqual( Sizzle( "*:lt(2) + *", null, [], Sizzle("#qunit-fixture > p") ), q("ap"),
"Seeded pos with trailing relative" );
// jQuery #12526
var context = jQuery("#qunit-fixture").append("<div id='jquery12526'></div>")[0];
assert.deepEqual( Sizzle( ":last", context ), q("jquery12526"),
"Post-manipulation positional" );
});
QUnit.test("pseudo - form", function( assert ) {
assert.expect( 10 );
var extraTexts = jQuery("<input id=\"impliedText\"/><input id=\"capitalText\" type=\"TEXT\">").appendTo("#form");
t( "Form element :input", "#form :input", ["text1", "text2", "radio1", "radio2", "check1", "check2", "hidden1", "hidden2", "name", "search", "button", "area1", "select1", "select2", "select3", "select4", "select5", "impliedText", "capitalText"] );
t( "Form element :radio", "#form :radio", ["radio1", "radio2"] );
t( "Form element :checkbox", "#form :checkbox", ["check1", "check2"] );
t( "Form element :text", "#form :text", ["text1", "text2", "hidden2", "name", "impliedText", "capitalText"] );
t( "Form element :radio:checked", "#form :radio:checked", ["radio2"] );
t( "Form element :checkbox:checked", "#form :checkbox:checked", ["check1"] );
t( "Form element :radio:checked, :checkbox:checked", "#form :radio:checked, #form :checkbox:checked", ["radio2", "check1"] );
t( "Selected option element",
"#form option:selected",
[ "option1a", "option2d", "option3b", "option3c", "option4b", "option4c", "option4d",
"option5a" ] );
t( "Selected option elements are also :checked", "#form option:checked",
[ "option1a", "option2d", "option3b", "option3c", "option4b", "option4c", "option4d",
"option5a" ] );
t( "Hidden inputs are still :enabled",
"#hidden1:enabled",
[ "hidden1" ] );
extraTexts.remove();
});
QUnit.test("pseudo - :(dis|en)abled, explicitly disabled", function( assert ) {
assert.expect( 2 );
// Set a meaningless disabled property on a common ancestor
var container = document.getElementById( "disabled-tests" );
container.disabled = true;
// Support: IE 6 - 11
// Unset the property where it is not meaningless
if ( document.getElementById( "enabled-input" ).isDisabled ) {
container.disabled = undefined;
}
t(
"Explicitly disabled elements",
"#enabled-fieldset :disabled",
[ "disabled-input", "disabled-textarea", "disabled-button",
"disabled-select", "disabled-optgroup", "disabled-option" ]
);
t(
"Enabled elements",
"#enabled-fieldset :enabled",
[ "enabled-input", "enabled-textarea", "enabled-button",
"enabled-select", "enabled-optgroup", "enabled-option" ]
);
});
QUnit.test("pseudo - :(dis|en)abled, optgroup and option", function( assert ) {
assert.expect( 2 );
t(
":disabled",
"#disabled-select-inherit :disabled, #enabled-select-inherit :disabled",
[ "disabled-optgroup-inherit", "disabled-optgroup-option", "en_disabled-optgroup-inherit",
"en_disabled-optgroup-option" ]
);
t(
":enabled",
"#disabled-select-inherit :enabled, #enabled-select-inherit :enabled",
[ "enabled-optgroup-inherit", "enabled-optgroup-option", "enabled-select-option" ]
);
});
// Support: PhantomJS
// fieldsetElement.disabled is undefined
if ( jQuery("<fieldset disabled='disabled'/>")[0].disabled ) {
QUnit.test("pseudo - fieldset:(dis|en)abled", function() {
t( "Disabled fieldset", "fieldset:disabled", [ "disabled-fieldset" ] );
t( "Enabled fieldset", "fieldset:enabled", [ "enabled-fieldset" ] );
});
QUnit.test("pseudo - :disabled by ancestry", function( assert ) {
assert.expect( 1 );
// Don't test for presence of select
// IE6 doesn't visibly or functionally disable them when the fieldset is disabled
t(
"Inputs inherit disabled from fieldset",
"#disabled-fieldset :disabled",
[ "disabled-fieldset-input", "disabled-fieldset-textarea",
"disabled-fieldset-button" ]
);
});
}
QUnit.test("pseudo - :target and :root", function( assert ) {
assert.expect( 2 );
// Target
var oldHash,
$link = jQuery("<a/>").attr({
href: "#",
id: "new-link"
}).appendTo("#qunit-fixture");
oldHash = window.location.hash;
window.location.hash = "new-link";
t( ":target", ":target", ["new-link"] );
$link.remove();
window.location.hash = oldHash;
// Root
assert.equal( Sizzle(":root")[0], document.documentElement, ":root selector" );
});
QUnit.test("pseudo - :lang", function( assert ) {
assert.expect( 105 );
var docElem = document.documentElement,
docXmlLang = docElem.getAttribute("xml:lang"),
docLang = docElem.lang,
foo = document.getElementById("foo"),
anchor = document.getElementById("anchor2"),
xml = createWithFriesXML(),
testLang = function( text, elem, container, lang, extra ) {
var message,
full = lang + "-" + extra;
message = "lang=" + lang + " " + text;
container.setAttribute( container.ownerDocument.documentElement.nodeName === "HTML" ? "lang" : "xml:lang", lang );
assertMatch( message, elem, ":lang(" + lang + ")" );
assertMatch( message, elem, ":lang(" + mixCase(lang) + ")" );
assertNoMatch( message, elem, ":lang(" + full + ")" );
assertNoMatch( message, elem, ":lang(" + mixCase(full) + ")" );
assertNoMatch( message, elem, ":lang(" + lang + "-)" );
assertNoMatch( message, elem, ":lang(" + full + "-)" );
assertNoMatch( message, elem, ":lang(" + lang + "glish)" );
assertNoMatch( message, elem, ":lang(" + full + "glish)" );
message = "lang=" + full + " " + text;
container.setAttribute( container.ownerDocument.documentElement.nodeName === "HTML" ? "lang" : "xml:lang", full );
assertMatch( message, elem, ":lang(" + lang + ")" );
assertMatch( message, elem, ":lang(" + mixCase(lang) + ")" );
assertMatch( message, elem, ":lang(" + full + ")" );
assertMatch( message, elem, ":lang(" + mixCase(full) + ")" );
assertNoMatch( message, elem, ":lang(" + lang + "-)" );
assertNoMatch( message, elem, ":lang(" + full + "-)" );
assertNoMatch( message, elem, ":lang(" + lang + "glish)" );
assertNoMatch( message, elem, ":lang(" + full + "glish)" );
},
mixCase = function( str ) {
var ret = str.split(""),
i = ret.length;
while ( i-- ) {
if ( i & 1 ) {
ret[i] = ret[i].toUpperCase();
}
}
return ret.join("");
},
assertMatch = function( text, elem, selector ) {
assert.ok( Sizzle.matchesSelector( elem, selector ), text + " match " + selector );
},
assertNoMatch = function( text, elem, selector ) {
assert.ok( !Sizzle.matchesSelector( elem, selector ), text + " fail " + selector );
};
// Prefixing and inheritance
assert.ok( Sizzle.matchesSelector( docElem, ":lang(" + docElem.lang + ")" ), "starting :lang" );
testLang( "document", anchor, docElem, "en", "us" );
testLang( "grandparent", anchor, anchor.parentNode.parentNode, "yue", "hk" );
assert.ok( !Sizzle.matchesSelector( anchor, ":lang(en), :lang(en-us)" ),
":lang does not look above an ancestor with specified lang" );
testLang( "self", anchor, anchor, "es", "419" );
assert.ok(
!Sizzle.matchesSelector( anchor, ":lang(en), :lang(en-us), :lang(yue), :lang(yue-hk)" ),
":lang does not look above self with specified lang"
);
// Searching by language tag
anchor.parentNode.parentNode.lang = "arab";
anchor.parentNode.lang = anchor.parentNode.id = "ara-sa";
anchor.lang = "ara";
assert.deepEqual( Sizzle( ":lang(ara)", foo ), [ anchor.parentNode, anchor ], "Find by :lang" );
// Selector validity
anchor.parentNode.lang = "ara";
anchor.lang = "ara\\b";
assert.deepEqual( Sizzle( ":lang(ara\\b)", foo ), [], ":lang respects backslashes" );
assert.deepEqual( Sizzle( ":lang(ara\\\\b)", foo ), [ anchor ],
":lang respects escaped backslashes" );
assert.throws(function() {
Sizzle.call( null, "#qunit-fixture:lang(c++)" );
}, function( e ) {
return e.message.indexOf("Syntax error") >= 0;
}, ":lang value must be a valid identifier" );
// XML
foo = jQuery( "response", xml )[0];
anchor = jQuery( "#seite1", xml )[0];
testLang( "XML document", anchor, xml.documentElement, "en", "us" );
testLang( "XML grandparent", anchor, foo, "yue", "hk" );
assert.ok( !Sizzle.matchesSelector( anchor, ":lang(en), :lang(en-us)" ),
"XML :lang does not look above an ancestor with specified lang" );
testLang( "XML self", anchor, anchor, "es", "419" );
assert.ok(
!Sizzle.matchesSelector( anchor, ":lang(en), :lang(en-us), :lang(yue), :lang(yue-hk)" ),
"XML :lang does not look above self with specified lang" );
// Cleanup
if ( docXmlLang == null ) {
docElem.removeAttribute("xml:lang");
} else {
docElem.setAttribute( "xml:lang", docXmlLang );
}
docElem.lang = docLang;
});
QUnit.test("context", function( assert ) {
assert.expect( 21 );
var context,
selector = ".blog",
expected = q( "mark", "simon" ),
iframe = document.getElementById( "iframe" ),
iframeDoc = iframe.contentDocument || iframe.contentWindow.document;
assert.deepEqual( Sizzle( selector, document ), expected, "explicit document context" );
assert.deepEqual( Sizzle( selector ), expected, "unspecified context becomes document" );
assert.deepEqual( Sizzle( selector, undefined ), expected,
"undefined context becomes document" );
assert.deepEqual( Sizzle( selector, null ), expected, "null context becomes document" );
iframeDoc.open();
iframeDoc.write( "<body><p id='foo'>bar</p></body>" );
iframeDoc.close();
expected = [ iframeDoc.getElementById( "foo" ) ];
assert.deepEqual( Sizzle( "p", iframeDoc ), expected, "Other document context (simple)");
assert.deepEqual( Sizzle( "p:contains(ar)", iframeDoc ), expected,
"Other document context (complex)");
assert.deepEqual( Sizzle( "span", iframeDoc ), [],
"Other document context (simple, no results)");
assert.deepEqual( Sizzle( "* span", iframeDoc ), [],
"Other document context (complex, no results)");
context = document.getElementById( "nothiddendiv" );
assert.deepEqual( Sizzle( "*", context ), q( "nothiddendivchild" ), "<div> context" );
assert.deepEqual( Sizzle( "* > *", context ), [], "<div> context (no results)" );
context.removeAttribute( "id" );
assert.deepEqual( Sizzle( "*", context ), q( "nothiddendivchild" ), "no-id element context" );
assert.deepEqual( Sizzle( "* > *", context ), [], "no-id element context (no results)" );
// Support: IE<8 only
// ID attroperty is never really gone
assert.strictEqual( context.getAttribute( "id" ) || "", "", "id not added by no-id selection" );
context = document.getElementById( "lengthtest" );
assert.deepEqual( Sizzle( "input", context ), q( "length", "idTest" ), "<form> context");
assert.deepEqual( Sizzle( "select", context ), [], "<form> context (no results)");
context = document.getElementById( "å°åTaÌibeÌi" );
expected = q( "å°åTaÌibeÌi-child" );
assert.deepEqual( Sizzle( "span[id]", context ), expected, "context with non-ASCII id");
assert.deepEqual( Sizzle( "#å°åTaÌibeÌi span[id]", context.parentNode ), expected,
"context with non-ASCII id selector prefix");
context = document.createDocumentFragment();
// Capture *independent* expected nodes before they're detached from the page
expected = q( "siblingnext", "siblingspan" );
context.appendChild( document.getElementById( "siblingTest" ) );
assert.deepEqual(
Sizzle( "em:nth-child(2)", context ),
expected.slice( 0, 1 ),
"DocumentFragment context"
);
assert.deepEqual( Sizzle( "span", context ), expected.slice( 1 ),
"DocumentFragment context by tag name" );
assert.deepEqual( Sizzle( "p", context ), [], "DocumentFragment context (no results)" );
assert.deepEqual(
Sizzle( "em + :not(:has(*)):not(:empty), foo", context.firstChild ),
expected.slice( 0, 1 ),
"Non-qSA path correctly sets detached context for sibling selectors (jQuery #14351)"
);
});
QUnit.test("caching", function( assert ) {
assert.expect( 3 );
var sap = document.getElementById("sap");
Sizzle( ":not(code)", document.getElementById("ap") );
assert.deepEqual(
Sizzle( ":not(code)", document.getElementById("foo") ),
q( "sndp", "en", "yahoo", "sap", "anchor2", "simon" ),
"Reusing selector with new context"
);
t( "Deep ancestry caching in post-positional element matcher (jQuery #14657)",
"#qunit-fixture a:lt(3):parent",
[ "simon1", "google", "groups" ] );
sap.className = "original";
Sizzle( "#qunit-fixture:noQSA .original" );
document.getElementById("nothiddendiv").appendChild(
sap.cloneNode( true ) ).className = "clone";
assert.equal( Sizzle( "#qunit-fixture:noQSA .clone [href*='2']" ).length, 1,
"Cloning does not poison caches" );
|
jquery/sizzle
|
26a1f3f6f156cb687d0d7adc7bf79f0e5454811a
|
Misc: Update isXML to recognize HTML-embedded elements
|
diff --git a/dist/sizzle.js b/dist/sizzle.js
index 5d234f0..150d90c 100644
--- a/dist/sizzle.js
+++ b/dist/sizzle.js
@@ -1,1077 +1,1081 @@
/*!
* Sizzle CSS Selector Engine v2.3.4-pre
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
- * Date: 2018-11-04
+ * Date: 2018-12-03
*/
(function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ({}).hasOwnProperty,
arr = [],
pop = arr.pop,
push_native = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[i] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
"*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
+ rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
funescape = function( _, escaped, escapedWhitespace ) {
var high = "0x" + escaped - 0x10000;
// NaN means non-codepoint
// Support: Firefox<24
// Workaround erroneous numeric interpretation of +"0x"
return high !== high || escapedWhitespace ?
escaped :
high < 0 ?
// BMP codepoint
String.fromCharCode( high + 0x10000 ) :
// Supplemental Plane codepoint (surrogate pair)
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
(arr = slice.call( preferredDoc.childNodes )),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
push_native.apply( target, slice.call(els) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( (target[j++] = els[i++]) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
// ID selector
if ( (m = match[1]) ) {
// Document context
if ( nodeType === 9 ) {
if ( (elem = context.getElementById( m )) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && (elem = newContext.getElementById( m )) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[2] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( (m = match[3]) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
// Support: IE 8 only
// Exclude object elements
(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( (nid = context.getAttribute( "id" )) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", (nid = expando) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[i] = "#" + nid + " " + toSelector( groups[i] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return (cache[ key + " " ] = value);
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement("fieldset");
try {
return !!fn( el );
} catch (e) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split("|"),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[i] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( (cur = cur.nextSibling) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return (name === "input" || name === "button") && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction(function( argument ) {
argument = +argument;
return markFunction(function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ (j = matchIndexes[i]) ] ) {
seed[j] = !(matches[j] = seed[j]);
}
}
});
});
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
- // documentElement is verified for cases where it doesn't yet exist
- // (such as loading iframes in IE - #4833)
- var documentElement = elem && (elem.ownerDocument || elem).documentElement;
- return documentElement ? documentElement.nodeName !== "HTML" : false;
+ var namespace = elem.namespaceURI,
+ docElem = (elem.ownerDocument || elem).documentElement;
+
+ // Support: IE <=8
+ // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+ // https://bugs.jquery.com/ticket/4833
+ return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
(subWindow = document.defaultView) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert(function( el ) {
el.className = "i";
return !el.getAttribute("className");
});
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert(function( el ) {
el.appendChild( document.createComment("") );
return !el.getElementsByTagName("*").length;
});
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert(function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
});
// ID filter and find
if ( support.getById ) {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute("id") === attrId;
};
};
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
var node = typeof elem.getAttributeNode !== "undefined" &&
elem.getAttributeNode("id");
return node && node.value === attrId;
};
};
// Support: IE 6 - 7 only
// getElementById is not reliable as a find shortcut
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var node, i, elems,
elem = context.getElementById( id );
if ( elem ) {
// Verify the id attribute
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
// Fall back on getElementsByName
elems = context.getElementsByName( id );
i = 0;
while ( (elem = elems[i++]) ) {
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
}
}
return [];
}
};
}
// Tag
Expr.find["TAG"] = support.getElementsByTagName ?
function( tag, context ) {
if ( typeof context.getElementsByTagName !== "undefined" ) {
return context.getElementsByTagName( tag );
// DocumentFragment nodes don't have gEBTN
} else if ( support.qsa ) {
return context.querySelectorAll( tag );
}
} :
function( tag, context ) {
var elem,
tmp = [],
i = 0,
// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
results = context.getElementsByTagName( tag );
// Filter out possible comments
if ( tag === "*" ) {
while ( (elem = results[i++]) ) {
if ( elem.nodeType === 1 ) {
tmp.push( elem );
}
}
return tmp;
}
return results;
};
// Class
Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) {
if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
return context.getElementsByClassName( className );
}
};
/* QSA/matchesSelector
---------------------------------------------------------------------- */
// QSA and matchesSelector support
// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
rbuggyMatches = [];
// qSa(:focus) reports false when true (Chrome 21)
// We allow this because of a bug in IE8/9 that throws an error
// whenever `document.activeElement` is accessed on an iframe
// So, we allow :focus to pass through QSA all the time to avoid the IE error
// See https://bugs.jquery.com/ticket/13378
rbuggyQSA = [];
if ( (support.qsa = rnative.test( document.querySelectorAll )) ) {
// Build QSA regex
// Regex strategy adopted from Diego Perini
assert(function( el ) {
// Select is set to empty string on purpose
// This is to test IE's treatment of not explicitly
// setting a boolean content attribute,
// since its presence should be enough
// https://bugs.jquery.com/ticket/12359
docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
"<select id='" + expando + "-\r\\' msallowcapture=''>" +
"<option selected=''></option></select>";
// Support: IE8, Opera 11-12.16
// Nothing should be selected when empty strings follow ^= or $= or *=
// The test attribute must be unknown in Opera but "safe" for WinRT
// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
if ( el.querySelectorAll("[msallowcapture^='']").length ) {
rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
}
// Support: IE8
// Boolean attributes and "value" are not treated correctly
if ( !el.querySelectorAll("[selected]").length ) {
rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
}
// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
rbuggyQSA.push("~=");
}
// Webkit/Opera - :checked should return selected option elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
// IE8 throws error here and will not see later tests
if ( !el.querySelectorAll(":checked").length ) {
rbuggyQSA.push(":checked");
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push(".#.+[+~]");
}
});
assert(function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement("input");
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll("[name=d]").length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll(":enabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll(":disabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll("*,:x");
rbuggyQSA.push(",.*:");
});
}
if ( (support.matchesSelector = rnative.test( (matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector) )) ) {
assert(function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
});
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
));
} :
function( a, b ) {
if ( b ) {
while ( (b = b.parentNode) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
(!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) {
// Choose the first element that is related to our preferred document
if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) {
return -1;
}
if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( (cur = cur.parentNode) ) {
ap.unshift( cur );
}
cur = b;
while ( (cur = cur.parentNode) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[i] === bp[i] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[i], bp[i] ) :
// Otherwise nodes in our document sort first
ap[i] === preferredDoc ? -1 :
bp[i] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch (e) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
(val = elem.getAttributeNode(name)) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return (sel + "").replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( (elem = results[i++]) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
diff --git a/dist/sizzle.min.js b/dist/sizzle.min.js
index d884567..d4ea5ac 100644
--- a/dist/sizzle.min.js
+++ b/dist/sizzle.min.js
@@ -1,3 +1,3 @@
/*! Sizzle v2.3.4-pre | (c) JS Foundation and other contributors | js.foundation */
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\ No newline at end of file
diff --git a/src/sizzle.js b/src/sizzle.js
index 78c5930..868342d 100644
--- a/src/sizzle.js
+++ b/src/sizzle.js
@@ -1,1077 +1,1081 @@
/*!
* Sizzle CSS Selector Engine v@VERSION
* https://sizzlejs.com/
*
* Copyright JS Foundation and other contributors
* Released under the MIT license
* https://js.foundation/
*
* Date: @DATE
*/
(function( window ) {
var i,
support,
Expr,
getText,
isXML,
tokenize,
compile,
select,
outermostContext,
sortInput,
hasDuplicate,
// Local document vars
setDocument,
document,
docElem,
documentIsHTML,
rbuggyQSA,
rbuggyMatches,
matches,
contains,
// Instance-specific data
expando = "sizzle" + 1 * new Date(),
preferredDoc = window.document,
dirruns = 0,
done = 0,
classCache = createCache(),
tokenCache = createCache(),
compilerCache = createCache(),
nonnativeSelectorCache = createCache(),
sortOrder = function( a, b ) {
if ( a === b ) {
hasDuplicate = true;
}
return 0;
},
// Instance methods
hasOwn = ({}).hasOwnProperty,
arr = [],
pop = arr.pop,
push_native = arr.push,
push = arr.push,
slice = arr.slice,
// Use a stripped-down indexOf as it's faster than native
// https://jsperf.com/thor-indexof-vs-for/5
indexOf = function( list, elem ) {
var i = 0,
len = list.length;
for ( ; i < len; i++ ) {
if ( list[i] === elem ) {
return i;
}
}
return -1;
},
booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
// Regular expressions
// http://www.w3.org/TR/css3-selectors/#whitespace
whitespace = "[\\x20\\t\\r\\n\\f]",
// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
// Operator (capture 2)
"*([*^$|!~]?=)" + whitespace +
// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
"*\\]",
pseudos = ":(" + identifier + ")(?:\\((" +
// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
// 1. quoted (capture 3; capture 4 or capture 5)
"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
// 2. simple (capture 6)
"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
// 3. anything else (capture 2)
".*" +
")\\)|)",
// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
rwhitespace = new RegExp( whitespace + "+", "g" ),
rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
rdescend = new RegExp( whitespace + "|>" ),
rpseudo = new RegExp( pseudos ),
ridentifier = new RegExp( "^" + identifier + "$" ),
matchExpr = {
"ID": new RegExp( "^#(" + identifier + ")" ),
"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
"TAG": new RegExp( "^(" + identifier + "|[*])" ),
"ATTR": new RegExp( "^" + attributes ),
"PSEUDO": new RegExp( "^" + pseudos ),
"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
// For use in libraries implementing .is()
// We use this for POS matching in `select`
"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
},
+ rhtml = /HTML$/i,
rinputs = /^(?:input|select|textarea|button)$/i,
rheader = /^h\d$/i,
rnative = /^[^{]+\{\s*\[native \w/,
// Easily-parseable/retrievable ID or TAG or CLASS selectors
rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
rsibling = /[+~]/,
// CSS escapes
// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
funescape = function( _, escaped, escapedWhitespace ) {
var high = "0x" + escaped - 0x10000;
// NaN means non-codepoint
// Support: Firefox<24
// Workaround erroneous numeric interpretation of +"0x"
return high !== high || escapedWhitespace ?
escaped :
high < 0 ?
// BMP codepoint
String.fromCharCode( high + 0x10000 ) :
// Supplemental Plane codepoint (surrogate pair)
String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
},
// CSS string/identifier serialization
// https://drafts.csswg.org/cssom/#common-serializing-idioms
rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
fcssescape = function( ch, asCodePoint ) {
if ( asCodePoint ) {
// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
if ( ch === "\0" ) {
return "\uFFFD";
}
// Control characters and (dependent upon position) numbers get escaped as code points
return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
}
// Other potentially-special ASCII characters get backslash-escaped
return "\\" + ch;
},
// Used for iframes
// See setDocument()
// Removing the function wrapper causes a "Permission Denied"
// error in IE
unloadHandler = function() {
setDocument();
},
inDisabledFieldset = addCombinator(
function( elem ) {
return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
},
{ dir: "parentNode", next: "legend" }
);
// Optimize for push.apply( _, NodeList )
try {
push.apply(
(arr = slice.call( preferredDoc.childNodes )),
preferredDoc.childNodes
);
// Support: Android<4.0
// Detect silently failing push.apply
arr[ preferredDoc.childNodes.length ].nodeType;
} catch ( e ) {
push = { apply: arr.length ?
// Leverage slice if possible
function( target, els ) {
push_native.apply( target, slice.call(els) );
} :
// Support: IE<9
// Otherwise append directly
function( target, els ) {
var j = target.length,
i = 0;
// Can't trust NodeList.length
while ( (target[j++] = els[i++]) ) {}
target.length = j - 1;
}
};
}
function Sizzle( selector, context, results, seed ) {
var m, i, elem, nid, match, groups, newSelector,
newContext = context && context.ownerDocument,
// nodeType defaults to 9, since context defaults to document
nodeType = context ? context.nodeType : 9;
results = results || [];
// Return early from calls with invalid selector or context
if ( typeof selector !== "string" || !selector ||
nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
return results;
}
// Try to shortcut find operations (as opposed to filters) in HTML documents
if ( !seed ) {
if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
setDocument( context );
}
context = context || document;
if ( documentIsHTML ) {
// If the selector is sufficiently simple, try using a "get*By*" DOM method
// (excepting DocumentFragment context, where the methods don't exist)
if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
// ID selector
if ( (m = match[1]) ) {
// Document context
if ( nodeType === 9 ) {
if ( (elem = context.getElementById( m )) ) {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( elem.id === m ) {
results.push( elem );
return results;
}
} else {
return results;
}
// Element context
} else {
// Support: IE, Opera, Webkit
// TODO: identify versions
// getElementById can match elements by name instead of ID
if ( newContext && (elem = newContext.getElementById( m )) &&
contains( context, elem ) &&
elem.id === m ) {
results.push( elem );
return results;
}
}
// Type selector
} else if ( match[2] ) {
push.apply( results, context.getElementsByTagName( selector ) );
return results;
// Class selector
} else if ( (m = match[3]) && support.getElementsByClassName &&
context.getElementsByClassName ) {
push.apply( results, context.getElementsByClassName( m ) );
return results;
}
}
// Take advantage of querySelectorAll
if ( support.qsa &&
!nonnativeSelectorCache[ selector + " " ] &&
(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
// Support: IE 8 only
// Exclude object elements
(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
newSelector = selector;
newContext = context;
// qSA considers elements outside a scoping root when evaluating child or
// descendant combinators, which is not what we want.
// In such cases, we work around the behavior by prefixing every selector in the
// list with an ID selector referencing the scope context.
// Thanks to Andrew Dupont for this technique.
if ( nodeType === 1 && rdescend.test( selector ) ) {
// Capture the context ID, setting it first if necessary
if ( (nid = context.getAttribute( "id" )) ) {
nid = nid.replace( rcssescape, fcssescape );
} else {
context.setAttribute( "id", (nid = expando) );
}
// Prefix every selector in the list
groups = tokenize( selector );
i = groups.length;
while ( i-- ) {
groups[i] = "#" + nid + " " + toSelector( groups[i] );
}
newSelector = groups.join( "," );
// Expand context for sibling selectors
newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
context;
}
try {
push.apply( results,
newContext.querySelectorAll( newSelector )
);
return results;
} catch ( qsaError ) {
nonnativeSelectorCache( selector, true );
} finally {
if ( nid === expando ) {
context.removeAttribute( "id" );
}
}
}
}
}
// All others
return select( selector.replace( rtrim, "$1" ), context, results, seed );
}
/**
* Create key-value caches of limited size
* @returns {function(string, object)} Returns the Object data after storing it on itself with
* property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
* deleting the oldest entry
*/
function createCache() {
var keys = [];
function cache( key, value ) {
// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
if ( keys.push( key + " " ) > Expr.cacheLength ) {
// Only keep the most recent entries
delete cache[ keys.shift() ];
}
return (cache[ key + " " ] = value);
}
return cache;
}
/**
* Mark a function for special use by Sizzle
* @param {Function} fn The function to mark
*/
function markFunction( fn ) {
fn[ expando ] = true;
return fn;
}
/**
* Support testing using an element
* @param {Function} fn Passed the created element and returns a boolean result
*/
function assert( fn ) {
var el = document.createElement("fieldset");
try {
return !!fn( el );
} catch (e) {
return false;
} finally {
// Remove from its parent by default
if ( el.parentNode ) {
el.parentNode.removeChild( el );
}
// release memory in IE
el = null;
}
}
/**
* Adds the same handler for all of the specified attrs
* @param {String} attrs Pipe-separated list of attributes
* @param {Function} handler The method that will be applied
*/
function addHandle( attrs, handler ) {
var arr = attrs.split("|"),
i = arr.length;
while ( i-- ) {
Expr.attrHandle[ arr[i] ] = handler;
}
}
/**
* Checks document order of two siblings
* @param {Element} a
* @param {Element} b
* @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
*/
function siblingCheck( a, b ) {
var cur = b && a,
diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
a.sourceIndex - b.sourceIndex;
// Use IE sourceIndex if available on both nodes
if ( diff ) {
return diff;
}
// Check if b follows a
if ( cur ) {
while ( (cur = cur.nextSibling) ) {
if ( cur === b ) {
return -1;
}
}
}
return a ? 1 : -1;
}
/**
* Returns a function to use in pseudos for input types
* @param {String} type
*/
function createInputPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return name === "input" && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for buttons
* @param {String} type
*/
function createButtonPseudo( type ) {
return function( elem ) {
var name = elem.nodeName.toLowerCase();
return (name === "input" || name === "button") && elem.type === type;
};
}
/**
* Returns a function to use in pseudos for :enabled/:disabled
* @param {Boolean} disabled true for :disabled; false for :enabled
*/
function createDisabledPseudo( disabled ) {
// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
return function( elem ) {
// Only certain elements can match :enabled or :disabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
if ( "form" in elem ) {
// Check for inherited disabledness on relevant non-disabled elements:
// * listed form-associated elements in a disabled fieldset
// https://html.spec.whatwg.org/multipage/forms.html#category-listed
// https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
// * option elements in a disabled optgroup
// https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
// All such elements have a "form" property.
if ( elem.parentNode && elem.disabled === false ) {
// Option elements defer to a parent optgroup if present
if ( "label" in elem ) {
if ( "label" in elem.parentNode ) {
return elem.parentNode.disabled === disabled;
} else {
return elem.disabled === disabled;
}
}
// Support: IE 6 - 11
// Use the isDisabled shortcut property to check for disabled fieldset ancestors
return elem.isDisabled === disabled ||
// Where there is no isDisabled, check manually
/* jshint -W018 */
elem.isDisabled !== !disabled &&
inDisabledFieldset( elem ) === disabled;
}
return elem.disabled === disabled;
// Try to winnow out elements that can't be disabled before trusting the disabled property.
// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
// even exist on them, let alone have a boolean value.
} else if ( "label" in elem ) {
return elem.disabled === disabled;
}
// Remaining elements are neither :enabled nor :disabled
return false;
};
}
/**
* Returns a function to use in pseudos for positionals
* @param {Function} fn
*/
function createPositionalPseudo( fn ) {
return markFunction(function( argument ) {
argument = +argument;
return markFunction(function( seed, matches ) {
var j,
matchIndexes = fn( [], seed.length, argument ),
i = matchIndexes.length;
// Match elements found at the specified indexes
while ( i-- ) {
if ( seed[ (j = matchIndexes[i]) ] ) {
seed[j] = !(matches[j] = seed[j]);
}
}
});
});
}
/**
* Checks a node for validity as a Sizzle context
* @param {Element|Object=} context
* @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
*/
function testContext( context ) {
return context && typeof context.getElementsByTagName !== "undefined" && context;
}
// Expose support vars for convenience
support = Sizzle.support = {};
/**
* Detects XML nodes
* @param {Element|Object} elem An element or a document
* @returns {Boolean} True iff elem is a non-HTML XML node
*/
isXML = Sizzle.isXML = function( elem ) {
- // documentElement is verified for cases where it doesn't yet exist
- // (such as loading iframes in IE - #4833)
- var documentElement = elem && (elem.ownerDocument || elem).documentElement;
- return documentElement ? documentElement.nodeName !== "HTML" : false;
+ var namespace = elem.namespaceURI,
+ docElem = (elem.ownerDocument || elem).documentElement;
+
+ // Support: IE <=8
+ // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+ // https://bugs.jquery.com/ticket/4833
+ return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
};
/**
* Sets document-related variables once based on the current document
* @param {Element|Object} [doc] An element or document object to use to set the document
* @returns {Object} Returns the current document
*/
setDocument = Sizzle.setDocument = function( node ) {
var hasCompare, subWindow,
doc = node ? node.ownerDocument || node : preferredDoc;
// Return early if doc is invalid or already selected
if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
return document;
}
// Update global variables
document = doc;
docElem = document.documentElement;
documentIsHTML = !isXML( document );
// Support: IE 9-11, Edge
// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
if ( preferredDoc !== document &&
(subWindow = document.defaultView) && subWindow.top !== subWindow ) {
// Support: IE 11, Edge
if ( subWindow.addEventListener ) {
subWindow.addEventListener( "unload", unloadHandler, false );
// Support: IE 9 - 10 only
} else if ( subWindow.attachEvent ) {
subWindow.attachEvent( "onunload", unloadHandler );
}
}
/* Attributes
---------------------------------------------------------------------- */
// Support: IE<8
// Verify that getAttribute really returns attributes and not properties
// (excepting IE8 booleans)
support.attributes = assert(function( el ) {
el.className = "i";
return !el.getAttribute("className");
});
/* getElement(s)By*
---------------------------------------------------------------------- */
// Check if getElementsByTagName("*") returns only elements
support.getElementsByTagName = assert(function( el ) {
el.appendChild( document.createComment("") );
return !el.getElementsByTagName("*").length;
});
// Support: IE<9
support.getElementsByClassName = rnative.test( document.getElementsByClassName );
// Support: IE<10
// Check if getElementById returns elements by name
// The broken getElementById methods don't pick up programmatically-set names,
// so use a roundabout getElementsByName test
support.getById = assert(function( el ) {
docElem.appendChild( el ).id = expando;
return !document.getElementsByName || !document.getElementsByName( expando ).length;
});
// ID filter and find
if ( support.getById ) {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
return elem.getAttribute("id") === attrId;
};
};
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var elem = context.getElementById( id );
return elem ? [ elem ] : [];
}
};
} else {
Expr.filter["ID"] = function( id ) {
var attrId = id.replace( runescape, funescape );
return function( elem ) {
var node = typeof elem.getAttributeNode !== "undefined" &&
elem.getAttributeNode("id");
return node && node.value === attrId;
};
};
// Support: IE 6 - 7 only
// getElementById is not reliable as a find shortcut
Expr.find["ID"] = function( id, context ) {
if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
var node, i, elems,
elem = context.getElementById( id );
if ( elem ) {
// Verify the id attribute
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
// Fall back on getElementsByName
elems = context.getElementsByName( id );
i = 0;
while ( (elem = elems[i++]) ) {
node = elem.getAttributeNode("id");
if ( node && node.value === id ) {
return [ elem ];
}
}
}
return [];
}
};
}
// Tag
Expr.find["TAG"] = support.getElementsByTagName ?
function( tag, context ) {
if ( typeof context.getElementsByTagName !== "undefined" ) {
return context.getElementsByTagName( tag );
// DocumentFragment nodes don't have gEBTN
} else if ( support.qsa ) {
return context.querySelectorAll( tag );
}
} :
function( tag, context ) {
var elem,
tmp = [],
i = 0,
// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
results = context.getElementsByTagName( tag );
// Filter out possible comments
if ( tag === "*" ) {
while ( (elem = results[i++]) ) {
if ( elem.nodeType === 1 ) {
tmp.push( elem );
}
}
return tmp;
}
return results;
};
// Class
Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) {
if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
return context.getElementsByClassName( className );
}
};
/* QSA/matchesSelector
---------------------------------------------------------------------- */
// QSA and matchesSelector support
// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
rbuggyMatches = [];
// qSa(:focus) reports false when true (Chrome 21)
// We allow this because of a bug in IE8/9 that throws an error
// whenever `document.activeElement` is accessed on an iframe
// So, we allow :focus to pass through QSA all the time to avoid the IE error
// See https://bugs.jquery.com/ticket/13378
rbuggyQSA = [];
if ( (support.qsa = rnative.test( document.querySelectorAll )) ) {
// Build QSA regex
// Regex strategy adopted from Diego Perini
assert(function( el ) {
// Select is set to empty string on purpose
// This is to test IE's treatment of not explicitly
// setting a boolean content attribute,
// since its presence should be enough
// https://bugs.jquery.com/ticket/12359
docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
"<select id='" + expando + "-\r\\' msallowcapture=''>" +
"<option selected=''></option></select>";
// Support: IE8, Opera 11-12.16
// Nothing should be selected when empty strings follow ^= or $= or *=
// The test attribute must be unknown in Opera but "safe" for WinRT
// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
if ( el.querySelectorAll("[msallowcapture^='']").length ) {
rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
}
// Support: IE8
// Boolean attributes and "value" are not treated correctly
if ( !el.querySelectorAll("[selected]").length ) {
rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
}
// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
rbuggyQSA.push("~=");
}
// Webkit/Opera - :checked should return selected option elements
// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
// IE8 throws error here and will not see later tests
if ( !el.querySelectorAll(":checked").length ) {
rbuggyQSA.push(":checked");
}
// Support: Safari 8+, iOS 8+
// https://bugs.webkit.org/show_bug.cgi?id=136851
// In-page `selector#id sibling-combinator selector` fails
if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
rbuggyQSA.push(".#.+[+~]");
}
});
assert(function( el ) {
el.innerHTML = "<a href='' disabled='disabled'></a>" +
"<select disabled='disabled'><option/></select>";
// Support: Windows 8 Native Apps
// The type and name attributes are restricted during .innerHTML assignment
var input = document.createElement("input");
input.setAttribute( "type", "hidden" );
el.appendChild( input ).setAttribute( "name", "D" );
// Support: IE8
// Enforce case-sensitivity of name attribute
if ( el.querySelectorAll("[name=d]").length ) {
rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
}
// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
// IE8 throws error here and will not see later tests
if ( el.querySelectorAll(":enabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Support: IE9-11+
// IE's :disabled selector does not pick up the children of disabled fieldsets
docElem.appendChild( el ).disabled = true;
if ( el.querySelectorAll(":disabled").length !== 2 ) {
rbuggyQSA.push( ":enabled", ":disabled" );
}
// Opera 10-11 does not throw on post-comma invalid pseudos
el.querySelectorAll("*,:x");
rbuggyQSA.push(",.*:");
});
}
if ( (support.matchesSelector = rnative.test( (matches = docElem.matches ||
docElem.webkitMatchesSelector ||
docElem.mozMatchesSelector ||
docElem.oMatchesSelector ||
docElem.msMatchesSelector) )) ) {
assert(function( el ) {
// Check to see if it's possible to do matchesSelector
// on a disconnected node (IE 9)
support.disconnectedMatch = matches.call( el, "*" );
// This should fail with an exception
// Gecko does not error, returns false instead
matches.call( el, "[s!='']:x" );
rbuggyMatches.push( "!=", pseudos );
});
}
rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") );
rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") );
/* Contains
---------------------------------------------------------------------- */
hasCompare = rnative.test( docElem.compareDocumentPosition );
// Element contains another
// Purposefully self-exclusive
// As in, an element does not contain itself
contains = hasCompare || rnative.test( docElem.contains ) ?
function( a, b ) {
var adown = a.nodeType === 9 ? a.documentElement : a,
bup = b && b.parentNode;
return a === bup || !!( bup && bup.nodeType === 1 && (
adown.contains ?
adown.contains( bup ) :
a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
));
} :
function( a, b ) {
if ( b ) {
while ( (b = b.parentNode) ) {
if ( b === a ) {
return true;
}
}
}
return false;
};
/* Sorting
---------------------------------------------------------------------- */
// Document order sorting
sortOrder = hasCompare ?
function( a, b ) {
// Flag for duplicate removal
if ( a === b ) {
hasDuplicate = true;
return 0;
}
// Sort on method existence if only one input has compareDocumentPosition
var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
if ( compare ) {
return compare;
}
// Calculate position if both inputs belong to the same document
compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
a.compareDocumentPosition( b ) :
// Otherwise we know they are disconnected
1;
// Disconnected nodes
if ( compare & 1 ||
(!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) {
// Choose the first element that is related to our preferred document
if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) {
return -1;
}
if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) {
return 1;
}
// Maintain original order
return sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
}
return compare & 4 ? -1 : 1;
} :
function( a, b ) {
// Exit early if the nodes are identical
if ( a === b ) {
hasDuplicate = true;
return 0;
}
var cur,
i = 0,
aup = a.parentNode,
bup = b.parentNode,
ap = [ a ],
bp = [ b ];
// Parentless nodes are either documents or disconnected
if ( !aup || !bup ) {
return a === document ? -1 :
b === document ? 1 :
aup ? -1 :
bup ? 1 :
sortInput ?
( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
0;
// If the nodes are siblings, we can do a quick check
} else if ( aup === bup ) {
return siblingCheck( a, b );
}
// Otherwise we need full lists of their ancestors for comparison
cur = a;
while ( (cur = cur.parentNode) ) {
ap.unshift( cur );
}
cur = b;
while ( (cur = cur.parentNode) ) {
bp.unshift( cur );
}
// Walk down the tree looking for a discrepancy
while ( ap[i] === bp[i] ) {
i++;
}
return i ?
// Do a sibling check if the nodes have a common ancestor
siblingCheck( ap[i], bp[i] ) :
// Otherwise nodes in our document sort first
ap[i] === preferredDoc ? -1 :
bp[i] === preferredDoc ? 1 :
0;
};
return document;
};
Sizzle.matches = function( expr, elements ) {
return Sizzle( expr, null, null, elements );
};
Sizzle.matchesSelector = function( elem, expr ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
if ( support.matchesSelector && documentIsHTML &&
!nonnativeSelectorCache[ expr + " " ] &&
( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
try {
var ret = matches.call( elem, expr );
// IE 9's matchesSelector returns false on disconnected nodes
if ( ret || support.disconnectedMatch ||
// As well, disconnected nodes are said to be in a document
// fragment in IE 9
elem.document && elem.document.nodeType !== 11 ) {
return ret;
}
} catch (e) {
nonnativeSelectorCache( expr, true );
}
}
return Sizzle( expr, document, null, [ elem ] ).length > 0;
};
Sizzle.contains = function( context, elem ) {
// Set document vars if needed
if ( ( context.ownerDocument || context ) !== document ) {
setDocument( context );
}
return contains( context, elem );
};
Sizzle.attr = function( elem, name ) {
// Set document vars if needed
if ( ( elem.ownerDocument || elem ) !== document ) {
setDocument( elem );
}
var fn = Expr.attrHandle[ name.toLowerCase() ],
// Don't get fooled by Object.prototype properties (jQuery #13807)
val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
fn( elem, name, !documentIsHTML ) :
undefined;
return val !== undefined ?
val :
support.attributes || !documentIsHTML ?
elem.getAttribute( name ) :
(val = elem.getAttributeNode(name)) && val.specified ?
val.value :
null;
};
Sizzle.escape = function( sel ) {
return (sel + "").replace( rcssescape, fcssescape );
};
Sizzle.error = function( msg ) {
throw new Error( "Syntax error, unrecognized expression: " + msg );
};
/**
* Document sorting and removing duplicates
* @param {ArrayLike} results
*/
Sizzle.uniqueSort = function( results ) {
var elem,
duplicates = [],
j = 0,
i = 0;
// Unless we *know* we can detect duplicates, assume their presence
hasDuplicate = !support.detectDuplicates;
sortInput = !support.sortStable && results.slice( 0 );
results.sort( sortOrder );
if ( hasDuplicate ) {
while ( (elem = results[i++]) ) {
if ( elem === results[ i ] ) {
j = duplicates.push( i );
}
}
while ( j-- ) {
results.splice( duplicates[ j ], 1 );
}
}
// Clear input after sorting to release objects
// See https://github.com/jquery/sizzle/pull/225
sortInput = null;
return results;
diff --git a/test/unit/utilities.js b/test/unit/utilities.js
index 036e9da..45bec64 100644
--- a/test/unit/utilities.js
+++ b/test/unit/utilities.js
@@ -1,296 +1,357 @@
QUnit.module( "utilities", { beforeEach: setup } );
function testAttr( doc, assert ) {
assert.expect( 9 );
var el;
if ( doc ) {
// XML
el = doc.createElement( "input" );
el.setAttribute( "type", "checkbox" );
} else {
// Set checked on creation by creating with a fragment
// See https://jsfiddle.net/8sVgA/1/show/light in oldIE
el = jQuery( "<input type='checkbox' checked='checked' />" )[0];
}
// Set it again for good measure
el.setAttribute( "checked", "checked" );
el.setAttribute( "id", "id" );
el.setAttribute( "value", "on" );
assert.strictEqual( Sizzle.attr( el, "nonexistent" ), null, "nonexistent" );
assert.strictEqual( Sizzle.attr( el, "id" ), "id", "existent" );
assert.strictEqual( Sizzle.attr( el, "value" ), "on", "value" );
assert.strictEqual( Sizzle.attr( el, "checked" ), "checked", "boolean" );
assert.strictEqual( Sizzle.attr( el, "href" ), null, "interpolation risk" );
assert.strictEqual( Sizzle.attr( el, "constructor" ), null,
"Object.prototype property \"constructor\" (negative)" );
assert.strictEqual( Sizzle.attr( el, "watch" ), null,
"Gecko Object.prototype property \"watch\" (negative)" );
el.setAttribute( "constructor", "foo" );
el.setAttribute( "watch", "bar" );
assert.strictEqual( Sizzle.attr( el, "constructor" ), "foo",
"Object.prototype property \"constructor\"" );
assert.strictEqual( Sizzle.attr( el, "watch" ), "bar",
"Gecko Object.prototype property \"watch\"" );
}
QUnit.test("Sizzle.attr (HTML)", function( assert ) {
testAttr( null, assert );
});
QUnit.test("Sizzle.attr (XML)", function( assert ) {
testAttr( jQuery.parseXML( "<root/>" ), assert );
});
QUnit.test("Sizzle.escape", function( assert ) {
// Edge cases
assert.equal( Sizzle.escape(), "undefined", "Converts undefined to string" );
assert.equal( Sizzle.escape("-"), "\\-", "Escapes standalone dash" );
assert.equal( Sizzle.escape("-a"), "-a", "Doesn't escape leading dash followed by non-number" );
assert.equal( Sizzle.escape("--"), "--", "Doesn't escape standalone double dash" );
assert.equal( Sizzle.escape( "\uFFFD" ), "\uFFFD",
"Doesn't escape standalone replacement character" );
assert.equal( Sizzle.escape( "a\uFFFD" ), "a\uFFFD",
"Doesn't escape trailing replacement character" );
assert.equal( Sizzle.escape( "\uFFFDb" ), "\uFFFDb",
"Doesn't escape leading replacement character" );
assert.equal( Sizzle.escape( "a\uFFFDb" ), "a\uFFFDb",
"Doesn't escape embedded replacement character" );
// Derived from CSSOM tests
// https://test.csswg.org/harness/test/cssom-1_dev/section/7.1/
// String conversion
assert.equal( Sizzle.escape( true ), "true", "Converts boolean true to string" );
assert.equal( Sizzle.escape( false ), "false", "Converts boolean true to string" );
assert.equal( Sizzle.escape( null ), "null", "Converts null to string" );
assert.equal( Sizzle.escape( "" ), "", "Doesn't modify empty string" );
// Null bytes
assert.equal( Sizzle.escape( "\0" ), "\uFFFD",
"Escapes null-character input as replacement character" );
assert.equal( Sizzle.escape( "a\0" ), "a\uFFFD",
"Escapes trailing-null input as replacement character" );
assert.equal( Sizzle.escape( "\0b" ), "\uFFFDb",
"Escapes leading-null input as replacement character" );
assert.equal( Sizzle.escape( "a\0b" ), "a\uFFFDb",
"Escapes embedded-null input as replacement character" );
// Number prefix
assert.equal( Sizzle.escape( "0a" ), "\\30 a", "Escapes leading 0" );
assert.equal( Sizzle.escape( "1a" ), "\\31 a", "Escapes leading 1" );
assert.equal( Sizzle.escape( "2a" ), "\\32 a", "Escapes leading 2" );
assert.equal( Sizzle.escape( "3a" ), "\\33 a", "Escapes leading 3" );
assert.equal( Sizzle.escape( "4a" ), "\\34 a", "Escapes leading 4" );
assert.equal( Sizzle.escape( "5a" ), "\\35 a", "Escapes leading 5" );
assert.equal( Sizzle.escape( "6a" ), "\\36 a", "Escapes leading 6" );
assert.equal( Sizzle.escape( "7a" ), "\\37 a", "Escapes leading 7" );
assert.equal( Sizzle.escape( "8a" ), "\\38 a", "Escapes leading 8" );
assert.equal( Sizzle.escape( "9a" ), "\\39 a", "Escapes leading 9" );
// Letter-number prefix
assert.equal( Sizzle.escape( "a0b" ), "a0b", "Doesn't escape embedded 0" );
assert.equal( Sizzle.escape( "a1b" ), "a1b", "Doesn't escape embedded 1" );
assert.equal( Sizzle.escape( "a2b" ), "a2b", "Doesn't escape embedded 2" );
assert.equal( Sizzle.escape( "a3b" ), "a3b", "Doesn't escape embedded 3" );
assert.equal( Sizzle.escape( "a4b" ), "a4b", "Doesn't escape embedded 4" );
assert.equal( Sizzle.escape( "a5b" ), "a5b", "Doesn't escape embedded 5" );
assert.equal( Sizzle.escape( "a6b" ), "a6b", "Doesn't escape embedded 6" );
assert.equal( Sizzle.escape( "a7b" ), "a7b", "Doesn't escape embedded 7" );
assert.equal( Sizzle.escape( "a8b" ), "a8b", "Doesn't escape embedded 8" );
assert.equal( Sizzle.escape( "a9b" ), "a9b", "Doesn't escape embedded 9" );
// Dash-number prefix
assert.equal( Sizzle.escape( "-0a" ), "-\\30 a", "Escapes 0 after leading dash" );
assert.equal( Sizzle.escape( "-1a" ), "-\\31 a", "Escapes 1 after leading dash" );
assert.equal( Sizzle.escape( "-2a" ), "-\\32 a", "Escapes 2 after leading dash" );
assert.equal( Sizzle.escape( "-3a" ), "-\\33 a", "Escapes 3 after leading dash" );
assert.equal( Sizzle.escape( "-4a" ), "-\\34 a", "Escapes 4 after leading dash" );
assert.equal( Sizzle.escape( "-5a" ), "-\\35 a", "Escapes 5 after leading dash" );
assert.equal( Sizzle.escape( "-6a" ), "-\\36 a", "Escapes 6 after leading dash" );
assert.equal( Sizzle.escape( "-7a" ), "-\\37 a", "Escapes 7 after leading dash" );
assert.equal( Sizzle.escape( "-8a" ), "-\\38 a", "Escapes 8 after leading dash" );
assert.equal( Sizzle.escape( "-9a" ), "-\\39 a", "Escapes 9 after leading dash" );
// Double dash prefix
assert.equal( Sizzle.escape( "--a" ), "--a", "Doesn't escape leading double dash" );
// Miscellany
assert.equal( Sizzle.escape( "\x01\x02\x1E\x1F" ), "\\1 \\2 \\1e \\1f ",
"Escapes C0 control characters" );
assert.equal( Sizzle.escape( "\x80\x2D\x5F\xA9" ), "\x80\x2D\x5F\xA9",
"Doesn't escape general punctuation or non-ASCII ISO-8859-1 characters" );
assert.equal(
Sizzle.escape( "\x7F\x80\x81\x82\x83\x84\x85\x86\x87\x88\x89\x8A\x8B\x8C\x8D\x8E\x8F\x90" +
"\x91\x92\x93\x94\x95\x96\x97\x98\x99\x9A\x9B\x9C\x9D\x9E\x9F" ),
"\\7f \x80\x81\x82\x83\x84\x85\x86\x87\x88\x89\x8A\x8B\x8C\x8D\x8E\x8F\x90" +
"\x91\x92\x93\x94\x95\x96\x97\x98\x99\x9A\x9B\x9C\x9D\x9E\x9F",
"Escapes DEL control character"
);
assert.equal( Sizzle.escape( "\xA0\xA1\xA2" ), "\xA0\xA1\xA2",
"Doesn't escape non-ASCII ISO-8859-1 characters" );
assert.equal( Sizzle.escape( "a0123456789b" ), "a0123456789b",
"Doesn't escape embedded numbers" );
assert.equal( Sizzle.escape( "abcdefghijklmnopqrstuvwxyz" ), "abcdefghijklmnopqrstuvwxyz",
"Doesn't escape lowercase ASCII letters" );
assert.equal( Sizzle.escape( "ABCDEFGHIJKLMNOPQRSTUVWXYZ" ), "ABCDEFGHIJKLMNOPQRSTUVWXYZ",
"Doesn't escape uppercase ASCII letters" );
assert.equal( Sizzle.escape( "\x20\x21\x78\x79" ), "\\ \\!xy",
"Escapes non-word ASCII characters" );
// Astral symbol (U+1D306 TETRAGRAM FOR CENTRE)
assert.equal( Sizzle.escape( "\uD834\uDF06" ), "\uD834\uDF06",
"Doesn't escape astral characters" );
// Lone surrogates
assert.equal( Sizzle.escape( "\uDF06" ), "\uDF06", "Doesn't escape lone low surrogate" );
assert.equal( Sizzle.escape( "\uD834" ), "\uD834", "Doesn't escape lone high surrogate" );
});
QUnit.test("Sizzle.contains", function( assert ) {
assert.expect( 16 );
var container = document.getElementById("nonnodes"),
element = container.firstChild,
text = element.nextSibling,
nonContained = container.nextSibling,
detached = document.createElement("a");
assert.ok( element && element.nodeType === 1, "preliminary: found element" );
assert.ok( text && text.nodeType === 3, "preliminary: found text" );
assert.ok( nonContained, "preliminary: found non-descendant" );
assert.ok( Sizzle.contains(container, element), "child" );
assert.ok( Sizzle.contains(container.parentNode, element), "grandchild" );
assert.ok( Sizzle.contains(container, text), "text child" );
assert.ok( Sizzle.contains(container.parentNode, text), "text grandchild" );
assert.ok( !Sizzle.contains(container, container), "self" );
assert.ok( !Sizzle.contains(element, container), "parent" );
assert.ok( !Sizzle.contains(container, nonContained), "non-descendant" );
assert.ok( !Sizzle.contains(container, document), "document" );
assert.ok( !Sizzle.contains(container, document.documentElement), "documentElement (negative)" );
assert.ok( !Sizzle.contains(container, null), "Passing null does not throw an error" );
assert.ok( Sizzle.contains(document, document.documentElement), "documentElement (positive)" );
assert.ok( Sizzle.contains(document, element), "document container (positive)" );
assert.ok( !Sizzle.contains(document, detached), "document container (negative)" );
});
if ( jQuery( "<svg xmlns='http://www.w3.org/2000/svg' version='1.1' height='1' width='1'><g/></svg>"
)[ 0 ].firstChild ) {
QUnit.test("Sizzle.contains in SVG (jQuery #10832)", function( assert ) {
assert.expect( 4 );
var svg = jQuery(
"<svg xmlns='http://www.w3.org/2000/svg' version='1.1' height='1' width='1'>" +
"<g><circle cx='1' cy='1' r='1' /></g>" +
"</svg>"
).appendTo("#qunit-fixture")[0];
assert.ok( Sizzle.contains( svg, svg.firstChild ), "root child" );
assert.ok( Sizzle.contains( svg.firstChild, svg.firstChild.firstChild ), "element child" );
assert.ok( Sizzle.contains( svg, svg.firstChild.firstChild ), "root granchild" );
assert.ok( !Sizzle.contains( svg.firstChild.firstChild, svg.firstChild ),
"parent (negative)" );
});
}
+QUnit.test("Sizzle.isXML", function( assert ) {
+ assert.expect( 10 );
+
+ var svgTree,
+ xmlTree = jQuery.parseXML( "<docElem><elem/></docElem>" ).documentElement,
+ htmlTree = jQuery( "<div>" +
+ "<svg xmlns='http://www.w3.org/2000/svg' version='1.1' height='1' width='1'>" +
+ "<desc></desc>" +
+ "</svg>" +
+ "</div>"
+ )[ 0 ],
+ supportsSVG = /svg/i.test( htmlTree.firstChild.namespaceURI );
+
+ // Support: IE<=8
+ // Omit the SVG DOCTYPE if it is not understood
+ try {
+ svgTree = jQuery.parseXML(
+ "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" " +
+ "\"http://www.w3.org/Gaphics/SVG/1.1/DTD/svg11.dtd\">" +
+ "<svg version='1.1' xmlns='http://www.w3.org/2000/svg'><desc/></svg>"
+ ).documentElement;
+ } catch ( ex ) {
+ svgTree = jQuery.parseXML(
+ "<svg version='1.1' xmlns='http://www.w3.org/2000/svg'><desc/></svg>"
+ ).documentElement;
+ }
+
+ assert.strictEqual( Sizzle.isXML( xmlTree ), true, "XML element" );
+ assert.strictEqual( Sizzle.isXML( xmlTree.firstChild ), true, "XML child element" );
+
+ assert.strictEqual( Sizzle.isXML( svgTree ), true, "SVG root element" );
+ assert.strictEqual( Sizzle.isXML( svgTree.firstChild ), true, "SVG child element" );
+
+ assert.strictEqual( Sizzle.isXML( htmlTree ), false, "disconnected div element" );
+ assert.strictEqual( Sizzle.isXML( htmlTree.firstChild ), supportsSVG,
+ "disconnected HTML-embedded SVG root element" );
+
+ // Support: IE 7 only
+ // The DOM under foreign elements can be incomplete
+ if ( htmlTree.firstChild.firstChild ) {
+ assert.strictEqual( Sizzle.isXML( htmlTree.firstChild.firstChild ), supportsSVG,
+ "disconnected HTML-embedded SVG child element" );
+ } else {
+ assert.ok( true, "Cannot test an incomplete DOM" );
+ }
+
+ document.getElementById( "qunit-fixture" ).appendChild( htmlTree );
+ assert.strictEqual( Sizzle.isXML( htmlTree ), false, "connected div element" );
+ assert.strictEqual( Sizzle.isXML( htmlTree.firstChild ), supportsSVG,
+ "connected HTML-embedded SVG root element" );
+
+ // Support: IE 7 only
+ // The DOM under foreign elements can be incomplete
+ if ( htmlTree.firstChild.firstChild ) {
+ assert.strictEqual( Sizzle.isXML( htmlTree.firstChild.firstChild ), supportsSVG,
+ "disconnected HTML-embedded SVG child element" );
+ } else {
+ assert.ok( true, "Cannot test an incomplete DOM" );
+ }
+});
+
QUnit.test("Sizzle.uniqueSort", function( assert ) {
assert.expect( 14 );
function Arrayish( arr ) {
var i = this.length = arr.length;
while ( i-- ) {
this[ i ] = arr[ i ];
}
}
Arrayish.prototype = {
slice: [].slice,
sort: [].sort,
splice: [].splice
};
var i, tests,
detached = [],
body = document.body,
fixture = document.getElementById("qunit-fixture"),
detached1 = document.createElement("p"),
detached2 = document.createElement("ul"),
detachedChild = detached1.appendChild( document.createElement("a") ),
detachedGrandchild = detachedChild.appendChild( document.createElement("b") );
for ( i = 0; i < 12; i++ ) {
detached.push( document.createElement("li") );
detached[i].id = "detached" + i;
detached2.appendChild( document.createElement("li") ).id = "detachedChild" + i;
}
tests = {
"Empty": {
input: [],
expected: []
},
"Single-element": {
input: [ fixture ],
expected: [ fixture ]
},
"No duplicates": {
input: [ fixture, body ],
expected: [ body, fixture ]
},
"Duplicates": {
input: [ body, fixture, fixture, body ],
expected: [ body, fixture ]
},
"Detached": {
input: detached.slice( 0 ),
expected: detached.slice( 0 )
},
"Detached children": {
input: [
detached2.childNodes[3],
detached2.childNodes[0],
detached2.childNodes[2],
detached2.childNodes[1]
],
expected: [
detached2.childNodes[0],
detached2.childNodes[1],
detached2.childNodes[2],
detached2.childNodes[3]
]
},
"Attached/detached mixture": {
input: [ detached1, fixture, detached2, document, detachedChild, body, detachedGrandchild ],
expected: [ document, body, fixture ],
length: 3
}
};
jQuery.each( tests, function( label, test ) {
var length = test.length || test.input.length;
assert.deepEqual(
Sizzle.uniqueSort( test.input ).slice( 0, length ),
test.expected,
label + " (array)"
);
assert.deepEqual(
Sizzle.uniqueSort( new Arrayish( test.input ) ).slice( 0, length ),
test.expected,
label + " (quasi-array)"
);
});
});
testIframeWithCallback( "Sizzle.uniqueSort works cross-window (jQuery #14381)", "mixed_sort.html",
function( actual, expected, message ) {
var assert = this;
assert.deepEqual( actual, expected, message );
}
);
testIframeWithCallback( "Sizzle.noConflict", "noConflict.html", function( reporter ) {
var assert = this;
reporter( assert );
} );
|
jquery/sizzle
|
54bc2dd385a54851c897bc371fed05921b5ab65f
|
Build: Update tested browsers, fix iOS configuration
|
diff --git a/Gruntfile.js b/Gruntfile.js
index 0db803e..645508d 100644
--- a/Gruntfile.js
+++ b/Gruntfile.js
@@ -1,288 +1,288 @@
module.exports = function( grunt ) {
"use strict";
var gzip = require( "gzip-js" ),
isBrowserStack = process.env.BROWSER_STACK_USERNAME && process.env.BROWSER_STACK_ACCESS_KEY,
browsers = {
phantom: [ "PhantomJS" ],
desktop: [],
android: [],
ios: [],
old: {
firefox: [],
chrome: [],
safari: [],
ie: [],
opera: [],
android: []
}
},
files = {
source: "src/sizzle.js",
speed: "speed/speed.js",
tests: "test/unit/*.js",
karma: "test/karma/*.js",
grunt: [ "Gruntfile.js", "tasks/*" ]
};
// if Browserstack is set up, assume we can use it
if ( isBrowserStack ) {
// See https://github.com/jquery/sizzle/wiki/Sizzle-Documentation#browsers
browsers.desktop = [
"bs_chrome-45", // shares V8 with Node.js 4 LTS
- "bs_chrome-69", "bs_chrome-70",
+ "bs_chrome-70", "bs_chrome-71",
"bs_firefox-52", "bs_firefox-60", // Firefox ESR
- "bs_firefox-61", "bs_firefox-62",
+ "bs_firefox-63", "bs_firefox-64",
- "bs_edge-16", "bs_edge-17",
+ "bs_edge-17", "bs_edge-18",
"bs_ie-9", "bs_ie-10", "bs_ie-11",
- "bs_opera-55", "bs_opera-56",
+ "bs_opera-56", "bs_opera-57",
// Real Safari 6.1 and 7.0 are not available
"bs_safari-6.0", "bs_safari-8.0", "bs_safari-9.1", "bs_safari-10.1",
"bs_safari-11.1", "bs_safari-12.0",
];
browsers.ios = [
"bs_ios-5.1", "bs_ios-6.0", "bs_ios-7.0", "bs_ios-8.3", "bs_ios-9.3", "bs_ios-10.3",
- "bs_ios-11.4", "bs_ios-12.0",
+ "bs_ios-11.4", "bs_ios-12.1",
];
browsers.android = [
"bs_android-4.0", "bs_android-4.1", "bs_android-4.2",
"bs_android-4.3", "bs_android-4.4"
];
browsers.old = {
firefox: [ "bs_firefox-3.6" ],
chrome: [ "bs_chrome-16" ],
safari: [ "bs_safari-4.0", "bs_safari-5.0", "bs_safari-5.1" ],
ie: [ "bs_ie-7", "bs_ie-8" ],
opera: [ "bs_opera-11.6", "bs_opera-12.16" ],
android: [ "bs_android-2.3" ]
};
}
// Project configuration
grunt.initConfig({
pkg: grunt.file.readJSON( "package.json" ),
dateString: new Date().toISOString().replace( /\..*Z/, "" ),
compile: {
all: {
dest: "dist/sizzle.js",
src: "src/sizzle.js"
}
},
version: {
files: [ "package.json", "bower.json" ]
},
uglify: {
all: {
files: {
"dist/sizzle.min.js": [ "dist/sizzle.js" ]
},
options: {
compress: {
"hoist_funs": false,
loops: false
},
output: {
ascii_only: true
},
banner: "/*! Sizzle v<%= pkg.version %> | (c) " +
"JS Foundation and other contributors | js.foundation */",
sourceMap: true,
sourceMapName: "dist/sizzle.min.map"
}
}
},
"ensure_ascii": {
files: [ "dist/*.js" ]
},
"compare_size": {
files: [ "dist/sizzle.js", "dist/sizzle.min.js" ],
options: {
compress: {
gz: function( contents ) {
return gzip.zip( contents, {} ).length;
}
},
cache: "dist/.sizecache.json"
}
},
npmcopy: {
all: {
options: {
destPrefix: "external"
},
files: {
"benchmark/benchmark.js": "benchmark/benchmark.js",
"benchmark/LICENSE.txt": "benchmark/LICENSE.txt",
"jquery/jquery.js": "jquery/jquery.js",
"jquery/MIT-LICENSE.txt": "jquery/MIT-LICENSE.txt",
"qunit/qunit.js": "qunitjs/qunit/qunit.js",
"qunit/qunit.css": "qunitjs/qunit/qunit.css",
"qunit/LICENSE.txt": "qunitjs/LICENSE.txt",
"requirejs/require.js": "requirejs/require.js",
"requirejs-domready/domReady.js": "requirejs-domready/domReady.js",
"requirejs-text/text.js": "requirejs-text/text.js",
}
}
},
jshint: {
options: {
jshintrc: true
},
all: {
src: [ files.source, files.grunt, files.karma, files.speed, files.tests ]
}
},
jscs: {
src: {
options: {
requireDotNotation: null
},
src: [ files.source ]
},
grunt: {
options: {
requireCamelCaseOrUpperCaseIdentifiers: null
},
src: [ files.grunt ]
},
speed: [ files.speed ],
tests: {
options: {
maximumLineLength: null
},
src: [ files.tests ]
},
karma: {
options: {
requireCamelCaseOrUpperCaseIdentifiers: null
},
src: [ files.karma ]
}
},
jsonlint: {
pkg: {
src: [ "package.json" ]
},
bower: {
src: [ "bower.json" ]
}
},
karma: {
options: {
configFile: "test/karma/karma.conf.js",
singleRun: true
},
watch: {
background: true,
singleRun: false,
browsers: browsers.phantom
},
phantom: {
browsers: browsers.phantom
},
desktop: {
browsers: browsers.desktop
},
android: {
browsers: browsers.android
},
ios: {
browsers: browsers.ios
},
oldIe: {
browsers: browsers.old.ie,
// Support: IE <=8 only
// Force use of JSONP polling
transports: [ "polling" ],
forceJSONP: true
},
oldOpera: {
browsers: browsers.old.opera
},
oldFirefox: {
browsers: browsers.old.firefox
},
oldChrome: {
browsers: browsers.old.chrome
},
oldSafari: {
browsers: browsers.old.safari
},
oldAndroid: {
browsers: browsers.old.android
},
all: {
browsers: browsers.phantom.concat(
browsers.desktop,
browsers.ios,
browsers.android,
browsers.old.firefox,
browsers.old.chrome,
browsers.old.safari,
browsers.old.ie,
browsers.old.opera,
browsers.old.android
)
}
},
watch: {
options: {
livereload: true
},
files: [
files.source,
files.grunt,
files.karma,
files.speed,
"test/**/*",
"test/*.html",
"{package,bower}.json"
],
tasks: [ "build", "karma:watch:run" ]
}
});
// Integrate Sizzle specific tasks
grunt.loadTasks( "tasks" );
// Load dev dependencies
require( "load-grunt-tasks" )( grunt );
grunt.registerTask( "lint", [ "jsonlint", "jshint", "jscs" ] );
grunt.registerTask( "start", [ "karma:watch:start", "watch" ] );
// Execute tests all browsers in sequential way,
// so slow connections would not affect other runs
grunt.registerTask( "tests", isBrowserStack ? [
"karma:phantom", "karma:desktop",
"karma:ios",
"karma:oldIe", "karma:oldFirefox", "karma:oldChrome",
"karma:oldSafari", "karma:oldOpera"
// See #314 :-(
// "karma:android", "karma:oldAndroid"
] : "karma:phantom" );
grunt.registerTask( "build", [ "lint", "compile", "uglify", "dist", "ensure_ascii" ] );
grunt.registerTask( "default", [ "build", "tests", "compare_size" ] );
grunt.registerTask( "bower", "bowercopy" );
};
diff --git a/test/karma/launchers.js b/test/karma/launchers.js
index 7bb36fc..f921031 100644
--- a/test/karma/launchers.js
+++ b/test/karma/launchers.js
@@ -1,307 +1,307 @@
"use strict";
module.exports = {
"bs_firefox-3.6": {
base: "BrowserStack",
browser: "firefox",
browser_version: "3.6",
os: "OS X",
os_version: "Mavericks"
},
"bs_firefox-52": {
base: "BrowserStack",
browser: "firefox",
browser_version: "52.0",
os: "OS X",
os_version: "Sierra"
},
"bs_firefox-60": {
base: "BrowserStack",
browser: "firefox",
browser_version: "60.0",
os: "OS X",
os_version: "High Sierra"
},
- "bs_firefox-61": {
+ "bs_firefox-63": {
base: "BrowserStack",
browser: "firefox",
- browser_version: "61.0",
+ browser_version: "63.0",
os: "OS X",
os_version: "Mojave"
},
- "bs_firefox-62": {
+ "bs_firefox-64": {
base: "BrowserStack",
browser: "firefox",
- browser_version: "62.0",
+ browser_version: "64.0",
os: "OS X",
os_version: "Mojave"
},
"bs_chrome-16": {
base: "BrowserStack",
browser: "chrome",
browser_version: "16.0",
os: "OS X",
os_version: "Mavericks"
},
"bs_chrome-45": {
base: "BrowserStack",
browser: "chrome",
browser_version: "45.0",
os: "OS X",
os_version: "Sierra"
},
- "bs_chrome-69": {
+ "bs_chrome-70": {
base: "BrowserStack",
browser: "chrome",
- browser_version: "69.0",
+ browser_version: "70.0",
os: "OS X",
os_version: "Mojave"
},
- "bs_chrome-70": {
+ "bs_chrome-71": {
base: "BrowserStack",
browser: "chrome",
- browser_version: "70.0",
+ browser_version: "71.0",
os: "OS X",
os_version: "Mojave"
},
- "bs_edge-16": {
+ "bs_edge-17": {
base: "BrowserStack",
browser: "edge",
- browser_version: "16.0",
+ browser_version: "17.0",
os: "Windows",
os_version: "10"
},
- "bs_edge-17": {
+ "bs_edge-18": {
base: "BrowserStack",
browser: "edge",
- browser_version: "17.0",
+ browser_version: "18.0",
os: "Windows",
os_version: "10"
},
"bs_ie-6": {
base: "BrowserStack",
browser: "ie",
browser_version: "6.0",
os: "Windows",
os_version: "XP"
},
"bs_ie-7": {
base: "BrowserStack",
browser: "ie",
browser_version: "7.0",
os: "Windows",
os_version: "XP"
},
"bs_ie-8": {
base: "BrowserStack",
browser: "ie",
browser_version: "8.0",
os: "Windows",
os_version: "7"
},
"bs_ie-9": {
base: "BrowserStack",
browser: "ie",
browser_version: "9.0",
os: "Windows",
os_version: "7"
},
"bs_ie-10": {
base: "BrowserStack",
browser: "ie",
browser_version: "10.0",
os: "Windows",
os_version: "8"
},
"bs_ie-11": {
base: "BrowserStack",
browser: "ie",
browser_version: "11.0",
os: "Windows",
os_version: "8.1"
},
"bs_opera-11.6": {
base: "BrowserStack",
browser: "opera",
browser_version: "11.6",
os: "Windows",
os_version: "7"
},
"bs_opera-12.16": {
base: "BrowserStack",
browser: "opera",
browser_version: "12.16",
os: "Windows",
os_version: "7"
},
- "bs_opera-55": {
+ "bs_opera-56": {
base: "BrowserStack",
browser: "opera",
- browser_version: "55.0",
+ browser_version: "56.0",
os: "OS X",
os_version: "Mojave"
},
- "bs_opera-56": {
+ "bs_opera-57": {
base: "BrowserStack",
browser: "opera",
- browser_version: "56.0",
+ browser_version: "57.0",
os: "OS X",
os_version: "Mojave"
},
"bs_safari-4.0": {
base: "BrowserStack",
browser: "safari",
browser_version: "4.0",
os: "OS X",
os_version: "Snow Leopard"
},
"bs_safari-5.0": {
base: "BrowserStack",
browser: "safari",
browser_version: "5.0",
os: "OS X",
os_version: "Snow Leopard"
},
"bs_safari-5.1": {
base: "BrowserStack",
browser: "safari",
browser_version: "5.1",
os: "OS X",
os_version: "Lion"
},
"bs_safari-6.0": {
base: "BrowserStack",
browser: "safari",
browser_version: "6.0",
os: "OS X",
os_version: "Lion"
},
"bs_safari-8.0": {
base: "BrowserStack",
browser: "safari",
browser_version: "8.0",
os: "OS X",
os_version: "Yosemite"
},
"bs_safari-9.1": {
base: "BrowserStack",
browser: "safari",
browser_version: "9.1",
os: "OS X",
os_version: "El Capitan"
},
"bs_safari-10.1": {
base: "BrowserStack",
browser: "safari",
browser_version: "10.1",
os: "OS X",
os_version: "Sierra"
},
"bs_safari-11.1": {
base: "BrowserStack",
browser: "safari",
browser_version: "11.1",
os: "OS X",
os_version: "High Sierra"
},
"bs_safari-12.0": {
base: "BrowserStack",
browser: "safari",
browser_version: "12.0",
os: "OS X",
os_version: "Mojave"
},
"bs_ios-5.1": {
base: "BrowserStack",
device: "iPhone 4S",
os: "ios",
os_version: "5.1"
},
"bs_ios-6.0": {
base: "BrowserStack",
device: "iPhone 5",
os: "ios",
os_version: "6.0"
},
"bs_ios-7.0": {
base: "BrowserStack",
device: "iPhone 5S",
os: "ios",
os_version: "7.0"
},
"bs_ios-8.3": {
base: "BrowserStack",
device: "iPhone 6",
os: "ios",
os_version: "8.3"
},
"bs_ios-9.3": {
base: "BrowserStack",
device: "iPhone 6S",
os: "ios",
os_version: "9.3"
},
"bs_ios-10.3": {
base: "BrowserStack",
device: "iPhone 7",
os: "ios",
os_version: "10.3"
},
"bs_ios-11.4": {
base: "BrowserStack",
device: "iPhone 6S",
os: "ios",
os_version: "11.4",
real_mobile: true
},
- "bs_ios-12.0": {
+ "bs_ios-12.1": {
base: "BrowserStack",
device: "iPhone XS",
os: "ios",
- os_version: "12.0",
+ os_version: "12.1",
real_mobile: true
},
"bs_android-2.3": {
base: "BrowserStack",
device: "Motorola Droid Razr",
os: "android",
os_version: "2.3"
},
"bs_android-4.0": {
base: "BrowserStack",
device: "Motorola Razr",
os: "android",
os_version: "4.0"
},
"bs_android-4.1": {
base: "BrowserStack",
device: "Google Nexus 7",
os: "android",
os_version: "4.1"
},
"bs_android-4.2": {
base: "BrowserStack",
device: "LG Nexus 4",
os: "android",
os_version: "4.2"
},
"bs_android-4.3": {
base: "BrowserStack",
device: "Samsung Galaxy S4",
os: "android",
os_version: "4.3"
},
"bs_android-4.4": {
base: "BrowserStack",
device: "Samsung Galaxy S5",
os: "android",
os_version: "4.4"
}
};
|
jquery/sizzle
|
686f08dc3493e2e1ed3d97e4e3f80f158b1c94c8
|
Release: Add jquery-release script
|
diff --git a/build/release.js b/build/release.js
new file mode 100644
index 0000000..9f12baf
--- /dev/null
+++ b/build/release.js
@@ -0,0 +1,28 @@
+/* eslint-env node */
+module.exports = function( Release ) {
+
+ var files = [
+ "dist/sizzle.js",
+ "dist/sizzle.min.js",
+ "dist/sizzle.min.map"
+ ];
+
+ Release.define( {
+ npmPublish: true,
+ issueTracker: "github",
+
+ generateArtifacts: function( done ) {
+ Release.exec( "grunt", "Grunt command failed" );
+ done( files );
+ },
+
+ // TODO Add Sizzle to the CDN, or add public opt-out interfaces to jquery-release
+ _copyCdnArtifacts: function() {
+ console.warn( "Skipping CDN artifact copy." );
+ },
+ _pushToCdn: function() {
+ console.warn( "Skipping CDN push." );
+ }
+ } );
+
+};
|
martindemello/clojure-swing
|
2e24e32767529a7eba441ba7fbd029d49eb84981
|
get-item method added
|
diff --git a/helpers/item-listener.clj b/helpers/item-listener.clj
index 9d904e1..0a498dc 100644
--- a/helpers/item-listener.clj
+++ b/helpers/item-listener.clj
@@ -1,17 +1,21 @@
(ns swing.helpers.item-listener
(:import (java.awt.event ItemListener ItemEvent)))
(defn add-item-listener
[component f & args]
(let [listener (proxy [ItemListener] []
(itemStateChanged [event]
(apply f event args))) ]
(.addItemListener component listener)))
(defn item-selected?
[event]
(= (.getStateChange event) ItemEvent/SELECTED))
(defn item-deselected?
[event]
(= (.getStateChange event) ItemEvent/DESELECTED))
+
+(defn get-item
+ [event]
+ (.getItem event))
|
martindemello/clojure-swing
|
61e41a71869d12d761996e26cefe0c24215d0e02
|
add more example slides
|
diff --git a/examples/borderlayout.clj b/examples/borderlayout.clj
index ccecb8a..3320be1 100644
--- a/examples/borderlayout.clj
+++ b/examples/borderlayout.clj
@@ -1,27 +1,29 @@
; http://download.oracle.com/docs/cd/E17409_01/javase/tutorial/uiswing/layout/border.html
(ns border-layout
(:import (java.awt BorderLayout Dimension ComponentOrientation))
(:import (javax.swing JButton JFrame)))
(defn- add-components-to-pane
[pane]
(let [page-start (JButton. "page start")
center (JButton. "center")
line-start (JButton. "line start")
page-end (JButton. "page end")
line-end (JButton. "line end") ]
(do
(.setComponentOrientation pane ComponentOrientation/RIGHT_TO_LEFT)
(doto pane
(.add page-start BorderLayout/PAGE_START)
(.add center BorderLayout/CENTER)
(.add line-start BorderLayout/LINE_START)
(.add page-end BorderLayout/PAGE_END)
(.add line-end BorderLayout/LINE_END))
(.setPreferredSize center (Dimension. 200 100)))))
(defn border-example []
(let [frame (JFrame. "border example") pane (.getContentPane frame) ]
(add-components-to-pane pane)
(.pack frame)
(.setVisible frame true)))
+
+(border-example)
diff --git a/presentation/content/presentation/_border.clj.txt b/presentation/content/presentation/_border.clj.txt
index aec8022..01d4b34 100644
--- a/presentation/content/presentation/_border.clj.txt
+++ b/presentation/content/presentation/_border.clj.txt
@@ -1,35 +1,32 @@
---
filter: erb
---
-<div style="font-size:50%">
+<div style="font-size:67%">
<% uv :lang => "scheme", :theme => 'twilight' do -%>
; http://download.oracle.com/docs/cd/E17409_01/javase/tutorial/uiswing/layout/border.html
-(ns border-layout
- (:import (java.awt BorderLayout Dimension ComponentOrientation))
- (:import (javax.swing JButton JFrame)))
-
(defn- add-components-to-pane
[pane]
(let [page-start (JButton. "page start")
center (JButton. "center")
line-start (JButton. "line start")
page-end (JButton. "page end")
line-end (JButton. "line end") ]
(do
(.setComponentOrientation pane ComponentOrientation/RIGHT_TO_LEFT)
(doto pane
- (.add page-start BorderLayout/PAGE_START)
+ (.add page-start BorderLayout/PAGE_START) ; static class constant
(.add center BorderLayout/CENTER)
(.add line-start BorderLayout/LINE_START)
(.add page-end BorderLayout/PAGE_END)
(.add line-end BorderLayout/LINE_END))
(.setPreferredSize center (Dimension. 200 100)))))
(defn border-example []
(let [frame (JFrame. "border example") pane (.getContentPane frame) ]
+ ; components get added to the frame's content pane
(add-components-to-pane pane)
(.pack frame)
(.setVisible frame true)))
<% end -%>
</div>
diff --git a/presentation/content/presentation/_listeners.clj.txt b/presentation/content/presentation/_listeners.clj.txt
new file mode 100644
index 0000000..e69de29
diff --git a/presentation/content/presentation/_miglayout.clj.txt b/presentation/content/presentation/_miglayout.clj.txt
new file mode 100644
index 0000000..98cdcb3
--- /dev/null
+++ b/presentation/content/presentation/_miglayout.clj.txt
@@ -0,0 +1,24 @@
+---
+filter: erb
+---
+<div style="font-size:75%">
+<% uv :lang => "scheme", :theme => 'twilight' do -%>
+(defn dynamic-non-editable-table
+ []
+ (let [ panel (miglayout
+ (JPanel.)
+ (JTextField. 20) {:id :search-key}
+ (JButton. "populate table") { :id :p-button } :span
+ (JButton. "clear table") { :id :c-button } :wrap
+ (JScrollPane. (JTable. my-dynamic-table-model)))
+
+ {:keys [p-button c-button search-key] } (components panel) ]
+ (add-action-listener p-button populate-table search-key)
+ (add-action-listener c-button clear-table)
+ (doto (JFrame.)
+ (.add panel)
+ (.setResizable false)
+ (.pack)
+ (.setVisible true))))
+<% end -%>
+</div>
diff --git a/presentation/content/presentation/index.txt b/presentation/content/presentation/index.txt
index 9d570ac..d5e7e15 100644
--- a/presentation/content/presentation/index.txt
+++ b/presentation/content/presentation/index.txt
@@ -1,49 +1,92 @@
---
title: Webby S5
created_at: 2008-05-18 22:10:21.995012 -06:00
author: You
company: Company
copyright: Creative Commons
filter:
- erb
- textile
- slides
layout: presentation
---
h1. Clojure and Swing
Using the Swing toolkit to write GUI desktop applications in Clojure
h1. Why Swing?
* Default java gui toolkit
* No native code needed
* Tons of documentation, examples and third-party widgets
h1. Hello World
It doesn't take much to get a Swing GUI up and running:
<% uv :lang => "scheme", :theme => 'twilight' do -%>
(import 'javax.swing.JOptionPane)
(. JOptionPane (showMessageDialog nil "Hello World"))
<% end -%>
h1. Translating from Java
An example from a Java Swing tutorial:
<%= render :partial => 'helloworld.java', :guard => true %>
h1. Translating from Java
And the same example in Clojure
<%= render :partial => 'helloworld.clj', :guard => true %>
+h1. Listeners
+
+<% uv :lang => "java", :theme => "twilight" do -%>
+public class Beeper ... implements ActionListener {
+ // argument to addActionListener is an object
+ // that implements ActionListener
+ button.addActionListener(this);
+
+ public void actionPerformed(ActionEvent e) {
+ makeBeepSound();
+ }
+}
+<% end %>
+
+and in clojure
+<% uv :lang => "scheme", :theme => "twilight" do -%>
+ (.addActionListener button
+ (proxy [ActionListener] []
+ (actionPerformed [e] (make-beep-sound))
+<% end %>
+
+h1. Listeners - Now with swing-utils
+<% uv :lang => "scheme", :theme => "twilight" do -%>
+ (ns examples.event
+ (:use (clojure.contrib
+ [swing-utils :only (add-action-listener)])))
+
+ ;; Usage: (add-action-listener component f & args)
+ (add-action-listener button make-beep-sound))
+<% end %>
+
h1. Simple BorderLayout example
<%= render :partial => 'border.clj', :guard => true %>
+
+h1. Simple BorderLayout example
+
+!screenshot-border.png!
+
+h1. MigLayout
+
+<%= render :partial => 'miglayout.clj', :guard => true %>
+
+h1. MigLayout
+
+!screenshot-mig.png!
diff --git a/presentation/content/presentation/screenshot-border.png b/presentation/content/presentation/screenshot-border.png
new file mode 100644
index 0000000..862fdc8
Binary files /dev/null and b/presentation/content/presentation/screenshot-border.png differ
diff --git a/presentation/content/presentation/screenshot-mig.png b/presentation/content/presentation/screenshot-mig.png
new file mode 100644
index 0000000..e530a92
Binary files /dev/null and b/presentation/content/presentation/screenshot-mig.png differ
|
martindemello/clojure-swing
|
c9d78728e9b92eb118658f526266b7fba05ac13e
|
add border layout example
|
diff --git a/presentation/content/presentation/_border.clj.txt b/presentation/content/presentation/_border.clj.txt
new file mode 100644
index 0000000..aec8022
--- /dev/null
+++ b/presentation/content/presentation/_border.clj.txt
@@ -0,0 +1,35 @@
+---
+filter: erb
+---
+<div style="font-size:50%">
+<% uv :lang => "scheme", :theme => 'twilight' do -%>
+
+; http://download.oracle.com/docs/cd/E17409_01/javase/tutorial/uiswing/layout/border.html
+(ns border-layout
+ (:import (java.awt BorderLayout Dimension ComponentOrientation))
+ (:import (javax.swing JButton JFrame)))
+
+(defn- add-components-to-pane
+ [pane]
+ (let [page-start (JButton. "page start")
+ center (JButton. "center")
+ line-start (JButton. "line start")
+ page-end (JButton. "page end")
+ line-end (JButton. "line end") ]
+ (do
+ (.setComponentOrientation pane ComponentOrientation/RIGHT_TO_LEFT)
+ (doto pane
+ (.add page-start BorderLayout/PAGE_START)
+ (.add center BorderLayout/CENTER)
+ (.add line-start BorderLayout/LINE_START)
+ (.add page-end BorderLayout/PAGE_END)
+ (.add line-end BorderLayout/LINE_END))
+ (.setPreferredSize center (Dimension. 200 100)))))
+
+(defn border-example []
+ (let [frame (JFrame. "border example") pane (.getContentPane frame) ]
+ (add-components-to-pane pane)
+ (.pack frame)
+ (.setVisible frame true)))
+<% end -%>
+</div>
diff --git a/presentation/content/presentation/index.txt b/presentation/content/presentation/index.txt
index 6e37fcf..9d570ac 100644
--- a/presentation/content/presentation/index.txt
+++ b/presentation/content/presentation/index.txt
@@ -1,46 +1,49 @@
---
title: Webby S5
created_at: 2008-05-18 22:10:21.995012 -06:00
author: You
company: Company
copyright: Creative Commons
filter:
- erb
- textile
- slides
layout: presentation
---
h1. Clojure and Swing
Using the Swing toolkit to write GUI desktop applications in Clojure
h1. Why Swing?
* Default java gui toolkit
* No native code needed
* Tons of documentation, examples and third-party widgets
h1. Hello World
It doesn't take much to get a Swing GUI up and running:
<% uv :lang => "scheme", :theme => 'twilight' do -%>
(import 'javax.swing.JOptionPane)
(. JOptionPane (showMessageDialog nil "Hello World"))
<% end -%>
h1. Translating from Java
An example from a Java Swing tutorial:
<%= render :partial => 'helloworld.java', :guard => true %>
h1. Translating from Java
And the same example in Clojure
<%= render :partial => 'helloworld.clj', :guard => true %>
+h1. Simple BorderLayout example
+
+<%= render :partial => 'border.clj', :guard => true %>
|
martindemello/clojure-swing
|
bf8237171606ac9db377c65a163a3dbd8a709664
|
s/defn-/defn
|
diff --git a/helpers/mouse.clj b/helpers/mouse.clj
index 2893389..ce282dc 100644
--- a/helpers/mouse.clj
+++ b/helpers/mouse.clj
@@ -1,26 +1,26 @@
(ns swing.helpers.mouse
(:import (SwingUtilities))
(:import (java.awt.event MouseAdapter MouseListener KeyEvent)))
-(defn- double-click?
+(defn double-click?
[event]
(= 2 (.getClickCount event)))
(defn left-click?
[event]
(SwingUtilities/isLeftMouseButton event))
(defn right-click?
[event]
(SwingUtilities/isRightMouseButton event))
(defn center-click?
[event]
(SwingUtilities/isMiddleMouseButton event))
(defn add-mouse-clicked-listener
[component f & args]
(let [listener (proxy [MouseAdapter] []
(mouseClicked [event] (apply f event args)))]
(.addMouseListener component listener)
listener))
|
martindemello/clojure-swing
|
b72d895cc403d4840b43b28494bf6276ca232a7d
|
item listener helper added
|
diff --git a/helpers/item-listener.clj b/helpers/item-listener.clj
new file mode 100644
index 0000000..9d904e1
--- /dev/null
+++ b/helpers/item-listener.clj
@@ -0,0 +1,17 @@
+(ns swing.helpers.item-listener
+ (:import (java.awt.event ItemListener ItemEvent)))
+
+(defn add-item-listener
+ [component f & args]
+ (let [listener (proxy [ItemListener] []
+ (itemStateChanged [event]
+ (apply f event args))) ]
+ (.addItemListener component listener)))
+
+(defn item-selected?
+ [event]
+ (= (.getStateChange event) ItemEvent/SELECTED))
+
+(defn item-deselected?
+ [event]
+ (= (.getStateChange event) ItemEvent/DESELECTED))
|
martindemello/clojure-swing
|
429549e493fa0526812017fe71a660596304f5ea
|
jtable usage with default constructor added
|
diff --git a/examples/jtable.clj b/examples/jtable.clj
new file mode 100644
index 0000000..95afabf
--- /dev/null
+++ b/examples/jtable.clj
@@ -0,0 +1,17 @@
+(ns jtable-example
+ (:import (javax.swing JFrame JTable JScrollPane JPanel))
+ (:import (java.awt Dimension)))
+
+(def columns ["Book" "Author"])
+
+(def data [["On Lisp" "Paul Graham"]
+ ["Practical Common Lisp" "Peter Seibel"]
+ ["Programming Clojure" "Stuart Holloway"]])
+
+(defn default-editable-table
+ []
+ (let [ frame (JFrame. "Default table demo") panel (JPanel.) scroll-pane (JScrollPane. (JTable. (to-array-2d data) (into-array columns)))]
+ (doto frame
+ (.add scroll-pane)
+ (.pack)
+ (.setVisible true))))
|
martindemello/clojure-swing
|
fd7e73546e6cefbb03fce3a9cffa7cdf9ce91190
|
added keyboard helpers
|
diff --git a/helpers/keyboard.clj b/helpers/keyboard.clj
new file mode 100644
index 0000000..2dbad18
--- /dev/null
+++ b/helpers/keyboard.clj
@@ -0,0 +1,17 @@
+(ns swing.helpers.keyboard
+ (:import
+ (java.awt.event KeyListener KeyAdapter KeyEvent InputEvent)))
+
+(defn char-of [e] (. KeyEvent getKeyText (. e getKeyCode)))
+(defn modifier [e] (. e getModifiers))
+(defn modtext [e] (. KeyEvent getKeyModifiersText (modifier e)))
+(def CTRL (. InputEvent CTRL_MASK))
+(def ALT (. InputEvent ALT_MASK))
+(defn ctrl? [e] (= CTRL (bit-and (modifier e) CTRL)))
+(defn alt? [e] (= ALT (bit-and (modifier e) ALT)))
+
+(defn add-key-pressed-listener [component f & args]
+ (let [listener (proxy [KeyAdapter] []
+ (keyPressed [e] (apply f e args)))]
+ (.addKeyListener component listener)
+ listener))
|
martindemello/clojure-swing
|
9ab1f1248f3498cbad2f0b37404c39e4e91537b2
|
helpers dir added, mouse event listener and helpers added
|
diff --git a/helpers/mouse.clj b/helpers/mouse.clj
new file mode 100644
index 0000000..2893389
--- /dev/null
+++ b/helpers/mouse.clj
@@ -0,0 +1,26 @@
+(ns swing.helpers.mouse
+ (:import (SwingUtilities))
+ (:import (java.awt.event MouseAdapter MouseListener KeyEvent)))
+
+(defn- double-click?
+ [event]
+ (= 2 (.getClickCount event)))
+
+(defn left-click?
+ [event]
+ (SwingUtilities/isLeftMouseButton event))
+
+(defn right-click?
+ [event]
+ (SwingUtilities/isRightMouseButton event))
+
+(defn center-click?
+ [event]
+ (SwingUtilities/isMiddleMouseButton event))
+
+(defn add-mouse-clicked-listener
+ [component f & args]
+ (let [listener (proxy [MouseAdapter] []
+ (mouseClicked [event] (apply f event args)))]
+ (.addMouseListener component listener)
+ listener))
|
martindemello/clojure-swing
|
90403e093d6f859bfffbb281c55d08699bc92daf
|
border layout example
|
diff --git a/examples/borderlayout.clj b/examples/borderlayout.clj
new file mode 100644
index 0000000..ccecb8a
--- /dev/null
+++ b/examples/borderlayout.clj
@@ -0,0 +1,27 @@
+; http://download.oracle.com/docs/cd/E17409_01/javase/tutorial/uiswing/layout/border.html
+(ns border-layout
+ (:import (java.awt BorderLayout Dimension ComponentOrientation))
+ (:import (javax.swing JButton JFrame)))
+
+(defn- add-components-to-pane
+ [pane]
+ (let [page-start (JButton. "page start")
+ center (JButton. "center")
+ line-start (JButton. "line start")
+ page-end (JButton. "page end")
+ line-end (JButton. "line end") ]
+ (do
+ (.setComponentOrientation pane ComponentOrientation/RIGHT_TO_LEFT)
+ (doto pane
+ (.add page-start BorderLayout/PAGE_START)
+ (.add center BorderLayout/CENTER)
+ (.add line-start BorderLayout/LINE_START)
+ (.add page-end BorderLayout/PAGE_END)
+ (.add line-end BorderLayout/LINE_END))
+ (.setPreferredSize center (Dimension. 200 100)))))
+
+(defn border-example []
+ (let [frame (JFrame. "border example") pane (.getContentPane frame) ]
+ (add-components-to-pane pane)
+ (.pack frame)
+ (.setVisible frame true)))
|
martindemello/clojure-swing
|
6c55a2398ccb6541a47afe6a07cc6cf95212e9d6
|
top-level project README
|
diff --git a/README b/README
new file mode 100644
index 0000000..ad2a9cb
--- /dev/null
+++ b/README
@@ -0,0 +1 @@
+Clojure and Swing stuff
|
martindemello/clojure-swing
|
d8a84863cfd5a5155cc8545939c68306bbcda051
|
add a few hello-world slides
|
diff --git a/presentation/content/presentation/_helloworld.clj.txt b/presentation/content/presentation/_helloworld.clj.txt
new file mode 100644
index 0000000..2e4cfe6
--- /dev/null
+++ b/presentation/content/presentation/_helloworld.clj.txt
@@ -0,0 +1,16 @@
+---
+filter: erb
+---
+
+<% uv :lang => "scheme", :theme => 'twilight' do -%>
+
+(ns hello
+ (:import (javax.swing JFrame)))
+
+(let [frame (JFrame.)]
+ (.setSize frame 200 100)
+ (.setDefaultCloseOperation frame JFrame/EXIT_ON_CLOSE)
+ (.setTitle frame "Hello World!")
+ (.setVisible frame true))
+
+<% end -%>
diff --git a/presentation/content/presentation/_helloworld.java.txt b/presentation/content/presentation/_helloworld.java.txt
new file mode 100644
index 0000000..e7f3e2b
--- /dev/null
+++ b/presentation/content/presentation/_helloworld.java.txt
@@ -0,0 +1,24 @@
+---
+filter: erb
+---
+
+<% uv :lang => "java", :theme => 'twilight' do -%>
+
+ import javax.swing.JFrame;
+
+ public class HelloFrame extends JFrame {
+ public static void main(String[] args) {
+ new HelloFrame();
+ }
+
+ public HelloFrame() {
+ this.setSize(200, 100);
+ this.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
+ this.setTitle("Hello World!");
+ this.setVisible(true);
+ }
+ }
+
+<% end -%>
+
+Code from http://www.java2s.com/Code/Java/Swing-JFC/TheSwingVersionoftheHelloWorldProgram.htm
diff --git a/presentation/content/presentation/index.txt b/presentation/content/presentation/index.txt
index c07aa7a..6e37fcf 100644
--- a/presentation/content/presentation/index.txt
+++ b/presentation/content/presentation/index.txt
@@ -1,63 +1,46 @@
---
title: Webby S5
created_at: 2008-05-18 22:10:21.995012 -06:00
author: You
company: Company
copyright: Creative Commons
filter:
- erb
- textile
- slides
layout: presentation
---
-h1. Webby S5 Generator
+h1. Clojure and Swing
-Clever introductory text that will grab the audience's attention.
+Using the Swing toolkit to write GUI desktop applications in Clojure
+h1. Why Swing?
-h1. Title of the First Slide
+* Default java gui toolkit
+* No native code needed
+* Tons of documentation, examples and third-party widgets
-A little more build up before really getting into the meat of it.
+h1. Hello World
+It doesn't take much to get a Swing GUI up and running:
-h1. Title of the Second Slide
+<% uv :lang => "scheme", :theme => 'twilight' do -%>
+(import 'javax.swing.JOptionPane)
-Finally, some code!
-
-<% uv :lang => "ragel", :theme => 'twilight' do -%>
-action dgt { printf("DGT: %c\n", fc); }
-action dec { printf("DEC: .\n"); }
-action exp { printf("EXP: %c\n", fc); }
-action exp_sign { printf("SGN: %c\n", fc); }
-action number { /*NUMBER*/ }
-
-number = (
- [0-9]+ $dgt ( '.' @dec [0-9]+ $dgt )?
- ( [eE] ( [+\-] $exp_sign )? [0-9]+ $exp )?
-) %number;
-
-main := ( number '\n' )*;
+(. JOptionPane (showMessageDialog nil "Hello World"))
<% end -%>
-h1. Title of the Third Slide
-
-This code comes from a partial
+h1. Translating from Java
-<%= render :partial => 'sample_code', :guard => true %>
+An example from a Java Swing tutorial:
+<%= render :partial => 'helloworld.java', :guard => true %>
-h1. Title of the Fourth Slide
-
-A quadratic equation with real or complex coefficients has two (not necessarily distinct) solutions, called roots, which may or may not be real, given by the quadratic formula:
-
-<% tex2img 'quadratic', :path => 'images', :alt => 'quadratic', :resolution => '300x300' do -%>
-x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a}
-<% end -%>
+h1. Translating from Java
-h1. The Final Slide
+And the same example in Clojure
-And that about sums it up!
+<%= render :partial => 'helloworld.clj', :guard => true %>
-Thanks for visiting
|
martindemello/clojure-swing
|
ea0280ecfe51e8b8b5c1dd031f976fbfdfaffea2
|
added README
|
diff --git a/presentation/README b/presentation/README
new file mode 100644
index 0000000..1af650d
--- /dev/null
+++ b/presentation/README
@@ -0,0 +1,5 @@
+* Generate slideshow:
+ webby
+
+* View presentation:
+ open output/presentation/index.html
|
martindemello/clojure-swing
|
b1f48c6b82310daf08664d1785ad0fb70bd695c5
|
add a basepath so we can run this without a webserver
|
diff --git a/presentation/Sitefile b/presentation/Sitefile
index 1debfbd..299f19e 100644
--- a/presentation/Sitefile
+++ b/presentation/Sitefile
@@ -1,10 +1,11 @@
-
task :default => :build
desc 'deploy the site to the webserver'
task :deploy => [:build, 'deploy:rsync']
SITE.uv.theme = 'twilight'
SITE.uv.line_numbers = false
+SITE.base = ".."
+
# EOF
diff --git a/presentation/layouts/presentation.txt b/presentation/layouts/presentation.txt
index 7d83933..7b7be01 100644
--- a/presentation/layouts/presentation.txt
+++ b/presentation/layouts/presentation.txt
@@ -1,43 +1,44 @@
---
extension: html
filter:
- erb
+ - basepath
---
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en-us">
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<title><%= h(@page.title) %></title>
<meta name="author" content="<%= h(@page.author) %>" />
<meta name="company" content="<%= h(@page.company) %>" />
<!-- configuration parameters -->
<meta name="defaultView" content="slideshow" />
<meta name="controlVis" content="hidden" />
<link rel="stylesheet" href="/presentation/s5/slides.css" type="text/css" media="projection" id="slideProj" />
<link rel="stylesheet" href="/presentation/s5/outline.css" type="text/css" media="screen" id="outlineStyle" />
<link rel="stylesheet" href="/css/uv/twilight.css" type="text/css" media="screen, projection" />
<!-- S5 JS -->
<script src="/presentation/s5/slides.js" type="text/javascript"></script>
</head>
<body>
<div class="layout">
<div id="controls"><!-- DO NOT EDIT --></div>
<div id="currentSlide"><!-- DO NOT EDIT --></div>
<div id="header"></div>
<div id="footer">
<h2>Copyright © <%= h(@page.copyright) %></h2>
</div>
</div>
<div class="presentation">
<%= @content %>
</div>
</body>
</html>
|
martindemello/clojure-swing
|
5108eecdf72473ef0e21e567cf77b5adf08232d1
|
webby-gen presentation
|
diff --git a/presentation/Sitefile b/presentation/Sitefile
new file mode 100644
index 0000000..1debfbd
--- /dev/null
+++ b/presentation/Sitefile
@@ -0,0 +1,10 @@
+
+task :default => :build
+
+desc 'deploy the site to the webserver'
+task :deploy => [:build, 'deploy:rsync']
+
+SITE.uv.theme = 'twilight'
+SITE.uv.line_numbers = false
+
+# EOF
diff --git a/presentation/content/css/uv/twilight.css b/presentation/content/css/uv/twilight.css
new file mode 100644
index 0000000..d6427dd
--- /dev/null
+++ b/presentation/content/css/uv/twilight.css
@@ -0,0 +1,137 @@
+pre.twilight .DiffInserted {
+ background-color: #253B22;
+ color: #F8F8F8;
+}
+pre.twilight .DiffHeader {
+ background-color: #0E2231;
+ color: #F8F8F8;
+ font-style: italic;
+}
+pre.twilight .CssPropertyValue {
+ color: #F9EE98;
+}
+pre.twilight .CCCPreprocessorDirective {
+ color: #AFC4DB;
+}
+pre.twilight .Constant {
+ color: #CF6A4C;
+}
+pre.twilight .DiffChanged {
+ background-color: #4A410D;
+ color: #F8F8F8;
+}
+pre.twilight .EmbeddedSource {
+ background-color: #A3A6AD;
+}
+pre.twilight .Support {
+ color: #9B859D;
+}
+pre.twilight .MarkupList {
+ color: #F9EE98;
+}
+pre.twilight .CssConstructorArgument {
+ color: #8F9D6A;
+}
+pre.twilight .Storage {
+ color: #F9EE98;
+}
+pre.twilight .line-numbers {
+ background-color: inherit;
+ color: #999999;
+}
+pre.twilight .CssClass {
+ color: #9B703F;
+}
+pre.twilight .StringConstant {
+ color: #DDF2A4;
+}
+pre.twilight .CssAtRule {
+ color: #8693A5;
+}
+pre.twilight .MetaTagInline {
+ color: #E0C589;
+}
+pre.twilight .MarkupHeading {
+ color: #CF6A4C;
+}
+pre.twilight .CssTagName {
+ color: #CDA869;
+}
+pre.twilight .SupportConstant {
+ color: #CF6A4C;
+}
+pre.twilight .DiffDeleted {
+ background-color: #420E09;
+ color: #F8F8F8;
+}
+pre.twilight .CCCPreprocessorLine {
+ color: #8996A8;
+}
+pre.twilight .StringRegexpSpecial {
+ color: #CF7D34;
+}
+pre.twilight .EmbeddedSourceBright {
+ background-color: #9C9EA4;
+}
+pre.twilight .InvalidIllegal {
+ background-color: #241A24;
+ color: #F8F8F8;
+}
+pre.twilight .SupportFunction {
+ color: #DAD085;
+}
+pre.twilight .CssAdditionalConstants {
+ color: #CA7840;
+}
+pre.twilight .MetaTagAll {
+ color: #AC885B;
+}
+pre.twilight .StringRegexp {
+ color: #E9C062;
+}
+pre.twilight .StringEmbeddedSource {
+ color: #DAEFA3;
+}
+pre.twilight .EntityInheritedClass {
+ color: #9B5C2E;
+ font-style: italic;
+}
+pre.twilight .CssId {
+ color: #8B98AB;
+}
+pre.twilight .CssPseudoClass {
+ color: #8F9D6A;
+}
+pre.twilight .StringVariable {
+ color: #8A9A95;
+}
+pre.twilight .String {
+ color: #8F9D6A;
+}
+pre.twilight .Keyword {
+ color: #CDA869;
+}
+pre.twilight {
+ background-color: #141414;
+ color: #F8F8F8;
+}
+pre.twilight .CssPropertyName {
+ color: #C5AF75;
+}
+pre.twilight .DoctypeXmlProcessing {
+ color: #494949;
+}
+pre.twilight .InvalidDeprecated {
+ color: #D2A8A1;
+ font-style: italic;
+}
+pre.twilight .Variable {
+ color: #7587A6;
+}
+pre.twilight .Entity {
+ color: #9B703F;
+}
+pre.twilight .Comment {
+ color: #5F5A60;
+ font-style: italic;
+}
diff --git a/presentation/content/presentation/_sample_code.txt b/presentation/content/presentation/_sample_code.txt
new file mode 100644
index 0000000..61976a0
--- /dev/null
+++ b/presentation/content/presentation/_sample_code.txt
@@ -0,0 +1,10 @@
+---
+filter: erb
+---
+<% uv :lang => "ruby", :theme => 'twilight' do -%>
+class A
+ def method()
+ puts "in class #{self.class.name}"
+ end
+end
+<% end -%>
diff --git a/presentation/content/presentation/index.txt b/presentation/content/presentation/index.txt
new file mode 100644
index 0000000..c07aa7a
--- /dev/null
+++ b/presentation/content/presentation/index.txt
@@ -0,0 +1,63 @@
+---
+title: Webby S5
+created_at: 2008-05-18 22:10:21.995012 -06:00
+author: You
+company: Company
+copyright: Creative Commons
+filter:
+ - erb
+ - textile
+ - slides
+layout: presentation
+---
+h1. Webby S5 Generator
+
+Clever introductory text that will grab the audience's attention.
+
+
+h1. Title of the First Slide
+
+A little more build up before really getting into the meat of it.
+
+
+h1. Title of the Second Slide
+
+Finally, some code!
+
+<% uv :lang => "ragel", :theme => 'twilight' do -%>
+action dgt { printf("DGT: %c\n", fc); }
+action dec { printf("DEC: .\n"); }
+action exp { printf("EXP: %c\n", fc); }
+action exp_sign { printf("SGN: %c\n", fc); }
+action number { /*NUMBER*/ }
+
+number = (
+ [0-9]+ $dgt ( '.' @dec [0-9]+ $dgt )?
+ ( [eE] ( [+\-] $exp_sign )? [0-9]+ $exp )?
+) %number;
+
+main := ( number '\n' )*;
+<% end -%>
+
+
+h1. Title of the Third Slide
+
+This code comes from a partial
+
+<%= render :partial => 'sample_code', :guard => true %>
+
+
+h1. Title of the Fourth Slide
+
+A quadratic equation with real or complex coefficients has two (not necessarily distinct) solutions, called roots, which may or may not be real, given by the quadratic formula:
+
+<% tex2img 'quadratic', :path => 'images', :alt => 'quadratic', :resolution => '300x300' do -%>
+x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a}
+<% end -%>
+
+
+h1. The Final Slide
+
+And that about sums it up!
+
+Thanks for visiting
diff --git a/presentation/content/presentation/s5/blank.gif b/presentation/content/presentation/s5/blank.gif
new file mode 100644
index 0000000..75b945d
Binary files /dev/null and b/presentation/content/presentation/s5/blank.gif differ
diff --git a/presentation/content/presentation/s5/bodybg.gif b/presentation/content/presentation/s5/bodybg.gif
new file mode 100644
index 0000000..5f448a1
Binary files /dev/null and b/presentation/content/presentation/s5/bodybg.gif differ
diff --git a/presentation/content/presentation/s5/framing.css b/presentation/content/presentation/s5/framing.css
new file mode 100644
index 0000000..14d8509
--- /dev/null
+++ b/presentation/content/presentation/s5/framing.css
@@ -0,0 +1,23 @@
+/* The following styles size, place, and layer the slide components.
+ Edit these if you want to change the overall slide layout.
+ The commented lines can be uncommented (and modified, if necessary)
+ to help you with the rearrangement process. */
+
+/* target = 1024x768 */
+
+div#header, div#footer, .slide {width: 100%; top: 0; left: 0;}
+div#header {top: 0; height: 3em; z-index: 1;}
+div#footer {top: auto; bottom: 0; height: 2.5em; z-index: 5;}
+.slide {top: 0; width: 92%; padding: 3.5em 4% 4%; z-index: 2; list-style: none;}
+div#controls {left: 50%; bottom: 0; width: 50%; z-index: 100;}
+div#controls form {position: absolute; bottom: 0; right: 0; width: 100%;
+ margin: 0;}
+#currentSlide {position: absolute; width: 10%; left: 45%; bottom: 1em; z-index: 10;}
+html>body #currentSlide {position: fixed;}
+
+/*
+div#header {background: #FCC;}
+div#footer {background: #CCF;}
+div#controls {background: #BBD;}
+div#currentSlide {background: #FFC;}
+*/
diff --git a/presentation/content/presentation/s5/iepngfix.htc b/presentation/content/presentation/s5/iepngfix.htc
new file mode 100644
index 0000000..bba2db7
--- /dev/null
+++ b/presentation/content/presentation/s5/iepngfix.htc
@@ -0,0 +1,42 @@
+<public:component>
+<public:attach event="onpropertychange" onevent="doFix()" />
+
+<script>
+
+// IE5.5+ PNG Alpha Fix v1.0 by Angus Turnbull http://www.twinhelix.com
+// Free usage permitted as long as this notice remains intact.
+
+// This must be a path to a blank image. That's all the configuration you need here.
+var blankImg = 'ui/default/blank.gif';
+
+var f = 'DXImageTransform.Microsoft.AlphaImageLoader';
+
+function filt(s, m) {
+ if (filters[f]) {
+ filters[f].enabled = s ? true : false;
+ if (s) with (filters[f]) { src = s; sizingMethod = m }
+ } else if (s) style.filter = 'progid:'+f+'(src="'+s+'",sizingMethod="'+m+'")';
+}
+
+function doFix() {
+ if ((parseFloat(navigator.userAgent.match(/MSIE (\S+)/)[1]) < 5.5) ||
+ (event && !/(background|src)/.test(event.propertyName))) return;
+
+ if (tagName == 'IMG') {
+ if ((/\.png$/i).test(src)) {
+ filt(src, 'image'); // was 'scale'
+ src = blankImg;
+ } else if (src.indexOf(blankImg) < 0) filt();
+ } else if (style.backgroundImage) {
+ if (style.backgroundImage.match(/^url[("']+(.*\.png)[)"']+$/i)) {
+ var s = RegExp.$1;
+ style.backgroundImage = '';
+ filt(s, 'crop');
+ } else filt();
+ }
+}
+
+doFix();
+
+</script>
+</public:component>
\ No newline at end of file
diff --git a/presentation/content/presentation/s5/opera.css b/presentation/content/presentation/s5/opera.css
new file mode 100644
index 0000000..9e9d2a3
--- /dev/null
+++ b/presentation/content/presentation/s5/opera.css
@@ -0,0 +1,7 @@
+/* DO NOT CHANGE THESE unless you really want to break Opera Show */
+.slide {
+ visibility: visible !important;
+ position: static !important;
+ page-break-before: always;
+}
+#slide0 {page-break-before: avoid;}
diff --git a/presentation/content/presentation/s5/outline.css b/presentation/content/presentation/s5/outline.css
new file mode 100644
index 0000000..62db519
--- /dev/null
+++ b/presentation/content/presentation/s5/outline.css
@@ -0,0 +1,15 @@
+/* don't change this unless you want the layout stuff to show up in the outline view! */
+
+.layout div, #footer *, #controlForm * {display: none;}
+#footer, #controls, #controlForm, #navLinks, #toggle {
+ display: block; visibility: visible; margin: 0; padding: 0;}
+#toggle {float: right; padding: 0.5em;}
+html>body #toggle {position: fixed; top: 0; right: 0;}
+
+/* making the outline look pretty-ish */
+
+#slide0 h1, #slide0 h2, #slide0 h3, #slide0 h4 {border: none; margin: 0;}
+#slide0 h1 {padding-top: 1.5em;}
+.slide h1 {margin: 1.5em 0 0; padding-top: 0.25em;
+ border-top: 1px solid #888; border-bottom: 1px solid #AAA;}
+#toggle {border: 1px solid; border-width: 0 0 1px 1px; background: #FFF;}
diff --git a/presentation/content/presentation/s5/pretty.css b/presentation/content/presentation/s5/pretty.css
new file mode 100644
index 0000000..3d3acef
--- /dev/null
+++ b/presentation/content/presentation/s5/pretty.css
@@ -0,0 +1,86 @@
+/* Following are the presentation styles -- edit away! */
+
+body {background: #FFF url(bodybg.gif) -16px 0 no-repeat; color: #000; font-size: 2em;}
+:link, :visited {text-decoration: none; color: #00C;}
+#controls :active {color: #88A !important;}
+#controls :focus {outline: 1px dotted #227;}
+h1, h2, h3, h4 {font-size: 100%; margin: 0; padding: 0; font-weight: inherit;}
+ul, pre {margin: 0; line-height: 1em;}
+html, body {margin: 0; padding: 0;}
+
+blockquote, q {font-style: italic;}
+blockquote {padding: 0 2em 0.5em; margin: 0 1.5em 0.5em; text-align: center; font-size: 1em;}
+blockquote p {margin: 0;}
+blockquote i {font-style: normal;}
+blockquote b {display: block; margin-top: 0.5em; font-weight: normal; font-size: smaller; font-style: normal;}
+blockquote b i {font-style: italic;}
+
+kbd {font-weight: bold; font-size: 1em;}
+sup {font-size: smaller; line-height: 1px;}
+
+.slide code {padding: 2px 0.25em; font-weight: bold; color: #533;}
+.slide code.bad, code del {color: red;}
+.slide code.old {color: silver;}
+.slide pre {padding: 0; margin: 0.25em 0 0.5em 0.5em; color: #533; font-size: 90%;}
+.slide pre code {display: block;}
+.slide ul {margin-left: 5%; margin-right: 7%; list-style: disc;}
+.slide li {margin-top: 0.75em; margin-right: 0;}
+.slide ul ul {line-height: 1;}
+.slide ul ul li {margin: .2em; font-size: 85%; list-style: square;}
+.slide img.leader {display: block; margin: 0 auto;}
+
+div#header, div#footer {background: #005; color: #AAB;
+ font-family: Verdana, Helvetica, sans-serif;}
+div#header {background: #005 url(bodybg.gif) -16px 0 no-repeat;
+ line-height: 1px;}
+div#footer {font-size: 0.5em; font-weight: bold; padding: 1em 0;}
+#footer h1, #footer h2 {display: block; padding: 0 1em;}
+#footer h2 {font-style: italic;}
+
+div.long {font-size: 0.75em;}
+.slide h1 {position: absolute; top: 0.7em; left: 87px; z-index: 1;
+ margin: 0; padding: 0.3em 0 0 50px; white-space: nowrap;
+ font: bold 150%/1em Helvetica, sans-serif; text-transform: capitalize;
+ color: #DDE; background: #005;}
+.slide h3 {font-size: 130%;}
+h1 abbr {font-variant: small-caps;}
+
+div#controls {position: absolute; left: 50%; bottom: 0;
+ width: 50%;
+ text-align: right; font: bold 0.9em Verdana, Helvetica, sans-serif;}
+html>body div#controls {position: fixed; padding: 0 0 1em 0;
+ top: auto;}
+div#controls form {position: absolute; bottom: 0; right: 0; width: 100%;
+ margin: 0; padding: 0;}
+#controls #navLinks a {padding: 0; margin: 0 0.5em;
+ background: #005; border: none; color: #779;
+ cursor: pointer;}
+#controls #navList {height: 1em;}
+#controls #navList #jumplist {position: absolute; bottom: 0; right: 0; background: #DDD; color: #227;}
+
+#currentSlide {text-align: center; font-size: 0.5em; color: #449;}
+
+#slide0 {padding-top: 3.5em; font-size: 90%;}
+#slide0 h1 {position: static; margin: 1em 0 0; padding: 0;
+ font: bold 2em Helvetica, sans-serif; white-space: normal;
+ color: #000; background: transparent;}
+#slide0 h2 {font: bold italic 1em Helvetica, sans-serif; margin: 0.25em;}
+#slide0 h3 {margin-top: 1.5em; font-size: 1.5em;}
+#slide0 h4 {margin-top: 0; font-size: 1em;}
+
+ul.urls {list-style: none; display: inline; margin: 0;}
+.urls li {display: inline; margin: 0;}
+.note {display: none;}
+.external {border-bottom: 1px dotted gray;}
+html>body .external {border-bottom: none;}
+.external:after {content: " \274F"; font-size: smaller; color: #77B;}
+
+.incremental, .incremental *, .incremental *:after {color: #DDE; visibility: visible;}
+img.incremental {visibility: hidden;}
+.slide .current {color: #B02;}
+
+
+/* diagnostics
+
+li:after {content: " [" attr(class) "]"; color: #F88;}
+ */
\ No newline at end of file
diff --git a/presentation/content/presentation/s5/print.css b/presentation/content/presentation/s5/print.css
new file mode 100644
index 0000000..458be69
--- /dev/null
+++ b/presentation/content/presentation/s5/print.css
@@ -0,0 +1,25 @@
+/* The following rule is necessary to have all slides appear in print! DO NOT REMOVE IT! */
+.slide, ul {page-break-inside: avoid; visibility: visible !important;}
+h1 {page-break-after: avoid;}
+
+body {font-size: 12pt; background: white;}
+* {color: black;}
+
+#slide0 h1 {font-size: 200%; border: none; margin: 0.5em 0 0.25em;}
+#slide0 h3 {margin: 0; padding: 0;}
+#slide0 h4 {margin: 0 0 0.5em; padding: 0;}
+#slide0 {margin-bottom: 3em;}
+
+h1 {border-top: 2pt solid gray; border-bottom: 1px dotted silver;}
+.extra {background: transparent !important;}
+div.extra, pre.extra, .example {font-size: 10pt; color: #333;}
+ul.extra a {font-weight: bold;}
+p.example {display: none;}
+
+#header {display: none;}
+#footer h1 {margin: 0; border-bottom: 1px solid; color: gray; font-style: italic;}
+#footer h2, #controls {display: none;}
+
+/* The following rule keeps the layout stuff out of print. Remove at your own risk! */
+.layout, .layout * {display: none !important;}
+
diff --git a/presentation/content/presentation/s5/s5-core.css b/presentation/content/presentation/s5/s5-core.css
new file mode 100644
index 0000000..86444e0
--- /dev/null
+++ b/presentation/content/presentation/s5/s5-core.css
@@ -0,0 +1,9 @@
+/* Do not edit or override these styles! The system will likely break if you do. */
+
+div#header, div#footer, div#controls, .slide {position: absolute;}
+html>body div#header, html>body div#footer,
+ html>body div#controls, html>body .slide {position: fixed;}
+.handout {display: none;}
+.layout {display: block;}
+.slide, .hideme, .incremental {visibility: hidden;}
+#slide0 {visibility: visible;}
diff --git a/presentation/content/presentation/s5/slides.css b/presentation/content/presentation/s5/slides.css
new file mode 100644
index 0000000..0786d7d
--- /dev/null
+++ b/presentation/content/presentation/s5/slides.css
@@ -0,0 +1,3 @@
+@import url(s5-core.css); /* required to make the slide show run at all */
+@import url(framing.css); /* sets basic placement and size of slide components */
+@import url(pretty.css); /* stuff that makes the slides look better than blah */
\ No newline at end of file
diff --git a/presentation/content/presentation/s5/slides.js b/presentation/content/presentation/s5/slides.js
new file mode 100644
index 0000000..38fe853
--- /dev/null
+++ b/presentation/content/presentation/s5/slides.js
@@ -0,0 +1,553 @@
+// S5 v1.1 slides.js -- released into the Public Domain
+//
+// Please see http://www.meyerweb.com/eric/tools/s5/credits.html for information
+// about all the wonderful and talented contributors to this code!
+
+var undef;
+var slideCSS = '';
+var snum = 0;
+var smax = 1;
+var incpos = 0;
+var number = undef;
+var s5mode = true;
+var defaultView = 'slideshow';
+var controlVis = 'visible';
+
+var isIE = navigator.appName == 'Microsoft Internet Explorer' && navigator.userAgent.indexOf('Opera') < 1 ? 1 : 0;
+var isOp = navigator.userAgent.indexOf('Opera') > -1 ? 1 : 0;
+var isGe = navigator.userAgent.indexOf('Gecko') > -1 && navigator.userAgent.indexOf('Safari') < 1 ? 1 : 0;
+
+function hasClass(object, className) {
+ if (!object.className) return false;
+ return (object.className.search('(^|\\s)' + className + '(\\s|$)') != -1);
+}
+
+function hasValue(object, value) {
+ if (!object) return false;
+ return (object.search('(^|\\s)' + value + '(\\s|$)') != -1);
+}
+
+function removeClass(object,className) {
+ if (!object) return;
+ object.className = object.className.replace(new RegExp('(^|\\s)'+className+'(\\s|$)'), RegExp.$1+RegExp.$2);
+}
+
+function addClass(object,className) {
+ if (!object || hasClass(object, className)) return;
+ if (object.className) {
+ object.className += ' '+className;
+ } else {
+ object.className = className;
+ }
+}
+
+function GetElementsWithClassName(elementName,className) {
+ var allElements = document.getElementsByTagName(elementName);
+ var elemColl = new Array();
+ for (var i = 0; i< allElements.length; i++) {
+ if (hasClass(allElements[i], className)) {
+ elemColl[elemColl.length] = allElements[i];
+ }
+ }
+ return elemColl;
+}
+
+function isParentOrSelf(element, id) {
+ if (element == null || element.nodeName=='BODY') return false;
+ else if (element.id == id) return true;
+ else return isParentOrSelf(element.parentNode, id);
+}
+
+function nodeValue(node) {
+ var result = "";
+ if (node.nodeType == 1) {
+ var children = node.childNodes;
+ for (var i = 0; i < children.length; ++i) {
+ result += nodeValue(children[i]);
+ }
+ }
+ else if (node.nodeType == 3) {
+ result = node.nodeValue;
+ }
+ return(result);
+}
+
+function slideLabel() {
+ var slideColl = GetElementsWithClassName('*','slide');
+ var list = document.getElementById('jumplist');
+ smax = slideColl.length;
+ for (var n = 0; n < smax; n++) {
+ var obj = slideColl[n];
+
+ var did = 'slide' + n.toString();
+ obj.setAttribute('id',did);
+ if (isOp) continue;
+
+ var otext = '';
+ var menu = obj.firstChild;
+ if (!menu) continue; // to cope with empty slides
+ while (menu && menu.nodeType == 3) {
+ menu = menu.nextSibling;
+ }
+ if (!menu) continue; // to cope with slides with only text nodes
+
+ var menunodes = menu.childNodes;
+ for (var o = 0; o < menunodes.length; o++) {
+ otext += nodeValue(menunodes[o]);
+ }
+ list.options[list.length] = new Option(n + ' : ' + otext, n);
+ }
+}
+
+function currentSlide() {
+ var cs;
+ if (document.getElementById) {
+ cs = document.getElementById('currentSlide');
+ } else {
+ cs = document.currentSlide;
+ }
+ cs.innerHTML = '<span id="csHere">' + snum + '<\/span> ' +
+ '<span id="csSep">\/<\/span> ' +
+ '<span id="csTotal">' + (smax-1) + '<\/span>';
+ if (snum == 0) {
+ cs.style.visibility = 'hidden';
+ } else {
+ cs.style.visibility = 'visible';
+ }
+}
+
+function go(step) {
+ if (document.getElementById('slideProj').disabled || step == 0) return;
+ var jl = document.getElementById('jumplist');
+ var cid = 'slide' + snum;
+ var ce = document.getElementById(cid);
+ if (incrementals[snum].length > 0) {
+ for (var i = 0; i < incrementals[snum].length; i++) {
+ removeClass(incrementals[snum][i], 'current');
+ removeClass(incrementals[snum][i], 'incremental');
+ }
+ }
+ if (step != 'j') {
+ snum += step;
+ lmax = smax - 1;
+ if (snum > lmax) snum = lmax;
+ if (snum < 0) snum = 0;
+ } else
+ snum = parseInt(jl.value);
+ var nid = 'slide' + snum;
+ var ne = document.getElementById(nid);
+ if (!ne) {
+ ne = document.getElementById('slide0');
+ snum = 0;
+ }
+ if (step < 0) {incpos = incrementals[snum].length} else {incpos = 0;}
+ if (incrementals[snum].length > 0 && incpos == 0) {
+ for (var i = 0; i < incrementals[snum].length; i++) {
+ if (hasClass(incrementals[snum][i], 'current'))
+ incpos = i + 1;
+ else
+ addClass(incrementals[snum][i], 'incremental');
+ }
+ }
+ if (incrementals[snum].length > 0 && incpos > 0)
+ addClass(incrementals[snum][incpos - 1], 'current');
+ ce.style.visibility = 'hidden';
+ ne.style.visibility = 'visible';
+ jl.selectedIndex = snum;
+ currentSlide();
+ number = 0;
+}
+
+function goTo(target) {
+ if (target >= smax || target == snum) return;
+ go(target - snum);
+}
+
+function subgo(step) {
+ if (step > 0) {
+ removeClass(incrementals[snum][incpos - 1],'current');
+ removeClass(incrementals[snum][incpos], 'incremental');
+ addClass(incrementals[snum][incpos],'current');
+ incpos++;
+ } else {
+ incpos--;
+ removeClass(incrementals[snum][incpos],'current');
+ addClass(incrementals[snum][incpos], 'incremental');
+ addClass(incrementals[snum][incpos - 1],'current');
+ }
+}
+
+function toggle() {
+ var slideColl = GetElementsWithClassName('*','slide');
+ var slides = document.getElementById('slideProj');
+ var outline = document.getElementById('outlineStyle');
+ if (!slides.disabled) {
+ slides.disabled = true;
+ outline.disabled = false;
+ s5mode = false;
+ fontSize('1em');
+ for (var n = 0; n < smax; n++) {
+ var slide = slideColl[n];
+ slide.style.visibility = 'visible';
+ }
+ } else {
+ slides.disabled = false;
+ outline.disabled = true;
+ s5mode = true;
+ fontScale();
+ for (var n = 0; n < smax; n++) {
+ var slide = slideColl[n];
+ slide.style.visibility = 'hidden';
+ }
+ slideColl[snum].style.visibility = 'visible';
+ }
+}
+
+function showHide(action) {
+ var obj = GetElementsWithClassName('*','hideme')[0];
+ switch (action) {
+ case 's': obj.style.visibility = 'visible'; break;
+ case 'h': obj.style.visibility = 'hidden'; break;
+ case 'k':
+ if (obj.style.visibility != 'visible') {
+ obj.style.visibility = 'visible';
+ } else {
+ obj.style.visibility = 'hidden';
+ }
+ break;
+ }
+}
+
+// 'keys' code adapted from MozPoint (http://mozpoint.mozdev.org/)
+function keys(key) {
+ if (!key) {
+ key = event;
+ key.which = key.keyCode;
+ }
+ if (key.which == 84) {
+ toggle();
+ return;
+ }
+ if (s5mode) {
+ switch (key.which) {
+ case 10: // return
+ case 13: // enter
+ if (window.event && isParentOrSelf(window.event.srcElement, 'controls')) return;
+ if (key.target && isParentOrSelf(key.target, 'controls')) return;
+ if(number != undef) {
+ goTo(number);
+ break;
+ }
+ case 32: // spacebar
+ case 34: // page down
+ case 39: // rightkey
+ case 40: // downkey
+ if(number != undef) {
+ go(number);
+ } else if (!incrementals[snum] || incpos >= incrementals[snum].length) {
+ go(1);
+ } else {
+ subgo(1);
+ }
+ break;
+ case 33: // page up
+ case 37: // leftkey
+ case 38: // upkey
+ if(number != undef) {
+ go(-1 * number);
+ } else if (!incrementals[snum] || incpos <= 0) {
+ go(-1);
+ } else {
+ subgo(-1);
+ }
+ break;
+ case 36: // home
+ goTo(0);
+ break;
+ case 35: // end
+ goTo(smax-1);
+ break;
+ case 67: // c
+ showHide('k');
+ break;
+ }
+ if (key.which < 48 || key.which > 57) {
+ number = undef;
+ } else {
+ if (window.event && isParentOrSelf(window.event.srcElement, 'controls')) return;
+ if (key.target && isParentOrSelf(key.target, 'controls')) return;
+ number = (((number != undef) ? number : 0) * 10) + (key.which - 48);
+ }
+ }
+ return false;
+}
+
+function clicker(e) {
+ number = undef;
+ var target;
+ if (window.event) {
+ target = window.event.srcElement;
+ e = window.event;
+ } else target = e.target;
+ if (target.getAttribute('href') != null || hasValue(target.rel, 'external') || isParentOrSelf(target, 'controls') || isParentOrSelf(target,'embed') || isParentOrSelf(target,'object')) return true;
+ if (!e.which || e.which == 1) {
+ if (!incrementals[snum] || incpos >= incrementals[snum].length) {
+ go(1);
+ } else {
+ subgo(1);
+ }
+ }
+}
+
+function findSlide(hash) {
+ var target = null;
+ var slides = GetElementsWithClassName('*','slide');
+ for (var i = 0; i < slides.length; i++) {
+ var targetSlide = slides[i];
+ if ( (targetSlide.name && targetSlide.name == hash)
+ || (targetSlide.id && targetSlide.id == hash) ) {
+ target = targetSlide;
+ break;
+ }
+ }
+ while(target != null && target.nodeName != 'BODY') {
+ if (hasClass(target, 'slide')) {
+ return parseInt(target.id.slice(5));
+ }
+ target = target.parentNode;
+ }
+ return null;
+}
+
+function slideJump() {
+ if (window.location.hash == null) return;
+ var sregex = /^#slide(\d+)$/;
+ var matches = sregex.exec(window.location.hash);
+ var dest = null;
+ if (matches != null) {
+ dest = parseInt(matches[1]);
+ } else {
+ dest = findSlide(window.location.hash.slice(1));
+ }
+ if (dest != null)
+ go(dest - snum);
+}
+
+function fixLinks() {
+ var thisUri = window.location.href;
+ thisUri = thisUri.slice(0, thisUri.length - window.location.hash.length);
+ var aelements = document.getElementsByTagName('A');
+ for (var i = 0; i < aelements.length; i++) {
+ var a = aelements[i].href;
+ var slideID = a.match('\#slide[0-9]{1,2}');
+ if ((slideID) && (slideID[0].slice(0,1) == '#')) {
+ var dest = findSlide(slideID[0].slice(1));
+ if (dest != null) {
+ if (aelements[i].addEventListener) {
+ aelements[i].addEventListener("click", new Function("e",
+ "if (document.getElementById('slideProj').disabled) return;" +
+ "go("+dest+" - snum); " +
+ "if (e.preventDefault) e.preventDefault();"), true);
+ } else if (aelements[i].attachEvent) {
+ aelements[i].attachEvent("onclick", new Function("",
+ "if (document.getElementById('slideProj').disabled) return;" +
+ "go("+dest+" - snum); " +
+ "event.returnValue = false;"));
+ }
+ }
+ }
+ }
+}
+
+function externalLinks() {
+ if (!document.getElementsByTagName) return;
+ var anchors = document.getElementsByTagName('a');
+ for (var i=0; i<anchors.length; i++) {
+ var anchor = anchors[i];
+ if (anchor.getAttribute('href') && hasValue(anchor.rel, 'external')) {
+ anchor.target = '_blank';
+ addClass(anchor,'external');
+ }
+ }
+}
+
+function createControls() {
+ var controlsDiv = document.getElementById("controls");
+ if (!controlsDiv) return;
+ var hider = ' onmouseover="showHide(\'s\');" onmouseout="showHide(\'h\');"';
+ var hideDiv, hideList = '';
+ if (controlVis == 'hidden') {
+ hideDiv = hider;
+ } else {
+ hideList = hider;
+ }
+ controlsDiv.innerHTML = '<form action="#" id="controlForm"' + hideDiv + '>' +
+ '<div id="navLinks">' +
+ '<a accesskey="t" id="toggle" href="javascript:toggle();">Ø<\/a>' +
+ '<a accesskey="z" id="prev" href="javascript:go(-1);">«<\/a>' +
+ '<a accesskey="x" id="next" href="javascript:go(1);">»<\/a>' +
+ '<div id="navList"' + hideList + '><select id="jumplist" onchange="go(\'j\');"><\/select><\/div>' +
+ '<\/div><\/form>';
+ if (controlVis == 'hidden') {
+ var hidden = document.getElementById('navLinks');
+ } else {
+ var hidden = document.getElementById('jumplist');
+ }
+ addClass(hidden,'hideme');
+}
+
+function fontScale() { // causes layout problems in FireFox that get fixed if browser's Reload is used; same may be true of other Gecko-based browsers
+ if (!s5mode) return false;
+ var vScale = 22; // both yield 32 (after rounding) at 1024x768
+ var hScale = 32; // perhaps should auto-calculate based on theme's declared value?
+ if (window.innerHeight) {
+ var vSize = window.innerHeight;
+ var hSize = window.innerWidth;
+ } else if (document.documentElement.clientHeight) {
+ var vSize = document.documentElement.clientHeight;
+ var hSize = document.documentElement.clientWidth;
+ } else if (document.body.clientHeight) {
+ var vSize = document.body.clientHeight;
+ var hSize = document.body.clientWidth;
+ } else {
+ var vSize = 700; // assuming 1024x768, minus chrome and such
+ var hSize = 1024; // these do not account for kiosk mode or Opera Show
+ }
+ var newSize = Math.min(Math.round(vSize/vScale),Math.round(hSize/hScale));
+ fontSize(newSize + 'px');
+ if (isGe) { // hack to counter incremental reflow bugs
+ var obj = document.getElementsByTagName('body')[0];
+ obj.style.display = 'none';
+ obj.style.display = 'block';
+ }
+}
+
+function fontSize(value) {
+ if (!(s5ss = document.getElementById('s5ss'))) {
+ if (!isIE) {
+ document.getElementsByTagName('head')[0].appendChild(s5ss = document.createElement('style'));
+ s5ss.setAttribute('media','screen, projection');
+ s5ss.setAttribute('id','s5ss');
+ } else {
+ document.createStyleSheet();
+ document.s5ss = document.styleSheets[document.styleSheets.length - 1];
+ }
+ }
+ if (!isIE) {
+ while (s5ss.lastChild) s5ss.removeChild(s5ss.lastChild);
+ s5ss.appendChild(document.createTextNode('body {font-size: ' + value + ' !important;}'));
+ } else {
+ document.s5ss.addRule('body','font-size: ' + value + ' !important;');
+ }
+}
+
+function notOperaFix() {
+ slideCSS = document.getElementById('slideProj').href;
+ var slides = document.getElementById('slideProj');
+ var outline = document.getElementById('outlineStyle');
+ slides.setAttribute('media','screen');
+ outline.disabled = true;
+ if (isGe) {
+ slides.setAttribute('href','null'); // Gecko fix
+ slides.setAttribute('href',slideCSS); // Gecko fix
+ }
+ if (isIE && document.styleSheets && document.styleSheets[0]) {
+ document.styleSheets[0].addRule('img', 'behavior: url(ui/default/iepngfix.htc)');
+ document.styleSheets[0].addRule('div', 'behavior: url(ui/default/iepngfix.htc)');
+ document.styleSheets[0].addRule('.slide', 'behavior: url(ui/default/iepngfix.htc)');
+ }
+}
+
+function getIncrementals(obj) {
+ var incrementals = new Array();
+ if (!obj)
+ return incrementals;
+ var children = obj.childNodes;
+ for (var i = 0; i < children.length; i++) {
+ var child = children[i];
+ if (hasClass(child, 'incremental')) {
+ if (child.nodeName == 'OL' || child.nodeName == 'UL') {
+ removeClass(child, 'incremental');
+ for (var j = 0; j < child.childNodes.length; j++) {
+ if (child.childNodes[j].nodeType == 1) {
+ addClass(child.childNodes[j], 'incremental');
+ }
+ }
+ } else {
+ incrementals[incrementals.length] = child;
+ removeClass(child,'incremental');
+ }
+ }
+ if (hasClass(child, 'show-first')) {
+ if (child.nodeName == 'OL' || child.nodeName == 'UL') {
+ removeClass(child, 'show-first');
+ if (child.childNodes[isGe].nodeType == 1) {
+ removeClass(child.childNodes[isGe], 'incremental');
+ }
+ } else {
+ incrementals[incrementals.length] = child;
+ }
+ }
+ incrementals = incrementals.concat(getIncrementals(child));
+ }
+ return incrementals;
+}
+
+function createIncrementals() {
+ var incrementals = new Array();
+ for (var i = 0; i < smax; i++) {
+ incrementals[i] = getIncrementals(document.getElementById('slide'+i));
+ }
+ return incrementals;
+}
+
+function defaultCheck() {
+ var allMetas = document.getElementsByTagName('meta');
+ for (var i = 0; i< allMetas.length; i++) {
+ if (allMetas[i].name == 'defaultView') {
+ defaultView = allMetas[i].content;
+ }
+ if (allMetas[i].name == 'controlVis') {
+ controlVis = allMetas[i].content;
+ }
+ }
+}
+
+// Key trap fix, new function body for trap()
+function trap(e) {
+ if (!e) {
+ e = event;
+ e.which = e.keyCode;
+ }
+ try {
+ modifierKey = e.ctrlKey || e.altKey || e.metaKey;
+ }
+ catch(e) {
+ modifierKey = false;
+ }
+ return modifierKey || e.which == 0;
+}
+
+function startup() {
+ defaultCheck();
+ if (!isOp)
+ createControls();
+ slideLabel();
+ fixLinks();
+ externalLinks();
+ fontScale();
+ if (!isOp) {
+ notOperaFix();
+ incrementals = createIncrementals();
+ slideJump();
+ if (defaultView == 'outline') {
+ toggle();
+ }
+ document.onkeyup = keys;
+ document.onkeypress = trap;
+ document.onclick = clicker;
+ }
+}
+
+window.onload = startup;
+window.onresize = function(){setTimeout('fontScale()', 50);}
\ No newline at end of file
diff --git a/presentation/layouts/presentation.txt b/presentation/layouts/presentation.txt
new file mode 100644
index 0000000..7d83933
--- /dev/null
+++ b/presentation/layouts/presentation.txt
@@ -0,0 +1,43 @@
+---
+extension: html
+filter:
+ - erb
+---
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
+ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en-us">
+<head>
+ <meta http-equiv="content-type" content="text/html; charset=utf-8" />
+ <title><%= h(@page.title) %></title>
+ <meta name="author" content="<%= h(@page.author) %>" />
+ <meta name="company" content="<%= h(@page.company) %>" />
+
+ <!-- configuration parameters -->
+ <meta name="defaultView" content="slideshow" />
+ <meta name="controlVis" content="hidden" />
+
+ <link rel="stylesheet" href="/presentation/s5/slides.css" type="text/css" media="projection" id="slideProj" />
+ <link rel="stylesheet" href="/presentation/s5/outline.css" type="text/css" media="screen" id="outlineStyle" />
+ <link rel="stylesheet" href="/css/uv/twilight.css" type="text/css" media="screen, projection" />
+
+ <!-- S5 JS -->
+ <script src="/presentation/s5/slides.js" type="text/javascript"></script>
+</head>
+<body>
+
+<div class="layout">
+ <div id="controls"><!-- DO NOT EDIT --></div>
+ <div id="currentSlide"><!-- DO NOT EDIT --></div>
+ <div id="header"></div>
+ <div id="footer">
+ <h2>Copyright © <%= h(@page.copyright) %></h2>
+ </div>
+</div>
+
+<div class="presentation">
+ <%= @content %>
+</div>
+
+</body>
+</html>
diff --git a/presentation/templates/_code_partial.erb b/presentation/templates/_code_partial.erb
new file mode 100644
index 0000000..bb8dc6c
--- /dev/null
+++ b/presentation/templates/_code_partial.erb
@@ -0,0 +1,13 @@
+---
+filter: erb
+---
+<%% uv :lang => 'ruby', :line_numbers => false, :theme => 'twilight' do -%>
+# This is a sample of Ruby code
+#
+class Object
+ def returning( obj, &block )
+ block.call obj
+ return obj
+ end
+end
+<%% end -%>
diff --git a/presentation/templates/presentation.erb b/presentation/templates/presentation.erb
new file mode 100644
index 0000000..b554221
--- /dev/null
+++ b/presentation/templates/presentation.erb
@@ -0,0 +1,40 @@
+---
+title: <%= title %>
+created_at: <%= Time.now.to_y %>
+author: You
+company: Company
+copyright: Creative Commons
+filter:
+ - erb
+ - textile
+ - slides
+layout: presentation
+---
+h1. Presentation Title
+
+Clever introductory text that will grab the audience's attention.
+
+
+h1. Title of the First Slide
+
+A little more build up before really getting into the meat of it.
+
+
+h1. Title of the Second Slide
+
+Finally, some code!
+
+<%% uv :lang => 'ruby', :line_numbers => false do -%>
+class EnglishMajor
+ def supercilious
+ 'behaving or looking as though one thinks one is superior to others'
+ end
+end
+<%% end -%>
+
+
+h1. The Final Slide
+
+And that about sums it up!
+
+Thanks for visiting
|
pc2/liftracc
|
1cdfca41a11fd5fa5a661767e6a0aea176aa379d
|
modifications for linpack testing
|
diff --git a/benchmarks/CMakeLists.txt b/benchmarks/CMakeLists.txt
index 26dcee3..d5949f6 100644
--- a/benchmarks/CMakeLists.txt
+++ b/benchmarks/CMakeLists.txt
@@ -1,67 +1,77 @@
cmake_minimum_required(VERSION 2.6.4)
set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${CMAKE_CURRENT_SOURCE_DIR}/cmake/modules)
project(benchmarks)
find_package(LIFTRACC REQUIRED)
include(${LIFTRACC_USE_FILE})
find_package(BLAS REQUIRED)
find_package(CBLAS REQUIRED)
find_package(Goto2)
include_directories(
${BLAS_INCLUDE_DIRS}
${CBLAS_INCLUDE_DIRS}
${GOTO2_INCLUDE_DIRS}
)
link_directories(
${BLAS_LIBRARY_DIR}
${CBLAS_LIBRARY_DIR}
${GOTO2_LIBRARY_DIR}
)
add_executable(linpack-new
${PROJECT_SOURCE_DIR}/src/linpack-new.c
)
target_link_libraries(linpack-new
m
)
add_executable(linpack-new-mod
${PROJECT_SOURCE_DIR}/src/linpack-new-mod.c
)
target_link_libraries(linpack-new-mod
m
)
add_executable(linpack-liftracc
${PROJECT_SOURCE_DIR}/src/linpack-liftracc.c
)
target_link_libraries(linpack-liftracc
liftracc
- cblas
- blas
)
+add_executable(linpack-testing
+ ${PROJECT_SOURCE_DIR}/src/linpack-testing.c
+)
+
+target_link_libraries(linpack-testing
+ liftracc
+)
+
+set(LIFTRACC_TESTING_SELECT "cblas" CACHE STRING "Options: cblas, liftracc.")
+string(TOUPPER "${LIFTRACC_TESTING_SELECT}" SELECT_VALUE)
+add_definitions(-D_SELECT_${SELECT_VALUE}_)
+
add_custom_command(
TARGET linpack-liftracc POST_BUILD
COMMAND ${CMAKE_COMMAND} -E copy_if_different
${PROJECT_SOURCE_DIR}/src/linpack-liftracc.sh
${PROJECT_BINARY_DIR}/linpack-liftracc.sh
COMMENT "copy linpack-liftracc.sh"
)
add_executable(linpack-cblas
${PROJECT_SOURCE_DIR}/src/linpack-cblas.c
)
target_link_libraries(linpack-cblas
cblas
blas
)
diff --git a/benchmarks/profiling/plot.py b/benchmarks/profiling/plot.py
index 83578c3..0829c1d 100755
--- a/benchmarks/profiling/plot.py
+++ b/benchmarks/profiling/plot.py
@@ -1,128 +1,140 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from matplotlib import *
use('PDF')
rcParams['text.usetex']=True
rcParams['text.latex.unicode']=True
rcParams['font.family']='serif'
import csv
import sys
import numpy as npy
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
import pylab
from math import sqrt
from decimal import Decimal as d
class tps:
calc = d(2261000000)
av = d(2268881244)
class DataClass:
def __init__(self):
self.label = r'no\_label'
self.sym = '-'
self.data_dict = {}
self.data_count_dict = {}
self.xrange = []
self.data = []
def count(list):
return d(len(list))
def calc_mean(list):
return d(sum(list)/count(list))
def calc_confi(val, list):
n = count(list)
mean = calc_mean(list)
tmp = [ d((d(x) - mean)**2) for x in list ]
std_abw = d(d(1/n)*sum(tmp)).sqrt() # maximum like-lihood
std_err = d(std_abw / n.sqrt())
return val * std_err
def read_data(file_name, conv_sec, sym=None, label=None):
print "Processing", file_name
csv_file = csv.reader(open(file_name), delimiter = ' ', skipinitialspace = True)
dc = DataClass()
if sym: dc.sym=sym
if label: dc.label=label
av_error = 0
for row in csv_file:
if len(row) and not row[0].startswith('#'):
print row[0], row[6]
if dc.data_dict.has_key(int(row[0])):
old = dc.data_dict[int(row[0])]
else:
old = 0
if dc.data_count_dict.has_key(int(row[0])):
count = dc.data_count_dict[int(row[0])]
else:
count = 0
dc.data_dict[int(row[0])] = int((old*count)+int(row[0])/(count+1))
dc.data_count_dict[int(row[0])] = count+1
for key in sorted(dc.data_dict.keys()):
dc.xrange.append(d(key))
dc.data.append(d(dc.data_dict[key]))
#for row in csv_file:
# if row[0].find("measuring_error") > -1:
# num_row = [ d(x) for x in row[3:] ]
# av_error = calc_mean(num_row)
# av_confi = calc_confi(d("1.96"), num_row)
# #print "Average Error:", av_error, "(", av_error-av_confi, ",", av_error+av_confi, ")"
# break
#for row in csv_file:
# if row[0].find("measuring_error") == -1:
# num_row = [ d(x) for x in row ]
# num_row[3:] = [ d(x-av_error) for x in num_row[3:]]
# num_row_sec = [ d((x-av_error)/d(conv_sec)) for x in num_row[3:]]
# dc.xrange.append(2**num_row[0])
# dc.data_tks.append(num_row[3:])
# dc.mean_tks.append(calc_mean(num_row[3:]))
# dc.confi_tks.append(calc_confi(d("1.96"), num_row[3:]))
# dc.data_sec.append(num_row_sec)
# dc.mean_sec.append(calc_mean(num_row_sec))
# dc.confi_sec.append(calc_confi(d("1.96"), num_row_sec))
return dc
def plot_graph(filename, data, title, x_label, y_label, x_lim=None, y_lim=None):
print "Plotting to", filename
pylab.figure()
for d in data:
pylab.plot(d.xrange, d.data, d.sym, ms=5, label=d.label, linewidth=1)
#pylab.errorbar(d.xrange, d.mean_sec, d.confi_sec, label=d.label, xerr=None,
# fmt=d.sym, elinewidth=3, ms=5, capsize=6)
pylab.legend(loc=0)
pylab.xlabel(x_label, fontsize=12)
pylab.ylabel(y_label, fontsize=12)
pylab.xscale('log', basex=2)
pylab.yscale('log', basey=10)
if x_lim: pylab.xlim(x_lim)
if y_lim: pylab.ylim(y_lim)
pylab.title(title, fontsize=12)
pylab.grid('on', '.')
pylab.savefig(filename)
if __name__ == "__main__":
lpn_new = read_data('linpack_new_200-4096.txt', tps.av, sym='-o', label=r'lpn\_new')
lpn_mod = read_data('linpack_new_mod_16-16384.txt', tps.av, sym='-s', label=r'lpn\_mod')
lpl_atl = read_data('linpack_liftracc_atlas_16-16384.txt', tps.av, sym='-o', label=r'lpl\_atl')
lpl_cbl = read_data('linpack_liftracc_cblas_16-16384.txt', tps.av, sym='->', label=r'lpl\_cbl')
lpl_cle = read_data('linpack_liftracc_clear_16-16384.txt', tps.av, sym='-D', label=r'lpl\_cle')
lpl_cub = read_data('linpack_liftracc_cublas_16-16384.txt', tps.av, sym='-v', label=r'lpl\_cub')
lpl_go2 = read_data('linpack_liftracc_goto2_16-16384.txt', tps.av, sym='-s', label=r'lpl\_go2')
plot_graph('test',
[lpn_new, lpn_mod, lpl_atl, lpl_cbl, lpl_cle, lpl_cub, lpl_go2],
r'Test',
r'Dimension [n]',
r'KFLOPS', x_lim=(2**3,2**15)
)
+ nlp_cblas = read_data('new_linpack_cblas.txt', tps.av, sym='-o', label=r'nlp\_cblas')
+ nlp_pre = read_data('new_linpack_ldpreload.txt', tps.av, sym='-s', label=r'nlp\_pre')
+ nlp_lift = read_data('new_linpack_liftracc.txt', tps.av, sym='-o', label=r'nlp\_lift')
+ nlp_new = read_data('new_linpack_new.txt', tps.av, sym='->', label=r'nlp\_new')
+
+ plot_graph('test2',
+ [nlp_cblas, nlp_pre, nlp_lift, nlp_new],
+ r'Test',
+ r'Dimension [n]',
+ r'KFLOPS', x_lim=(2**3,2**15)
+ )
+
diff --git a/benchmarks/src/linpack-testing.c b/benchmarks/src/linpack-testing.c
new file mode 100644
index 0000000..04d1d8e
--- /dev/null
+++ b/benchmarks/src/linpack-testing.c
@@ -0,0 +1,277 @@
+/*
+**
+** LINPACK.C Linpack benchmark, calculates FLOPS.
+** (FLoating Point Operations Per Second)
+**
+** Translated to C by Bonnie Toy 5/88
+**
+** Modified by Will Menninger, 10/93, with these features:
+** (modified on 2/25/94 to fix a problem with daxpy for
+** unequal increments or equal increments not equal to 1.
+** Jack Dongarra)
+**
+** Modified by Manuel Niekamp <niekma@upb.de>
+** (modified on 19.11.2010)
+**
+** To compile:
+** gcc -O3 -I<liftracc_incdir> -L<liftracc_libdir> -lliftracc -o linpack linpack.c
+**
+*/
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+
+#define ZERO 0.0e0
+#define ONE 1.0e0
+
+/* CBLAS selected */
+#if defined(_SELECT_CBLAS_)
+
+#include "cblas.h"
+const char *info_str = "cblas version";
+#define call_idamax cblas_idamax
+#define call_dscal cblas_dscal
+#define call_daxpy cblas_daxpy
+#define call_ddot cblas_ddot
+
+/* LIFTRACC selected */
+#elif defined(_SELECT_LIFTRACC_)
+
+#include "liftracc.h"
+const char *info_str = "liftracc version";
+#define call_idamax liftracc_idamax
+#define call_dscal liftracc_dscal
+#define call_daxpy liftracc_daxpy
+#define call_ddot liftracc_ddot
+
+/* nothing selected */
+#else
+
+#error "No compiler option -D_SELECT_(CBLAS|LIFTRACC)_ found."
+#define call_idamax no_idamax
+#define call_dscal no_dscal
+#define call_daxpy no_daxpy
+#define call_ddot no_ddot
+
+#endif
+
+static double linpack_dyn(long nreps, int arsize);
+static void matgen_dyn(double *a, int lda, int n, double *b, double *norma);
+static void dgefa_dyn(double *a, int lda, int n, int *ipvt, int *info);
+static void dgesl_dyn(double *a, int lda, int n, int *ipvt, double *b, int job);
+static double second(void);
+
+static void print_mempool(void *mempool, int ar2dsize, int arsize, int intsize);
+
+static void *mempool;
+
+#define MAX_DIM 16384
+
+int main(void)
+{
+ char buf[80];
+ int arsize;
+ long arsize2d, memreq, nreps;
+ size_t malloc_arg;
+
+ printf("\n\nUsing %s.\n\n", info_str);
+ printf("Average performance:\n");
+ printf("N Reps Time(s) DGEFA DGESL OVERHEAD KFLOPS\n");
+ printf("------------------------------------------\n");
+
+ for (arsize=16; arsize<=MAX_DIM; arsize*=2) {
+ arsize/=2;
+ arsize*=2;
+ arsize2d = (long)arsize*(long)arsize;
+ memreq=arsize2d*sizeof(double)+(long)arsize*sizeof(double)+(long)arsize*sizeof(int);
+ malloc_arg=(size_t)memreq;
+ if (malloc_arg!=memreq || (mempool=malloc(malloc_arg))==NULL) {
+ printf("Not enough memory available for given array size.\n\n");
+ return 1;
+ }
+ nreps=1;
+ while (linpack_dyn(nreps, arsize)<10.)
+ nreps*=2;
+ /* print mempool array */
+ print_mempool(mempool, arsize2d*sizeof(double), (long)arsize*sizeof(double), (long)arsize*sizeof(int));
+ free(mempool);
+ }
+}
+
+static double linpack_dyn(long nreps, int arsize)
+{
+ double *a, *b;
+ double norma, t1, kflops, tdgesl, tdgefa, totalt, toverhead, ops;
+ int *ipvt, n, info, lda;
+ long i, arsize2d;
+
+ lda = arsize;
+ n = arsize/2;
+ arsize2d = (long)arsize*(long)arsize;
+ ops=((2.0*n*n*n)/3.0+2.0*n*n);
+ a=(double *)mempool;
+ b=a+arsize2d;
+ ipvt=(int *)&b[arsize];
+ tdgesl=0;
+ tdgefa=0;
+ totalt=second();
+ for (i=0; i<nreps; i++) {
+ matgen_dyn(a, lda, n, b, &norma);
+ t1 = second();
+ dgefa_dyn(a, lda, n, ipvt, &info);
+ tdgefa += second()-t1;
+ t1 = second();
+ dgesl_dyn(a, lda, n, ipvt, b, 0);
+ tdgesl += second()-t1;
+ }
+ totalt=second()-totalt;
+ if (totalt<0.5 || tdgefa+tdgesl<0.2)
+ return(0.);
+ kflops=2.*nreps*ops/(1000.*(tdgefa+tdgesl));
+ toverhead=totalt-tdgefa-tdgesl;
+ if (tdgefa<0.) tdgefa=0.;
+ if (tdgesl<0.) tdgesl=0.;
+ if (toverhead<0.) toverhead=0.;
+ printf("%d %ld %.2f %.2f%% %.2f%% %.2f%% %.3f\n",
+ arsize, nreps, totalt, 100.*tdgefa/totalt,
+ 100.*tdgesl/totalt, 100.*toverhead/totalt,
+ kflops);
+
+ return(totalt);
+}
+
+static void matgen_dyn(double *a, int lda, int n, double *b, double *norma)
+{
+ int init, i, j;
+
+ init = 1325;
+ *norma = 0.0;
+ for (j = 0; j < n; j++)
+ for (i = 0; i < n; i++) {
+ init = (int)((long)3125*(long)init % 65536L);
+ a[lda*j+i] = (init - 32768.0)/16384.0;
+ *norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
+ }
+ for (i = 0; i < n; i++)
+ b[i] = 0.0;
+ for (j = 0; j < n; j++)
+ for (i = 0; i < n; i++)
+ b[i] = b[i] + a[lda*j+i];
+
+ printf("Matrix A:\n");
+ for (j=0; j<n; j++)
+ for (i=0; i<n; i++)
+ printf("%f ", a[lda*j+i]);
+ printf("\n");
+
+ printf("Matrix B:\n");
+ for (j=0; j<n; j++)
+ for (i=0; i<n; i++)
+ printf("%f ", b[lda*j+i]);
+ printf("\n");
+}
+
+static void dgefa_dyn(double *a, int lda, int n, int *ipvt, int *info)
+{
+ double t;
+ int j, k, kp1, l, nm1;
+
+ /* gaussian elimination with partial pivoting */
+ *info = 0;
+ nm1 = n - 1;
+ if (nm1 >= 0)
+ for (k = 0; k < nm1; k++) {
+ kp1 = k + 1;
+ /* find l = pivot index */
+ l = call_idamax(n-k,&a[lda*k+k],1) + k;
+ ipvt[k] = l;
+ /* zero pivot implies this column already triangularized */
+ if (a[lda*k+l] != ZERO) {
+ /* interchange if necessary */
+ if (l != k) {
+ t = a[lda*k+l];
+ a[lda*k+l] = a[lda*k+k];
+ a[lda*k+k] = t;
+ }
+ /* compute multipliers */
+ t = -ONE/a[lda*k+k];
+ call_dscal(n-(k+1),t,&a[lda*k+k+1],1);
+ /* row elimination with column indexing */
+ for (j = kp1; j < n; j++) {
+ t = a[lda*j+l];
+ if (l != k) {
+ a[lda*j+l] = a[lda*j+k];
+ a[lda*j+k] = t;
+ }
+ call_daxpy(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
+ }
+ } else
+ (*info) = k;
+ }
+ ipvt[n-1] = n-1;
+ if (a[lda*(n-1)+(n-1)] == ZERO)
+ (*info) = n-1;
+}
+
+static void dgesl_dyn(double *a, int lda, int n, int *ipvt, double *b, int job)
+{
+ double t;
+ int k, kb, l, nm1;
+
+ nm1 = n - 1;
+ if (job == 0) {
+ /* job = 0 , solve a * x = b */
+ /* first solve l*y = b */
+ if (nm1 >= 1)
+ for (k = 0; k < nm1; k++) {
+ l = ipvt[k];
+ t = b[l];
+ if (l != k) {
+ b[l] = b[k];
+ b[k] = t;
+ }
+ call_daxpy(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1);
+ }
+ /* now solve u*x = y */
+ for (kb = 0; kb < n; kb++) {
+ k = n - (kb + 1);
+ b[k] = b[k]/a[lda*k+k];
+ t = -b[k];
+ call_daxpy(k,t,&a[lda*k+0],1,&b[0],1);
+ }
+ } else {
+ /* job = nonzero, solve trans(a) * x = b */
+ /* first solve trans(u)*y = b */
+ for (k = 0; k < n; k++) {
+ t = call_ddot(k,&a[lda*k+0],1,&b[0],1);
+ b[k] = (b[k] - t)/a[lda*k+k];
+ }
+ /* now solve trans(l)*x = y */
+ if (nm1 >= 1)
+ for (kb = 1; kb < nm1; kb++) {
+ k = n - (kb+1);
+ b[k] = b[k] + call_ddot(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
+ l = ipvt[k];
+ if (l != k) {
+ t = b[l];
+ b[l] = b[k];
+ b[k] = t;
+ }
+ }
+ }
+}
+
+static double second(void)
+{
+ return ((double)((double)clock()/(double)CLOCKS_PER_SEC));
+}
+
+static void print_mempool(void *mempool, int ar2dsize, int arsize, int intsize)
+{
+ /* TODO */
+ double *a = (double*)mempool;
+ double *b = (double*)a+ar2dsize;
+ double *c = (double*)b+arsize;
+}
+
diff --git a/library/src/liftracc_testing.c b/library/src/liftracc_testing.c
index f373f1e..703faaa 100644
--- a/library/src/liftracc_testing.c
+++ b/library/src/liftracc_testing.c
@@ -1,417 +1,434 @@
/**
* @file liftracc_testing.c
* @brief C file to test new functionality
*
* @author Manuel Niekamp <niekma@upb.de>
* @version 0.1
*
* This file implements the main functionality of the library.
* It is intended to use this file for testing purpose.
* If the here implemented code works and is tested it can
* be easily transfered to the xsl file to auto generate the
* complete library.
*/
#include "liftracc.h"
#include "liftracc_logging.h"
#include "liftracc_selector.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
extern profiling_data_t liftracc_function_profiling_data[];
#endif
liftracc_selector_problem_info_t pinfo = { };
float liftracc_sdsdot(const int n, const float alpha, const float *x,
const int incx, const float *y, const int incy)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_SDSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
float (*liftracc_plugin_func)();
float ret = 0.0;
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_SDSDOT, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_sdsdot");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
ret = (*liftracc_plugin_func)(n, alpha, x, incx, y, incy);
} else
ERROR("liftracc_sdsdot not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_SDSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
return ret;
}
float liftracc_sdsdot_(const int *n, const float *alpha, const float *x,
const int *incx, const float *y, const int *incy)
{
return liftracc_sdsdot(*n, *alpha, x, *incx, y, *incy);
}
double liftracc_dsdot(const int n, const float *x, const int incx, const float *y, const int incy)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DSDOT]));
#endif // _LIFTRACC_PROFILING_
double (*liftracc_plugin_func)();
double ret = 0.0;
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_DSDOT, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_dsdot");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
ret = (*liftracc_plugin_func)(n, x, incx, y, incy);
} else
ERROR("liftracc_dsdot not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
return ret;
}
double liftracc_dsdot_(const int *n, const float *x, const int *incx,
const float *y, const int *incy)
{
return liftracc_dsdot(*n, x, *incx, y, *incy);
}
float liftracc_sdot(const int n, const float *x, const int incx,
const float *y, const int incy)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_SDOT]));
#endif /* _LIFTRACC_PROFILING_ */
float (*liftracc_plugin_func)();
float ret = 0.0;
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_SDOT, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_sdot");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
ret = (*liftracc_plugin_func)(n, x, incx, y, incy);
} else
ERROR("liftracc_sdot not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_SDOT]));
#endif /* _LIFTRACC_PROFILING_ */
return ret;
}
float liftracc_sdot_(const int *n, const float *x, const int *incx,
const float *y, const int *incy)
{
return liftracc_sdot(*n, x, *incx, y, *incy);
}
liftracc_index_t liftracc_idamax(const int n, const double *x, const int incx)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
liftracc_index_t (*liftracc_plugin_func)();
liftracc_index_t ret = 0.0;
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_IDAMAX, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_idamax");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
ret = (*liftracc_plugin_func)(n, x, incx);
} else
ERROR("liftracc_idamax not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
return ret;
}
liftracc_index_t liftracc_idamax_(const int *n, const double *x, const int *incx)
{
return liftracc_idamax(*n, x, *incx);
}
void liftracc_dscal(const int n, const double alpha, double * x, const int incx)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
void (*liftracc_plugin_func)();
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_DSCAL, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_dscal");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
(*liftracc_plugin_func)(n, alpha, x, incx);
} else
ERROR("liftracc_dscal not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
}
void liftracc_dscal_(const int *n, const double *alpha, double *x, const int *incx)
{
liftracc_dscal(*n, *alpha, x, *incx);
}
void liftracc_daxpy(const int n, const double alpha, const double *x,
const int incx, double *y, const int incy)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
void (*liftracc_plugin_func)();
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_DAXPY, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_daxpy");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
(*liftracc_plugin_func)(n, alpha, x, incx, y, incy);
} else
ERROR("liftracc_daxpy not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
}
void liftracc_daxpy_(const int *n, const double *alpha, const double *x,
const int *incx, double *y, const int *incy)
{
liftracc_daxpy(*n, *alpha, x, *incx, y, *incy);
}
double liftracc_ddot(const int n, const double *x, const int incx,
const double *y, const int incy)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
double (*liftracc_plugin_func)();
double ret = 0.0;
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = n;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_DDOT, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_ddot");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
ret = (*liftracc_plugin_func)(n, x, incx, y, incy);
} else
ERROR("liftracc_ddot not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
return ret;
}
double liftracc_ddot_(const int *n, const double *x, const int *incx,
const double *y, const int *incy)
{
return liftracc_ddot(*n, x, *incx, y, *incy);
}
void liftracc_dgemm(const liftracc_order_t order,
const liftracc_transpose_t transa,
const liftracc_transpose_t transb,
const int m,
const int n,
const int k,
const double alpha,
const double *a,
const int lda,
const double *b,
const int ldb,
const double beta,
double *c,
const int ldc)
{
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_start(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
+ printf("LIFTRACC_DGEMM_USED\n");
+
void (*liftracc_plugin_func)();
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_start(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_SELECTOR_NEW_
pinfo.info1 = m;
*(void **) (&liftracc_plugin_func) = liftracc_selector_select(SELECT_DGEMM, &pinfo);
#else
*(void **) (&liftracc_plugin_func) = liftracc_selector_select("liftracc_plugin_dgemm");
#endif /* _LIFTRACC_SELECTOR_NEW_ */
#if _LIFTRACC_PROFILING_ == 2
liftracc_function_timing_stop(&(liftracc_profiling_data[SELECT_CALL]));
#endif /* _LIFTRACC_PROFILING_ */
if (liftracc_plugin_func != 0) {
(*liftracc_plugin_func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
} else
ERROR("liftracc_dgemm not executed");
#if _LIFTRACC_PROFILING_ == 1
liftracc_function_timing_stop(&(liftracc_function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
}
void liftracc_dgemm_(const char *transa,
const char *transb,
const int *m,
const int *n,
const int *k,
const double *alpha,
const double *a,
const int *lda,
const double *b,
const int *ldb,
const double *beta,
double *c,
const int *ldc)
{
liftracc_transpose_t ta, tb;
switch (*transa) {
case 'N':
case 'n': ta = liftracc_no_trans; break;
case 'T':
case 't': ta = liftracc_trans; break;
case 'C':
case 'c': ta = liftracc_conj_trans; break;
default: ta = liftracc_no_trans; break;
}
switch (*transb) {
case 'N':
case 'n': tb = liftracc_no_trans; break;
case 'T':
case 't': tb = liftracc_trans; break;
case 'C':
case 'c': tb = liftracc_conj_trans; break;
default: tb = liftracc_no_trans; break;
}
liftracc_dgemm(liftracc_col_major, ta, tb,
*m, *n, *k,
*alpha, a, *lda,
b, *ldb, *beta,
c, *ldc);
}
-/* CBLAS interface */
-/*
-__typeof__ (liftracc_dgemm_) cblas_dgemm __attribute__ ((alias("liftracc_dgemm")));
-*/
-
-/* MKL interface */
-/*
-__typeof__ (liftracc_dgemm_) dgemm_ __attribute__ ((alias("liftracc_dgemm_")));
-*/
+#ifdef _LIFTRACC_CBLAS_INTERFACE_
+__typeof__ (liftracc_sdsdot) cblas_sdsdot __attribute__ ((alias("liftracc_sdsdot")));
+__typeof__ (liftracc_dsdot) cblas_dsdot __attribute__ ((alias("liftracc_dsdot")));
+__typeof__ (liftracc_sdot) cblas_sdot __attribute__ ((alias("liftracc_sdot")));
+__typeof__ (liftracc_idamax) cblas_idamax __attribute__ ((alias("liftracc_idamax")));
+__typeof__ (liftracc_dscal) cblas_dscal __attribute__ ((alias("liftracc_dscal")));
+__typeof__ (liftracc_daxpy) cblas_daxpy __attribute__ ((alias("liftracc_daxpy")));
+__typeof__ (liftracc_ddot) cblas_ddot __attribute__ ((alias("liftracc_ddot")));
+__typeof__ (liftracc_dgemm) cblas_dgemm __attribute__ ((alias("liftracc_dgemm")));
+
+__typeof__ (liftracc_sdsdot) f2c_sdsdot __attribute__ ((alias("liftracc_sdsdot")));
+__typeof__ (liftracc_dsdot) f2c_dsdot __attribute__ ((alias("liftracc_dsdot")));
+__typeof__ (liftracc_sdot) f2c_sdot __attribute__ ((alias("liftracc_sdot")));
+__typeof__ (liftracc_idamax) f2c_idamax __attribute__ ((alias("liftracc_idamax")));
+__typeof__ (liftracc_dscal) f2c_dscal __attribute__ ((alias("liftracc_dscal")));
+__typeof__ (liftracc_daxpy) f2c_daxpy __attribute__ ((alias("liftracc_daxpy")));
+__typeof__ (liftracc_ddot) f2c_ddot __attribute__ ((alias("liftracc_ddot")));
+__typeof__ (liftracc_dgemm) f2c_dgemm __attribute__ ((alias("liftracc_dgemm")));
+#endif // _LIFTRACC_CBLAS_INTERFACE_
+
+#ifdef _LIFTRACC_MKL_INTERFACE_
+__typeof__ (liftracc_dgemm_) DGEMM __attribute__ ((alias("liftracc_dgemm_")));
+__typeof__ (liftracc_dgemm_) dgemm __attribute__ ((alias("liftracc_dgemm_")));
+#endif // _LIFTRACC_MKL_INTERFACE_
|
pc2/liftracc
|
fcdaec195e40740db478170d03eddf4f7c3f0a05
|
- fixed some bugs
|
diff --git a/benchmarks/src/linpack-cblas.c b/benchmarks/src/linpack-cblas.c
index 85f747b..c03c003 100644
--- a/benchmarks/src/linpack-cblas.c
+++ b/benchmarks/src/linpack-cblas.c
@@ -1,341 +1,347 @@
/*
**
** LINPACK.C Linpack benchmark, calculates FLOPS.
** (FLoating Point Operations Per Second)
**
** Translated to C by Bonnie Toy 5/88
**
** Modified by Will Menninger, 10/93, with these features:
** (modified on 2/25/94 to fix a problem with daxpy for
** unequal increments or equal increments not equal to 1.
** Jack Dongarra)
**
** Modified by Manuel Niekamp <niekma@upb.de>
** (modified on 06.02.2010 to direct calls through
** liftracc wrapper-library)
**
** To compile:
** gcc -O3 -I<liftracc_incdir> -L<liftracc_libdir> -lliftracc -o linpack linpack.c
**
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define ZERO 0.0e0
#define ONE 1.0e0
#include "cblas.h"
+/* only testing */
+#define cblas_idamax inner_cblas_idamax
+#define cblas_dscal inner_cblas_dscal
+#define cblas_daxpy inner_cblas_daxpy
+#define cblas_ddot inner_cblas_ddot
+
static double linpack_dyn(long nreps, int arsize);
static void matgen_dyn(double *a, int lda, int n, double *b, double *norma);
static void dgefa_dyn(double *a, int lda, int n, int *ipvt, int *info);
static void dgesl_dyn(double *a, int lda, int n, int *ipvt, double *b, int job);
static double second(void);
static void *mempool;
-#define MAX_DIM 1024
+#define MAX_DIM 8192
int main(void)
{
char buf[80];
int arsize;
long arsize2d, memreq, nreps;
size_t malloc_arg;
printf("Average performance:\n\n");
printf("N Reps Time(s) DGEFA DGESL OVERHEAD KFLOPS\n");
printf("------------------------------------------\n");
- for (arsize=2; arsize<=MAX_DIM; arsize+=2) {
+ for (arsize=16; arsize<=MAX_DIM; arsize*=2) {
arsize/=2;
arsize*=2;
arsize2d = (long)arsize*(long)arsize;
memreq=arsize2d*sizeof(double)+(long)arsize*sizeof(double)+(long)arsize*sizeof(int);
malloc_arg=(size_t)memreq;
if (malloc_arg!=memreq || (mempool=malloc(malloc_arg))==NULL) {
printf("Not enough memory available for given array size.\n\n");
return 1;
}
nreps=1;
while (linpack_dyn(nreps, arsize)<10.)
nreps*=2;
free(mempool);
}
}
static double linpack_dyn(long nreps, int arsize)
{
double *a, *b;
double norma, t1, kflops, tdgesl, tdgefa, totalt, toverhead, ops;
int *ipvt, n, info, lda;
long i, arsize2d;
lda = arsize;
n = arsize/2;
arsize2d = (long)arsize*(long)arsize;
ops=((2.0*n*n*n)/3.0+2.0*n*n);
a=(double *)mempool;
b=a+arsize2d;
ipvt=(int *)&b[arsize];
tdgesl=0;
tdgefa=0;
totalt=second();
for (i=0; i<nreps; i++) {
matgen_dyn(a, lda, n, b, &norma);
t1 = second();
dgefa_dyn(a, lda, n, ipvt, &info);
tdgefa += second()-t1;
t1 = second();
dgesl_dyn(a, lda, n, ipvt, b, 0);
tdgesl += second()-t1;
}
totalt=second()-totalt;
if (totalt<0.5 || tdgefa+tdgesl<0.2)
return(0.);
kflops=2.*nreps*ops/(1000.*(tdgefa+tdgesl));
toverhead=totalt-tdgefa-tdgesl;
if (tdgefa<0.) tdgefa=0.;
if (tdgesl<0.) tdgesl=0.;
if (toverhead<0.) toverhead=0.;
printf("%d %ld %.2f %.2f%% %.2f%% %.2f%% %.3f\n",
arsize, nreps, totalt, 100.*tdgefa/totalt,
100.*tdgesl/totalt, 100.*toverhead/totalt,
kflops);
return(totalt);
}
/*
** For matgen,
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
*/
static void matgen_dyn(double *a, int lda, int n, double *b, double *norma)
{
int init, i, j;
init = 1325;
*norma = 0.0;
for (j = 0; j < n; j++)
for (i = 0; i < n; i++) {
init = (int)((long)3125*(long)init % 65536L);
a[lda*j+i] = (init - 32768.0)/16384.0;
*norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
}
for (i = 0; i < n; i++)
b[i] = 0.0;
for (j = 0; j < n; j++)
for (i = 0; i < n; i++)
b[i] = b[i] + a[lda*j+i];
}
/*
**
** DGEFA benchmark
**
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
**
** dgefa factors a double precision matrix by gaussian elimination.
**
** dgefa is usually called by dgeco, but it can be called
** directly with a saving in time if rcond is not needed.
** (time for dgeco) = (1 + 9/n)*(time for dgefa) .
**
** on entry
**
** a REAL precision[n][lda]
** the matrix to be factored.
**
** lda integer
** the leading dimension of the array a .
**
** n integer
** the order of the matrix a .
**
** on return
**
** a an upper triangular matrix and the multipliers
** which were used to obtain it.
** the factorization can be written a = l*u where
** l is a product of permutation and unit lower
** triangular matrices and u is upper triangular.
**
** ipvt integer[n]
** an integer vector of pivot indices.
**
** info integer
** = 0 normal value.
** = k if u[k][k] .eq. 0.0 . this is not an error
** condition for this subroutine, but it does
** indicate that dgesl or dgedi will divide by zero
** if called. use rcond in dgeco for a reliable
** indication of singularity.
**
** linpack. this version dated 08/14/78 .
** cleve moler, university of New Mexico, argonne national lab.
**
** functions
**
** blas daxpy, dscal, idamax
**
*/
static void dgefa_dyn(double *a, int lda, int n, int *ipvt, int *info)
{
double t;
int j, k, kp1, l, nm1;
/* gaussian elimination with partial pivoting */
*info = 0;
nm1 = n - 1;
if (nm1 >= 0)
for (k = 0; k < nm1; k++) {
kp1 = k + 1;
/* find l = pivot index */
l = cblas_idamax(n-k,&a[lda*k+k],1) + k;
ipvt[k] = l;
/* zero pivot implies this column already triangularized */
if (a[lda*k+l] != ZERO) {
/* interchange if necessary */
if (l != k) {
t = a[lda*k+l];
a[lda*k+l] = a[lda*k+k];
a[lda*k+k] = t;
}
/* compute multipliers */
t = -ONE/a[lda*k+k];
cblas_dscal(n-(k+1),t,&a[lda*k+k+1],1);
/* row elimination with column indexing */
for (j = kp1; j < n; j++) {
t = a[lda*j+l];
if (l != k) {
a[lda*j+l] = a[lda*j+k];
a[lda*j+k] = t;
}
cblas_daxpy(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
}
} else
(*info) = k;
}
ipvt[n-1] = n-1;
if (a[lda*(n-1)+(n-1)] == ZERO)
(*info) = n-1;
}
/*
**
** DGESL benchmark
**
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
**
** dgesl solves the double precision system
** a * x = b or trans(a) * x = b
** using the factors computed by dgeco or dgefa.
**
** on entry
**
** a double precision[n][lda]
** the output from dgeco or dgefa.
**
** lda integer
** the leading dimension of the array a .
**
** n integer
** the order of the matrix a .
**
** ipvt integer[n]
** the pivot vector from dgeco or dgefa.
**
** b double precision[n]
** the right hand side vector.
**
** job integer
** = 0 to solve a*x = b ,
** = nonzero to solve trans(a)*x = b where
** trans(a) is the transpose.
**
** on return
**
** b the solution vector x .
**
** error condition
**
** a division by zero will occur if the input factor contains a
** zero on the diagonal. technically this indicates singularity
** but it is often caused by improper arguments or improper
** setting of lda . it will not occur if the subroutines are
** called correctly and if dgeco has set rcond .gt. 0.0
** or dgefa has set info .eq. 0 .
**
** to compute inverse(a) * c where c is a matrix
** with p columns
** dgeco(a,lda,n,ipvt,rcond,z)
** if (!rcond is too small){
** for (j=0,j<p,j++)
** dgesl(a,lda,n,ipvt,c[j][0],0);
** }
**
** linpack. this version dated 08/14/78 .
** cleve moler, university of new mexico, argonne national lab.
**
** functions
**
** blas daxpy, ddot
*/
static void dgesl_dyn(double *a, int lda, int n, int *ipvt, double *b, int job)
{
double t;
int k, kb, l, nm1;
nm1 = n - 1;
if (job == 0) {
/* job = 0 , solve a * x = b */
/* first solve l*y = b */
if (nm1 >= 1)
for (k = 0; k < nm1; k++) {
l = ipvt[k];
t = b[l];
if (l != k) {
b[l] = b[k];
b[k] = t;
}
cblas_daxpy(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1);
}
/* now solve u*x = y */
for (kb = 0; kb < n; kb++) {
k = n - (kb + 1);
b[k] = b[k]/a[lda*k+k];
t = -b[k];
cblas_daxpy(k,t,&a[lda*k+0],1,&b[0],1);
}
} else {
/* job = nonzero, solve trans(a) * x = b */
/* first solve trans(u)*y = b */
for (k = 0; k < n; k++) {
t = cblas_ddot(k,&a[lda*k+0],1,&b[0],1);
b[k] = (b[k] - t)/a[lda*k+k];
}
/* now solve trans(l)*x = y */
if (nm1 >= 1)
for (kb = 1; kb < nm1; kb++) {
k = n - (kb+1);
b[k] = b[k] + cblas_ddot(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
l = ipvt[k];
if (l != k) {
t = b[l];
b[l] = b[k];
b[k] = t;
}
}
}
}
static double second(void)
{
return ((double)((double)clock()/(double)CLOCKS_PER_SEC));
}
diff --git a/benchmarks/src/linpack-new-mod.c b/benchmarks/src/linpack-new-mod.c
index 96453e6..20c16ea 100644
--- a/benchmarks/src/linpack-new-mod.c
+++ b/benchmarks/src/linpack-new-mod.c
@@ -1,597 +1,597 @@
/*
**
** LINPACK.C Linpack benchmark, calculates FLOPS.
** (FLoating Point Operations Per Second)
**
** Translated to C by Bonnie Toy 5/88
**
** Modified by Will Menninger, 10/93, with these features:
** (modified on 2/25/94 to fix a problem with daxpy for
** unequal increments or equal increments not equal to 1.
** Jack Dongarra)
**
** - Defaults to double precision.
** - Averages ROLLed and UNROLLed performance.
** - User selectable array sizes.
** - Automatically does enough repetitions to take at least 10 CPU seconds.
** - Prints machine precision.
** - ANSI prototyping.
**
** Modified by Manuel Niekamp <niekma@upb.de>
** (modified on 07.02.2010 run from dim 2 to
** MAX_DIM)
**
** To compile: cc -O -o linpack linpack.c -lm
**
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <float.h>
#define DP
#ifdef SP
#define ZERO 0.0
#define ONE 1.0
#define PREC "Single"
#define BASE10DIG FLT_DIG
typedef float REAL;
#endif
#ifdef DP
#define ZERO 0.0e0
#define ONE 1.0e0
#define PREC "Double"
#define BASE10DIG DBL_DIG
typedef double REAL;
#endif
static REAL linpack (long nreps,int arsize);
static void matgen (REAL *a,int lda,int n,REAL *b,REAL *norma);
static void dgefa (REAL *a,int lda,int n,int *ipvt,int *info,int roll);
static void dgesl (REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll);
static void daxpy_r (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
static REAL ddot_r (int n,REAL *dx,int incx,REAL *dy,int incy);
static void dscal_r (int n,REAL da,REAL *dx,int incx);
static void daxpy_ur (int n,REAL da,REAL *dx,int incx,REAL *dy,int incy);
static REAL ddot_ur (int n,REAL *dx,int incx,REAL *dy,int incy);
static void dscal_ur (int n,REAL da,REAL *dx,int incx);
static int idamax (int n,REAL *dx,int incx);
static REAL second (void);
static void *mempool;
#define MAX_DIM 16384
int main(void)
{
char buf[80];
int arsize;
long arsize2d,memreq,nreps;
size_t malloc_arg;
printf("\n\nLINPACK benchmark, %s precision.\n",PREC);
printf("Machine precision: %d digits.\n",BASE10DIG);
printf("Average rolled and unrolled performance:\n\n");
printf("N Reps Time(s) DGEFA DGESL OVERHEAD KFLOPS\n");
printf("------------------------------------------\n");
- for (arsize=8192; arsize<=MAX_DIM; arsize*=2) {
+ for (arsize=10; arsize<=MAX_DIM; arsize*=2) {
arsize/=2;
arsize*=2;
arsize2d = (long)arsize*(long)arsize;
memreq=arsize2d*sizeof(REAL)+(long)arsize*sizeof(REAL)+(long)arsize*sizeof(int);
malloc_arg=(size_t)memreq;
if (malloc_arg!=memreq || (mempool=malloc(malloc_arg))==NULL)
{
printf("Not enough memory available for given array size.\n\n");
continue;
}
nreps=1;
while (linpack(nreps,arsize)<10.)
nreps*=2;
free(mempool);
}
return 0;
}
static REAL linpack(long nreps,int arsize)
{
REAL *a,*b;
REAL norma,t1,kflops,tdgesl,tdgefa,totalt,toverhead,ops;
int *ipvt,n,info,lda;
long i,arsize2d;
lda = arsize;
n = arsize/2;
arsize2d = (long)arsize*(long)arsize;
ops=((2.0*n*n*n)/3.0+2.0*n*n);
a=(REAL *)mempool;
b=a+arsize2d;
ipvt=(int *)&b[arsize];
tdgesl=0;
tdgefa=0;
totalt=second();
for (i=0;i<nreps;i++)
{
matgen(a,lda,n,b,&norma);
t1 = second();
dgefa(a,lda,n,ipvt,&info,1);
tdgefa += second()-t1;
t1 = second();
dgesl(a,lda,n,ipvt,b,0,1);
tdgesl += second()-t1;
}
for (i=0;i<nreps;i++)
{
matgen(a,lda,n,b,&norma);
t1 = second();
dgefa(a,lda,n,ipvt,&info,0);
tdgefa += second()-t1;
t1 = second();
dgesl(a,lda,n,ipvt,b,0,0);
tdgesl += second()-t1;
}
totalt=second()-totalt;
if (totalt<0.5 || tdgefa+tdgesl<0.2)
return(0.);
kflops=2.*nreps*ops/(1000.*(tdgefa+tdgesl));
toverhead=totalt-tdgefa-tdgesl;
if (tdgefa<0.)
tdgefa=0.;
if (tdgesl<0.)
tdgesl=0.;
if (toverhead<0.)
toverhead=0.;
printf("%d %ld %.2f %.2f%% %.2f%% %.2f%% %.3f\n",
arsize, nreps, totalt, 100.*tdgefa/totalt,
100.*tdgesl/totalt, 100.*toverhead/totalt,
kflops);
return(totalt);
}
/*
** For matgen,
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
*/
static void matgen(REAL *a,int lda,int n,REAL *b,REAL *norma)
{
int init,i,j;
init = 1325;
*norma = 0.0;
for (j = 0; j < n; j++)
for (i = 0; i < n; i++)
{
init = (int)((long)3125*(long)init % 65536L);
a[lda*j+i] = (init - 32768.0)/16384.0;
*norma = (a[lda*j+i] > *norma) ? a[lda*j+i] : *norma;
}
for (i = 0; i < n; i++)
b[i] = 0.0;
for (j = 0; j < n; j++)
for (i = 0; i < n; i++)
b[i] = b[i] + a[lda*j+i];
}
/*
**
** DGEFA benchmark
**
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
**
** dgefa factors a double precision matrix by gaussian elimination.
**
** dgefa is usually called by dgeco, but it can be called
** directly with a saving in time if rcond is not needed.
** (time for dgeco) = (1 + 9/n)*(time for dgefa) .
**
** on entry
**
** a REAL precision[n][lda]
** the matrix to be factored.
**
** lda integer
** the leading dimension of the array a .
**
** n integer
** the order of the matrix a .
**
** on return
**
** a an upper triangular matrix and the multipliers
** which were used to obtain it.
** the factorization can be written a = l*u where
** l is a product of permutation and unit lower
** triangular matrices and u is upper triangular.
**
** ipvt integer[n]
** an integer vector of pivot indices.
**
** info integer
** = 0 normal value.
** = k if u[k][k] .eq. 0.0 . this is not an error
** condition for this subroutine, but it does
** indicate that dgesl or dgedi will divide by zero
** if called. use rcond in dgeco for a reliable
** indication of singularity.
**
** linpack. this version dated 08/14/78 .
** cleve moler, university of New Mexico, argonne national lab.
**
** functions
**
** blas daxpy,dscal,idamax
**
*/
static void dgefa(REAL *a,int lda,int n,int *ipvt,int *info,int roll)
{
REAL t;
int idamax(),j,k,kp1,l,nm1;
/* gaussian elimination with partial pivoting */
if (roll)
{
*info = 0;
nm1 = n - 1;
if (nm1 >= 0)
for (k = 0; k < nm1; k++)
{
kp1 = k + 1;
/* find l = pivot index */
l = idamax(n-k,&a[lda*k+k],1) + k;
ipvt[k] = l;
/* zero pivot implies this column already
triangularized */
if (a[lda*k+l] != ZERO)
{
/* interchange if necessary */
if (l != k)
{
t = a[lda*k+l];
a[lda*k+l] = a[lda*k+k];
a[lda*k+k] = t;
}
/* compute multipliers */
t = -ONE/a[lda*k+k];
dscal_r(n-(k+1),t,&a[lda*k+k+1],1);
/* row elimination with column indexing */
for (j = kp1; j < n; j++)
{
t = a[lda*j+l];
if (l != k)
{
a[lda*j+l] = a[lda*j+k];
a[lda*j+k] = t;
}
daxpy_r(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
}
}
else
(*info) = k;
}
ipvt[n-1] = n-1;
if (a[lda*(n-1)+(n-1)] == ZERO)
(*info) = n-1;
}
else
{
*info = 0;
nm1 = n - 1;
if (nm1 >= 0)
for (k = 0; k < nm1; k++)
{
kp1 = k + 1;
/* find l = pivot index */
l = idamax(n-k,&a[lda*k+k],1) + k;
ipvt[k] = l;
/* zero pivot implies this column already
triangularized */
if (a[lda*k+l] != ZERO)
{
/* interchange if necessary */
if (l != k)
{
t = a[lda*k+l];
a[lda*k+l] = a[lda*k+k];
a[lda*k+k] = t;
}
/* compute multipliers */
t = -ONE/a[lda*k+k];
dscal_ur(n-(k+1),t,&a[lda*k+k+1],1);
/* row elimination with column indexing */
for (j = kp1; j < n; j++)
{
t = a[lda*j+l];
if (l != k)
{
a[lda*j+l] = a[lda*j+k];
a[lda*j+k] = t;
}
daxpy_ur(n-(k+1),t,&a[lda*k+k+1],1,&a[lda*j+k+1],1);
}
}
else
(*info) = k;
}
ipvt[n-1] = n-1;
if (a[lda*(n-1)+(n-1)] == ZERO)
(*info) = n-1;
}
}
/*
**
** DGESL benchmark
**
** We would like to declare a[][lda], but c does not allow it. In this
** function, references to a[i][j] are written a[lda*i+j].
**
** dgesl solves the double precision system
** a * x = b or trans(a) * x = b
** using the factors computed by dgeco or dgefa.
**
** on entry
**
** a double precision[n][lda]
** the output from dgeco or dgefa.
**
** lda integer
** the leading dimension of the array a .
**
** n integer
** the order of the matrix a .
**
** ipvt integer[n]
** the pivot vector from dgeco or dgefa.
**
** b double precision[n]
** the right hand side vector.
**
** job integer
** = 0 to solve a*x = b ,
** = nonzero to solve trans(a)*x = b where
** trans(a) is the transpose.
**
** on return
**
** b the solution vector x .
**
** error condition
**
** a division by zero will occur if the input factor contains a
** zero on the diagonal. technically this indicates singularity
** but it is often caused by improper arguments or improper
** setting of lda . it will not occur if the subroutines are
** called correctly and if dgeco has set rcond .gt. 0.0
** or dgefa has set info .eq. 0 .
**
** to compute inverse(a) * c where c is a matrix
** with p columns
** dgeco(a,lda,n,ipvt,rcond,z)
** if (!rcond is too small){
** for (j=0,j<p,j++)
** dgesl(a,lda,n,ipvt,c[j][0],0);
** }
**
** linpack. this version dated 08/14/78 .
** cleve moler, university of new mexico, argonne national lab.
**
** functions
**
** blas daxpy,ddot
*/
static void dgesl(REAL *a,int lda,int n,int *ipvt,REAL *b,int job,int roll)
{
REAL t;
int k,kb,l,nm1;
if (roll)
{
nm1 = n - 1;
if (job == 0)
{
/* job = 0 , solve a * x = b */
/* first solve l*y = b */
if (nm1 >= 1)
for (k = 0; k < nm1; k++)
{
l = ipvt[k];
t = b[l];
if (l != k)
{
b[l] = b[k];
b[k] = t;
}
daxpy_r(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1);
}
/* now solve u*x = y */
for (kb = 0; kb < n; kb++)
{
k = n - (kb + 1);
b[k] = b[k]/a[lda*k+k];
t = -b[k];
daxpy_r(k,t,&a[lda*k+0],1,&b[0],1);
}
}
else
{
/* job = nonzero, solve trans(a) * x = b */
/* first solve trans(u)*y = b */
for (k = 0; k < n; k++)
{
t = ddot_r(k,&a[lda*k+0],1,&b[0],1);
b[k] = (b[k] - t)/a[lda*k+k];
}
/* now solve trans(l)*x = y */
if (nm1 >= 1)
for (kb = 1; kb < nm1; kb++)
{
k = n - (kb+1);
b[k] = b[k] + ddot_r(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
l = ipvt[k];
if (l != k)
{
t = b[l];
b[l] = b[k];
b[k] = t;
}
}
}
}
else
{
nm1 = n - 1;
if (job == 0)
{
/* job = 0 , solve a * x = b */
/* first solve l*y = b */
if (nm1 >= 1)
for (k = 0; k < nm1; k++)
{
l = ipvt[k];
t = b[l];
if (l != k)
{
b[l] = b[k];
b[k] = t;
}
daxpy_ur(n-(k+1),t,&a[lda*k+k+1],1,&b[k+1],1);
}
/* now solve u*x = y */
for (kb = 0; kb < n; kb++)
{
k = n - (kb + 1);
b[k] = b[k]/a[lda*k+k];
t = -b[k];
daxpy_ur(k,t,&a[lda*k+0],1,&b[0],1);
}
}
else
{
/* job = nonzero, solve trans(a) * x = b */
/* first solve trans(u)*y = b */
for (k = 0; k < n; k++)
{
t = ddot_ur(k,&a[lda*k+0],1,&b[0],1);
b[k] = (b[k] - t)/a[lda*k+k];
}
/* now solve trans(l)*x = y */
if (nm1 >= 1)
for (kb = 1; kb < nm1; kb++)
{
k = n - (kb+1);
b[k] = b[k] + ddot_ur(n-(k+1),&a[lda*k+k+1],1,&b[k+1],1);
l = ipvt[k];
if (l != k)
{
t = b[l];
b[l] = b[k];
b[k] = t;
}
}
}
}
}
/*
** Constant times a vector plus a vector.
** Jack Dongarra, linpack, 3/11/78.
** ROLLED version
*/
static void daxpy_r(int n,REAL da,REAL *dx,int incx,REAL *dy,int incy)
{
int i,ix,iy;
if (n <= 0)
return;
if (da == ZERO)
return;
if (incx != 1 || incy != 1)
{
/* code for unequal increments or equal increments != 1 */
ix = 1;
iy = 1;
if(incx < 0) ix = (-n+1)*incx + 1;
if(incy < 0)iy = (-n+1)*incy + 1;
for (i = 0;i < n; i++)
{
dy[iy] = dy[iy] + da*dx[ix];
ix = ix + incx;
iy = iy + incy;
}
return;
}
/* code for both increments equal to 1 */
for (i = 0;i < n; i++)
dy[i] = dy[i] + da*dx[i];
}
/*
** Forms the dot product of two vectors.
** Jack Dongarra, linpack, 3/11/78.
** ROLLED version
*/
static REAL ddot_r(int n,REAL *dx,int incx,REAL *dy,int incy)
diff --git a/library/generate/stylesheets/cblas_plugin.c.xsl b/library/generate/stylesheets/cblas_plugin.c.xsl
index f71173f..f1978e0 100644
--- a/library/generate/stylesheets/cblas_plugin.c.xsl
+++ b/library/generate/stylesheets/cblas_plugin.c.xsl
@@ -1,207 +1,212 @@
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:func="http://exslt.org/functions"
xmlns:dyn="http://exslt.org/dynamic"
xmlns:helper="helper"
extension-element-prefixes="func dyn helper">
<!-- import type definitions -->
<xsl:import href="ctypes.xsl"/>
<!-- import my user defined functions -->
<xsl:import href="helper_functions.xsl"/>
<xsl:param name="PREFIX">liftracc_plugin_</xsl:param>
<xsl:param name="UUID">f4a17438-80ed-4f9f-90f1-1728df8ea630</xsl:param>
<xsl:param name="PRIO">1</xsl:param>
<xsl:param name="NAME">liftracc_cblas_plugin</xsl:param>
<xsl:param name="DESC">wrapper to standard blas library</xsl:param>
<!-- document output options -->
<xsl:output method="text"/>
<xsl:strip-space elements="*"/>
<xsl:template match="*">
<xsl:apply-templates/>
</xsl:template>
<xsl:template match="/blas_functions">
<![CDATA[/**
* \file cblas_plugin.c
* \brief [generated file]
*/
/* This file is generated automatically, do not edit manually! */
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <stdlib.h>
#include "cblas_autogen.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
#include "liftracc_selector.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = { };
#endif /* _LIFTRACC_PROFILING_ */
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = { };
void *liftracc_plugin_fptr[CBLAS_FUNCTIONS_COUNT] = { };
plugin_info_t liftracc_plugin_info = {
.uuid = "]]><xsl:value-of select="$UUID"/><![CDATA[",
.name = "]]><xsl:value-of select="$NAME"/><![CDATA[",
.desc = "]]><xsl:value-of select="$DESC"/><![CDATA[",
.prio = ]]><xsl:value-of select="$PRIO"/><![CDATA[
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
char *libname = getenv("USE_CBLAS_LIB");
if (libname)
handle = dlopen(libname, RTLD_LAZY);
if (!handle)
- handle = dlopen("libcblas.so", RTLD_LAZY);
+ handle = dlopen("libcblas_inner.so", RTLD_LAZY);
if (!handle)
ERROR("%s", dlerror());
else
INFO("%s loaded.", liftracc_plugin_info.name);
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
int i;
for (i=0; i<CBLAS_FUNCTIONS_COUNT; i++) {
liftracc_plugin_fptr[i] = dlsym(handle, liftracc_cblas_function_names[i]);
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (handle) dlclose(handle);
handle = 0;
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
#if _LIFTRACC_PROFILING_ == 1
int liftracc_plugin_calltest_dynamic(int a, int b, int c)
{
liftracc_function_timing_stop(&(liftracc_profiling_data[CALL_DYNAMIC]));
/* INFO("liftracc_plugin_calltest_dynamic"); */
return rand()-a*b+c;
}
#endif /* _LIFTRACC_PROFILING_ */
]]>
<xsl:apply-templates/>
</xsl:template>
<xsl:template match="/blas_functions//*//function">
<xsl:value-of select="dyn:evaluate(concat('$',@type))"/><xsl:text> </xsl:text><xsl:value-of select="concat($PREFIX, @name, '(')"/><xsl:value-of select="helper:type-param-str()"/><![CDATA[)
{
INFO("%s]]><xsl:value-of select="concat('_', @name)"/><![CDATA[", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
]]><xsl:value-of select="dyn:evaluate(concat('$',@type))"/><![CDATA[ (*func)();
]]><xsl:if test="@type!='VOID_TYPE'"><xsl:value-of select="dyn:evaluate(concat('$',@type))"/><![CDATA[ ret = 0.0;
]]></xsl:if><![CDATA[
*(void **) (&func) = liftracc_plugin_fptr[]]><xsl:value-of select="concat('CBLAS_FUNCTION_', helper:upper-case(@name))"/><![CDATA[];
if (func != 0) {
]]><xsl:if test="@type!='VOID_TYPE'"><![CDATA[ret = ]]></xsl:if><![CDATA[(*func)(]]><xsl:value-of select="helper:param-str()"/><![CDATA[);]]><![CDATA[
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[]));
-#endif /* _LIFTRACC_PROFILING_ */]]><xsl:if test="@type!='VOID_TYPE'"><![CDATA[
-
- return ret;]]></xsl:if><![CDATA[
+#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
]]><xsl:choose>
<xsl:when test="@name='srotg'"><![CDATA[ int n = 0;]]></xsl:when>
<xsl:when test="@name='srotmg'"><![CDATA[ int n = 0;]]></xsl:when>
<xsl:when test="@name='drotg'"><![CDATA[ int n = 0;]]></xsl:when>
<xsl:when test="@name='drotmg'"><![CDATA[ int n = 0;]]></xsl:when>
<xsl:when test="@name='xerbla'"><![CDATA[ int n = 0;]]></xsl:when>
<xsl:otherwise><![CDATA[]]></xsl:otherwise>
</xsl:choose><![CDATA[
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[, SELECT_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[, SELECT_]]><xsl:value-of select="helper:upper-case(@name)"/><![CDATA[);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
-}]]>
+]]><xsl:if test="@type!='VOID_TYPE'"><![CDATA[
+
+ return ret;
+
+]]></xsl:if><![CDATA[}]]>
<xsl:text>
</xsl:text>
</xsl:template>
</xsl:stylesheet>
diff --git a/library/src/liftracc_plugin.h b/library/src/liftracc_plugin.h
index 19b69cd..7b76ab2 100644
--- a/library/src/liftracc_plugin.h
+++ b/library/src/liftracc_plugin.h
@@ -1,80 +1,83 @@
/**
* \file liftracc_plugin.h
* \brief Definitions needed by the plugins
*
* \author Manuel Niekamp <niekma@upb.de>
* \version 0.1
* \date 10/2009-03/2010
*
* This File defines things related to the plugins.
* Mainly this is the plugin info structur.
*/
#ifndef __LIFTRACC_PLUGIN_H__
#define __LIFTRACC_PLUGIN_H__
#include "liftracc_selector.h"
#include "liftracc_logging.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
#endif
/**
* \brief Plugin information structur
* This struct contains all the info to describe a
* plugin in detail.
*/
typedef const struct {
char *uuid; /**< unique id generated for example by uuidgen */
char *name; /**< short name to identify the plugin */
char *desc; /**< long description with additional info */
unsigned char prio; /**< plugin priority 0:reserved! 1-255:from low to high */
} plugin_info_t;
/**
* \brief Calculate the index in array.
*
* Inline assembler function to calculate the index in LUT.
* As numbers to the power of two are used, this can be done
* with the bsr instruction.
*
* \param probsize
* Get the index to this number
* \param max
* To not jump behind the bounds of the array, the maximum
* index return is max.
*
* \return
* The index to use in LUT array
*/
static __inline__ unsigned int get_inx(unsigned int probsize, unsigned int max) {
unsigned int ret = 0;
__asm__ __volatile__ ( /* "Op-code src dst" AT&T syntax !!! */
"bsr %1, %0;" /* get left most 1 in bit field */
"cmp %2, %0;" /* compare to max (%0-%2) */
"jb 0f;" /* jump if below ((%0-%2)<0) */
"mov %2, %0;" /* else set output to max */
"0:"
: "+r" (ret) /* outputs */
: "r" (probsize), "r" (max) /* inputs */
);
return (unsigned int) ret;
}
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
-void set_decision_data(decision_data_t *data,
+void set_decision_data(int success,
+ decision_data_t *data,
profiling_data_t *func_data,
int value,
int func_id,
int select_id)
{
decision_data_t new_value = func_data[func_id].last_time;
decision_data_t old_value = data[select_id*ARRAY_SIZE+get_inx(value, ARRAY_SIZE)];
+ if (old_value == 0) old_value = new_value;
data[select_id*ARRAY_SIZE+get_inx(value, ARRAY_SIZE)] = (new_value+old_value)/2;
- ERROR("set_decision_data(%d, %d, %d) = %llu+%llu/2", value, func_id, select_id, new_value, old_value);
+ if (!success || new_value == 0) data[select_id*ARRAY_SIZE+get_inx(value, ARRAY_SIZE)] = 0 - 1;
+ ERROR("set_decision_data(%d, %d, %d) = (%llu+%llu)/2", value, func_id, select_id, new_value, old_value);
}
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
#endif // __LIFTRACC_PLUGIN_H__
diff --git a/library/src/plugins/atlas_plugin.c b/library/src/plugins/atlas_plugin.c
index 3bb1f3c..0bd7aa3 100644
--- a/library/src/plugins/atlas_plugin.c
+++ b/library/src/plugins/atlas_plugin.c
@@ -1,268 +1,279 @@
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include "atlas_aux.h"
#include "atlas_level1.h"
#include "atlas_level2.h"
#include "atlas_level3.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = {};
#endif
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = {};
typedef enum {
ATLAS_DAXPY_ID,
ATLAS_DDOT_ID,
ATLAS_DGEMM_ID,
ATLAS_DSCAL_ID,
ATLAS_IDAMAX_ID,
ATLAS_FUNCTIONS_COUNT
} liftracc_atlas_functions_t;
const char *liftracc_atlas_function_names[] = {
"ATL_daxpy",
"ATL_ddot",
"ATL_dgemm",
"ATL_dscal",
"ATL_idamax",
"size_entry"
};
void *liftracc_plugin_fptr[ATLAS_FUNCTIONS_COUNT] = { };
plugin_info_t liftracc_plugin_info = {
.uuid = "95cd6e1c-9f7e-4628-a265-5f9e1fab6abd",
.name = "liftracc_atlas_plugin",
.desc = "wrapper to atlas blas library",
.prio = 10
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
char *libname = getenv("USE_ATLAS_LIB");
if (libname)
handle = dlopen(libname, RTLD_LAZY);
if (!handle)
handle = dlopen("libatlas.so", RTLD_LAZY);
if (!handle)
ERROR("%s", dlerror());
else
INFO("%s loaded.", liftracc_plugin_info.name);
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
int i;
for (i=0; i<ATLAS_FUNCTIONS_COUNT; i++) {
liftracc_plugin_fptr[i] = dlsym(handle, liftracc_atlas_function_names[i]);
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (handle) dlclose(handle);
handle = 0;
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
/* START OF BLAS FUNCTION IMPLEMENTATION */
void liftracc_plugin_daxpy(const int n, const double alpha, const double * x, const int incx, double * y, const int incy)
{
INFO("%s_daxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
void (*func)();
-
*(void **) (&func) = liftracc_plugin_fptr[ATLAS_DAXPY_ID];
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#if _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DAXPY, SELECT_DAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
double liftracc_plugin_ddot(const int n, const double *x, const int incx, const double *y, const int incy)
{
INFO("%s_ddot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double (*func)();
+ double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[ATLAS_DDOT_ID];
- if ((error = dlerror()) != 0) {
- ERROR("%s", error);
- return 0.0;
+ if (func != 0) {
+ ret = (*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
- double ret = (*func)(n, x, incx, y, incy);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
#if _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
void liftracc_plugin_dgemm(const liftracc_order_t order,
const liftracc_transpose_t transa, const liftracc_transpose_t transb,
const int m, const int n, const int k,
const double alpha, const double *a, const int lda,
const double *b, const int ldb, const double beta,
double *c, const int ldc)
{
INFO("%s_dgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
+
if (order != liftracc_col_major) {
ERROR("Matrix not in column-major order.");
return;
}
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[ATLAS_DGEMM_ID];
- if ((error = dlerror()) != 0) {
- ERROR("%s", error);
- return;
+ if (func != 0) {
+ (*func)(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
- (*func)(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dscal(const int n, const double alpha, double * x, const int incx)
{
INFO("%s_dscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
void (*func)();
-
*(void **) (&func) = liftracc_plugin_fptr[ATLAS_DSCAL_ID];
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
liftracc_index_t liftracc_plugin_idamax(const int n, const double * x, const int incx)
{
INFO("%s_idamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
+ liftracc_index_t ret = 0;
liftracc_index_t (*func)();
- liftracc_index_t ret = 0.0;
-
*(void **) (&func) = liftracc_plugin_fptr[ATLAS_IDAMAX_ID];
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
diff --git a/library/src/plugins/cblas_plugin.c b/library/src/plugins/cblas_plugin.c
index 0a943e5..57444ca 100644
--- a/library/src/plugins/cblas_plugin.c
+++ b/library/src/plugins/cblas_plugin.c
@@ -1,3899 +1,4360 @@
/**
* \file cblas_plugin.c
* \brief [generated file]
*/
/* This file is generated automatically, do not edit manually! */
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <stdlib.h>
#include "cblas_autogen.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
#include "liftracc_selector.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = { };
#endif /* _LIFTRACC_PROFILING_ */
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = { };
void *liftracc_plugin_fptr[CBLAS_FUNCTIONS_COUNT] = { };
plugin_info_t liftracc_plugin_info = {
.uuid = "f4a17438-80ed-4f9f-90f1-1728df8ea630",
.name = "liftracc_cblas_plugin",
.desc = "wrapper to standard blas library",
.prio = 1
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
char *libname = getenv("USE_CBLAS_LIB");
if (libname)
handle = dlopen(libname, RTLD_LAZY);
if (!handle)
- handle = dlopen("libcblas.so", RTLD_LAZY);
+ handle = dlopen("libcblas_inner.so", RTLD_LAZY);
if (!handle)
ERROR("%s", dlerror());
else
INFO("%s loaded.", liftracc_plugin_info.name);
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
int i;
for (i=0; i<CBLAS_FUNCTIONS_COUNT; i++) {
liftracc_plugin_fptr[i] = dlsym(handle, liftracc_cblas_function_names[i]);
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (handle) dlclose(handle);
handle = 0;
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
#if _LIFTRACC_PROFILING_ == 1
int liftracc_plugin_calltest_dynamic(int a, int b, int c)
{
liftracc_function_timing_stop(&(liftracc_profiling_data[CALL_DYNAMIC]));
/* INFO("liftracc_plugin_calltest_dynamic"); */
return rand()-a*b+c;
}
#endif /* _LIFTRACC_PROFILING_ */
float liftracc_plugin_sdsdot(const int n, const float alpha, const float * x, const int incx, const float * y, const int incy)
{
INFO("%s_sdsdot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SDSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SDSDOT];
if (func != 0) {
ret = (*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SDSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SDSDOT, SELECT_SDSDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SDSDOT, SELECT_SDSDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_dsdot(const int n, const float * x, const int incx, const float * y, const int incy)
{
INFO("%s_dsdot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSDOT];
if (func != 0) {
ret = (*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSDOT]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSDOT, SELECT_DSDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSDOT, SELECT_DSDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
float liftracc_plugin_sdot(const int n, const float * x, const int incx, const float * y, const int incy)
{
INFO("%s_sdot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SDOT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SDOT];
if (func != 0) {
ret = (*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SDOT]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SDOT, SELECT_SDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SDOT, SELECT_SDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_ddot(const int n, const double * x, const int incx, const double * y, const int incy)
{
INFO("%s_ddot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DDOT];
if (func != 0) {
ret = (*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
void liftracc_plugin_cdotu_sub(const int n, const void * x, const int incx, const void * y, const int incy, void * dotu)
{
INFO("%s_cdotu_sub", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CDOTU_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CDOTU_SUB];
if (func != 0) {
(*func)(n, x, incx, y, incy, dotu);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CDOTU_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CDOTU_SUB, SELECT_CDOTU_SUB);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CDOTU_SUB, SELECT_CDOTU_SUB);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cdotc_sub(const int n, const void * x, const int incx, const void * y, const int incy, void * dotc)
{
INFO("%s_cdotc_sub", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CDOTC_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CDOTC_SUB];
if (func != 0) {
(*func)(n, x, incx, y, incy, dotc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CDOTC_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CDOTC_SUB, SELECT_CDOTC_SUB);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CDOTC_SUB, SELECT_CDOTC_SUB);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zdotu_sub(const int n, const void * x, const int incx, const void * y, const int incy, void * dotu)
{
INFO("%s_zdotu_sub", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZDOTU_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZDOTU_SUB];
if (func != 0) {
(*func)(n, x, incx, y, incy, dotu);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZDOTU_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDOTU_SUB, SELECT_ZDOTU_SUB);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDOTU_SUB, SELECT_ZDOTU_SUB);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zdotc_sub(const int n, const void * x, const int incx, const void * y, const int incy, void * dotc)
{
INFO("%s_zdotc_sub", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZDOTC_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZDOTC_SUB];
if (func != 0) {
(*func)(n, x, incx, y, incy, dotc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZDOTC_SUB]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDOTC_SUB, SELECT_ZDOTC_SUB);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDOTC_SUB, SELECT_ZDOTC_SUB);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
float liftracc_plugin_snrm2(const int n, const float * x, const int incx)
{
INFO("%s_snrm2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SNRM2];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SNRM2, SELECT_SNRM2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SNRM2, SELECT_SNRM2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
float liftracc_plugin_sasum(const int n, const float * x, const int incx)
{
INFO("%s_sasum", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SASUM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SASUM];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SASUM]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SASUM, SELECT_SASUM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SASUM, SELECT_SASUM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_dnrm2(const int n, const double * x, const int incx)
{
INFO("%s_dnrm2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DNRM2];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DNRM2, SELECT_DNRM2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DNRM2, SELECT_DNRM2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_dasum(const int n, const double * x, const int incx)
{
INFO("%s_dasum", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DASUM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DASUM];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DASUM]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DASUM, SELECT_DASUM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DASUM, SELECT_DASUM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
float liftracc_plugin_scnrm2(const int n, const void * x, const int incx)
{
INFO("%s_scnrm2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SCNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SCNRM2];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SCNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCNRM2, SELECT_SCNRM2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCNRM2, SELECT_SCNRM2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
float liftracc_plugin_scasum(const int n, const void * x, const int incx)
{
INFO("%s_scasum", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SCASUM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
float (*func)();
float ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SCASUM];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SCASUM]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCASUM, SELECT_SCASUM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCASUM, SELECT_SCASUM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_dznrm2(const int n, const void * x, const int incx)
{
INFO("%s_dznrm2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DZNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DZNRM2];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DZNRM2]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DZNRM2, SELECT_DZNRM2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DZNRM2, SELECT_DZNRM2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
double liftracc_plugin_dzasum(const int n, const void * x, const int incx)
{
INFO("%s_dzasum", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DZASUM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
double (*func)();
double ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DZASUM];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DZASUM]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DZASUM, SELECT_DZASUM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DZASUM, SELECT_DZASUM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
liftracc_index_t liftracc_plugin_isamax(const int n, const float * x, const int incx)
{
INFO("%s_isamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ISAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
liftracc_index_t (*func)();
liftracc_index_t ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ISAMAX];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ISAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ISAMAX, SELECT_ISAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ISAMAX, SELECT_ISAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
liftracc_index_t liftracc_plugin_idamax(const int n, const double * x, const int incx)
{
INFO("%s_idamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
liftracc_index_t (*func)();
liftracc_index_t ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_IDAMAX];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
liftracc_index_t liftracc_plugin_icamax(const int n, const void * x, const int incx)
{
INFO("%s_icamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ICAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
liftracc_index_t (*func)();
liftracc_index_t ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ICAMAX];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ICAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ICAMAX, SELECT_ICAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ICAMAX, SELECT_ICAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
liftracc_index_t liftracc_plugin_izamax(const int n, const void * x, const int incx)
{
INFO("%s_izamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_IZAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
liftracc_index_t (*func)();
liftracc_index_t ret = 0.0;
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_IZAMAX];
if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_IZAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
- return ret;
-
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IZAMAX, SELECT_IZAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IZAMAX, SELECT_IZAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
+
+
+ return ret;
+
}
void liftracc_plugin_sswap(const int n, float * x, const int incx, float * y, const int incy)
{
INFO("%s_sswap", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSWAP];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSWAP, SELECT_SSWAP);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSWAP, SELECT_SSWAP);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_scopy(const int n, const float * x, const int incx, float * y, const int incy)
{
INFO("%s_scopy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SCOPY];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCOPY, SELECT_SCOPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SCOPY, SELECT_SCOPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_saxpy(const int n, const float alpha, const float * x, const int incx, float * y, const int incy)
{
INFO("%s_saxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SAXPY];
if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SAXPY, SELECT_SAXPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SAXPY, SELECT_SAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dswap(const int n, double * x, const int incx, double * y, const int incy)
{
INFO("%s_dswap", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSWAP];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSWAP, SELECT_DSWAP);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSWAP, SELECT_DSWAP);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dcopy(const int n, const double * x, const int incx, double * y, const int incy)
{
INFO("%s_dcopy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DCOPY];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DCOPY, SELECT_DCOPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DCOPY, SELECT_DCOPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_daxpy(const int n, const double alpha, const double * x, const int incx, double * y, const int incy)
{
INFO("%s_daxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DAXPY];
if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DAXPY, SELECT_DAXPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DAXPY, SELECT_DAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cswap(const int n, void * x, const int incx, void * y, const int incy)
{
INFO("%s_cswap", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSWAP];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSWAP, SELECT_CSWAP);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSWAP, SELECT_CSWAP);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ccopy(const int n, const void * x, const int incx, void * y, const int incy)
{
INFO("%s_ccopy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CCOPY];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CCOPY, SELECT_CCOPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CCOPY, SELECT_CCOPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_caxpy(const int n, const void * alpha, const void * x, const int incx, void * y, const int incy)
{
INFO("%s_caxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CAXPY];
if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CAXPY, SELECT_CAXPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CAXPY, SELECT_CAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zswap(const int n, void * x, const int incx, void * y, const int incy)
{
INFO("%s_zswap", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZSWAP];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZSWAP]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSWAP, SELECT_ZSWAP);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSWAP, SELECT_ZSWAP);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zcopy(const int n, const void * x, const int incx, void * y, const int incy)
{
INFO("%s_zcopy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZCOPY];
if (func != 0) {
(*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZCOPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZCOPY, SELECT_ZCOPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZCOPY, SELECT_ZCOPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zaxpy(const int n, const void * alpha, const void * x, const int incx, void * y, const int incy)
{
INFO("%s_zaxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZAXPY];
if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZAXPY, SELECT_ZAXPY);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZAXPY, SELECT_ZAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_srotg(float * a, float * b, float * c, float * s)
{
INFO("%s_srotg", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SROTG]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SROTG];
if (func != 0) {
(*func)(a, b, c, s);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SROTG]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
int n = 0;
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTG, SELECT_SROTG);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTG, SELECT_SROTG);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_srotmg(float * d1, float * d2, float * b1, const float b2, float * p)
{
INFO("%s_srotmg", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SROTMG]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SROTMG];
if (func != 0) {
(*func)(d1, d2, b1, b2, p);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SROTMG]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
int n = 0;
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTMG, SELECT_SROTMG);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTMG, SELECT_SROTMG);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_srot(const int n, float * x, const int incx, float * y, const int incy, const float c, const float s)
{
INFO("%s_srot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SROT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SROT];
if (func != 0) {
(*func)(n, x, incx, y, incy, c, s);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SROT]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROT, SELECT_SROT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROT, SELECT_SROT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_srotm(const int n, float * x, const int incx, float * y, const int incy, const float * p)
{
INFO("%s_srotm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SROTM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SROTM];
if (func != 0) {
(*func)(n, x, incx, y, incy, p);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SROTM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTM, SELECT_SROTM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SROTM, SELECT_SROTM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_drotg(double * a, double * b, double * c, double * s)
{
INFO("%s_drotg", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DROTG]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DROTG];
if (func != 0) {
(*func)(a, b, c, s);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DROTG]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
int n = 0;
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTG, SELECT_DROTG);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTG, SELECT_DROTG);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_drotmg(double * d1, double * d2, double * b1, const double b2, double * p)
{
INFO("%s_drotmg", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DROTMG]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DROTMG];
if (func != 0) {
(*func)(d1, d2, b1, b2, p);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DROTMG]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
int n = 0;
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTMG, SELECT_DROTMG);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTMG, SELECT_DROTMG);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_drot(const int n, double * x, const int incx, double * y, const int incy, const double c, const double s)
{
INFO("%s_drot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DROT]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DROT];
if (func != 0) {
(*func)(n, x, incx, y, incy, c, s);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DROT]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROT, SELECT_DROT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROT, SELECT_DROT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_drotm(const int n, double * x, const int incx, double * y, const int incy, const double * p)
{
INFO("%s_drotm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DROTM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DROTM];
if (func != 0) {
(*func)(n, x, incx, y, incy, p);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DROTM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTM, SELECT_DROTM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DROTM, SELECT_DROTM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sscal(const int n, const float alpha, float * x, const int incx)
{
INFO("%s_sscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSCAL, SELECT_SSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSCAL, SELECT_SSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dscal(const int n, const double alpha, double * x, const int incx)
{
INFO("%s_dscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cscal(const int n, const void * alpha, void * x, const int incx)
{
INFO("%s_cscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSCAL, SELECT_CSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSCAL, SELECT_CSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zscal(const int n, const void * alpha, void * x, const int incx)
{
INFO("%s_zscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSCAL, SELECT_ZSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSCAL, SELECT_ZSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_csscal(const int n, const float alpha, void * x, const int incx)
{
INFO("%s_csscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSSCAL, SELECT_CSSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSSCAL, SELECT_CSSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zdscal(const int n, const double alpha, void * x, const int incx)
{
INFO("%s_zdscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZDSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZDSCAL];
if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZDSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDSCAL, SELECT_ZDSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZDSCAL, SELECT_ZDSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sgemv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const float alpha, const float * a, const int lda, const float * x, const int incx, const float beta, float * y, const int incy)
{
INFO("%s_sgemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SGEMV];
if (func != 0) {
(*func)(order, transa, m, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGEMV, SELECT_SGEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGEMV, SELECT_SGEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sgbmv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const int kl, const int ku, const float alpha, const float * a, const int lda, const float * x, const int incx, const float beta, float * y, const int incy)
{
INFO("%s_sgbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SGBMV];
if (func != 0) {
(*func)(order, transa, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGBMV, SELECT_SGBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGBMV, SELECT_SGBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_strmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const float * a, const int lda, float * x, const int incx)
{
INFO("%s_strmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STRMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STRMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STRMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRMV, SELECT_STRMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRMV, SELECT_STRMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_stbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const float * a, const int lda, float * x, const int incx)
{
INFO("%s_stbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STBMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STBMV, SELECT_STBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STBMV, SELECT_STBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_stpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const float * ap, float * x, const int incx)
{
INFO("%s_stpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STPMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STPMV, SELECT_STPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STPMV, SELECT_STPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_strsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const float * a, const int lda, float * x, const int incx)
{
INFO("%s_strsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STRSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STRSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STRSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRSV, SELECT_STRSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRSV, SELECT_STRSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_stbsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const float * a, const int lda, float * x, const int incx)
{
INFO("%s_stbsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STBSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STBSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STBSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STBSV, SELECT_STBSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STBSV, SELECT_STBSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_stpsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const float * ap, float * x, const int incx)
{
INFO("%s_stpsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STPSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STPSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STPSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STPSV, SELECT_STPSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STPSV, SELECT_STPSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dgemv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const double alpha, const double * a, const int lda, const double * x, const int incx, const double beta, double * y, const int incy)
{
INFO("%s_dgemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DGEMV];
if (func != 0) {
(*func)(order, transa, m, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMV, SELECT_DGEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMV, SELECT_DGEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dgbmv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const int kl, const int ku, const double alpha, const double * a, const int lda, const double * x, const int incx, const double beta, double * y, const int incy)
{
INFO("%s_dgbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DGBMV];
if (func != 0) {
(*func)(order, transa, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGBMV, SELECT_DGBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGBMV, SELECT_DGBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtrmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const double * a, const int lda, double * x, const int incx)
{
INFO("%s_dtrmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTRMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRMV, SELECT_DTRMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRMV, SELECT_DTRMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const double * a, const int lda, double * x, const int incx)
{
INFO("%s_dtbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTBMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTBMV, SELECT_DTBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTBMV, SELECT_DTBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const double * ap, double * x, const int incx)
{
INFO("%s_dtpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTPMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTPMV, SELECT_DTPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTPMV, SELECT_DTPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtrsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const double * a, const int lda, double * x, const int incx)
{
INFO("%s_dtrsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTRSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRSV, SELECT_DTRSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRSV, SELECT_DTRSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtbsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const double * a, const int lda, double * x, const int incx)
{
INFO("%s_dtbsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTBSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTBSV, SELECT_DTBSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTBSV, SELECT_DTBSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtpsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const double * ap, double * x, const int incx)
{
INFO("%s_dtpsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTPSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTPSV, SELECT_DTPSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTPSV, SELECT_DTPSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cgemv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_cgemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CGEMV];
if (func != 0) {
(*func)(order, transa, m, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGEMV, SELECT_CGEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGEMV, SELECT_CGEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cgbmv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const int kl, const int ku, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_cgbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CGBMV];
if (func != 0) {
(*func)(order, transa, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGBMV, SELECT_CGBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGBMV, SELECT_CGBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctrmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ctrmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTRMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRMV, SELECT_CTRMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRMV, SELECT_CTRMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ctbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTBMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTBMV, SELECT_CTBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTBMV, SELECT_CTBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * ap, void * x, const int incx)
{
INFO("%s_ctpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTPMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTPMV, SELECT_CTPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTPMV, SELECT_CTPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctrsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ctrsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTRSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRSV, SELECT_CTRSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRSV, SELECT_CTRSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctbsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ctbsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTBSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTBSV, SELECT_CTBSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTBSV, SELECT_CTBSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctpsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * ap, void * x, const int incx)
{
INFO("%s_ctpsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTPSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTPSV, SELECT_CTPSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTPSV, SELECT_CTPSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zgemv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_zgemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZGEMV];
if (func != 0) {
(*func)(order, transa, m, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZGEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGEMV, SELECT_ZGEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGEMV, SELECT_ZGEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zgbmv(const liftracc_order_t order, const liftracc_transpose_t transa, const int m, const int n, const int kl, const int ku, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_zgbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZGBMV];
if (func != 0) {
(*func)(order, transa, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZGBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGBMV, SELECT_ZGBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGBMV, SELECT_ZGBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztrmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ztrmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTRMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRMV, SELECT_ZTRMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRMV, SELECT_ZTRMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ztbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTBMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTBMV, SELECT_ZTBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTBMV, SELECT_ZTBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * ap, void * x, const int incx)
{
INFO("%s_ztpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTPMV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTPMV, SELECT_ZTPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTPMV, SELECT_ZTPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztrsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ztrsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTRSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRSV, SELECT_ZTRSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRSV, SELECT_ZTRSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztbsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const int k, const void * a, const int lda, void * x, const int incx)
{
INFO("%s_ztbsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTBSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, k, a, lda, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTBSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTBSV, SELECT_ZTBSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTBSV, SELECT_ZTBSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztpsv(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int n, const void * ap, void * x, const int incx)
{
INFO("%s_ztpsv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTPSV];
if (func != 0) {
(*func)(order, uplo, transa, diag, n, ap, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTPSV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTPSV, SELECT_ZTPSV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTPSV, SELECT_ZTPSV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssymv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * a, const int lda, const float * x, const int incx, const float beta, float * y, const int incy)
{
INFO("%s_ssymv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYMV, SELECT_SSYMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYMV, SELECT_SSYMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const int k, const float alpha, const float * a, const int lda, const float * x, const int incx, const float beta, float * y, const int incy)
{
INFO("%s_ssbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSBMV];
if (func != 0) {
(*func)(order, uplo, n, k, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSBMV, SELECT_SSBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSBMV, SELECT_SSBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sspmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * ap, const float * x, const int incx, const float beta, float * y, const int incy)
{
INFO("%s_sspmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSPMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, ap, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPMV, SELECT_SSPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPMV, SELECT_SSPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sger(const liftracc_order_t order, const int m, const int n, const float alpha, const float * x, const int incx, const float * y, const int incy, float * a, const int lda)
{
INFO("%s_sger", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SGER]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SGER];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SGER]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGER, SELECT_SGER);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGER, SELECT_SGER);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssyr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * x, const int incx, float * a, const int lda)
{
INFO("%s_ssyr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR, SELECT_SSYR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR, SELECT_SSYR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sspr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * x, const int incx, float * ap)
{
INFO("%s_sspr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSPR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSPR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, ap);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSPR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPR, SELECT_SSPR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPR, SELECT_SSPR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssyr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * x, const int incx, const float * y, const int incy, float * a, const int lda)
{
INFO("%s_ssyr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR2, SELECT_SSYR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR2, SELECT_SSYR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sspr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const float * x, const int incx, const float * y, const int incy, float * a)
{
INFO("%s_sspr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSPR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSPR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSPR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPR2, SELECT_SSPR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSPR2, SELECT_SSPR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsymv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * a, const int lda, const double * x, const int incx, const double beta, double * y, const int incy)
{
INFO("%s_dsymv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYMV, SELECT_DSYMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYMV, SELECT_DSYMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const int k, const double alpha, const double * a, const int lda, const double * x, const int incx, const double beta, double * y, const int incy)
{
INFO("%s_dsbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSBMV];
if (func != 0) {
(*func)(order, uplo, n, k, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSBMV, SELECT_DSBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSBMV, SELECT_DSBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dspmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * ap, const double * x, const int incx, const double beta, double * y, const int incy)
{
INFO("%s_dspmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSPMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, ap, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPMV, SELECT_DSPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPMV, SELECT_DSPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dger(const liftracc_order_t order, const int m, const int n, const double alpha, const double * x, const int incx, const double * y, const int incy, double * a, const int lda)
{
INFO("%s_dger", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGER]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DGER];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGER]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGER, SELECT_DGER);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGER, SELECT_DGER);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsyr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * x, const int incx, double * a, const int lda)
{
INFO("%s_dsyr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR, SELECT_DSYR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR, SELECT_DSYR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dspr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * x, const int incx, double * ap)
{
INFO("%s_dspr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSPR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSPR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, ap);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSPR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPR, SELECT_DSPR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPR, SELECT_DSPR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsyr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * x, const int incx, const double * y, const int incy, double * a, const int lda)
{
INFO("%s_dsyr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR2, SELECT_DSYR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR2, SELECT_DSYR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dspr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const double * x, const int incx, const double * y, const int incy, double * a)
{
INFO("%s_dspr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSPR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSPR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSPR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPR2, SELECT_DSPR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSPR2, SELECT_DSPR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chemv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_chemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHEMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHEMV, SELECT_CHEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHEMV, SELECT_CHEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const int k, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_chbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHBMV];
if (func != 0) {
(*func)(order, uplo, n, k, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHBMV, SELECT_CHBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHBMV, SELECT_CHBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * ap, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_chpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHPMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, ap, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPMV, SELECT_CHPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPMV, SELECT_CHPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cgeru(const liftracc_order_t order, const int m, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_cgeru", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CGERU]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CGERU];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CGERU]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGERU, SELECT_CGERU);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGERU, SELECT_CGERU);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cgerc(const liftracc_order_t order, const int m, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_cgerc", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CGERC]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CGERC];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CGERC]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGERC, SELECT_CGERC);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGERC, SELECT_CGERC);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cher(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const void * x, const int incx, void * a, const int lda)
{
INFO("%s_cher", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHER]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHER];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHER]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER, SELECT_CHER);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER, SELECT_CHER);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chpr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const float alpha, const void * x, const int incx, void * a)
{
INFO("%s_chpr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHPR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHPR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHPR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPR, SELECT_CHPR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPR, SELECT_CHPR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cher2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_cher2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHER2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHER2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHER2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER2, SELECT_CHER2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER2, SELECT_CHER2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chpr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * ap)
{
INFO("%s_chpr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHPR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHPR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, ap);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHPR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPR2, SELECT_CHPR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHPR2, SELECT_CHPR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhemv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_zhemv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHEMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHEMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHEMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHEMV, SELECT_ZHEMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHEMV, SELECT_ZHEMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhbmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const int k, const void * alpha, const void * a, const int lda, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_zhbmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHBMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHBMV];
if (func != 0) {
(*func)(order, uplo, n, k, alpha, a, lda, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHBMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHBMV, SELECT_ZHBMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHBMV, SELECT_ZHBMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhpmv(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * ap, const void * x, const int incx, const void * beta, void * y, const int incy)
{
INFO("%s_zhpmv", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPMV]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHPMV];
if (func != 0) {
(*func)(order, uplo, n, alpha, ap, x, incx, beta, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPMV]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPMV, SELECT_ZHPMV);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPMV, SELECT_ZHPMV);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zgeru(const liftracc_order_t order, const int m, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_zgeru", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZGERU]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZGERU];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZGERU]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGERU, SELECT_ZGERU);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGERU, SELECT_ZGERU);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zgerc(const liftracc_order_t order, const int m, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_zgerc", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZGERC]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZGERC];
if (func != 0) {
(*func)(order, m, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZGERC]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGERC, SELECT_ZGERC);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGERC, SELECT_ZGERC);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zher(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const void * x, const int incx, void * a, const int lda)
{
INFO("%s_zher", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHER];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER, SELECT_ZHER);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER, SELECT_ZHER);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhpr(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const double alpha, const void * x, const int incx, void * a)
{
INFO("%s_zhpr", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPR]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHPR];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, a);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPR]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPR, SELECT_ZHPR);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPR, SELECT_ZHPR);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zher2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * a, const int lda)
{
INFO("%s_zher2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHER2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, a, lda);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER2, SELECT_ZHER2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER2, SELECT_ZHER2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhpr2(const liftracc_order_t order, const liftracc_uplo_t uplo, const int n, const void * alpha, const void * x, const int incx, const void * y, const int incy, void * ap)
{
INFO("%s_zhpr2", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPR2]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHPR2];
if (func != 0) {
(*func)(order, uplo, n, alpha, x, incx, y, incy, ap);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHPR2]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPR2, SELECT_ZHPR2);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHPR2, SELECT_ZHPR2);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_sgemm(const liftracc_order_t order, const liftracc_transpose_t transa, const liftracc_transpose_t transb, const int m, const int n, const int k, const float alpha, const float * a, const int lda, const float * b, const int ldb, const float beta, float * c, const int ldc)
{
INFO("%s_sgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SGEMM];
if (func != 0) {
(*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGEMM, SELECT_SGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SGEMM, SELECT_SGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssymm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const float alpha, const float * a, const int lda, const float * b, const int ldb, const float beta, float * c, const int ldc)
{
INFO("%s_ssymm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYMM, SELECT_SSYMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYMM, SELECT_SSYMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssyrk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const float alpha, const float * a, const int lda, const float beta, float * c, const int ldc)
{
INFO("%s_ssyrk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYRK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYRK, SELECT_SSYRK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYRK, SELECT_SSYRK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ssyr2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const float alpha, const float * a, const int lda, const float * b, const int ldb, const float beta, float * c, const int ldc)
{
INFO("%s_ssyr2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_SSYR2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_SSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR2K, SELECT_SSYR2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_SSYR2K, SELECT_SSYR2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_strmm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const float alpha, const float * a, const int lda, float * b, const int ldb)
{
INFO("%s_strmm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STRMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STRMM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STRMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRMM, SELECT_STRMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRMM, SELECT_STRMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_strsm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const float alpha, const float * a, const int lda, float * b, const int ldb)
{
INFO("%s_strsm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_STRSM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_STRSM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_STRSM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRSM, SELECT_STRSM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_STRSM, SELECT_STRSM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dgemm(const liftracc_order_t order, const liftracc_transpose_t transa, const liftracc_transpose_t transb, const int m, const int n, const int k, const double alpha, const double * a, const int lda, const double * b, const int ldb, const double beta, double * c, const int ldc)
{
INFO("%s_dgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DGEMM];
if (func != 0) {
(*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsymm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const double alpha, const double * a, const int lda, const double * b, const int ldb, const double beta, double * c, const int ldc)
{
INFO("%s_dsymm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYMM, SELECT_DSYMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYMM, SELECT_DSYMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsyrk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const double alpha, const double * a, const int lda, const double beta, double * c, const int ldc)
{
INFO("%s_dsyrk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYRK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYRK, SELECT_DSYRK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYRK, SELECT_DSYRK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dsyr2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const double alpha, const double * a, const int lda, const double * b, const int ldb, const double beta, double * c, const int ldc)
{
INFO("%s_dsyr2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DSYR2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR2K, SELECT_DSYR2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSYR2K, SELECT_DSYR2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtrmm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const double alpha, const double * a, const int lda, double * b, const int ldb)
{
INFO("%s_dtrmm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTRMM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRMM, SELECT_DTRMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRMM, SELECT_DTRMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dtrsm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const double alpha, const double * a, const int lda, double * b, const int ldb)
{
INFO("%s_dtrsm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_DTRSM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRSM, SELECT_DTRSM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DTRSM, SELECT_DTRSM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cgemm(const liftracc_order_t order, const liftracc_transpose_t transa, const liftracc_transpose_t transb, const int m, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_cgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CGEMM];
if (func != 0) {
(*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGEMM, SELECT_CGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CGEMM, SELECT_CGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_csymm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_csymm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSYMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYMM, SELECT_CSYMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYMM, SELECT_CSYMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_csyrk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * beta, void * c, const int ldc)
{
INFO("%s_csyrk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSYRK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYRK, SELECT_CSYRK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYRK, SELECT_CSYRK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_csyr2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_csyr2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CSYR2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYR2K, SELECT_CSYR2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CSYR2K, SELECT_CSYR2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctrmm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const void * alpha, const void * a, const int lda, void * b, const int ldb)
{
INFO("%s_ctrmm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTRMM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRMM, SELECT_CTRMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRMM, SELECT_CTRMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ctrsm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const void * alpha, const void * a, const int lda, void * b, const int ldb)
{
INFO("%s_ctrsm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CTRSM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRSM, SELECT_CTRSM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CTRSM, SELECT_CTRSM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zgemm(const liftracc_order_t order, const liftracc_transpose_t transa, const liftracc_transpose_t transb, const int m, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_zgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZGEMM];
if (func != 0) {
(*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGEMM, SELECT_ZGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZGEMM, SELECT_ZGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zsymm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_zsymm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZSYMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYMM, SELECT_ZSYMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYMM, SELECT_ZSYMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zsyrk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * beta, void * c, const int ldc)
{
INFO("%s_zsyrk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZSYRK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYRK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYRK, SELECT_ZSYRK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYRK, SELECT_ZSYRK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zsyr2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_zsyr2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZSYR2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZSYR2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYR2K, SELECT_ZSYR2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZSYR2K, SELECT_ZSYR2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztrmm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const void * alpha, const void * a, const int lda, void * b, const int ldb)
{
INFO("%s_ztrmm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTRMM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRMM, SELECT_ZTRMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRMM, SELECT_ZTRMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_ztrsm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const liftracc_transpose_t transa, const liftracc_diag_t diag, const int m, const int n, const void * alpha, const void * a, const int lda, void * b, const int ldb)
{
INFO("%s_ztrsm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZTRSM];
if (func != 0) {
(*func)(order, side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZTRSM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRSM, SELECT_ZTRSM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZTRSM, SELECT_ZTRSM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_chemm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_chemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHEMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHEMM, SELECT_CHEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHEMM, SELECT_CHEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cherk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const float alpha, const void * a, const int lda, const float beta, void * c, const int ldc)
{
INFO("%s_cherk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHERK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHERK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHERK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHERK, SELECT_CHERK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHERK, SELECT_CHERK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_cher2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const float beta, void * c, const int ldc)
{
INFO("%s_cher2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_CHER2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_CHER2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_CHER2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER2K, SELECT_CHER2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_CHER2K, SELECT_CHER2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zhemm(const liftracc_order_t order, const liftracc_side_t side, const liftracc_uplo_t uplo, const int m, const int n, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const void * beta, void * c, const int ldc)
{
INFO("%s_zhemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHEMM]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHEMM];
if (func != 0) {
(*func)(order, side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHEMM, SELECT_ZHEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHEMM, SELECT_ZHEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zherk(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const double alpha, const void * a, const int lda, const double beta, void * c, const int ldc)
{
INFO("%s_zherk", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHERK]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHERK];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHERK]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHERK, SELECT_ZHERK);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHERK, SELECT_ZHERK);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_zher2k(const liftracc_order_t order, const liftracc_uplo_t uplo, const liftracc_transpose_t trans, const int n, const int k, const void * alpha, const void * a, const int lda, const void * b, const int ldb, const double beta, void * c, const int ldc)
{
INFO("%s_zher2k", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER2K]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_ZHER2K];
if (func != 0) {
(*func)(order, uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_ZHER2K]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER2K, SELECT_ZHER2K);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_ZHER2K, SELECT_ZHER2K);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_xerbla(int p, const char * rout, const char * form)
{
INFO("%s_xerbla", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_XERBLA]));
#endif /* _LIFTRACC_PROFILING_ */
-
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CBLAS_FUNCTION_XERBLA];
if (func != 0) {
(*func)(p, rout, form);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_XERBLA]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
int n = 0;
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_XERBLA, SELECT_XERBLA);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_XERBLA, SELECT_XERBLA);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
diff --git a/library/src/plugins/clearspeed_plugin.c b/library/src/plugins/clearspeed_plugin.c
index 769e359..f8b2b5d 100644
--- a/library/src/plugins/clearspeed_plugin.c
+++ b/library/src/plugins/clearspeed_plugin.c
@@ -1,175 +1,177 @@
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = {};
#endif
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = {};
typedef enum {
CLEAR_DGEMM_ID,
CLEAR_FUNCTIONS_COUNT
} liftracc_clear_functions_t;
const char *liftracc_clear_function_names[] = {
"DGEMM",
"size_entry"
};
void *liftracc_plugin_fptr[CLEAR_FUNCTIONS_COUNT] = { };
plugin_info_t liftracc_plugin_info = {
.uuid = "7bedd79d-62b6-4210-b221-98ebf540057a",
.name = "liftracc_clearspeed_plugin",
.desc = "wrapper to clearspeed blas library",
.prio = 30
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
char *libname = getenv("USE_CSXL_LIB");
if (libname)
handle = dlopen(libname, RTLD_LAZY);
if (!handle)
handle = dlopen("libcsxl_mkl.so", RTLD_LAZY);
if (!handle)
ERROR("%s", dlerror());
else
INFO("%s loaded.", liftracc_plugin_info.name);
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
int i;
for (i=0; i<CLEAR_FUNCTIONS_COUNT; i++) {
liftracc_plugin_fptr[i] = dlsym(handle, liftracc_clear_function_names[i]);
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (handle) dlclose(handle);
handle = 0;
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
/* START OF BLAS FUNCTION IMPLEMENTATION */
void liftracc_plugin_dgemm(const liftracc_order_t order,
const liftracc_transpose_t transa, const liftracc_transpose_t transb,
const int m, const int n, const int k,
const double alpha, const double *a, const int lda,
const double *b, const int ldb, const double beta,
double *c, const int ldc)
{
INFO("%s_dgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
+
if (order != liftracc_col_major) {
ERROR("Matrix not in column-major order.");
return;
}
+
+ int success = 1;
void (*func)();
*(void **) (&func) = liftracc_plugin_fptr[CLEAR_DGEMM_ID];
- if ((error = dlerror()) != 0) {
- ERROR("%s", error);
- return;
- }
-
char ta, tb;
switch (transa) {
case liftracc_no_trans: ta = 'N'; break;
case liftracc_trans: ta = 'T'; break;
case liftracc_conj_trans: ta = 'C'; break;
default: ta = 'N'; break;
}
switch (transb) {
case liftracc_no_trans: tb = 'N'; break;
case liftracc_trans: tb = 'T'; break;
case liftracc_conj_trans: tb = 'C'; break;
default: tb = 'N'; break;
}
- (*func)((const char *) &ta, (const char *) &tb,
- &m, &n, &k,
- &alpha, a, &lda,
- b, &ldb, &beta,
- c, &ldc);
+ if (func != 0) {
+ (*func)((const char *) &ta, (const char *) &tb,
+ &m, &n, &k,
+ &alpha, a, &lda,
+ b, &ldb, &beta,
+ c, &ldc);
+ } else {
+ success = 0;
+ }
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
diff --git a/library/src/plugins/cublas_plugin.c b/library/src/plugins/cublas_plugin.c
index 8122439..43f28a2 100644
--- a/library/src/plugins/cublas_plugin.c
+++ b/library/src/plugins/cublas_plugin.c
@@ -1,309 +1,338 @@
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include "cublas.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = {};
#endif
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = {};
plugin_info_t liftracc_plugin_info = {
.uuid = "4241c224-99c9-4c44-979f-32c6ac5fc9a4",
.name = "liftracc_cublas_plugin",
.desc = "wrapper to cublas library",
.prio = 20
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
if (cublasInit()==CUBLAS_STATUS_SUCCESS)
INFO("%s loaded.", liftracc_plugin_info.name);
else
ERROR("cublasInit() failed!");
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (cublasShutdown()==CUBLAS_STATUS_SUCCESS)
INFO("%s unloaded.", liftracc_plugin_info.name);
else
ERROR("cublasShutdown() failed!");
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
/* START OF BLAS FUNCTION IMPLEMENTATION */
void liftracc_plugin_daxpy(const int n, const double alpha, const double * x, const int incx, double * y, const int incy)
{
INFO("%s_daxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double* dev_x;
double* dev_y;
cublasAlloc(n, sizeof(*x), (void**)&dev_x);
cublasAlloc(n, sizeof(*y), (void**)&dev_y);
cublasSetVector(n, sizeof(*x), x, incx, dev_x, incx);
cublasSetVector(n, sizeof(*y), y, incy, dev_y, incy);
cublasDaxpy(n, alpha, dev_x, incx, dev_y, incy);
- if (cublasGetError()!=CUBLAS_STATUS_SUCCESS)
+ if (cublasGetError()!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
ERROR("cublas function ERROR");
+ }
cublasGetVector(n, sizeof(*y), dev_y, incy, y, incy);
cublasFree(dev_x);
cublasFree(dev_y);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DAXPY, SELECT_DAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
double liftracc_plugin_ddot(const int n, const double *x, const int incx, const double *y, const int incy)
{
INFO("%s_ddot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double* dev_x;
double* dev_y;
+ double ret = 0.0;
cublasAlloc(n, sizeof(*x), (void**)&dev_x);
cublasAlloc(n, sizeof(*y), (void**)&dev_y);
cublasSetVector(n, sizeof(*x), x, incx, dev_x, incx);
cublasSetVector(n, sizeof(*y), y, incy, dev_y, incy);
- double ret = cublasDdot(n, dev_x, incx, dev_y, incy);
+ ret = cublasDdot(n, dev_x, incx, dev_y, incy);
- if (cublasGetError()!=CUBLAS_STATUS_SUCCESS)
+ if (cublasGetError()!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
ERROR("cublas function ERROR");
+ }
cublasFree(dev_x);
cublasFree(dev_y);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
void liftracc_plugin_dgemm(const liftracc_order_t order,
const liftracc_transpose_t transa, const liftracc_transpose_t transb,
const int m, const int n, const int k,
const double alpha, const double *a, const int lda,
const double *b, const int ldb, const double beta,
double *c, const int ldc)
{
INFO("%s_dgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#if _LIFTRACC_PROFILING_ == 10
liftracc_function_timing_start(&(liftracc_profiling_data[PARAM_CONV]));
#endif /* _LIFTRACC_PROFILING_ */
+
if (order != liftracc_col_major) {
ERROR("Matrix not in column-major order.");
return;
}
char ta, tb;
switch (transa) {
case liftracc_no_trans: ta = 'N'; break;
case liftracc_trans: ta = 'T'; break;
case liftracc_conj_trans: ta = 'C'; break;
default: ta = 'N'; break;
}
switch (transb) {
case liftracc_no_trans: tb = 'N'; break;
case liftracc_trans: tb = 'T'; break;
case liftracc_conj_trans: tb = 'C'; break;
default: tb = 'N'; break;
}
#if _LIFTRACC_PROFILING_ == 10
liftracc_function_timing_stop(&(liftracc_profiling_data[PARAM_CONV]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double* dev_a;
double* dev_b;
double* dev_c;
- cublasAlloc(m*k, sizeof(*a), (void**)&dev_a);
- cublasAlloc(k*n, sizeof(*b), (void**)&dev_b);
- cublasAlloc(m*n, sizeof(*c), (void**)&dev_c);
+ if (cublasAlloc(m*k, sizeof(*a), (void**)&dev_a)!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
+ ERROR("cublas alloc");
+ }
+
+ if (cublasAlloc(k*n, sizeof(*b), (void**)&dev_b)!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
+ ERROR("cublas alloc");
+ }
+
+ if (cublasAlloc(m*n, sizeof(*c), (void**)&dev_c)!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
+ ERROR("cublas alloc");
+ }
cublasSetMatrix(m, k, sizeof(*a), a, lda, dev_a, lda);
cublasSetMatrix(k, n, sizeof(*a), a, ldb, dev_b, ldb);
cublasSetMatrix(m, n, sizeof(*a), a, ldc, dev_c, ldc);
cublasDgemm(ta, tb, m, n, k,
alpha, dev_a, lda,
dev_b, ldb, beta,
dev_c, ldc);
- if (cublasGetError()!=CUBLAS_STATUS_SUCCESS)
- ERROR("cublas function ERROR");
+ if (cublasGetError()!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
+ ERROR("cublas function exec");
+ }
cublasGetMatrix(m, n, sizeof(*c), dev_c, ldc, c, ldc);
cublasFree(dev_a);
cublasFree(dev_b);
cublasFree(dev_c);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dscal(const int n, const double alpha, double * x, const int incx)
{
INFO("%s_dscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double* dev_x;
cublasAlloc(n, sizeof(*x), (void**)&dev_x);
cublasSetVector(n, sizeof(*x), x, incx, dev_x, incx);
cublasDscal(n, alpha, dev_x, incx);
- if (cublasGetError()!=CUBLAS_STATUS_SUCCESS)
+ if (cublasGetError()!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
ERROR("cublas function ERROR");
+ }
cublasGetVector(n, sizeof(*x), dev_x, incx, x, incx);
cublasFree(dev_x);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
liftracc_index_t liftracc_plugin_idamax(const int n, const double * x, const int incx)
{
INFO("%s_idamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
double* dev_x;
+ int ret = 0;
cublasAlloc(n, sizeof(*x), (void**)&dev_x);
cublasSetVector(n, sizeof(*x), x, incx, dev_x, incx);
- int ret = cublasIdamax(n, dev_x, incx);
+ ret = cublasIdamax(n, dev_x, incx);
- if (cublasGetError()!=CUBLAS_STATUS_SUCCESS)
+ if (cublasGetError()!=CUBLAS_STATUS_SUCCESS) {
+ success = 0;
ERROR("cublas function ERROR");
+ }
cublasFree(dev_x);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
diff --git a/library/src/plugins/goto2_plugin.c b/library/src/plugins/goto2_plugin.c
index f03837f..d23cf22 100644
--- a/library/src/plugins/goto2_plugin.c
+++ b/library/src/plugins/goto2_plugin.c
@@ -1,263 +1,272 @@
#include "liftracc.h"
#include "liftracc_plugin.h"
#include "liftracc_logging.h"
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include "cblas.h"
#if _LIFTRACC_PROFILING_ > 0
#include "liftracc_profiling.h"
profiling_data_t function_profiling_data[LIFTRACC_FUNCTIONS_COUNT] = {};
#endif
decision_data_t decision_data[FUNCTION_COUNT*ARRAY_SIZE] = {};
typedef enum {
GOTO_DAXPY_ID,
GOTO_DDOT_ID,
GOTO_DGEMM_ID,
GOTO_DSCAL_ID,
GOTO_IDAMAX_ID,
GOTO_FUNCTIONS_COUNT
} liftracc_atlas_functions_t;
const char *liftracc_goto_function_names[] = {
"cblas_daxpy",
"cblas_ddot",
"cblas_dgemm",
"cblas_dscal",
"cblas_idamax",
"size_entry"
};
void *liftracc_plugin_fptr[GOTO_FUNCTIONS_COUNT] = { };
plugin_info_t liftracc_plugin_info = {
.uuid = "829a1670-46b0-450e-9f85-3d6a65a9efcb",
.name = "liftracc_libgoto2_plugin",
.desc = "wrapper to libgoto2 blas library",
.prio = 40,
};
void *handle = 0;
char *error = 0;
void __attribute__ ((constructor)) liftracc_plugin_load(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
char *libname = getenv("USE_GOTO2_LIB");
if (libname)
handle = dlopen(libname, RTLD_LAZY);
if (!handle)
handle = dlopen("libgoto2.so", RTLD_LAZY);
if (!handle)
ERROR("%s", dlerror());
else
INFO("%s loaded.", liftracc_plugin_info.name);
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
#ifdef _LIFTRACC_AUTOMODE_
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#else /* _LIFTRACC_AUTOMODE_ */
strncat(plugin_data_filename, ".txt", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
#endif /* _LIFTRACC_AUTOMODE_ */
liftracc_selector_loadinfo(plugin_data_filename, &decision_data[0]);
int i;
for (i=0; i<GOTO_FUNCTIONS_COUNT; i++) {
liftracc_plugin_fptr[i] = dlsym(handle, liftracc_goto_function_names[i]);
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_INIT]));
#endif /* _LIFTRACC_PROFILING_ */
}
void __attribute__ ((destructor)) liftracc_plugin_unload(void)
{
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FINI]));
#endif /* _LIFTRACC_PROFILING_ */
if (handle) dlclose(handle);
handle = 0;
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
char plugin_data_filename[PATH_MAX];
Dl_info info;
dladdr(liftracc_plugin_load, &info);
strncpy(plugin_data_filename, info.dli_fname, PATH_MAX);
strncat(plugin_data_filename, ".data", PATH_MAX-strlen(plugin_data_filename)-1);
MSG("plugin_data_filename: %s", plugin_data_filename);
liftracc_selector_saveinfo(plugin_data_filename, &decision_data[0]);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
INFO("%s unloaded.", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FINI]));
print_profiling_data(liftracc_plugin_info.name, &(function_profiling_data[0]), liftracc_function_names, LIFTRACC_FUNCTIONS_COUNT);
#endif /* _LIFTRACC_PROFILING_ */
}
decision_data_t liftracc_plugin_getdecision(liftracc_selector_funcid_t id, int index)
{
#ifdef _LIFTRACC_AUTOMODE_
return decision_data[id*ARRAY_SIZE+index];
#else
if (decision_data[id*ARRAY_SIZE+index] > 0)
return decision_data[id*ARRAY_SIZE+index];
return liftracc_plugin_info.prio;
#endif /* _LIFTRACC_AUTOMODE_ */
}
/* START OF BLAS FUNCTION IMPLEMENTATION */
void liftracc_plugin_daxpy(const int n, const double alpha, const double * x, const int incx, double * y, const int incy)
{
INFO("%s_daxpy", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
void (*func)();
+ *(void **) (&func) = liftracc_plugin_fptr[GOTO_DAXPY_ID];
- *(void **) (&func) = dlsym(handle, "cblas_daxpy");
-
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
(*func)(n, alpha, x, incx, y, incy);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DAXPY]));
#endif /* _LIFTRACC_PROFILING_ */
#if _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DAXPY, SELECT_DAXPY);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
double liftracc_plugin_ddot(const int n, const double *x, const int incx, const double *y, const int incy)
{
INFO("%s_ddot", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
+ double ret = 0.0;
double (*func)();
- *(void **) (&func) = dlsym(handle, "cblas_ddot");
+ *(void **) (&func) = liftracc_plugin_fptr[GOTO_DDOT_ID];
- if ((error = dlerror()) != 0) {
- ERROR("%s", error);
- return 0.0;
+ if (func != 0) {
+ ret = (*func)(n, x, incx, y, incy);
+ } else {
+ success = 0;
}
- double ret = (*func)(n, x, incx, y, incy);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DDOT]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DDOT, SELECT_DDOT);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
void liftracc_plugin_dgemm(const liftracc_order_t order,
const liftracc_transpose_t transa, const liftracc_transpose_t transb,
const int m, const int n, const int k,
const double alpha, const double *a, const int lda,
const double *b, const int ldb, const double beta,
double *c, const int ldc)
{
INFO("%s_dgemm", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
void (*func)();
- *(void **) (&func) = dlsym(handle, "cblas_dgemm");
+ *(void **) (&func) = liftracc_plugin_fptr[GOTO_DGEMM_ID];
- if ((error = dlerror()) != 0) {
- ERROR("%s", error);
- return;
+ if (func != 0) {
+ (*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
+ } else {
+ success = 0;
}
- (*func)(order, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DGEMM]));
#endif /* _LIFTRACC_PROFILING_ */
#if _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DGEMM, SELECT_DGEMM);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
void liftracc_plugin_dscal(const int n, const double alpha, double * x, const int incx)
{
INFO("%s_dscal", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
void (*func)();
+ *(void **) (&func) = liftracc_plugin_fptr[GOTO_DSCAL_ID];
- *(void **) (&func) = dlsym(handle, "cblas_dscal");
-
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
(*func)(n, alpha, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_DSCAL]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_DSCAL, SELECT_DSCAL);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
}
liftracc_index_t liftracc_plugin_idamax(const int n, const double * x, const int incx)
{
INFO("%s_idamax", liftracc_plugin_info.name);
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_start(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
+ int success = 1;
+ liftracc_index_t ret = 0;
liftracc_index_t (*func)();
- liftracc_index_t ret = 0.0;
-
- *(void **) (&func) = dlsym(handle, "cblas_idamax");
+ *(void **) (&func) = liftracc_plugin_fptr[GOTO_IDAMAX_ID];
- if ((error = dlerror()) == 0) {
+ if (func != 0) {
ret = (*func)(n, x, incx);
+ } else {
+ success = 0;
}
#if _LIFTRACC_PROFILING_ == 3
liftracc_function_timing_stop(&(function_profiling_data[LIFTRACC_FUNCTION_IDAMAX]));
#endif /* _LIFTRACC_PROFILING_ */
#ifdef _LIFTRACC_AUTOMODE_TRAINING_
- set_decision_data(&decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
+ set_decision_data(success, &decision_data[0], &function_profiling_data[0], n, LIFTRACC_FUNCTION_IDAMAX, SELECT_IDAMAX);
#endif /* _LIFTRACC_AUTOMODE_TRAINING_ */
return ret;
}
diff --git a/library/tests/test05.cpp b/library/tests/test05.cpp
index 9a11e4d..2ad7af8 100644
--- a/library/tests/test05.cpp
+++ b/library/tests/test05.cpp
@@ -1,113 +1,118 @@
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <unistd.h>
#include <time.h>
#include <math.h>
#ifndef __USE_GNU
#define __USE_GNU
#endif
#include <dlfcn.h>
#include "liftracc.h"
#include "liftracc_logging.h"
#include "liftracc_profiling.h"
extern "C" {
#include "cblas.h"
}
int main(int argc, char** argv)
{
- printf("TEST\n");
#ifdef _LIFTRACC_PROFILING_
for (int i=0; i<100; i++) {
liftracc_function_timing_start(&(liftracc_profiling_data[MEASURING_ERROR]));
liftracc_function_timing_stop(&(liftracc_profiling_data[MEASURING_ERROR]));
}
#endif /* _LIFTRACC_PROFILING_ */
unsigned int error_count = 0;
const int max_runs = 10;
const int max_dim = 1024; //8192;
const int max_entries = max_dim * max_dim;
#ifdef _LIFTRACC_PROFILING_
profiling_data_t data[max_dim] = { };
#endif /* _LIFTRACC_PROFILING_ */
double *dA = (double*) malloc( sizeof(double) * max_entries );
double *dB = (double*) malloc( sizeof(double) * max_entries );
double *dC = (double*) malloc( sizeof(double) * max_entries );
double *dM = (double*) malloc( sizeof(double) * max_entries );
double dAlpha = 1.3;
double dBeta = 3.7;
srand(time(0));
// init libraries
void *cblas_handle = 0;
char *error = 0;
- cblas_handle = dlopen("libcblas.so", RTLD_LAZY);
+ cblas_handle = dlopen("libcblas_inner.so", RTLD_LAZY);
if (!cblas_handle)
ERROR("%s", dlerror());
if (cblas_handle) INFO("lib init ok.");
// function init
void (*cblas_dgemm)(const liftracc_order_t order,
const liftracc_transpose_t transa,
const liftracc_transpose_t transb,
const int m,
const int n,
const int k,
const double alpha,
const double *a,
const int lda,
const double *b,
const int ldb,
const double beta,
double *c,
const int ldc);
*(void **) (&cblas_dgemm) = dlsym(cblas_handle, "inner_cblas_dgemm");
if ((error = dlerror()) != 0) {
ERROR("%s", error);
}
// benchmark
int j,i;
for (j=0;j<max_runs;j++) {
for (i=0; i<max_entries; i++) dA[i] = (double)(rand()%500/100.0);
for (i=0; i<max_entries; i++) dB[i] = (double)(rand()%500/100.0);
for (i=0; i<max_entries; i++) dM[i] = (double)(rand()%500/100.0);
memcpy(dC, dM, max_entries);
for (i=2; i<max_dim; i++) {
#ifdef _LIFTRACC_PROFILING_
liftracc_function_timing_start(&(data[i]));
#endif /* _LIFTRACC_PROFILING_ */
(*cblas_dgemm)(liftracc_col_major, liftracc_no_trans, liftracc_no_trans,
i,i,i,
dAlpha, dA, i,
dB, i,
dBeta,
dC, i);
+ int different = 0;
+ int c;
+ for (c=0; c<max_entries; c++) {
+ if (dM[c] != dC[c]) different++;
+ }
+ MSG("Entries: %d -- Different: %d -- Same: %d", max_entries, different, max_entries-different);
#ifdef _LIFTRACC_PROFILING_
liftracc_function_timing_stop(&(data[i]));
#endif /* _LIFTRACC_PROFILING_ */
memcpy(dC, dM, max_entries);
MSG("%d_%d.run", j, i);
}
}
#ifdef _LIFTRACC_PROFILING_
print_profiling_data("cblas_RESULT", &(data[0]), 0, max_dim);
#endif /* _LIFTRACC_PROFILING_ */
return error_count;
}
|
pc2/liftracc
|
f740775d57b1c9f292c04be75448518a53739f82
|
missed some gitignores
|
diff --git a/.gitignore b/.gitignore
index 4c5f08a..32b8a02 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,3 @@
library/build/*
+benchmarks/build/*
+testapps/build/*
|
pc2/liftracc
|
2aa1c87168d839979c0ccaddf37f17ae9f8e3fac
|
github generated gh-pages branch
|
diff --git a/index.html b/index.html
new file mode 100644
index 0000000..908c541
--- /dev/null
+++ b/index.html
@@ -0,0 +1,78 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
+ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
+<head>
+ <meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
+
+ <title>pc2/liftracc @ GitHub</title>
+
+ <style type="text/css">
+ body {
+ margin-top: 1.0em;
+ background-color: #e1ca9d;
+ font-family: "Helvetica,Arial,FreeSans";
+ color: #000000;
+ }
+ #container {
+ margin: 0 auto;
+ width: 700px;
+ }
+ h1 { font-size: 3.8em; color: #1e3562; margin-bottom: 3px; }
+ h1 .small { font-size: 0.4em; }
+ h1 a { text-decoration: none }
+ h2 { font-size: 1.5em; color: #1e3562; }
+ h3 { text-align: center; color: #1e3562; }
+ a { color: #1e3562; }
+ .description { font-size: 1.2em; margin-bottom: 30px; margin-top: 30px; font-style: italic;}
+ .download { float: right; }
+ pre { background: #000; color: #fff; padding: 15px;}
+ hr { border: 0; width: 80%; border-bottom: 1px solid #aaa}
+ .footer { text-align:center; padding-top:30px; font-style: italic; }
+ </style>
+
+</head>
+
+<body>
+ <a href="http://github.com/pc2/liftracc"><img style="position: absolute; top: 0; right: 0; border: 0;" src="http://s3.amazonaws.com/github/ribbons/forkme_right_darkblue_121621.png" alt="Fork me on GitHub" /></a>
+
+ <div id="container">
+
+ <div class="download">
+ <a href="http://github.com/pc2/liftracc/zipball/master">
+ <img border="0" width="90" src="http://github.com/images/modules/download/zip.png"></a>
+ <a href="http://github.com/pc2/liftracc/tarball/master">
+ <img border="0" width="90" src="http://github.com/images/modules/download/tar.png"></a>
+ </div>
+
+ <h1><a href="http://github.com/pc2/liftracc">liftracc</a>
+ <span class="small">by <a href="http://github.com/pc2">pc2</a></span></h1>
+
+ <div class="description">
+ Dynamic Shared Library Interposing Framework for Transparent Accelerator Utilization
+ </div>
+
+ <h2>Contact</h2>
+<p>Paderborn Center for Parallel Computing</p>
+
+
+ <h2>Download</h2>
+ <p>
+ You can download this project in either
+ <a href="http://github.com/pc2/liftracc/zipball/master">zip</a> or
+ <a href="http://github.com/pc2/liftracc/tarball/master">tar</a> formats.
+ </p>
+ <p>You can also clone the project with <a href="http://git-scm.com">Git</a>
+ by running:
+ <pre>$ git clone git://github.com/pc2/liftracc</pre>
+ </p>
+
+ <div class="footer">
+ get the source code on GitHub : <a href="http://github.com/pc2/liftracc">pc2/liftracc</a>
+ </div>
+
+ </div>
+
+
+</body>
+</html>
|
dyoo/js-numbers
|
2cf776f6017858a30488a4ec768be3e67bb0a6c4
|
use strict
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index f8294ce..850d506 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,550 +1,551 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
+ 'use strict';
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(expandExponent(x+''));
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
var expandExponent = function(s) {
var match = s.match(scientificPattern), mantissaChunks, exponent;
if (match) {
mantissaChunks = match[1].match(/^([^.]*)(.*)$/);
exponent = Number(match[2]);
if (mantissaChunks[2].length === 0) {
return mantissaChunks[1] + zfill(exponent);
}
if (exponent >= mantissaChunks[2].length - 1) {
return (mantissaChunks[1] +
mantissaChunks[2].substring(1) +
zfill(exponent - (mantissaChunks[2].length - 1)));
} else {
return (mantissaChunks[1] +
mantissaChunks[2].substring(1, 1+exponent));
}
} else {
return s;
}
};
// zfill: integer -> string
// builds a string of "0"'s of length n.
var zfill = function(n) {
var buffer = [];
buffer.length = n;
for (var i = 0; i < n; i++) {
buffer[i] = '0';
}
return buffer.join('');
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = function(x, y) {
var sum;
if (typeof(x) === 'number' && typeof(y) === 'number') {
sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
}
}
if (x instanceof FloatPoint && y instanceof FloatPoint) {
return x.add(y);
}
return addSlow(x, y);
};
var addSlow = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = function(x, y) {
var prod;
if (typeof(x) === 'number' && typeof(y) === 'number') {
prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
}
if (x instanceof FloatPoint && y instanceof FloatPoint) {
return x.multiply(y);
}
return multiplySlow(x, y);
};
var multiplySlow = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isXSpecialCase: function(x) {
return (eqv(x, 0));
},
onXSpecialCase: function(x, y) {
if (eqv(y, 0)) {
throwRuntimeError("/: division by zero", x, y);
}
return 0;
},
isYSpecialCase: function(y) {
return (eqv(y, 0)); },
onYSpecialCase: function(x, y) {
throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
|
dyoo/js-numbers
|
d23ccf19cb36bff5786688680b4a707fc9c1b3f9
|
trying to fast-path a few common functions
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 0192b47..f8294ce 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,799 +1,828 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(expandExponent(x+''));
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
var expandExponent = function(s) {
var match = s.match(scientificPattern), mantissaChunks, exponent;
if (match) {
mantissaChunks = match[1].match(/^([^.]*)(.*)$/);
exponent = Number(match[2]);
if (mantissaChunks[2].length === 0) {
return mantissaChunks[1] + zfill(exponent);
}
if (exponent >= mantissaChunks[2].length - 1) {
return (mantissaChunks[1] +
mantissaChunks[2].substring(1) +
zfill(exponent - (mantissaChunks[2].length - 1)));
} else {
return (mantissaChunks[1] +
mantissaChunks[2].substring(1, 1+exponent));
}
} else {
return s;
}
};
// zfill: integer -> string
// builds a string of "0"'s of length n.
var zfill = function(n) {
var buffer = [];
buffer.length = n;
for (var i = 0; i < n; i++) {
buffer[i] = '0';
}
return buffer.join('');
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
- var add = makeNumericBinop(
+ var add = function(x, y) {
+ var sum;
+ if (typeof(x) === 'number' && typeof(y) === 'number') {
+ sum = x + y;
+ if (isOverflow(sum)) {
+ return (makeBignum(x)).add(makeBignum(y));
+ }
+ }
+ if (x instanceof FloatPoint && y instanceof FloatPoint) {
+ return x.add(y);
+ }
+ return addSlow(x, y);
+ };
+
+ var addSlow = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
- var multiply = makeNumericBinop(
+ var multiply = function(x, y) {
+ var prod;
+ if (typeof(x) === 'number' && typeof(y) === 'number') {
+ prod = x * y;
+ if (isOverflow(prod)) {
+ return (makeBignum(x)).multiply(makeBignum(y));
+ } else {
+ return prod;
+ }
+ }
+ if (x instanceof FloatPoint && y instanceof FloatPoint) {
+ return x.multiply(y);
+ }
+ return multiplySlow(x, y);
+ };
+ var multiplySlow = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isXSpecialCase: function(x) {
return (eqv(x, 0));
},
onXSpecialCase: function(x, y) {
if (eqv(y, 0)) {
throwRuntimeError("/: division by zero", x, y);
}
return 0;
},
isYSpecialCase: function(y) {
return (eqv(y, 0)); },
onYSpecialCase: function(x, y) {
throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (! isInteger(x)) {
throwRuntimeError('integer-sqrt: the argument ' + x.toString() +
" is not an integer.", x);
}
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
|
dyoo/js-numbers
|
608b38f21c53684e4310ad36b06bf47c1a4f4fc3
|
changing the behavior of tan, atan, and makeComplexPolar when given exact 0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index bfe4a28..0192b47 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -107,1216 +107,1218 @@ if (typeof(exports) !== 'undefined') {
mantissaChunks[2].substring(1, 1+exponent));
}
} else {
return s;
}
};
// zfill: integer -> string
// builds a string of "0"'s of length n.
var zfill = function(n) {
var buffer = [];
buffer.length = n;
for (var i = 0; i < n; i++) {
buffer[i] = '0';
}
return buffer.join('');
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isXSpecialCase: function(x) {
return (eqv(x, 0));
},
onXSpecialCase: function(x, y) {
if (eqv(y, 0)) {
throwRuntimeError("/: division by zero", x, y);
}
return 0;
},
isYSpecialCase: function(y) {
return (eqv(y, 0)); },
onYSpecialCase: function(x, y) {
throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
+ if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
+ if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (! isInteger(x)) {
throwRuntimeError('integer-sqrt: the argument ' + x.toString() +
" is not an integer.", x);
}
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
- if (equals(theta, 0)) {
+ if (eqv(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
|
dyoo/js-numbers
|
185e321241353ba9f958491265baab84c4734dd4
|
fixing bug: asin(0) = exact 0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index a0ceac9..bfe4a28 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -150,1024 +150,1025 @@ if (typeof(exports) !== 'undefined') {
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isXSpecialCase: function(x) {
return (eqv(x, 0));
},
onXSpecialCase: function(x, y) {
if (eqv(y, 0)) {
throwRuntimeError("/: division by zero", x, y);
}
return 0;
},
isYSpecialCase: function(y) {
return (eqv(y, 0)); },
onYSpecialCase: function(x, y) {
throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
+ if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (! isInteger(x)) {
throwRuntimeError('integer-sqrt: the argument ' + x.toString() +
" is not an integer.", x);
}
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
diff --git a/test/tests.js b/test/tests.js
index 2506cff..b27943a 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -3065,861 +3065,860 @@ describe('integerSqrt', {
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
assertTrue(eqv(integerSqrt(negative_zero),
negative_zero));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('repeating decimals', {
tests: function() {
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
},
limitRendering: function() {
var OPTIONS = {limit: 5};
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1, OPTIONS));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2, OPTIONS));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3, OPTIONS));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4, OPTIONS));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5, OPTIONS));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6, OPTIONS));
assertEquals(['0', '05882', '...'],
toRepeatingDecimal(1, 17, {limit : 5}));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8, {limit : 4}));
assertEquals(['0', '125', '...'], toRepeatingDecimal(1, 8, {limit : 3}));
assertEquals(['0', '12', '...'], toRepeatingDecimal(1, 8, {limit : 2}));
assertEquals(['0', '1', '...'], toRepeatingDecimal(1, 8, {limit : 1}));
assertEquals(['0', '', '...'], toRepeatingDecimal(1, 8, {limit : 0}));
assertEquals(['10012718086',
'8577149703838870007766167',
'...'],
toRepeatingDecimal(makeBignum("239872983562893234879"),
makeBignum("23956829852"),
{limit:25}));
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertEqv(divide(makeFloat(1),makeFloat(0)),
inf);
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
- assertTrue(equals(asin(0),
- 0));
+ assertTrue(eqv(asin(0), 0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(diffPercent(realPart(asin(makeComplex(1, 5))),
makeFloat(0.1937931365549321))
< 1e-2);
assertTrue(diffPercent(imaginaryPart(asin(makeComplex(1, 5))),
makeFloat(2.3309746530493123))
< 1e-2);
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
assertEquals("5.0+0.0i",
(makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
(makeComplex(5, 1)).toString());
assertEquals("4-2i",
(makeComplex(4, -2)).toString());
},
testQuotient : function(){
assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
assertTrue(eqv(1, quotient(7, 5)));
},
testRemainder : function(){
assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
makeFloat(3)));
assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, modulo(n1, n2));
assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(isReal(pi));
assertTrue(isReal(1));
assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!isReal("hi"));
},
testRound : function(){
assertTrue(equals(round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(round(makeRational(3)),
makeRational(3)));
assertTrue(equals(round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(round(makeRational(-17, 4)),
makeRational(-4)));
},
// testSgn : function(){
// assertTrue(equals(sgn(makeFloat(4)), 1));
// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
// assertTrue(equals(sgn(0), 0));
// },
// testZero_question_ : function(){
// assertTrue(Kernel.zero_question_(0));
// assertTrue(!Kernel.zero_question_(1));
// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
// }
});
|
dyoo/js-numbers
|
d7fd36e5ace3c74a59182dff5723e78491453a99
|
added another test case
|
diff --git a/test/tests.js b/test/tests.js
index 34b7e2b..2506cff 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,679 +1,681 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertEqv = function(x, y) {
value_of(eqv(x, y)).should_be_true();
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
value_of(toFixnum(makeRational(1, 5)) === 0.2)
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
assertTrue(eqv(makeComplexPolar(1, 2),
makeComplex(makeFloat(-0.4161468365471424),
makeFloat(0.9092974268256817))));
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
+ assertEquals(makeFloat(1000000000000000.2),
+ fromString("1000000000000000.2"));
assertEquals(makeFloat(10000000000000000.2),
fromString("10000000000000000.2"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertTrue(equals(fromString("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100)));
assertTrue(equals(fromString("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200)));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(makeRational(1024), makeFloat(1024))).should_be_false();
value_of(eqv(makeRational(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
// If any component of a complex is inexact, both
// the real and imaginary parts get turned into
// inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
assertFalse(isRational(makeComplex(makeFloat(0), makeFloat(0))));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
|
dyoo/js-numbers
|
b3d6f8b8e1a9bc67d360fec14e0124f06a47ade6
|
Passing test cases again
|
diff --git a/README b/README
index dc9bcd2..28f28a5 100644
--- a/README
+++ b/README
@@ -1,320 +1,324 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a toplevel namespace called
jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
- Convert from a javascript number to a scheme-number.
+ Convert from a javascript number to a scheme number. If the
+ number looks like an integer, represents as an exact integer.
+ Otherwise, represents as a float. If you need more precision over
+ the representation, use makeFloat or makeRational instead.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
- the denominator is 1.
+ the denominator is 1. The numerator and denominator must be
+ integers.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInexact: scheme-number -> boolean
Produces true if the number is inexact.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
toInexact: scheme-number -> scheme-number
Converts the number to an inexact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
quotient: scheme-number scheme-number -> scheme-number
Produces the quotient. Both inputs must be integers.
remainder: scheme-number scheme-number -> scheme-number
Produces the remainder. Both inputs must be integers.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
toRepeatedDecimal: scheme-number scheme-number {limit: number}? -> [string, string, string]
Produces a string representation of the decimal expansion; the first and second
argument must be integers. Returns an array of three parts: the portion before
the decimal, the non-repeating part, and then the repeating part.
If the expansion goes beyond the limit (by default, 256 characters), then
the expansion will be cut off, and the third portion will be '...'.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, sgn
* Add real documentation.
======================================================================
Related work
There appears to be another Scheme numeric tower implementation that
just came out in the last month or so, by Matt Might and John Tobey:
https://github.com/jtobey/javascript-bignum
http://silentmatt.com/biginteger/
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
June 2010: got implementation of integer-sqrt from Ugur Cekmez;
brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index e1f0f4c..a0ceac9 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,600 +1,634 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
- if (isOverflow(nf)) {
- return makeBignum(x);
- } else {
+ if (isOverflow(nf)) {
+ return makeBignum(expandExponent(x+''));
+ } else {
return nf;
}
} else {
- return FloatPoint.makeInstance(x);
+ return FloatPoint.makeInstance(x);
+ }
+ };
+
+ var expandExponent = function(s) {
+ var match = s.match(scientificPattern), mantissaChunks, exponent;
+ if (match) {
+ mantissaChunks = match[1].match(/^([^.]*)(.*)$/);
+ exponent = Number(match[2]);
+
+ if (mantissaChunks[2].length === 0) {
+ return mantissaChunks[1] + zfill(exponent);
+ }
+
+ if (exponent >= mantissaChunks[2].length - 1) {
+ return (mantissaChunks[1] +
+ mantissaChunks[2].substring(1) +
+ zfill(exponent - (mantissaChunks[2].length - 1)));
+ } else {
+ return (mantissaChunks[1] +
+ mantissaChunks[2].substring(1, 1+exponent));
+ }
+ } else {
+ return s;
+ }
+ };
+
+ // zfill: integer -> string
+ // builds a string of "0"'s of length n.
+ var zfill = function(n) {
+ var buffer = [];
+ buffer.length = n;
+ for (var i = 0; i < n; i++) {
+ buffer[i] = '0';
}
+ return buffer.join('');
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isXSpecialCase: function(x) {
return (eqv(x, 0));
},
onXSpecialCase: function(x, y) {
if (eqv(y, 0)) {
throwRuntimeError("/: division by zero", x, y);
}
return 0;
},
isYSpecialCase: function(y) {
return (eqv(y, 0)); },
onYSpecialCase: function(x, y) {
throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
@@ -988,1885 +1022,1887 @@ if (typeof(exports) !== 'undefined') {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
- return fromFixnum(fl);
+ return fl;
}
else {
- return fromFixnum(ce);
+ return ce;
}
} else {
- return fromFixnum(Math.round(this.n / this.d));
+ return Math.round(this.n / this.d);
}
};
-
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(-0.0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
} else if (n === 0) {
if ((1/n) === -Infinity) {
return NEGATIVE_ZERO;
} else {
return INEXACT_ZERO;
}
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n - other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
return FloatPoint.makeInstance(this.n * other.n);
};
FloatPoint.prototype.divide = function(other) {
return FloatPoint.makeInstance(this.n / other.n);
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
return FloatPoint.makeInstance(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
- if (typeof(r) === 'number') { r = fromFixnum(r); }
- if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
if (this.isInexact() || other.isInexact()) {
// http://portal.acm.org/citation.cfm?id=1039814
// We currently use Smith's method, though we should
// probably switch over to Priest's method.
a = this.r;
b = this.i;
c = other.r;
d = other.i;
if (lessThanOrEqual(abs(d), abs(c))) {
r = divide(d, c);
x = divide(add(a, multiply(b, r)),
add(c, multiply(d, r)));
y = divide(subtract(b, multiply(a, r)),
add(c, multiply(d, r)));
} else {
r = divide(c, d);
x = divide(add(multiply(a, r), b),
add(multiply(c, r), d));
y = divide(subtract(multiply(b, r), a),
add(multiply(c, r), d));
}
return Complex.makeInstance(x, y);
} else {
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
}
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
- var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
- var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
- var digitRegexp = new RegExp("\\d");
+ var digitRegexp = new RegExp("^[+-]?\\d+$");
+ var flonumRegexp = new RegExp("^([+-]?\\d*)\\.(\\d*)$");
+ var scientificPattern = new RegExp("^([+-]?\\d*\\.?\\d*)[Ee](\\+?\\d+)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
+ // Floating point tests
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
- if (x.match(digitRegexp) &&
- (x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
+ if (x.match(flonumRegexp) || x.match(scientificPattern)) {
+ return FloatPoint.makeInstance(Number(x));
+ }
+
+ // Finally, integer tests.
+ if (x.match(digitRegexp)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
- return fromFixnum(n);
+ return n;
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
// use am to combine the multiply-shift-add into one call
j = i+this.m.t;
x[j] += this.m.am(0,u0,x,i,0,this.m.t);
// propagate carry
@@ -3110,949 +3146,944 @@ if (typeof(exports) !== 'undefined') {
// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
// (public) ~this
function bnNot() {
var r = nbi();
for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
r.t = this.t;
r.s = ~this.s;
return r;
}
// (public) this << n
function bnShiftLeft(n) {
var r = nbi();
if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
return r;
}
// (public) this >> n
function bnShiftRight(n) {
var r = nbi();
if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
return r;
}
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if(x == 0) return -1;
var r = 0;
if((x&0xffff) == 0) { x >>= 16; r += 16; }
if((x&0xff) == 0) { x >>= 8; r += 8; }
if((x&0xf) == 0) { x >>= 4; r += 4; }
if((x&3) == 0) { x >>= 2; r += 2; }
if((x&1) == 0) ++r;
return r;
}
// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
for(var i = 0; i < this.t; ++i)
if(this[i] != 0) return i*this.DB+lbit(this[i]);
if(this.s < 0) return this.t*this.DB;
return -1;
}
// return number of 1 bits in x
function cbit(x) {
var r = 0;
while(x != 0) { x &= x-1; ++r; }
return r;
}
// (public) return number of set bits
function bnBitCount() {
var r = 0, x = this.s&this.DM;
for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
return r;
}
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this.DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this.DB)))!=0);
}
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
var r = BigInteger.ONE.shiftLeft(n);
this.bitwiseTo(r,op,r);
return r;
}
// (public) this | (1<<n)
function bnSetBit(n) { return this.changeBit(n,op_or); }
// (public) this & ~(1<<n)
function bnClearBit(n) { return this.changeBit(n,op_andnot); }
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this.changeBit(n,op_xor); }
// (protected) r = this + a
function bnpAddTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]+a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this.DV+c;
r.t = i;
r.clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
- var match = s.match(bignumScientificPattern);
- if (match) {
- return new BigInteger(match[1]+match[2] +
- zerostring(Number(match[3]) - match[2].length),
- 10);
- } else {
- return new BigInteger(s, 10);
- }
+ s = expandExponent(s);
+ return new BigInteger(s, 10);
};
+
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))))) {
guess = floor(divide(add(guess,
floor(divide(n, guess))),
2));
}
return guess;
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
var n;
if(sign(this) >= 0) {
return searchIter(this, this);
} else {
n = this.negate();
return Complex.makeInstance(0, searchIter(n, n));
}
};
})();
(function() {
// Get an approximation using integerSqrt, and then start another
// Newton-Ralphson search if necessary.
BigInteger.prototype.sqrt = function() {
var approx = this.integerSqrt(), fix;
if (eqv(sqr(approx), this)) {
return approx;
}
fix = toFixnum(this);
if (isFinite(fix)) {
if (fix >= 0) {
return FloatPoint.makeInstance(Math.sqrt(fix));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-fix)));
}
} else {
return approx;
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
//
// An optional limit on the decimal expansion can be provided, in which
// case the search cuts off if we go past the limit.
// If this happens, the third argument returned becomes '...' to indicate
// that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
if (limit-- <= 0) {
return [digits.join(''), '...']
}
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d, options) {
// default limit on decimal expansion; can be overridden
var limit = 512;
if (options && typeof(options.limit) !== 'undefined') {
limit = options.limit;
}
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
// The following exposes the class representations for easier
// integration with other projects.
Numbers['BigInteger'] = BigInteger;
Numbers['Rational'] = Rational;
Numbers['FloatPoint'] = FloatPoint;
Numbers['Complex'] = Complex;
Numbers['MIN_FIXNUM'] = MIN_FIXNUM;
Numbers['MAX_FIXNUM'] = MAX_FIXNUM;
})();
diff --git a/test/tests.js b/test/tests.js
index c5cebc9..34b7e2b 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,1036 +1,1036 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertEqv = function(x, y) {
value_of(eqv(x, y)).should_be_true();
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
value_of(toFixnum(makeRational(1, 5)) === 0.2)
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
assertTrue(eqv(makeComplexPolar(1, 2),
makeComplex(makeFloat(-0.4161468365471424),
makeFloat(0.9092974268256817))));
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
- assertEquals(makeFloat(0.1), fromString(".1"));
- assertEquals(makeFloat(0.23), fromString("0.23"));
- assertEquals(makeFloat(0.1), fromString("+.1"));
- assertEquals(makeFloat(-0.1), fromString("-.1"));
- assertEquals(makeFloat(-0.123423), fromString("-.123423"));
- assertEquals(makeFloat(123.45), fromString("123.45"));
- assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
- assertEquals(makeFloat(10000000000000000.2),
- fromString("10000000000000000.2"));
+ assertEquals(makeFloat(0.1), fromString(".1"));
+ assertEquals(makeFloat(0.23), fromString("0.23"));
+ assertEquals(makeFloat(0.1), fromString("+.1"));
+ assertEquals(makeFloat(-0.1), fromString("-.1"));
+ assertEquals(makeFloat(-0.123423), fromString("-.123423"));
+ assertEquals(makeFloat(123.45), fromString("123.45"));
+ assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
+ assertEquals(makeFloat(10000000000000000.2),
+ fromString("10000000000000000.2"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
- assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
- fromFixnum(10e100));
+ assertTrue(equals(fromString("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
+ fromFixnum(10e100)));
- assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
- fromFixnum(10e200));
+ assertTrue(equals(fromString("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
+ fromFixnum(10e200)));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
- value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
- value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
+ value_of(eqv(makeRational(1024), makeFloat(1024))).should_be_false();
+ value_of(eqv(makeRational(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
// If any component of a complex is inexact, both
// the real and imaginary parts get turned into
// inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
assertFalse(isRational(makeComplex(makeFloat(0), makeFloat(0))));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
assertTrue(isReal(makeBignum("1e1000")));
assertTrue(isReal(makeBignum("-1e1000")));
assertTrue(isReal(makeBignum("1e23784")));
assertTrue(isReal(makeBignum("-7.241e23784")));
},
'rationals': function() {
assertTrue(isReal(makeRational(0, 1)));
assertTrue(isReal(makeRational(0, 12342)));
assertTrue(isReal(makeRational(-2324, 12342)));
assertTrue(isReal(makeRational(1, 2)));
},
'floats': function() {
assertTrue(isReal(makeFloat(1.0)));
assertTrue(isReal(makeFloat(25.0)));
assertTrue(isReal(e));
assertTrue(isReal(pi));
assertTrue(isReal(inf));
assertTrue(isReal(negative_inf));
assertTrue(isReal(nan));
},
'complex': function() {
assertTrue(isReal(makeComplex(0, 0)));
assertTrue(isReal(makeComplex(e, 0)));
assertTrue(isReal(makeComplex(pi, 0)));
assertTrue(isReal(makeComplex(nan, 0)));
assertTrue(isReal(makeComplex(inf, 0)));
assertTrue(isReal(makeComplex(negative_inf, 0)));
assertFalse(isReal(makeComplex(0, 1)));
assertFalse(isReal(makeComplex(0, negative_inf)));
assertFalse(isReal(makeComplex(pi, inf)));
assertFalse(isReal(makeComplex(234, nan)));
assertFalse(isReal(makeComplex(makeFloat(3),
makeFloat(0))));
},
'others': function() {
assertFalse(isReal("0"));
assertFalse(isReal("hello"));
assertFalse(isReal([]));
assertFalse(isReal({}));
assertFalse(isReal(false));
}
});
describe('isExact', {
'fixnums': function() {
assertTrue(isExact(19));
assertTrue(isExact(0));
assertTrue(isExact(-1));
assertTrue(isExact(1));
},
'bignums': function() {
assertTrue(isExact(makeBignum("0")));
assertTrue(isExact(makeBignum("1")));
assertTrue(isExact(makeBignum("-1")));
assertTrue(isExact(makeBignum("23497842398287924789232439723")));
assertTrue(isExact(makeBignum("1e1000")));
assertTrue(isExact(makeBignum("-1e1000")));
assertTrue(isExact(makeBignum("12342357892297851728921374891327893")));
assertTrue(isExact(makeBignum("4.1321e200")));
assertTrue(isExact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertTrue(isExact(makeRational(19)));
assertTrue(isExact(makeRational(0)));
assertTrue(isExact(makeRational(-1)));
assertTrue(isExact(makeRational(1)));
assertTrue(isExact(makeRational(1, 2)));
assertTrue(isExact(makeRational(1, 29291)));
},
'floats': function() {
assertFalse(isExact(e));
assertFalse(isExact(pi));
assertFalse(isExact(inf));
assertFalse(isExact(negative_inf));
assertFalse(isExact(nan));
assertFalse(isExact(makeFloat(0)));
assertFalse(isExact(makeFloat(1111.1)));
},
'complex': function() {
assertTrue(isExact(makeComplex(0, 0)));
assertTrue(isExact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertFalse(isExact(makeComplex(e,
makeRational(1, 17))));
assertFalse(isExact(makeComplex(makeRational(1,2),
pi)));
assertFalse(isExact(makeComplex(makeRational(1,2),
nan)));
assertFalse(isExact(makeComplex(negative_inf,
nan)));
}
});
describe('isInexact', {
'fixnums': function() {
assertFalse(isInexact(19));
assertFalse(isInexact(0));
assertFalse(isInexact(-1));
assertFalse(isInexact(1));
},
'bignums': function() {
assertFalse(isInexact(makeBignum("0")));
assertFalse(isInexact(makeBignum("1")));
assertFalse(isInexact(makeBignum("-1")));
assertFalse(isInexact(makeBignum("23497842398287924789232439723")));
assertFalse(isInexact(makeBignum("1e1000")));
assertFalse(isInexact(makeBignum("-1e1000")));
assertFalse(isInexact(makeBignum("12342357892297851728921374891327893")));
assertFalse(isInexact(makeBignum("4.1321e200")));
assertFalse(isInexact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertFalse(isInexact(makeRational(19)));
assertFalse(isInexact(makeRational(0)));
assertFalse(isInexact(makeRational(-1)));
assertFalse(isInexact(makeRational(1)));
assertFalse(isInexact(makeRational(1, 2)));
assertFalse(isInexact(makeRational(1, 29291)));
},
'floats': function() {
assertTrue(isInexact(e));
assertTrue(isInexact(pi));
assertTrue(isInexact(inf));
assertTrue(isInexact(negative_inf));
assertTrue(isInexact(nan));
assertTrue(isInexact(makeFloat(0)));
assertTrue(isInexact(makeFloat(1111.1)));
},
'complex': function() {
assertFalse(isInexact(makeComplex(0, 0)));
assertFalse(isInexact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(e,
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(makeRational(1,2),
pi)));
assertTrue(isInexact(makeComplex(makeRational(1,2),
nan)));
assertTrue(isInexact(makeComplex(negative_inf,
nan)));
}
});
describe('isInteger', {
'fixnums': function() {
assertTrue(isInteger(1));
assertTrue(isInteger(-1));
},
'bignums': function() {
assertTrue(isInteger(makeBignum("2983473189472187414789132743928148151617364")));
assertTrue(isInteger(makeBignum("-99999999999999999999999999999999999999")));
},
'rationals': function() {
assertTrue(isInteger(makeRational(1, 1)));
assertFalse(isInteger(makeRational(1, 2)));
assertFalse(isInteger(makeRational(9999, 10000)));
assertFalse(isInteger(makeRational(9999, 1000)));
},
'floats': function() {
assertFalse(isInteger(makeFloat(2.3)));
assertTrue(isInteger(makeFloat(4.0)));
assertFalse(isInteger(inf));
assertFalse(isInteger(negative_inf));
assertFalse(isInteger(nan));
},
'complex': function() {
assertTrue(isInteger(makeComplex(42, 0)));
assertFalse(isInteger(makeComplex(makeFloat(42), makeFloat(0))));
assertFalse(isInteger(makeComplex(42, 42)));
assertFalse(isInteger(i));
assertFalse(isInteger(negative_i));
},
'others': function() {
assertFalse(isInteger("hello"));
assertFalse(isInteger("0"));
}
});
describe('toFixnum', {
'fixnums': function() {
assertEquals(42, toFixnum(42));
assertEquals(-20, toFixnum(-20));
assertEquals(0, toFixnum(0));
},
'bignums': function() {
assertEquals(123456789, toFixnum(makeBignum("123456789")));
assertEquals(0, toFixnum(makeBignum("0")));
assertEquals(-123, toFixnum(makeBignum("-123")));
assertEquals(123456, toFixnum(makeBignum("123456")));
// We're dealing with big numbers, where the numerical error
// makes it difficult to compare for equality. We just go for
// percentage and see that it is ok.
assertTrue(diffPercent(1e200, toFixnum(makeBignum("1e200")))
< 1e-10);
assertTrue(diffPercent(-1e200, toFixnum(makeBignum("-1e200")))
< 1e-10);
},
'rationals': function() {
assertEquals(0, toFixnum(zero));
assertEquals(17/2, toFixnum(makeRational(17, 2)));
assertEquals(1926/3, toFixnum(makeRational(1926, 3)));
assertEquals(-11150/17, toFixnum(makeRational(-11150, 17)));
},
'floats': function() {
assertEquals(12345.6789, toFixnum(makeFloat(12345.6789)));
assertEquals(Math.PI, toFixnum(pi));
assertEquals(Math.E, toFixnum(e));
assertEquals(Number.POSITIVE_INFINITY, toFixnum(inf));
assertEquals(Number.NEGATIVE_INFINITY, toFixnum(negative_inf));
assertTrue(isNaN(toFixnum(nan)));
},
'complex': function() {
assertFails(function() { toFixnum(makeComplex(2, 1)); });
assertFails(function() { toFixnum(i); });
assertFails(function() { toFixnum(negative_i); });
assertEquals(2, toFixnum(makeComplex(2, 0)));
assertEquals(1/2, toFixnum(makeComplex(makeRational(1, 2),
0)));
assertEquals(Number.POSITIVE_INFINITY,
toFixnum(makeComplex(inf, 0)));
assertEquals(Number.NEGATIVE_INFINITY,
toFixnum(makeComplex(negative_inf, 0)));
assertTrue(isNaN(toFixnum(makeComplex(nan, 0))));
}
});
describe('toExact', {
'fixnums': function() {
assertEquals(1792, toExact(1792));
assertEquals(0, toExact(0));
assertEquals(-1, toExact(-1));
},
'bignums': function() {
assertEquals(makeBignum("4.2e100"),
toExact(makeBignum("4.2e100")));
assertEquals(makeBignum("0"),
toExact(makeBignum("0")));
assertEquals(makeBignum("1"),
toExact(makeBignum("1")));
assertEquals(makeBignum("-1"),
toExact(makeBignum("-1")));
assertEquals(makeBignum("-12345"),
toExact(makeBignum("-12345")));
assertEquals(makeBignum("-1.723e500"),
toExact(makeBignum("-1.723e500")));
},
'rationals': function() {
assertEquals(makeRational(1, 2), toExact(makeRational(1, 2)));
assertEquals(makeRational(1, 9999), toExact(makeRational(1, 9999)));
assertEquals(makeRational(0, 1), toExact(makeRational(0, 9999)));
assertEquals(makeRational(-290, 1), toExact(makeRational(-290, 1)));
},
'floats': function() {
assertEquals(makeRational(1, 2), toExact(makeFloat(0.5)));
assertEquals(makeRational(1, 10), toExact(makeFloat(0.1)));
assertEquals(makeRational(9, 10), toExact(makeFloat(0.9)));
assertTrue(isExact(toExact(makeFloat(10234.7))));
assertTrue(diffPercent(makeRational(102347, 10),
toExact(makeFloat(10234.7))) < 1);
assertEquals(-1, toExact(makeFloat(-1)));
assertEquals(0, toExact(makeFloat(0)));
assertEquals(1024, toExact(makeFloat(1024)));
assertFails(function() { toExact(nan); });
assertFails(function() { toExact(inf); });
assertFails(function() { toExact(negative_inf); });
},
'complex': function() {
assertEquals(0, toExact(makeComplex(0, 0)));
assertEquals(99, toExact(makeComplex(99, 0)));
assertEquals(makeRational(-1, 2),
toExact(makeComplex(makeRational(-1, 2), 0)));
assertEquals(makeRational(1, 4),
toExact(makeComplex(makeFloat(.25), 0)));
assertFails(function() { toExact(makeComplex(nan, 0)); });
assertFails(function() { toExact(makeComplex(inf, 0)); });
assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
assertTrue(eqv(toExact(makeComplex(0, 1)), makeComplex(0, 1)));
assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
|
dyoo/js-numbers
|
c8c4fbc63b73dadd8a45d37b6f2608ec9c4982d1
|
adding test case from report by manuel simoni
|
diff --git a/test/tests.js b/test/tests.js
index 45b8654..c5cebc9 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,679 +1,681 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertEqv = function(x, y) {
value_of(eqv(x, y)).should_be_true();
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
value_of(toFixnum(makeRational(1, 5)) === 0.2)
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
assertTrue(eqv(makeComplexPolar(1, 2),
makeComplex(makeFloat(-0.4161468365471424),
makeFloat(0.9092974268256817))));
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
+ assertEquals(makeFloat(10000000000000000.2),
+ fromString("10000000000000000.2"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
// If any component of a complex is inexact, both
// the real and imaginary parts get turned into
// inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
assertFalse(isRational(makeComplex(makeFloat(0), makeFloat(0))));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
assertTrue(isReal(makeBignum("1e1000")));
assertTrue(isReal(makeBignum("-1e1000")));
|
dyoo/js-numbers
|
caaef42a23855fa05481710e06ee642f71de530e
|
exposing min and max fixnum constants as well
|
diff --git a/README b/README
index e981b3c..dc9bcd2 100644
--- a/README
+++ b/README
@@ -1,322 +1,320 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a toplevel namespace called
jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInexact: scheme-number -> boolean
Produces true if the number is inexact.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
toInexact: scheme-number -> scheme-number
Converts the number to an inexact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
quotient: scheme-number scheme-number -> scheme-number
Produces the quotient. Both inputs must be integers.
remainder: scheme-number scheme-number -> scheme-number
Produces the remainder. Both inputs must be integers.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
toRepeatedDecimal: scheme-number scheme-number {limit: number}? -> [string, string, string]
Produces a string representation of the decimal expansion; the first and second
argument must be integers. Returns an array of three parts: the portion before
the decimal, the non-repeating part, and then the repeating part.
If the expansion goes beyond the limit (by default, 256 characters), then
the expansion will be cut off, and the third portion will be '...'.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, sgn
-* Bring over the numeric test cases from Moby.
-
* Add real documentation.
======================================================================
Related work
There appears to be another Scheme numeric tower implementation that
just came out in the last month or so, by Matt Might and John Tobey:
https://github.com/jtobey/javascript-bignum
http://silentmatt.com/biginteger/
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
June 2010: got implementation of integer-sqrt from Ugur Cekmez;
brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index c28d5bc..e1f0f4c 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3541,516 +3541,518 @@ if (typeof(exports) !== 'undefined') {
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))))) {
guess = floor(divide(add(guess,
floor(divide(n, guess))),
2));
}
return guess;
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
var n;
if(sign(this) >= 0) {
return searchIter(this, this);
} else {
n = this.negate();
return Complex.makeInstance(0, searchIter(n, n));
}
};
})();
(function() {
// Get an approximation using integerSqrt, and then start another
// Newton-Ralphson search if necessary.
BigInteger.prototype.sqrt = function() {
var approx = this.integerSqrt(), fix;
if (eqv(sqr(approx), this)) {
return approx;
}
fix = toFixnum(this);
if (isFinite(fix)) {
if (fix >= 0) {
return FloatPoint.makeInstance(Math.sqrt(fix));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-fix)));
}
} else {
return approx;
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
//
// An optional limit on the decimal expansion can be provided, in which
// case the search cuts off if we go past the limit.
// If this happens, the third argument returned becomes '...' to indicate
// that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
if (limit-- <= 0) {
return [digits.join(''), '...']
}
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d, options) {
// default limit on decimal expansion; can be overridden
var limit = 512;
if (options && typeof(options.limit) !== 'undefined') {
limit = options.limit;
}
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
// The following exposes the class representations for easier
// integration with other projects.
Numbers['BigInteger'] = BigInteger;
Numbers['Rational'] = Rational;
Numbers['FloatPoint'] = FloatPoint;
- Numbers['Complex'] = Complex;
-
+ Numbers['Complex'] = Complex;
+
+ Numbers['MIN_FIXNUM'] = MIN_FIXNUM;
+ Numbers['MAX_FIXNUM'] = MAX_FIXNUM;
})();
|
dyoo/js-numbers
|
11fcb0f7724dd247f15b68feb34c7472e5211a26
|
adding exports for Manuel Simoni
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 6064239..c28d5bc 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3534,513 +3534,523 @@ if (typeof(exports) !== 'undefined') {
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))))) {
guess = floor(divide(add(guess,
floor(divide(n, guess))),
2));
}
return guess;
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
var n;
if(sign(this) >= 0) {
return searchIter(this, this);
} else {
n = this.negate();
return Complex.makeInstance(0, searchIter(n, n));
}
};
})();
(function() {
// Get an approximation using integerSqrt, and then start another
// Newton-Ralphson search if necessary.
BigInteger.prototype.sqrt = function() {
var approx = this.integerSqrt(), fix;
if (eqv(sqr(approx), this)) {
return approx;
}
fix = toFixnum(this);
if (isFinite(fix)) {
if (fix >= 0) {
return FloatPoint.makeInstance(Math.sqrt(fix));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-fix)));
}
} else {
return approx;
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
//
// An optional limit on the decimal expansion can be provided, in which
// case the search cuts off if we go past the limit.
// If this happens, the third argument returned becomes '...' to indicate
// that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
if (limit-- <= 0) {
return [digits.join(''), '...']
}
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d, options) {
// default limit on decimal expansion; can be overridden
var limit = 512;
if (options && typeof(options.limit) !== 'undefined') {
limit = options.limit;
}
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
+
+
+ // The following exposes the class representations for easier
+ // integration with other projects.
+ Numbers['BigInteger'] = BigInteger;
+ Numbers['Rational'] = Rational;
+ Numbers['FloatPoint'] = FloatPoint;
+ Numbers['Complex'] = Complex;
+
+
})();
|
dyoo/js-numbers
|
69c9197adf1d0a96600d0bc82f746465669642ef
|
noting related work
|
diff --git a/README b/README
index e9c9449..e981b3c 100644
--- a/README
+++ b/README
@@ -1,310 +1,322 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a toplevel namespace called
jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInexact: scheme-number -> boolean
Produces true if the number is inexact.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
toInexact: scheme-number -> scheme-number
Converts the number to an inexact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
quotient: scheme-number scheme-number -> scheme-number
Produces the quotient. Both inputs must be integers.
remainder: scheme-number scheme-number -> scheme-number
Produces the remainder. Both inputs must be integers.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
toRepeatedDecimal: scheme-number scheme-number {limit: number}? -> [string, string, string]
Produces a string representation of the decimal expansion; the first and second
argument must be integers. Returns an array of three parts: the portion before
the decimal, the non-repeating part, and then the repeating part.
If the expansion goes beyond the limit (by default, 256 characters), then
the expansion will be cut off, and the third portion will be '...'.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
+======================================================================
+
+Related work
+
+There appears to be another Scheme numeric tower implementation that
+just came out in the last month or so, by Matt Might and John Tobey:
+
+ https://github.com/jtobey/javascript-bignum
+ http://silentmatt.com/biginteger/
+
+
+
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
June 2010: got implementation of integer-sqrt from Ugur Cekmez;
brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
|
dyoo/js-numbers
|
e5bdeaa4edb66c4e6968d4810f7561ed820fa0da
|
removing deprecated comment
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 0af77b0..6064239 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -832,1026 +832,1024 @@ if (typeof(exports) !== 'undefined') {
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
- // FIXME: up to this point I've modified Rational to use the _integer functions.
- // I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(-0.0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
} else if (n === 0) {
if ((1/n) === -Infinity) {
return NEGATIVE_ZERO;
} else {
return INEXACT_ZERO;
}
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n - other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
return FloatPoint.makeInstance(this.n * other.n);
};
FloatPoint.prototype.divide = function(other) {
return FloatPoint.makeInstance(this.n / other.n);
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
return FloatPoint.makeInstance(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
|
dyoo/js-numbers
|
d6afb0468bff83bc783efe49621d81da207a6614
|
fallback on biginteger.sqrt: just switch over to floating point if we can't get the exact answer
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index eec0d97..0af77b0 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3240,841 +3240,809 @@ if (typeof(exports) !== 'undefined') {
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
- while(!(goodEnough(n, guess))) {
- guess = average(guess,
- floor(divide(n, guess)));
+ while(!(lessThanOrEqual(sqr(guess),n) &&
+ lessThan(n,sqr(add(guess, 1))))) {
+ guess = floor(divide(add(guess,
+ floor(divide(n, guess))),
+ 2));
}
return guess;
};
-
- var average = function (x,y) {
- return floor(divide(add(x,y), 2));
- };
-
- var goodEnough = function(n, guess) {
- return (lessThanOrEqual(sqr(guess),n) &&
- lessThan(n,sqr(add(guess, 1))));
- };
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
- if(this.s == 0) {
+ var n;
+ if(sign(this) >= 0) {
return searchIter(this, this);
} else {
- var tmpThis = multiply(this, -1);
- return Complex.makeInstance(0,
- searchIter(tmpThis, tmpThis));
+ n = this.negate();
+ return Complex.makeInstance(0, searchIter(n, n));
}
};
})();
- (function() {
-
-
- // Classic implementation of Newton-Ralphson square-root search.
- // http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
- var searchIter = function(n, guess) {
- var maxIterations = 100;
- while(Math.abs(guess*guess - n) > 0.000001 &&
- (maxIterations--) > 0) {
- guess = (guess + n/guess) / 2
-
- }
- return guess;
- };
-
+ (function() {
// Get an approximation using integerSqrt, and then start another
// Newton-Ralphson search if necessary.
BigInteger.prototype.sqrt = function() {
- var approx = this.integerSqrt();
- var f;
+ var approx = this.integerSqrt(), fix;
if (eqv(sqr(approx), this)) {
return approx;
}
-
- if (isReal(approx)) {
- if (isFinite(toFixnum(this)) &&
- isFinite(toFixnum(approx))) {
- return FloatPoint.makeInstance(
- searchIter(toFixnum(this), toFixnum(approx)));
+ fix = toFixnum(this);
+ if (isFinite(fix)) {
+ if (fix >= 0) {
+ return FloatPoint.makeInstance(Math.sqrt(fix));
} else {
- return approx;
- }
- } else {
- if (isFinite(toFixnum(this)) &&
- isFinite(toFixnum(imaginaryPart(approx)))) {
return Complex.makeInstance(
- 0,
- FloatPoint.makeInstance(
- searchIter(
- (-toFixnum(this)),
- toFixnum(imaginaryPart(approx)))));
- } else {
- return approx;
+ 0,
+ FloatPoint.makeInstance(Math.sqrt(-fix)));
}
+ } else {
+ return approx;
}
- }
+ };
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
//
// An optional limit on the decimal expansion can be provided, in which
// case the search cuts off if we go past the limit.
// If this happens, the third argument returned becomes '...' to indicate
// that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
if (limit-- <= 0) {
return [digits.join(''), '...']
}
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d, options) {
// default limit on decimal expansion; can be overridden
var limit = 512;
if (options && typeof(options.limit) !== 'undefined') {
limit = options.limit;
}
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
diff --git a/test/tests.js b/test/tests.js
index 8a44597..45b8654 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1685,1063 +1685,1071 @@ describe('divide', {
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeComplex(makeFloat(.25), makeFloat(0.0))));
assertTrue(eqv(divide(makeComplex(2, 6),
makeComplex(4, 1)),
makeComplex(makeRational(14, 17),
makeRational(22, 17))));
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
assertTrue(eqv(sqrt(makeBignum("4")),
2))
assertTrue(eqv(sqrt(makeBignum("-4")),
makeComplex(0, 2)))
assertTrue(diffPercent(makeFloat(4893703081.846022),
sqrt(makeBignum("23948329853269253680")))
< 1e-2)
+ assertTrue(diffPercent(sqrt(expt(15, 21)).toFixnum(),
+ 2233357359474.6265)
+ < 2e-10);
+ assertTrue(eqv(sqrt(expt(15, 22)),
+ expt(15, 11)));
+ assertTrue(eqv(sqrt(expt(15, 22)),
+ expt(15, 11)));
},
'rationals': function() {
assertTrue(eqv(sqrt(makeRational(1, 4)),
makeRational(1, 2)));
assertTrue(eqv(sqrt(makeRational(-1, 4)),
makeComplex(0, makeRational(1, 2))));
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
+
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertFails(function() { floor(makeComplex(nan, negative_zero))} );
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertFails(function() { floor(makeComplex(makeFloat(-1.999),
makeFloat(0.0)))});
assertFails(function() { floor(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0))) });
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234568),
ceiling(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234567),
ceiling(makeFloat(-1234567891234567.8)));
assertEqv(nan, ceiling(nan));
assertEqv(inf, ceiling(inf));
assertEqv(negative_inf, ceiling(negative_inf));
assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(nan)));
assertFails(function() { ceiling(makeComplex(makeFloat(0), nan))});
assertFails(function() { ceiling(makeComplex(nan, makeFloat(1)))});
assertFails(function() { ceiling(makeComplex(makeFloat(1), nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertFails(function() { ceiling(makeComplex(nan, negative_zero))} );
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(makeFloat(0),inf))});
assertFails(function() { ceiling(makeComplex(inf,makeFloat(0)))});
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertFails(function() { ceiling(makeComplex(makeFloat(-1.999),
makeFloat(0)))});
assertFails(function() { ceiling(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))});
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
4926282f436492a272880b9247460c722ecf3da9
|
biginteger sqrt should behave a little better now
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index cfe27f7..eec0d97 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3270,776 +3270,811 @@ if (typeof(exports) !== 'undefined') {
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess,
floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
(function() {
- // Get an approximation using integerSqrt,
+
+
+ // Classic implementation of Newton-Ralphson square-root search.
+ // http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
+ var searchIter = function(n, guess) {
+ var maxIterations = 100;
+ while(Math.abs(guess*guess - n) > 0.000001 &&
+ (maxIterations--) > 0) {
+ guess = (guess + n/guess) / 2
+
+ }
+ return guess;
+ };
+
+ // Get an approximation using integerSqrt, and then start another
+ // Newton-Ralphson search if necessary.
BigInteger.prototype.sqrt = function() {
var approx = this.integerSqrt();
+ var f;
if (eqv(sqr(approx), this)) {
return approx;
}
- // TODO: get closer to the result by Newton's method if
- // we can do so by floating-point
- return approx;
+
+ if (isReal(approx)) {
+ if (isFinite(toFixnum(this)) &&
+ isFinite(toFixnum(approx))) {
+ return FloatPoint.makeInstance(
+ searchIter(toFixnum(this), toFixnum(approx)));
+ } else {
+ return approx;
+ }
+ } else {
+ if (isFinite(toFixnum(this)) &&
+ isFinite(toFixnum(imaginaryPart(approx)))) {
+ return Complex.makeInstance(
+ 0,
+ FloatPoint.makeInstance(
+ searchIter(
+ (-toFixnum(this)),
+ toFixnum(imaginaryPart(approx)))));
+ } else {
+ return approx;
+ }
+ }
}
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
//
// An optional limit on the decimal expansion can be provided, in which
// case the search cuts off if we go past the limit.
// If this happens, the third argument returned becomes '...' to indicate
// that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
if (limit-- <= 0) {
return [digits.join(''), '...']
}
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d, options) {
// default limit on decimal expansion; can be overridden
var limit = 512;
if (options && typeof(options.limit) !== 'undefined') {
limit = options.limit;
}
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
|
dyoo/js-numbers
|
74ca5ecd5daa1fdf7c36b7c5da642e744097708b
|
some simplifications
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 7520712..cfe27f7 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,850 +1,831 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
- { isYSpecialCase: function(y) {
- return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
- onYSpecialCase: function(x, y) {
- var pos = (y !== NEGATIVE_ZERO);
-
-
- if (isReal(x)) {
- if (isExact(x)) {
- if (greaterThan(x, 0)) {
- return pos ? inf : neginf;
- } else if (lessThan(x, 0)) {
- return pos ? neginf : inf;
- } else {
- return 0;
- }
- } else {
- // both x and y are inexact
- if (isNaN(toFixnum(x))) {
- return NaN;
- } else if (greaterThan(x, 0)) {
- return pos ? inf : neginf;
- } else if (lessThan(x, 0)) {
- return pos ? neginf : inf;
- } else {
- return NaN;
- }
- }
- } else {
- if (x.level < y.level) x = x.liftTo(y);
- if (y.level < x.level) y = y.liftTo(x);
- return x.divide(y);
+ { isXSpecialCase: function(x) {
+ return (eqv(x, 0));
+ },
+ onXSpecialCase: function(x, y) {
+ if (eqv(y, 0)) {
+ throwRuntimeError("/: division by zero", x, y);
}
+ return 0;
+ },
+ isYSpecialCase: function(y) {
+ return (eqv(y, 0)); },
+ onYSpecialCase: function(x, y) {
+ throwRuntimeError("/: division by zero", x, y);
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (! isInteger(x)) {
throwRuntimeError('integer-sqrt: the argument ' + x.toString() +
" is not an integer.", x);
}
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
@@ -1239,1119 +1220,1073 @@ if (typeof(exports) !== 'undefined') {
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(-0.0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
} else if (n === 0) {
if ((1/n) === -Infinity) {
return NEGATIVE_ZERO;
} else {
return INEXACT_ZERO;
}
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
return FloatPoint.makeInstance(this.n - other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
- if (this.n === 0 || other.n === 0) {
- if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
- return INEXACT_ZERO;
- } else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
- return NEGATIVE_ZERO;
- }
- return INEXACT_ZERO;
- }
-
- if (this.isFinite() && other.isFinite()) {
- var product = this.n * other.n;
- if (product !== 0) {
- return FloatPoint.makeInstance(product);
- }
- return sign(this) * sign(other) == 1 ?
- FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
- } else if (isNaN(this.n) || isNaN(other.n)) {
- return NaN;
- } else {
- return ((sign(this) * sign(other) === 1) ? inf : neginf);
- }
+ return FloatPoint.makeInstance(this.n * other.n);
};
FloatPoint.prototype.divide = function(other) {
- if (this.isFinite() && other.isFinite()) {
- if (other.n === 0) {
- return throwRuntimeError("/: division by zero", this, other);
- }
- return FloatPoint.makeInstance(this.n / other.n);
- } else if (isNaN(this.n) || isNaN(other.n)) {
- return NaN;
- } else if (! this.isFinite() && !other.isFinite()) {
- return NaN;
- } else if (this.isFinite() && !other.isFinite()) {
- return FloatPoint.makeInstance(0.0);
- } else if (! this.isFinite() && other.isFinite()) {
- return ((sign(this) * sign(other) === 1) ? inf : neginf);
- } else {
- return throwRuntimeError("impossible", this, other);
- }
+ return FloatPoint.makeInstance(this.n / other.n);
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
- if (! isFinite(this.n)) {
- return this;
- } else if (this === NEGATIVE_ZERO) {
- return this;
- } else {
- return FloatPoint.makeInstance(Math.floor(this.n));
- }
+ return FloatPoint.makeInstance(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
- if (! isFinite(this.n)) {
- return this;
- } else if (this === NEGATIVE_ZERO) {
- return this;
- } return FloatPoint.makeInstance(Math.ceil(this.n));
+ return FloatPoint.makeInstance(Math.ceil(this.n));
};
-
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
if (this.isInexact() || other.isInexact()) {
// http://portal.acm.org/citation.cfm?id=1039814
// We currently use Smith's method, though we should
// probably switch over to Priest's method.
a = this.r;
b = this.i;
c = other.r;
d = other.i;
if (lessThanOrEqual(abs(d), abs(c))) {
r = divide(d, c);
x = divide(add(a, multiply(b, r)),
add(c, multiply(d, r)));
y = divide(subtract(b, multiply(a, r)),
add(c, multiply(d, r)));
} else {
r = divide(c, d);
x = divide(add(multiply(a, r), b),
add(multiply(c, r), d));
y = divide(subtract(multiply(b, r), a),
add(multiply(c, r), d));
}
return Complex.makeInstance(x, y);
} else {
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
}
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
diff --git a/test/tests.js b/test/tests.js
index 1edb2ba..8a44597 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,578 +1,580 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertEqv = function(x, y) {
value_of(eqv(x, y)).should_be_true();
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
+ value_of(toFixnum(makeRational(1, 5)) === 0.2)
+ .should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
assertTrue(eqv(makeComplexPolar(1, 2),
makeComplex(makeFloat(-0.4161468365471424),
makeFloat(0.9092974268256817))));
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
@@ -996,1025 +998,1035 @@ describe('toExact', {
assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
assertTrue(eqv(toExact(makeComplex(0, 1)), makeComplex(0, 1)));
assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(-1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(234), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(200), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(34), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(-24), makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(24), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(toFixnum(makeRational(16, 17))),
makeFloat(1.1234)),
subtract(1, makeComplex(makeFloat(toFixnum(makeRational(1, 17))),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
+
'floating / floating' : function() {
+ assertTrue(eqv(subtract(makeFloat(1.2), makeFloat(0.2)),
+ makeFloat(1.2-0.2)));
+
+ assertTrue(eqv(subtract(nan, nan),
+ nan));
+ assertTrue(eqv(subtract(nan, makeFloat(3.0)),
+ nan));
+ assertTrue(eqv(subtract(nan, makeFloat(-3.0)),
+ nan));
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, 0)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(negative_zero,
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(0, 0),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeComplex(makeFloat(.25), makeFloat(0.0))));
assertTrue(eqv(divide(makeComplex(2, 6),
makeComplex(4, 1)),
makeComplex(makeRational(14, 17),
makeRational(22, 17))));
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
|
dyoo/js-numbers
|
b133bf5476ac67477d77ce6b4bcf5905ae8db974
|
simplifying some of the logic
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index d8a0539..7520712 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1200,1076 +1200,1059 @@ if (typeof(exports) !== 'undefined') {
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(-0.0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
} else if (n === 0) {
if ((1/n) === -Infinity) {
return NEGATIVE_ZERO;
} else {
return INEXACT_ZERO;
}
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
- if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
- return NEGATIVE_ZERO;
- }
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
- var result = this.n - other.n;
- if (result === 0.0) {
- if (other === NEGATIVE_ZERO) {
- return FloatPoint.makeInstance(result);
- }
- else if (this === NEGATIVE_ZERO) {
- return NEGATIVE_ZERO;
- }
- }
- return FloatPoint.makeInstance(result);
+ return FloatPoint.makeInstance(this.n - other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
- if (this === NEGATIVE_ZERO) {
- return FloatPoint.makeInstance(0);
- } else if (this.n === 0) {
- return NEGATIVE_ZERO;
- }
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return INEXACT_ZERO;
} else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return INEXACT_ZERO;
}
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
if (this.isInexact() || other.isInexact()) {
// http://portal.acm.org/citation.cfm?id=1039814
// We currently use Smith's method, though we should
// probably switch over to Priest's method.
a = this.r;
b = this.i;
c = other.r;
d = other.i;
if (lessThanOrEqual(abs(d), abs(c))) {
r = divide(d, c);
x = divide(add(a, multiply(b, r)),
add(c, multiply(d, r)));
y = divide(subtract(b, multiply(a, r)),
add(c, multiply(d, r)));
} else {
r = divide(c, d);
x = divide(add(multiply(a, r), b),
add(multiply(c, r), d));
y = divide(subtract(multiply(b, r), a),
add(multiply(c, r), d));
}
return Complex.makeInstance(x, y);
} else {
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
}
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
|
dyoo/js-numbers
|
2c6ddbff9e31db6bebacaf8aaa284f2f4adabb1d
|
added test for negative zero. I need to simplify all the floatpoint stuff now that I know how to test for negative zero. How embarrassing... :)
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index c8f9480..d8a0539 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1065,1040 +1065,1046 @@ if (typeof(exports) !== 'undefined') {
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
- var NEGATIVE_ZERO = new FloatPoint(0);
+ var NEGATIVE_ZERO = new FloatPoint(-0.0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
+ } else if (n === 0) {
+ if ((1/n) === -Infinity) {
+ return NEGATIVE_ZERO;
+ } else {
+ return INEXACT_ZERO;
+ }
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return INEXACT_ZERO;
} else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return INEXACT_ZERO;
}
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
|
dyoo/js-numbers
|
986cf3eff4871d2a2587e8470ab9bb1e3902bcfa
|
fixing typo
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index ac9252f..c8f9480 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1694,1025 +1694,1025 @@ if (typeof(exports) !== 'undefined') {
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return INEXACT_ZERO;
} else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return INEXACT_ZERO;
}
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
} else {
return Complex.makeInstance(
INEXACT_ZERO,
FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
if (this.isInexact() || other.isInexact()) {
// http://portal.acm.org/citation.cfm?id=1039814
// We currently use Smith's method, though we should
// probably switch over to Priest's method.
a = this.r;
b = this.i;
c = other.r;
d = other.i;
if (lessThanOrEqual(abs(d), abs(c))) {
r = divide(d, c);
x = divide(add(a, multiply(b, r)),
add(c, multiply(d, r)));
y = divide(subtract(b, multiply(a, r)),
add(c, multiply(d, r)));
} else {
r = divide(c, d);
x = divide(add(multiply(a, r), b),
add(multiply(c, r), d));
y = divide(subtract(multiply(b, r), a),
add(multiply(c, r), d));
}
- return makeComplex(x, y);
+ return Complex.makeInstance(x, y);
} else {
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
}
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(digitRegexp) &&
(x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
|
dyoo/js-numbers
|
4d2f4d1205fa2118200d1248e40655867dfc70e8
|
fixing expansion of toRepeatedDecimal
|
diff --git a/README b/README
index f5bd228..e9c9449 100644
--- a/README
+++ b/README
@@ -1,306 +1,310 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a toplevel namespace called
jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInexact: scheme-number -> boolean
Produces true if the number is inexact.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
toInexact: scheme-number -> scheme-number
Converts the number to an inexact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
quotient: scheme-number scheme-number -> scheme-number
Produces the quotient. Both inputs must be integers.
remainder: scheme-number scheme-number -> scheme-number
Produces the remainder. Both inputs must be integers.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
+toRepeatedDecimal: scheme-number scheme-number {limit: number}? -> [string, string, string]
+ Produces a string representation of the decimal expansion; the first and second
+ argument must be integers. Returns an array of three parts: the portion before
+ the decimal, the non-repeating part, and then the repeating part.
-
-
+ If the expansion goes beyond the limit (by default, 256 characters), then
+ the expansion will be cut off, and the third portion will be '...'.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
June 2010: got implementation of integer-sqrt from Ugur Cekmez;
brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index f5a34f2..ac9252f 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3432,676 +3432,690 @@ if (typeof(exports) !== 'undefined') {
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess,
floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
(function() {
// Get an approximation using integerSqrt,
BigInteger.prototype.sqrt = function() {
var approx = this.integerSqrt();
if (eqv(sqr(approx), this)) {
return approx;
}
// TODO: get closer to the result by Newton's method if
// we can do so by floating-point
return approx;
}
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
- // toRepeatingDecimal: jsnum jsnum -> [string, string, string]
+ // toRepeatingDecimal: jsnum jsnum {limit: number}? -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
+ //
+ // An optional limit on the decimal expansion can be provided, in which
+ // case the search cuts off if we go past the limit.
+ // If this happens, the third argument returned becomes '...' to indicate
+ // that the search was prematurely cut off.
var toRepeatingDecimal = (function() {
- var getResidue = function(r, d) {
+ var getResidue = function(r, d, limit) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
+ if (limit-- <= 0) {
+ return [digits.join(''), '...']
+ }
+
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
- return function(n, d) {
+ return function(n, d, options) {
+ // default limit on decimal expansion; can be overridden
+ var limit = 512;
+ if (options && typeof(options.limit) !== 'undefined') {
+ limit = options.limit;
+ }
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
- var afterDecimals = getResidue(remainder(n, d), d);
+ var afterDecimals = getResidue(remainder(n, d), d, limit);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
diff --git a/test/tests.js b/test/tests.js
index 1724d64..1edb2ba 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2723,1025 +2723,1052 @@ describe('asin', {
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
assertTrue(eqv(integerSqrt(negative_zero),
negative_zero));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('repeating decimals', {
tests: function() {
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
+ },
+
+ limitRendering: function() {
+ var OPTIONS = {limit: 5};
+ assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1, OPTIONS));
+ assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2, OPTIONS));
+ assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3, OPTIONS));
+ assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4, OPTIONS));
+ assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5, OPTIONS));
+ assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6, OPTIONS));
+ assertEquals(['0', '05882', '...'],
+ toRepeatingDecimal(1, 17, {limit : 5}));
+
+ assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8, {limit : 4}));
+ assertEquals(['0', '125', '...'], toRepeatingDecimal(1, 8, {limit : 3}));
+ assertEquals(['0', '12', '...'], toRepeatingDecimal(1, 8, {limit : 2}));
+ assertEquals(['0', '1', '...'], toRepeatingDecimal(1, 8, {limit : 1}));
+ assertEquals(['0', '', '...'], toRepeatingDecimal(1, 8, {limit : 0}));
+
+ assertEquals(['10012718086',
+ '8577149703838870007766167',
+ '...'],
+ toRepeatingDecimal(makeBignum("239872983562893234879"),
+ makeBignum("23956829852"),
+ {limit:25}));
+
}
+
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertEqv(divide(makeFloat(1),makeFloat(0)),
inf);
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(diffPercent(realPart(asin(makeComplex(1, 5))),
makeFloat(0.1937931365549321))
< 1e-2);
assertTrue(diffPercent(imaginaryPart(asin(makeComplex(1, 5))),
makeFloat(2.3309746530493123))
< 1e-2);
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
|
dyoo/js-numbers
|
ef7a31805cb4a5cd695af7eca425431442711e62
|
repairing the test case for asin
|
diff --git a/test/tests.js b/test/tests.js
index 37ff826..1724d64 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -3018,854 +3018,857 @@ describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
assertTrue(eqv(integerSqrt(negative_zero),
negative_zero));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('repeating decimals', {
tests: function() {
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertEqv(divide(makeFloat(1),makeFloat(0)),
inf);
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
- assertTrue(equals(asin(1),
- divide(pi, 2)));
- assertTrue(equals(asin(makeRational(1, 4)),
- makeFloat(0.25268025514207865)));
- assertTrue(equals(asin(makeComplex(1, 5)),
- makeComplex(makeFloat(0.1937931365549321),
- makeFloat(2.3309746530493123))));
+ assertTrue(equals(asin(1),
+ divide(pi, 2)));
+ assertTrue(equals(asin(makeRational(1, 4)),
+ makeFloat(0.25268025514207865)));
+ assertTrue(diffPercent(realPart(asin(makeComplex(1, 5))),
+ makeFloat(0.1937931365549321))
+ < 1e-2);
+ assertTrue(diffPercent(imaginaryPart(asin(makeComplex(1, 5))),
+ makeFloat(2.3309746530493123))
+ < 1e-2);
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
assertEquals("5.0+0.0i",
(makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
(makeComplex(5, 1)).toString());
assertEquals("4-2i",
(makeComplex(4, -2)).toString());
},
testQuotient : function(){
assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
assertTrue(eqv(1, quotient(7, 5)));
},
testRemainder : function(){
assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
makeFloat(3)));
assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, modulo(n1, n2));
assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(isReal(pi));
assertTrue(isReal(1));
assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!isReal("hi"));
},
testRound : function(){
assertTrue(equals(round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(round(makeRational(3)),
makeRational(3)));
assertTrue(equals(round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(round(makeRational(-17, 4)),
makeRational(-4)));
},
// testSgn : function(){
// assertTrue(equals(sgn(makeFloat(4)), 1));
// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
// assertTrue(equals(sgn(0), 0));
// },
// testZero_question_ : function(){
// assertTrue(Kernel.zero_question_(0));
// assertTrue(!Kernel.zero_question_(1));
// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
// }
});
|
dyoo/js-numbers
|
5b15b1d412d25e52ca27d5341694994c19603a0c
|
fixing FloatPoint.prototype.integerSqrt
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index c84a860..f5a34f2 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -175,1033 +175,1036 @@ if (typeof(exports) !== 'undefined') {
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
var pos = (y !== NEGATIVE_ZERO);
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return 0;
}
} else {
// both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
+ if (! isInteger(x)) {
+ throwRuntimeError('integer-sqrt: the argument ' + x.toString() +
+ " is not an integer.", x);
+ }
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
-
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
@@ -1360,1032 +1363,1033 @@ if (typeof(exports) !== 'undefined') {
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return INEXACT_ZERO;
} else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return INEXACT_ZERO;
}
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
+ if (this === NEGATIVE_ZERO) { return this; }
if (isInteger(this)) {
if(this.n >= 0) {
- return FloatPoint.makeInstance(floor(sqrt(this.n)));
- }else {
- return Complex.makeInstance(0,
- FloatPoint.makeInstance(floor(sqrt(-this.n))))
+ return FloatPoint.makeInstance(Math.floor(Math.sqrt(this.n)));
+ } else {
+ return Complex.makeInstance(
+ INEXACT_ZERO,
+ FloatPoint.makeInstance(Math.floor(Math.sqrt(-this.n))));
}
-
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
if (this.isInexact() || other.isInexact()) {
// http://portal.acm.org/citation.cfm?id=1039814
// We currently use Smith's method, though we should
// probably switch over to Priest's method.
a = this.r;
b = this.i;
c = other.r;
d = other.i;
if (lessThanOrEqual(abs(d), abs(c))) {
r = divide(d, c);
x = divide(add(a, multiply(b, r)),
add(c, multiply(d, r)));
y = divide(subtract(b, multiply(a, r)),
add(c, multiply(d, r)));
} else {
r = divide(c, d);
x = divide(add(multiply(a, r), b),
add(multiply(c, r), d));
y = divide(subtract(multiply(b, r), a),
add(multiply(c, r), d));
}
return makeComplex(x, y);
} else {
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
}
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
diff --git a/test/tests.js b/test/tests.js
index de87ade..37ff826 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2560,1056 +2560,1057 @@ describe('magnitude', {
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
-
+
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
-
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
- assertTrue(eqv(makeFloat(1.0),
+ assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
- integerSqrt(makeFloat(12345.0))));
+ integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
- integerSqrt(makeFloat(-12345.0))));
+ integerSqrt(makeFloat(-12345.0))));
+ assertTrue(eqv(integerSqrt(negative_zero),
+ negative_zero));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('repeating decimals', {
tests: function() {
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertEqv(divide(makeFloat(1),makeFloat(0)),
inf);
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
|
dyoo/js-numbers
|
cf1ad136ed0558f9cd43873c9ddab210be1ed2b2
|
repairing the test cases on ceiling
|
diff --git a/test/tests.js b/test/tests.js
index 97a952e..de87ade 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1978,1069 +1978,1068 @@ describe('expt', {
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
assertTrue(eqv(sqrt(makeBignum("4")),
2))
assertTrue(eqv(sqrt(makeBignum("-4")),
makeComplex(0, 2)))
assertTrue(diffPercent(makeFloat(4893703081.846022),
sqrt(makeBignum("23948329853269253680")))
< 1e-2)
},
'rationals': function() {
assertTrue(eqv(sqrt(makeRational(1, 4)),
makeRational(1, 2)));
assertTrue(eqv(sqrt(makeRational(-1, 4)),
makeComplex(0, makeRational(1, 2))));
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertFails(function() { floor(makeComplex(nan, negative_zero))} );
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertFails(function() { floor(makeComplex(makeFloat(-1.999),
makeFloat(0.0)))});
assertFails(function() { floor(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0))) });
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234568),
ceiling(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234567),
ceiling(makeFloat(-1234567891234567.8)));
assertEqv(nan, ceiling(nan));
assertEqv(inf, ceiling(inf));
assertEqv(negative_inf, ceiling(negative_inf));
assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
- assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
- assertFails(function() { ceiling(makeComplex(0, nan))});
- assertFails(function() { ceiling(makeComplex(nan, 1))});
- assertFails(function() { ceiling(makeComplex(1, nan))});
- assertFails(function() { ceiling(makeComplex(nan, inf))});
- assertFails(function() { ceiling(makeComplex(inf, nan))});
- assertEquals(nan,floor(makeComplex(nan, negative_zero)));
+ assertTrue(eqv(nan, ceiling(nan)));
+ assertFails(function() { ceiling(makeComplex(makeFloat(0), nan))});
+ assertFails(function() { ceiling(makeComplex(nan, makeFloat(1)))});
+ assertFails(function() { ceiling(makeComplex(makeFloat(1), nan))});
+ assertFails(function() { ceiling(makeComplex(nan, inf))});
+ assertFails(function() { ceiling(makeComplex(inf, nan))});
+ assertFails(function() { ceiling(makeComplex(nan, negative_zero))} );
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
- assertFails(function() { ceiling(makeComplex(0,inf))});
- assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
+ assertFails(function() { ceiling(makeComplex(makeFloat(0),inf))});
+ assertFails(function() { ceiling(makeComplex(inf,makeFloat(0)))});
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
- ceiling(makeComplex(makeRational(makeBignum("9919"),
- makeBignum("9")),
- 0))));
+ ceiling(makeComplex(makeRational(makeBignum("9919"),
+ makeBignum("9")),
+ 0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
- makeBignum("0")))));
+ makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
- makeBignum("0")))));
+ makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
- makeBignum("0")))));
+ makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
- makeBignum("0")))));
+ makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
- makeBignum("2")),
- makeBignum("0")))));
+ makeBignum("2")),
+ makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
- assertTrue(eqv(makeFloat(-1), ceiling(makeComplex(makeFloat(-1.999),
- makeFloat(0)))));
- assertTrue(eqv(makeFloat(1234567891234568),
- ceiling(makeComplex(makeFloat(1234567891234567.8),
- makeFloat(0)))));
+ assertFails(function() { ceiling(makeComplex(makeFloat(-1.999),
+ makeFloat(0)))});
+ assertFails(function() { ceiling(makeComplex(makeFloat(1234567891234567.8),
+ makeFloat(0)))});
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
|
dyoo/js-numbers
|
4c844e9552fc6a36594e9eccfb879f86f0873b6d
|
repairing floor test cases
|
diff --git a/test/tests.js b/test/tests.js
index 020e314..97a952e 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1842,1068 +1842,1067 @@ describe('lessThanOrEqual', {
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
assertTrue(eqv(sqrt(makeBignum("4")),
2))
assertTrue(eqv(sqrt(makeBignum("-4")),
makeComplex(0, 2)))
assertTrue(diffPercent(makeFloat(4893703081.846022),
sqrt(makeBignum("23948329853269253680")))
< 1e-2)
},
'rationals': function() {
assertTrue(eqv(sqrt(makeRational(1, 4)),
makeRational(1, 2)));
assertTrue(eqv(sqrt(makeRational(-1, 4)),
makeComplex(0, makeRational(1, 2))));
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
- assertFails(function() { floor(makeComplex(0, nan))});
- assertFails(function() { floor(makeComplex(nan, 1))});
- assertFails(function() { floor(makeComplex(1, nan))});
- assertFails(function() { floor(makeComplex(nan, inf))});
- assertFails(function() { floor(makeComplex(inf, nan))});
+ assertFails(function() { floor(makeComplex(0, nan))});
+ assertFails(function() { floor(makeComplex(nan, 1))});
+ assertFails(function() { floor(makeComplex(1, nan))});
+ assertFails(function() { floor(makeComplex(nan, inf))});
+ assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
- assertEquals(nan,floor(makeComplex(nan, negative_zero)));
- assertFails(function() { floor(makeComplex(inf,inf))});
- assertFails(function() { floor(makeComplex(0,inf))});
- assertTrue(eqv(inf, floor(makeComplex(inf,0))));
+ assertFails(function() { floor(makeComplex(nan, negative_zero))} );
+ assertFails(function() { floor(makeComplex(inf,inf))});
+ assertFails(function() { floor(makeComplex(0,inf))});
+ assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
- floor(makeComplex(makeRational(makeBignum("9919"),
- makeBignum("9")),
- 0))));
+ floor(makeComplex(makeRational(makeBignum("9919"),
+ makeBignum("9")),
+ 0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
- floor(makeComplex(
- makeRational(makeBignum("100000000000000000000"),
- makeBignum("200000000000000000000")),
- makeBignum("0")))));
- assertTrue(eqv(makeFloat(-2), floor(makeComplex(makeFloat(-1.999),
- makeFloat(0.0)))));
- assertTrue(eqv(makeFloat(1234567891234567),
- floor(makeComplex(makeFloat(1234567891234567.8),
- makeFloat(0)))));
+ floor(makeComplex(
+ makeRational(makeBignum("100000000000000000000"),
+ makeBignum("200000000000000000000")),
+ makeBignum("0")))));
+ assertFails(function() { floor(makeComplex(makeFloat(-1.999),
+ makeFloat(0.0)))});
+ assertFails(function() { floor(makeComplex(makeFloat(1234567891234567.8),
+ makeFloat(0))) });
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234568),
ceiling(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234567),
ceiling(makeFloat(-1234567891234567.8)));
assertEqv(nan, ceiling(nan));
assertEqv(inf, ceiling(inf));
assertEqv(negative_inf, ceiling(negative_inf));
assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-1), ceiling(makeComplex(makeFloat(-1.999),
makeFloat(0)))));
assertTrue(eqv(makeFloat(1234567891234568),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
|
dyoo/js-numbers
|
ce68f8f6bf8f7d2b8f60d666b1cc7337379efca3
|
repairing inexact complex division so it uses Smith's method to avoid overflow.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index dde6d52..c84a860 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1656,1050 +1656,1077 @@ if (typeof(exports) !== 'undefined') {
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return INEXACT_ZERO;
} else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return INEXACT_ZERO;
}
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
+
+
+
+
Complex.prototype.divide = function(other){
+ var a, b, c, d, r, x, y;
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
+ if (this.isInexact() || other.isInexact()) {
+ // http://portal.acm.org/citation.cfm?id=1039814
+ // We currently use Smith's method, though we should
+ // probably switch over to Priest's method.
+ a = this.r;
+ b = this.i;
+ c = other.r;
+ d = other.i;
+ if (lessThanOrEqual(abs(d), abs(c))) {
+ r = divide(d, c);
+ x = divide(add(a, multiply(b, r)),
+ add(c, multiply(d, r)));
+ y = divide(subtract(b, multiply(a, r)),
+ add(c, multiply(d, r)));
+ } else {
+ r = divide(c, d);
+ x = divide(add(multiply(a, r), b),
+ add(multiply(c, r), d));
+ y = divide(subtract(multiply(b, r), a),
+ add(multiply(c, r), d));
+ }
+ return makeComplex(x, y);
+ } else {
+ var con = conjugate(other);
+ var up = multiply(this, con);
- var con = conjugate(other);
- var up = multiply(this, con);
-
- // Down is guaranteed to be real by this point.
- var down = realPart(multiply(other, con));
+ // Down is guaranteed to be real by this point.
+ var down = realPart(multiply(other, con));
- var result = Complex.makeInstance(
- divide(realPart(up), down),
- divide(imaginaryPart(up), down));
- return result;
+ var result = Complex.makeInstance(
+ divide(realPart(up), down),
+ divide(imaginaryPart(up), down));
+ return result;
+ }
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
- subtract(0,
- this.i));
+ subtract(0, this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(digitRegexp) &&
(x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
diff --git a/test/tests.js b/test/tests.js
index 83ff01e..020e314 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,602 +1,604 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertEqv = function(x, y) {
value_of(eqv(x, y)).should_be_true();
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
- // FIXME: add tests for polar construction
+ assertTrue(eqv(makeComplexPolar(1, 2),
+ makeComplex(makeFloat(-0.4161468365471424),
+ makeFloat(0.9092974268256817))));
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
// If any component of a complex is inexact, both
// the real and imaginary parts get turned into
// inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
@@ -1205,1026 +1207,1030 @@ describe('add', {
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(-1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(234), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(200), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(34), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(-24), makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(24), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(toFixnum(makeRational(16, 17))),
makeFloat(1.1234)),
subtract(1, makeComplex(makeFloat(toFixnum(makeRational(1, 17))),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, 0)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(negative_zero,
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(0, 0),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
- makeFloat(.25)))
- // FIXME: we're missing this
+ makeComplex(makeFloat(.25), makeFloat(0.0))));
+ assertTrue(eqv(divide(makeComplex(2, 6),
+ makeComplex(4, 1)),
+ makeComplex(makeRational(14, 17),
+ makeRational(22, 17))));
+
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
assertTrue(eqv(sqrt(makeBignum("4")),
2))
assertTrue(eqv(sqrt(makeBignum("-4")),
makeComplex(0, 2)))
assertTrue(diffPercent(makeFloat(4893703081.846022),
sqrt(makeBignum("23948329853269253680")))
< 1e-2)
},
'rationals': function() {
assertTrue(eqv(sqrt(makeRational(1, 4)),
makeRational(1, 2)));
assertTrue(eqv(sqrt(makeRational(-1, 4)),
makeComplex(0, makeRational(1, 2))));
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
|
dyoo/js-numbers
|
87d64fcedd330f3018fdf4b2e0b0b6bf041df74c
|
fixing the implementation of FloatPoint.proottype.multiply with regard to negative zero
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 27fa91a..dde6d52 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1247,1025 +1247,1032 @@ if (typeof(exports) !== 'undefined') {
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
- if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
+ if (this.n === 0 || other.n === 0) {
+ if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
+ return INEXACT_ZERO;
+ } else if (this === NEGATIVE_ZERO || other === NEGATIVE_ZERO) {
+ return NEGATIVE_ZERO;
+ }
+ return INEXACT_ZERO;
+ }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
diff --git a/test/tests.js b/test/tests.js
index ab1e4a4..83ff01e 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1102,1034 +1102,1034 @@ describe('add', {
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(-1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(234), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(200), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(34), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(-24), makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(24), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(toFixnum(makeRational(16, 17))),
makeFloat(1.1234)),
subtract(1, makeComplex(makeFloat(toFixnum(makeRational(1, 17))),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, 0)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
- assertTrue(eqv(makeFloat(0),
- multiply(makeFloat(0), negative_zero)));
- assertTrue(eqv(negative_zero,
- multiply(negative_zero, makeFloat(0))));
- assertTrue(eqv(makeComplex(negative_zero, negative_zero),
- multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
- assertTrue(eqv(makeComplex(negative_zero, negative_zero),
- multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
- assertTrue(eqv(makeComplex(negative_zero, negative_zero),
- multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
+ assertTrue(eqv(negative_zero,
+ multiply(makeFloat(0), negative_zero)));
+ assertTrue(eqv(negative_zero,
+ multiply(negative_zero, makeFloat(0))));
+ assertTrue(eqv(makeComplex(0, 0),
+ multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
+ assertTrue(eqv(makeComplex(negative_zero, negative_zero),
+ multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
+ assertTrue(eqv(makeComplex(negative_zero, negative_zero),
+ multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
|
dyoo/js-numbers
|
46fc2190cd62661ec000cb6ef7ca275ead0bd195
|
fixing bug in FloatPoint.prototype.subtract: it wasn't comparing NEGATIVE_ZERO properly.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 62b8b93..27fa91a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1213,1048 +1213,1048 @@ if (typeof(exports) !== 'undefined') {
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
- if (other.n === NEGATIVE_ZERO) {
+ if (other === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
- else if (this.n === NEGATIVE_ZERO) {
+ else if (this === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
-
};
+
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
diff --git a/test/tests.js b/test/tests.js
index 458bacb..ab1e4a4 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1001,1031 +1001,1032 @@ describe('toExact', {
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(-1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(234), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(200), makeFloat(1.1234)),
subtract(234, makeComplex(makeFloat(34), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(-24), makeFloat(1.1234)),
subtract(0, makeComplex(makeFloat(24), makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeFloat(toFixnum(makeRational(16, 17))),
makeFloat(1.1234)),
subtract(1, makeComplex(makeFloat(toFixnum(makeRational(1, 17))),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
- assertTrue(eqv(makeFloat(0.0),
- subtract(makeFloat(0), negative_zero)));
- assertTrue(eqv(negative_zero,
- subtract(negative_zero, makeFloat(0))));
-
- assertTrue(eqv(makeComplex(negative_zero, negative_zero),
- subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
+ assertTrue(eqv(makeFloat(0.0),
+ subtract(makeFloat(0), negative_zero)));
+ assertTrue(eqv(negative_zero,
+ subtract(negative_zero, 0)));
+ assertTrue(eqv(negative_zero,
+ subtract(negative_zero, makeFloat(0))));
+ assertTrue(eqv(makeComplex(negative_zero, negative_zero),
+ subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
2d1fd44be017bdbe8c92992bc4edd8e86aa25db5
|
repairing damage to the subtraction test case
|
diff --git a/test/tests.js b/test/tests.js
index 1078fd3..458bacb 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -962,1039 +962,1038 @@ describe('toExact', {
'rationals': function() {
assertEquals(makeRational(1, 2), toExact(makeRational(1, 2)));
assertEquals(makeRational(1, 9999), toExact(makeRational(1, 9999)));
assertEquals(makeRational(0, 1), toExact(makeRational(0, 9999)));
assertEquals(makeRational(-290, 1), toExact(makeRational(-290, 1)));
},
'floats': function() {
assertEquals(makeRational(1, 2), toExact(makeFloat(0.5)));
assertEquals(makeRational(1, 10), toExact(makeFloat(0.1)));
assertEquals(makeRational(9, 10), toExact(makeFloat(0.9)));
assertTrue(isExact(toExact(makeFloat(10234.7))));
assertTrue(diffPercent(makeRational(102347, 10),
toExact(makeFloat(10234.7))) < 1);
assertEquals(-1, toExact(makeFloat(-1)));
assertEquals(0, toExact(makeFloat(0)));
assertEquals(1024, toExact(makeFloat(1024)));
assertFails(function() { toExact(nan); });
assertFails(function() { toExact(inf); });
assertFails(function() { toExact(negative_inf); });
},
'complex': function() {
assertEquals(0, toExact(makeComplex(0, 0)));
assertEquals(99, toExact(makeComplex(99, 0)));
assertEquals(makeRational(-1, 2),
toExact(makeComplex(makeRational(-1, 2), 0)));
assertEquals(makeRational(1, 4),
toExact(makeComplex(makeFloat(.25), 0)));
assertFails(function() { toExact(makeComplex(nan, 0)); });
assertFails(function() { toExact(makeComplex(inf, 0)); });
assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
assertTrue(eqv(toExact(makeComplex(0, 1)), makeComplex(0, 1)));
assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
- assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
- subtract(0, makeComplex(0, makeFloat(1.1234)))));
- assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
- subtract(0, makeComplex(0, makeFloat(-1.1234)))));
- assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
- subtract(234, makeComplex(0, makeFloat(-1.1234)))));
- assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
- subtract(234, makeComplex(34, makeFloat(-1.1234)))));
- assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
- subtract(0, makeComplex(24, makeFloat(-1.1234)))));
-
- assertTrue(eqv(makeComplex(makeRational(16, 17),
- makeFloat(1.1234)),
- subtract(1, makeComplex(makeRational(1, 17),
- makeFloat(-1.1234)))));
+ assertTrue(eqv(makeComplex(negative_zero, makeFloat(-1.1234)),
+ subtract(0, makeComplex(makeFloat(0), makeFloat(1.1234)))));
+ assertTrue(eqv(makeComplex(negative_zero, makeFloat(1.1234)),
+ subtract(0, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
+ assertTrue(eqv(makeComplex(makeFloat(234), makeFloat(1.1234)),
+ subtract(234, makeComplex(makeFloat(0), makeFloat(-1.1234)))));
+ assertTrue(eqv(makeComplex(makeFloat(200), makeFloat(1.1234)),
+ subtract(234, makeComplex(makeFloat(34), makeFloat(-1.1234)))));
+ assertTrue(eqv(makeComplex(makeFloat(-24), makeFloat(1.1234)),
+ subtract(0, makeComplex(makeFloat(24), makeFloat(-1.1234)))));
+ assertTrue(eqv(makeComplex(makeFloat(toFixnum(makeRational(16, 17))),
+ makeFloat(1.1234)),
+ subtract(1, makeComplex(makeFloat(toFixnum(makeRational(1, 17))),
+ makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
|
dyoo/js-numbers
|
885a587d944af9a7753d1bdef8685cd44373bc70
|
adding initial implementation that just reuses integersqrt
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 53737c3..62b8b93 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -3279,776 +3279,791 @@ if (typeof(exports) !== 'undefined') {
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
- guess = average(guess, floor(divide(n, guess)));
+ guess = average(guess,
+ floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
+ (function() {
+ // Get an approximation using integerSqrt,
+ BigInteger.prototype.sqrt = function() {
+ var approx = this.integerSqrt();
+ if (eqv(sqr(approx), this)) {
+ return approx;
+ }
+ // TODO: get closer to the result by Newton's method if
+ // we can do so by floating-point
+ return approx;
+ }
+ })();
+
+
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
var toRepeatingDecimal = (function() {
var getResidue = function(r, d) {
var digits = [];
var seenRemainders = {};
seenRemainders[r] = true;
while(true) {
var nextDigit = quotient(
multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
r = nextRemainder;
}
}
var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
multiply(r, 10),
d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d) {
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
var sign = (lessThan(n, 0) ? "-" : "");
n = abs(n);
var beforeDecimalPoint = sign + quotient(n, d);
var afterDecimals = getResidue(remainder(n, d), d);
return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
diff --git a/test/tests.js b/test/tests.js
index 027762b..1078fd3 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1670,1025 +1670,1029 @@ describe('divide', {
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
assertTrue(eqv(sqrt(makeBignum("4")),
2))
assertTrue(eqv(sqrt(makeBignum("-4")),
makeComplex(0, 2)))
assertTrue(diffPercent(makeFloat(4893703081.846022),
sqrt(makeBignum("23948329853269253680")))
< 1e-2)
},
'rationals': function() {
- // FIXME: we're missing this
+ assertTrue(eqv(sqrt(makeRational(1, 4)),
+ makeRational(1, 2)));
+
+ assertTrue(eqv(sqrt(makeRational(-1, 4)),
+ makeComplex(0, makeRational(1, 2))));
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-2), floor(makeComplex(makeFloat(-1.999),
makeFloat(0.0)))));
assertTrue(eqv(makeFloat(1234567891234567),
floor(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234568),
ceiling(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234567),
ceiling(makeFloat(-1234567891234567.8)));
assertEqv(nan, ceiling(nan));
assertEqv(inf, ceiling(inf));
assertEqv(negative_inf, ceiling(negative_inf));
assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-1), ceiling(makeComplex(makeFloat(-1.999),
makeFloat(0)))));
assertTrue(eqv(makeFloat(1234567891234568),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
|
dyoo/js-numbers
|
ac4bf0acbc918cb6c04bd54210ed0b58e398a55a
|
adding missing test for sqrt of bignums
|
diff --git a/test/tests.js b/test/tests.js
index 934237c..027762b 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1658,1025 +1658,1033 @@ describe('multiply', {
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
- // FIXME: we're missing this
+ assertTrue(eqv(sqrt(makeBignum("4")),
+ 2))
+
+ assertTrue(eqv(sqrt(makeBignum("-4")),
+ makeComplex(0, 2)))
+
+ assertTrue(diffPercent(makeFloat(4893703081.846022),
+ sqrt(makeBignum("23948329853269253680")))
+ < 1e-2)
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-2), floor(makeComplex(makeFloat(-1.999),
makeFloat(0.0)))));
assertTrue(eqv(makeFloat(1234567891234567),
floor(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234568),
ceiling(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234567),
ceiling(makeFloat(-1234567891234567.8)));
assertEqv(nan, ceiling(nan));
assertEqv(inf, ceiling(inf));
assertEqv(negative_inf, ceiling(negative_inf));
assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-1), ceiling(makeComplex(makeFloat(-1.999),
makeFloat(0)))));
assertTrue(eqv(makeFloat(1234567891234568),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
|
dyoo/js-numbers
|
c09f7e831fd174b63a12551e33794571828af8c3
|
(sin 0) == 0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index b7e7b2a..53737c3 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -117,1024 +117,1025 @@ if (typeof(exports) !== 'undefined') {
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
var pos = (y !== NEGATIVE_ZERO);
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return 0;
}
} else {
// both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
+ if (eqv(n, 0)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
if (eqv(x, 0)) {
return FloatPoint.makeInstance(1.0);
}
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
|
dyoo/js-numbers
|
5df8f8d1781588fc0f845137f2038437494b2dc3
|
cosh on 0 === 1.0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 494ad33..b7e7b2a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -261,1024 +261,1027 @@ if (typeof(exports) !== 'undefined') {
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
var pos = (y !== NEGATIVE_ZERO);
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return 0;
}
} else {
// both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
+ if (eqv(x, 0)) {
+ return FloatPoint.makeInstance(1.0);
+ }
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
|
dyoo/js-numbers
|
fa89d8a78556a35891188b79d1645f64ec4dd02c
|
exactness of cos on 0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 9c9e13e..494ad33 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -108,1024 +108,1025 @@ if (typeof(exports) !== 'undefined') {
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
var pos = (y !== NEGATIVE_ZERO);
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return 0;
}
} else {
// both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
+ if (eqv(n, 0)) { return 1; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
|
dyoo/js-numbers
|
eaef780b32e1d5f2fdc06a0498c9492ddc7718a9
|
acos 1 == 0
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 40fa1fc..9c9e13e 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -124,1024 +124,1025 @@ if (typeof(exports) !== 'undefined') {
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
var pos = (y !== NEGATIVE_ZERO);
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return 0;
}
} else {
// both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
+ if (eqv(n, 1)) { return 0; }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
|
dyoo/js-numbers
|
70c84fc2c2fbeeebec9f6e22ad0b697f5199c6bb
|
fixing definition of complex's isReal, isRational, and isInteger so it uses exactness
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 3ed6fb7..40fa1fc 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1511,1195 +1511,1195 @@ if (typeof(exports) !== 'undefined') {
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (this === NEGATIVE_ZERO) {
return this;
}
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return FloatPoint.makeInstance(Math.floor(this.n));
return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
- return isRational(this.r) && equals(this.i, 0);
+ return isRational(this.r) && eqv(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
- equals(this.i, 0));
+ eqv(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
- return equals(this.i, 0);
+ return eqv(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(digitRegexp) &&
(x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
diff --git a/test/tests.js b/test/tests.js
index fe1431f..934237c 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -137,1244 +137,1248 @@ describe('fromString', {
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
// If any component of a complex is inexact, both
// the real and imaginary parts get turned into
// inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
+ assertFalse(isRational(makeComplex(makeFloat(0), makeFloat(0))));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
assertTrue(isReal(makeBignum("1e1000")));
assertTrue(isReal(makeBignum("-1e1000")));
assertTrue(isReal(makeBignum("1e23784")));
assertTrue(isReal(makeBignum("-7.241e23784")));
},
'rationals': function() {
assertTrue(isReal(makeRational(0, 1)));
assertTrue(isReal(makeRational(0, 12342)));
assertTrue(isReal(makeRational(-2324, 12342)));
assertTrue(isReal(makeRational(1, 2)));
},
'floats': function() {
assertTrue(isReal(makeFloat(1.0)));
assertTrue(isReal(makeFloat(25.0)));
assertTrue(isReal(e));
assertTrue(isReal(pi));
assertTrue(isReal(inf));
assertTrue(isReal(negative_inf));
assertTrue(isReal(nan));
},
'complex': function() {
assertTrue(isReal(makeComplex(0, 0)));
assertTrue(isReal(makeComplex(e, 0)));
assertTrue(isReal(makeComplex(pi, 0)));
assertTrue(isReal(makeComplex(nan, 0)));
assertTrue(isReal(makeComplex(inf, 0)));
assertTrue(isReal(makeComplex(negative_inf, 0)));
assertFalse(isReal(makeComplex(0, 1)));
assertFalse(isReal(makeComplex(0, negative_inf)));
assertFalse(isReal(makeComplex(pi, inf)));
assertFalse(isReal(makeComplex(234, nan)));
+ assertFalse(isReal(makeComplex(makeFloat(3),
+ makeFloat(0))));
},
'others': function() {
assertFalse(isReal("0"));
assertFalse(isReal("hello"));
assertFalse(isReal([]));
assertFalse(isReal({}));
assertFalse(isReal(false));
}
});
describe('isExact', {
'fixnums': function() {
assertTrue(isExact(19));
assertTrue(isExact(0));
assertTrue(isExact(-1));
assertTrue(isExact(1));
},
'bignums': function() {
assertTrue(isExact(makeBignum("0")));
assertTrue(isExact(makeBignum("1")));
assertTrue(isExact(makeBignum("-1")));
assertTrue(isExact(makeBignum("23497842398287924789232439723")));
assertTrue(isExact(makeBignum("1e1000")));
assertTrue(isExact(makeBignum("-1e1000")));
assertTrue(isExact(makeBignum("12342357892297851728921374891327893")));
assertTrue(isExact(makeBignum("4.1321e200")));
assertTrue(isExact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertTrue(isExact(makeRational(19)));
assertTrue(isExact(makeRational(0)));
assertTrue(isExact(makeRational(-1)));
assertTrue(isExact(makeRational(1)));
assertTrue(isExact(makeRational(1, 2)));
assertTrue(isExact(makeRational(1, 29291)));
},
'floats': function() {
assertFalse(isExact(e));
assertFalse(isExact(pi));
assertFalse(isExact(inf));
assertFalse(isExact(negative_inf));
assertFalse(isExact(nan));
assertFalse(isExact(makeFloat(0)));
assertFalse(isExact(makeFloat(1111.1)));
},
'complex': function() {
assertTrue(isExact(makeComplex(0, 0)));
assertTrue(isExact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertFalse(isExact(makeComplex(e,
makeRational(1, 17))));
assertFalse(isExact(makeComplex(makeRational(1,2),
pi)));
assertFalse(isExact(makeComplex(makeRational(1,2),
nan)));
assertFalse(isExact(makeComplex(negative_inf,
nan)));
}
});
describe('isInexact', {
'fixnums': function() {
assertFalse(isInexact(19));
assertFalse(isInexact(0));
assertFalse(isInexact(-1));
assertFalse(isInexact(1));
},
'bignums': function() {
assertFalse(isInexact(makeBignum("0")));
assertFalse(isInexact(makeBignum("1")));
assertFalse(isInexact(makeBignum("-1")));
assertFalse(isInexact(makeBignum("23497842398287924789232439723")));
assertFalse(isInexact(makeBignum("1e1000")));
assertFalse(isInexact(makeBignum("-1e1000")));
assertFalse(isInexact(makeBignum("12342357892297851728921374891327893")));
assertFalse(isInexact(makeBignum("4.1321e200")));
assertFalse(isInexact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertFalse(isInexact(makeRational(19)));
assertFalse(isInexact(makeRational(0)));
assertFalse(isInexact(makeRational(-1)));
assertFalse(isInexact(makeRational(1)));
assertFalse(isInexact(makeRational(1, 2)));
assertFalse(isInexact(makeRational(1, 29291)));
},
'floats': function() {
assertTrue(isInexact(e));
assertTrue(isInexact(pi));
assertTrue(isInexact(inf));
assertTrue(isInexact(negative_inf));
assertTrue(isInexact(nan));
assertTrue(isInexact(makeFloat(0)));
assertTrue(isInexact(makeFloat(1111.1)));
},
'complex': function() {
assertFalse(isInexact(makeComplex(0, 0)));
assertFalse(isInexact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(e,
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(makeRational(1,2),
pi)));
assertTrue(isInexact(makeComplex(makeRational(1,2),
nan)));
assertTrue(isInexact(makeComplex(negative_inf,
nan)));
}
});
describe('isInteger', {
'fixnums': function() {
assertTrue(isInteger(1));
assertTrue(isInteger(-1));
},
'bignums': function() {
assertTrue(isInteger(makeBignum("2983473189472187414789132743928148151617364")));
assertTrue(isInteger(makeBignum("-99999999999999999999999999999999999999")));
},
'rationals': function() {
assertTrue(isInteger(makeRational(1, 1)));
assertFalse(isInteger(makeRational(1, 2)));
assertFalse(isInteger(makeRational(9999, 10000)));
assertFalse(isInteger(makeRational(9999, 1000)));
},
'floats': function() {
assertFalse(isInteger(makeFloat(2.3)));
assertTrue(isInteger(makeFloat(4.0)));
assertFalse(isInteger(inf));
assertFalse(isInteger(negative_inf));
assertFalse(isInteger(nan));
},
'complex': function() {
assertTrue(isInteger(makeComplex(42, 0)));
+ assertFalse(isInteger(makeComplex(makeFloat(42), makeFloat(0))));
assertFalse(isInteger(makeComplex(42, 42)));
assertFalse(isInteger(i));
assertFalse(isInteger(negative_i));
},
'others': function() {
assertFalse(isInteger("hello"));
assertFalse(isInteger("0"));
}
});
describe('toFixnum', {
'fixnums': function() {
assertEquals(42, toFixnum(42));
assertEquals(-20, toFixnum(-20));
assertEquals(0, toFixnum(0));
},
'bignums': function() {
assertEquals(123456789, toFixnum(makeBignum("123456789")));
assertEquals(0, toFixnum(makeBignum("0")));
assertEquals(-123, toFixnum(makeBignum("-123")));
assertEquals(123456, toFixnum(makeBignum("123456")));
// We're dealing with big numbers, where the numerical error
// makes it difficult to compare for equality. We just go for
// percentage and see that it is ok.
assertTrue(diffPercent(1e200, toFixnum(makeBignum("1e200")))
< 1e-10);
assertTrue(diffPercent(-1e200, toFixnum(makeBignum("-1e200")))
< 1e-10);
},
'rationals': function() {
assertEquals(0, toFixnum(zero));
assertEquals(17/2, toFixnum(makeRational(17, 2)));
assertEquals(1926/3, toFixnum(makeRational(1926, 3)));
assertEquals(-11150/17, toFixnum(makeRational(-11150, 17)));
},
'floats': function() {
assertEquals(12345.6789, toFixnum(makeFloat(12345.6789)));
assertEquals(Math.PI, toFixnum(pi));
assertEquals(Math.E, toFixnum(e));
assertEquals(Number.POSITIVE_INFINITY, toFixnum(inf));
assertEquals(Number.NEGATIVE_INFINITY, toFixnum(negative_inf));
assertTrue(isNaN(toFixnum(nan)));
},
'complex': function() {
assertFails(function() { toFixnum(makeComplex(2, 1)); });
assertFails(function() { toFixnum(i); });
assertFails(function() { toFixnum(negative_i); });
assertEquals(2, toFixnum(makeComplex(2, 0)));
assertEquals(1/2, toFixnum(makeComplex(makeRational(1, 2),
0)));
assertEquals(Number.POSITIVE_INFINITY,
toFixnum(makeComplex(inf, 0)));
assertEquals(Number.NEGATIVE_INFINITY,
toFixnum(makeComplex(negative_inf, 0)));
assertTrue(isNaN(toFixnum(makeComplex(nan, 0))));
}
});
describe('toExact', {
'fixnums': function() {
assertEquals(1792, toExact(1792));
assertEquals(0, toExact(0));
assertEquals(-1, toExact(-1));
},
'bignums': function() {
assertEquals(makeBignum("4.2e100"),
toExact(makeBignum("4.2e100")));
assertEquals(makeBignum("0"),
toExact(makeBignum("0")));
assertEquals(makeBignum("1"),
toExact(makeBignum("1")));
assertEquals(makeBignum("-1"),
toExact(makeBignum("-1")));
assertEquals(makeBignum("-12345"),
toExact(makeBignum("-12345")));
assertEquals(makeBignum("-1.723e500"),
toExact(makeBignum("-1.723e500")));
},
'rationals': function() {
assertEquals(makeRational(1, 2), toExact(makeRational(1, 2)));
assertEquals(makeRational(1, 9999), toExact(makeRational(1, 9999)));
assertEquals(makeRational(0, 1), toExact(makeRational(0, 9999)));
assertEquals(makeRational(-290, 1), toExact(makeRational(-290, 1)));
},
'floats': function() {
assertEquals(makeRational(1, 2), toExact(makeFloat(0.5)));
assertEquals(makeRational(1, 10), toExact(makeFloat(0.1)));
assertEquals(makeRational(9, 10), toExact(makeFloat(0.9)));
assertTrue(isExact(toExact(makeFloat(10234.7))));
assertTrue(diffPercent(makeRational(102347, 10),
toExact(makeFloat(10234.7))) < 1);
assertEquals(-1, toExact(makeFloat(-1)));
assertEquals(0, toExact(makeFloat(0)));
assertEquals(1024, toExact(makeFloat(1024)));
assertFails(function() { toExact(nan); });
assertFails(function() { toExact(inf); });
assertFails(function() { toExact(negative_inf); });
},
'complex': function() {
assertEquals(0, toExact(makeComplex(0, 0)));
assertEquals(99, toExact(makeComplex(99, 0)));
assertEquals(makeRational(-1, 2),
toExact(makeComplex(makeRational(-1, 2), 0)));
assertEquals(makeRational(1, 4),
toExact(makeComplex(makeFloat(.25), 0)));
assertFails(function() { toExact(makeComplex(nan, 0)); });
assertFails(function() { toExact(makeComplex(inf, 0)); });
assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
assertTrue(eqv(toExact(makeComplex(0, 1)), makeComplex(0, 1)));
assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
|
dyoo/js-numbers
|
d3bf179f4a2ccec6b07247abe5158b9b59a79a9e
|
fixing round to preserve inexactness
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 227f543..3ed6fb7 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1446,1030 +1446,1033 @@ if (typeof(exports) !== 'undefined') {
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} else {
return FloatPoint.makeInstance(Math.floor(this.n));
}
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
} else if (this === NEGATIVE_ZERO) {
return this;
} return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
+ if (this === NEGATIVE_ZERO) {
+ return this;
+ }
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
- return fromFixnum(Math.floor(this.n));
- return fromFixnum(Math.ceil(this.n));
+ return FloatPoint.makeInstance(Math.floor(this.n));
+ return FloatPoint.makeInstance(Math.ceil(this.n));
} else {
- return fromFixnum(Math.round(this.n));
+ return FloatPoint.makeInstance(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(digitRegexp) &&
(x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
|
dyoo/js-numbers
|
8a308a25935b3905db9c4e87ca4d245fb3574f52
|
fixing one of the tests with division
|
diff --git a/test/tests.js b/test/tests.js
index c4ad425..fe1431f 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2779,1071 +2779,1072 @@ describe('realPart', {
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('repeating decimals', {
tests: function() {
assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
- assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
+ assertEqv(divide(makeFloat(1),makeFloat(0)),
+ inf);
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
assertEquals("5.0+0.0i",
(makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
(makeComplex(5, 1)).toString());
assertEquals("4-2i",
(makeComplex(4, -2)).toString());
},
testQuotient : function(){
assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
assertTrue(eqv(1, quotient(7, 5)));
},
testRemainder : function(){
assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
makeFloat(3)));
assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, modulo(n1, n2));
assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(isReal(pi));
assertTrue(isReal(1));
assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!isReal("hi"));
},
testRound : function(){
assertTrue(equals(round(makeFloat(3.499999)),
- makeFloat(3)));
+ makeFloat(3)));
assertTrue(equals(round(makeFloat(3.5)),
- makeFloat(4)));
+ makeFloat(4)));
assertTrue(equals(round(makeFloat(3.51)),
- makeFloat(4)));
+ makeFloat(4)));
assertTrue(equals(round(makeRational(3)),
- makeRational(3)));
-
+ makeRational(3)));
+
assertTrue(equals(round(makeRational(17, 4)),
- makeRational(4)));
-
-
+ makeRational(4)));
+
+
assertTrue(equals(round(makeRational(-17, 4)),
- makeRational(-4)));
+ makeRational(-4)));
},
// testSgn : function(){
// assertTrue(equals(sgn(makeFloat(4)), 1));
// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
// assertTrue(equals(sgn(0), 0));
// },
// testZero_question_ : function(){
// assertTrue(Kernel.zero_question_(0));
// assertTrue(!Kernel.zero_question_(1));
// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
// }
});
|
dyoo/js-numbers
|
260da58dc1b7757afedc2b4f5b5f228961925f8e
|
correcting bugs with ceiling tests
|
diff --git a/test/tests.js b/test/tests.js
index 0c06ed0..c4ad425 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1940,1084 +1940,1086 @@ describe('lessThan', {
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.0)));
assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
assertEqv(makeFloat(1), floor(makeFloat(1.1)));
assertEqv(makeFloat(1), floor(makeFloat(1.999)));
assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
assertEqv(makeFloat(1234567891234567),
floor(makeFloat(1234567891234567.8)));
assertEqv(makeFloat(-1234567891234568),
floor(makeFloat(-1234567891234567.8)));
assertEqv(nan, floor(nan));
assertEqv(inf, floor(inf));
assertEqv(negative_inf, floor(negative_inf));
assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeFloat(-2), floor(makeComplex(makeFloat(-1.999),
makeFloat(0.0)))));
assertTrue(eqv(makeFloat(1234567891234567),
floor(makeComplex(makeFloat(1234567891234567.8),
makeFloat(0)))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
- assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
- assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
- assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
- assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
- assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
- assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
- assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
- assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
- assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
- assertEquals(nan, ceiling(nan));
- assertEquals(inf, ceiling(inf));
- assertEquals(negative_inf, ceiling(negative_inf));
- assertEquals(negative_zero, ceiling(negative_zero));
+ assertEqv(makeFloat(0), ceiling(makeFloat(0.0)));
+ assertEqv(makeFloat(1), ceiling(makeFloat(1.0)));
+ assertEqv(makeFloat(-1), ceiling(makeFloat(-1.0)));
+ assertEqv(makeFloat(2), ceiling(makeFloat(1.1)));
+ assertEqv(makeFloat(2), ceiling(makeFloat(1.999)));
+ assertEqv(makeFloat(-1), ceiling(makeFloat(-1.999)));
+ assertEqv(makeFloat(123457), ceiling(makeFloat(123456.789)));
+ assertEqv(makeFloat(1234567891234568),
+ ceiling(makeFloat(1234567891234567.8)));
+ assertEqv(makeFloat(-1234567891234567),
+ ceiling(makeFloat(-1234567891234567.8)));
+ assertEqv(nan, ceiling(nan));
+ assertEqv(inf, ceiling(inf));
+ assertEqv(negative_inf, ceiling(negative_inf));
+ assertEqv(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
- assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
+ assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
- assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
- makeBignum("0")))));
- assertTrue(eqv(makeBignum("1234567891234568"),
+ assertTrue(eqv(makeFloat(-1), ceiling(makeComplex(makeFloat(-1.999),
+ makeFloat(0)))));
+ assertTrue(eqv(makeFloat(1234567891234568),
ceiling(makeComplex(makeFloat(1234567891234567.8),
- makeBignum("0")))));
+ makeFloat(0)))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
|
dyoo/js-numbers
|
c9dd9c829f26bdcb1cda2784b2778e01738677d0
|
repairing tests with floor
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index e12ac8a..227f543 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1312,1033 +1312,1037 @@ if (typeof(exports) !== 'undefined') {
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
+ } else if (this === NEGATIVE_ZERO) {
+ return this;
+ } else {
+ return FloatPoint.makeInstance(Math.floor(this.n));
}
- return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
- }
- return fromFixnum(Math.ceil(this.n));
+ } else if (this === NEGATIVE_ZERO) {
+ return this;
+ } return FloatPoint.makeInstance(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
diff --git a/test/tests.js b/test/tests.js
index c00565a..0c06ed0 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,533 +1,538 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
+
+var assertEqv = function(x, y) {
+ value_of(eqv(x, y)).should_be_true();
+};
+
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
// FIXME: add tests for polar construction
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
@@ -1796,1085 +1801,1087 @@ describe('lessThanOrEqual', {
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
assertTrue(eqv(1,
floor(makeRational(7, 5))));
},
'floats': function() {
- assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
- assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
- assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
- assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
- assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
- assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
- assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
- assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
- assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
- assertEquals(nan, floor(nan));
- assertEquals(inf, floor(inf));
- assertEquals(negative_inf, floor(negative_inf));
- assertEquals(negative_zero, floor(negative_zero));
+ assertEqv(makeFloat(0.0), floor(makeFloat(0.0)));
+ assertEqv(makeFloat(1), floor(makeFloat(1.0)));
+ assertEqv(makeFloat(-1), floor(makeFloat(-1.0)));
+ assertEqv(makeFloat(1), floor(makeFloat(1.1)));
+ assertEqv(makeFloat(1), floor(makeFloat(1.999)));
+ assertEqv(makeFloat(-2), floor(makeFloat(-1.999)));
+ assertEqv(makeFloat(123456), floor(makeFloat(123456.789)));
+ assertEqv(makeFloat(1234567891234567),
+ floor(makeFloat(1234567891234567.8)));
+ assertEqv(makeFloat(-1234567891234568),
+ floor(makeFloat(-1234567891234567.8)));
+ assertEqv(nan, floor(nan));
+ assertEqv(inf, floor(inf));
+ assertEqv(negative_inf, floor(negative_inf));
+ assertEqv(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
- assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
+ assertFails(function() { floor(makeComplex(makeFloat(4.25), makeFloat(1.5)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
- assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
- makeBignum("0")))));
- assertTrue(eqv(makeBignum("1234567891234567"),
+ assertTrue(eqv(makeFloat(-2), floor(makeComplex(makeFloat(-1.999),
+ makeFloat(0.0)))));
+ assertTrue(eqv(makeFloat(1234567891234567),
floor(makeComplex(makeFloat(1234567891234567.8),
- makeBignum("0")))));
+ makeFloat(0)))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
|
dyoo/js-numbers
|
448e17c70399b874c8cee6362c33c1420ee0584d
|
fixing some division-by-zero bugs
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 0b0cc6a..e12ac8a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,837 +1,841 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
- return (eqv(y, INEXACT_ZERO))},
+ return (eqv(y, INEXACT_ZERO) || eqv(y, NEGATIVE_ZERO))},
onYSpecialCase: function(x, y) {
+ var pos = (y !== NEGATIVE_ZERO);
+
+
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
- return inf;
+ return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
- return neginf;
+ return pos ? neginf : inf;
} else {
return 0;
}
} else {
+ // both x and y are inexact
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
- return inf;
+ return pos ? inf : neginf;
} else if (lessThan(x, 0)) {
- return neginf;
+ return pos ? neginf : inf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
diff --git a/test/tests.js b/test/tests.js
index 6fe6efd..c00565a 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1205,1034 +1205,1033 @@ describe('add', {
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
makeFloat(1e300)),
makeComplex(makeFloat(4e300),
makeFloat(4e300))),
makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
- assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
- assertTrue(eqv(negative_inf, divide(1, negative_zero)));
-
- assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
- assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
- assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
- assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
-
- assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
- assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
+ assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
+ assertTrue(eqv(negative_inf, divide(1, negative_zero)));
+
+ assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
+ assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
+ assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
+ assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
+ assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
+ assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
|
dyoo/js-numbers
|
38c6cb56bb6e7662661b8d37a7506d2a94a440f0
|
trying to fix some of the cases involving zero
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index b5d8632..0b0cc6a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,2668 +1,2669 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
- throwRuntimeError("division by zero", x, y);
+ throwRuntimeError("/: division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
},
{ isYSpecialCase: function(y) {
- return (isInexact(y) && isReal(y) && equals(y, 0))},
+ return (eqv(y, INEXACT_ZERO))},
onYSpecialCase: function(x, y) {
if (isReal(x)) {
if (isExact(x)) {
if (greaterThan(x, 0)) {
return inf;
} else if (lessThan(x, 0)) {
return neginf;
} else {
return 0;
}
} else {
if (isNaN(toFixnum(x))) {
return NaN;
} else if (greaterThan(x, 0)) {
return inf;
} else if (lessThan(x, 0)) {
return neginf;
} else {
return NaN;
}
}
} else {
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return x.divide(y);
}
}
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
- "greaterThanOrEqual: couldn't be applied to complex number", x, y);
+ ">=: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
- throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
+ throwRuntimeError("<=: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
- throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
+ throwRuntimeError(">: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
- throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
+ throwRuntimeError("<: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
- throwRuntimeError("division by zero", this, other);
+ throwRuntimeError("/: division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
+ var INEXACT_ZERO = new FloatPoint(0.0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
- return throwRuntimeError("division by zero", this, other);
+ return throwRuntimeError("/: division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
- var down = multiply(other, con);
+ var down = realPart(multiply(other, con));
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(digitRegexp) &&
(x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
diff --git a/test/tests.js b/test/tests.js
index 67fdfd4..6fe6efd 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1192,1024 +1192,1029 @@ describe('add', {
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
+ assertTrue(eqv(divide(makeComplex(makeFloat(1e300),
+ makeFloat(1e300)),
+ makeComplex(makeFloat(4e300),
+ makeFloat(4e300))),
+ makeFloat(.25)))
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
|
dyoo/js-numbers
|
5491aefcfdf954c61b82aa1eb109015dfaf742e8
|
trying to treat divisino by zero more carefully
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 1ddb34d..0d30bfe 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,817 +1,847 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
+ },
+ { isYSpecialCase: function(y) {
+ return (isInexact(y) && isReal(y) && equals(y, 0))},
+ onYSpecialCase: function(x, y) {
+ if (isReal(x)) {
+ if (isExact(x)) {
+ if (greaterThan(x, 0)) {
+ return inf;
+ } else if (lessThan(x, 0)) {
+ return neginf;
+ } else {
+ return 0;
+ }
+ } else {
+ if (isNaN(toFixnum(x))) {
+ return NaN;
+ } else if (greaterThan(x, 0)) {
+ return inf;
+ } else if (lessThan(x, 0)) {
+ return neginf;
+ } else {
+ return NaN;
+ }
+ }
+ } else {
+ if (x.level < y.level) x = x.liftTo(y);
+ if (y.level < x.level) y = y.liftTo(x);
+ return x.divide(y);
+ }
+ }
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
diff --git a/test/tests.js b/test/tests.js
index 1e4fc71..8c38a6a 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1215,1025 +1215,1025 @@ describe('add', {
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
- assertTrue(eqv(negative_zero,
+ assertTrue(eqv(nan,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
|
dyoo/js-numbers
|
40537a3dc1c698a7b3f4b825dda3f67b5ed19057
|
corrections to fromString
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 1ddb34d..2281f9f 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1809,1049 +1809,1051 @@ if (typeof(exports) !== 'undefined') {
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
if (isInexact(r) || isInexact(i)) {
r = toInexact(r);
i = toInexact(i);
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
+ var digitRegexp = new RegExp("\\d");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
- if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
+ if (x.match(digitRegexp) &&
+ (x.match(flonumRegexp) || x.match(bignumScientificPattern))) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
if ( this.s < 0 ) {
r = a.t - i;
}
else {
r = i - a.t;
}
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
|
dyoo/js-numbers
|
db4a83dec70e1969c4f6c6dec7a6755d3fc0e079
|
our assertFalse function is wrong.
|
diff --git a/test/tests.js b/test/tests.js
index a3fb2ac..0852ba3 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,539 +1,539 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
- value_of(aVal).should_be_false();
+ value_of(aVal === false).should_be_true();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
// FIXME: add tests for polar construction
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
|
dyoo/js-numbers
|
e8b27c39ccef3d7c98b7e45461905de8a18d5750
|
adding some tests for jsnums
|
diff --git a/test/tests.js b/test/tests.js
index 1e4fc71..a3fb2ac 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1785,1024 +1785,1027 @@ describe('greaterThanOrEqual', {
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
+
+ assertTrue(eqv(1,
+ floor(makeRational(7, 5))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
@@ -3235,595 +3238,599 @@ describe('old tests from Moby Scheme', {
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
assertEquals("5.0+0.0i",
(makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
(makeComplex(5, 1)).toString());
assertEquals("4-2i",
(makeComplex(4, -2)).toString());
},
testQuotient : function(){
assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
+
+
+
+ assertTrue(eqv(1, quotient(7, 5)));
},
testRemainder : function(){
assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
makeFloat(3)));
assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, modulo(n1, n2));
assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(isReal(pi));
assertTrue(isReal(1));
assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!isReal("hi"));
},
testRound : function(){
assertTrue(equals(round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(round(makeRational(3)),
makeRational(3)));
assertTrue(equals(round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(round(makeRational(-17, 4)),
makeRational(-4)));
},
// testSgn : function(){
// assertTrue(equals(sgn(makeFloat(4)), 1));
// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
// assertTrue(equals(sgn(0), 0));
// },
// testZero_question_ : function(){
// assertTrue(Kernel.zero_question_(0));
// assertTrue(!Kernel.zero_question_(1));
// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
// }
});
|
dyoo/js-numbers
|
ed320ccc61cd20da66b84e9ccdee8138a78f792e
|
fixing implementation of integer quotient
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 01076bf..1ddb34d 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -490,1025 +490,1025 @@ if (typeof(exports) !== 'undefined') {
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
- return ((m / n) - ((m % n) / n));
+ return ((m - (m % n))/ n);
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
@@ -3337,670 +3337,668 @@ if (typeof(exports) !== 'undefined') {
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess, floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
//////////////////////////////////////////////////////////////////////
// toRepeatingDecimal: jsnum jsnum -> [string, string, string]
//
// Given the numerator and denominator parts of a rational,
// produces the repeating-decimal representation, where the first
// part are the digits before the decimal, the second are the
// non-repeating digits after the decimal, and the third are the
// remaining repeating decimals.
var toRepeatingDecimal = (function() {
- var getResidue = function(remainder, divisor) {
+ var getResidue = function(r, d) {
var digits = [];
var seenRemainders = {};
- seenRemainders[remainder] = true;
+ seenRemainders[r] = true;
while(true) {
var nextDigit = quotient(
- multiply(remainder, 10), divisor);
+ multiply(r, 10), d);
var nextRemainder = remainder(
- multiply(remainder, 10),
- divisor);
-
+ multiply(r, 10),
+ d);
digits.push(nextDigit.toString());
if (seenRemainders[nextRemainder]) {
- remainder = nextRemainder;
+ r = nextRemainder;
break;
} else {
seenRemainders[nextRemainder] = true;
- remainder = nextRemainder;
+ r = nextRemainder;
}
}
- var firstRepeatingRemainder = remainder;
+ var firstRepeatingRemainder = r;
var repeatingDigits = [];
while (true) {
- var nextDigit = quotient(
- multiply(remainder, 10), divisor);
+ var nextDigit = quotient(multiply(r, 10), d);
var nextRemainder = remainder(
- multiply(remainder, 10),
- divisor);
+ multiply(r, 10),
+ d);
repeatingDigits.push(nextDigit.toString());
if (equals(nextRemainder, firstRepeatingRemainder)) {
break;
} else {
- remainder = nextRemainder;
+ r = nextRemainder;
}
};
var digitString = digits.join('');
var repeatingDigitString = repeatingDigits.join('');
while (digitString.length >= repeatingDigitString.length &&
(digitString.substring(
digitString.length - repeatingDigitString.length)
=== repeatingDigitString)) {
digitString = digitString.substring(
0, digitString.length - repeatingDigitString.length);
}
return [digitString, repeatingDigitString];
};
return function(n, d) {
if (! isInteger(n)) {
throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
" is not an integer.");
}
if (! isInteger(d)) {
throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
" is not an integer.");
}
if (equals(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d equals 0');
}
if (lessThan(d, 0)) {
throwRuntimeError('toRepeatingDecimal: d < 0');
}
- var sign = (lessThan(n, 0) ? "-" : "");
- n = abs(n);
- var beforeDecimalPoint = sign + quotient(n, d);
- var afterDecimals = getResidue(remainder(n, d), d);
- return [beforeDecimalPoint].concat(afterDecimals);
+ var sign = (lessThan(n, 0) ? "-" : "");
+ n = abs(n);
+ var beforeDecimalPoint = sign + quotient(n, d);
+ var afterDecimals = getResidue(remainder(n, d), d);
+ return [beforeDecimalPoint].concat(afterDecimals);
};
})();
//////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
diff --git a/test/tests.js b/test/tests.js
index 6b96a56..1e4fc71 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2666,1024 +2666,1048 @@ describe('acos', {
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
+describe('repeating decimals', {
+ tests: function() {
+ assertEquals(['1', '', '0'], toRepeatingDecimal(1, 1));
+ assertEquals(['0', '5', '0'], toRepeatingDecimal(1, 2));
+ assertEquals(['0', '', '3'], toRepeatingDecimal(1, 3));
+ assertEquals(['0', '25', '0'], toRepeatingDecimal(1, 4));
+ assertEquals(['0', '2', '0'], toRepeatingDecimal(1, 5));
+ assertEquals(['0', '1', '6'], toRepeatingDecimal(1, 6));
+ assertEquals(['0', '', '142857'], toRepeatingDecimal(1, 7));
+ assertEquals(['0', '125', '0'], toRepeatingDecimal(1, 8));
+ assertEquals(['0', '', '1'], toRepeatingDecimal(1, 9));
+ assertEquals(['0', '1', '0'], toRepeatingDecimal(1, 10));
+ assertEquals(['0', '', '09'], toRepeatingDecimal(1, 11));
+ assertEquals(['0', '08', '3'], toRepeatingDecimal(1, 12));
+ assertEquals(['0', '', '076923'], toRepeatingDecimal(1, 13));
+ assertEquals(['0', '0', '714285'], toRepeatingDecimal(1, 14));
+ assertEquals(['0', '0', '6'], toRepeatingDecimal(1, 15));
+ assertEquals(['0', '0625', '0'], toRepeatingDecimal(1, 16));
+ assertEquals(['0', '', '0588235294117647'], toRepeatingDecimal(1, 17));
+ assertEquals(['5', '8', '144'], toRepeatingDecimal(3227, 555));
+ }
+});
+
+
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
assertEquals("5.0+0.0i",
|
dyoo/js-numbers
|
c5629f91f465d87384a9a0dc8de0f9da052a3beb
|
adding implementation for repeating decimal representation.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 3a7a4e8..01076bf 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,618 +1,618 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
- return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
+ throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if ( eqv(n, 1) ) {
return 0;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
@@ -3328,594 +3328,679 @@ if (typeof(exports) !== 'undefined') {
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.isInexact = function() {
return false;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess, floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
+ //////////////////////////////////////////////////////////////////////
+ // toRepeatingDecimal: jsnum jsnum -> [string, string, string]
+ //
+ // Given the numerator and denominator parts of a rational,
+ // produces the repeating-decimal representation, where the first
+ // part are the digits before the decimal, the second are the
+ // non-repeating digits after the decimal, and the third are the
+ // remaining repeating decimals.
+ var toRepeatingDecimal = (function() {
+ var getResidue = function(remainder, divisor) {
+ var digits = [];
+ var seenRemainders = {};
+ seenRemainders[remainder] = true;
+ while(true) {
+ var nextDigit = quotient(
+ multiply(remainder, 10), divisor);
+ var nextRemainder = remainder(
+ multiply(remainder, 10),
+ divisor);
+
+ digits.push(nextDigit.toString());
+ if (seenRemainders[nextRemainder]) {
+ remainder = nextRemainder;
+ break;
+ } else {
+ seenRemainders[nextRemainder] = true;
+ remainder = nextRemainder;
+ }
+ }
+
+ var firstRepeatingRemainder = remainder;
+ var repeatingDigits = [];
+ while (true) {
+ var nextDigit = quotient(
+ multiply(remainder, 10), divisor);
+ var nextRemainder = remainder(
+ multiply(remainder, 10),
+ divisor);
+ repeatingDigits.push(nextDigit.toString());
+ if (equals(nextRemainder, firstRepeatingRemainder)) {
+ break;
+ } else {
+ remainder = nextRemainder;
+ }
+ };
+
+ var digitString = digits.join('');
+ var repeatingDigitString = repeatingDigits.join('');
+
+ while (digitString.length >= repeatingDigitString.length &&
+ (digitString.substring(
+ digitString.length - repeatingDigitString.length)
+ === repeatingDigitString)) {
+ digitString = digitString.substring(
+ 0, digitString.length - repeatingDigitString.length);
+ }
+
+ return [digitString, repeatingDigitString];
+
+ };
+
+ return function(n, d) {
+ if (! isInteger(n)) {
+ throwRuntimeError('toRepeatingDecimal: n ' + n.toString() +
+ " is not an integer.");
+ }
+ if (! isInteger(d)) {
+ throwRuntimeError('toRepeatingDecimal: d ' + d.toString() +
+ " is not an integer.");
+ }
+ if (equals(d, 0)) {
+ throwRuntimeError('toRepeatingDecimal: d equals 0');
+ }
+ if (lessThan(d, 0)) {
+ throwRuntimeError('toRepeatingDecimal: d < 0');
+ }
+ var sign = (lessThan(n, 0) ? "-" : "");
+ n = abs(n);
+ var beforeDecimalPoint = sign + quotient(n, d);
+ var afterDecimals = getResidue(remainder(n, d), d);
+ return [beforeDecimalPoint].concat(afterDecimals);
+ };
+ })();
+ //////////////////////////////////////////////////////////////////////
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
+ Numbers['toRepeatingDecimal'] = toRepeatingDecimal;
})();
|
dyoo/js-numbers
|
5ca9fc4635c706ea6fc07c345a3a0ea358a6a9e7
|
fixing issue with bignums
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 35a356a..3a7a4e8 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,521 +1,521 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
- this['jsnums'] = {};
+ this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
//var Numbers = jsnums;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if ( eqv(n, 0) ) {
return 1;
}
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
@@ -761,1025 +761,1025 @@ if (typeof(exports) !== 'undefined') {
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
- return Rational.makeInstance(-this.n, d)
+ return Rational.makeInstance(-this.n, this.d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var intPart = parseInt(match[1]);
var fracPart = parseInt(match[2]);
var tenToDecimalPlaces = Math.pow(10, match[2].length);
return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
tenToDecimalPlaces);
}
else {
return this.n;
}
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
var partialResult = this.n.toString();
if (! partialResult.match('\\.')) {
return partialResult + ".0";
} else {
return partialResult;
}
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
var multFactor = factorToInt / extraFactor;
return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
var afterDecimal = parseInt(match[2]);
var factorToInt = Math.pow(10, match[2].length);
var extraFactor = _integerGcd(factorToInt, afterDecimal);
return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
return FloatPoint.makeInstance(1);
}
};
@@ -2070,1025 +2070,1030 @@ if (typeof(exports) !== 'undefined') {
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
- r = i-a.t;
+ if ( this.s < 0 ) {
+ r = a.t - i;
+ }
+ else {
+ r = i - a.t;
+ }
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
// use am to combine the multiply-shift-add into one call
j = i+this.m.t;
x[j] += this.m.am(0,u0,x,i,0,this.m.t);
// propagate carry
while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
}
x.clamp();
x.drShiftTo(this.m.t,x);
if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = "x^2/R mod m"; x != r
function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = "xy/R mod m"; x,y != r
function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;
// (protected) true iff this is even
function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e,z) {
if(e > 0xffffffff || e < 1) return BigInteger.ONE;
var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
g.copyTo(r);
while(--i >= 0) {
z.sqrTo(r,r2);
if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
else { var t = r; r = r2; r2 = t; }
}
return z.revert(r);
}
// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e,m) {
var z;
if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
return this.exp(e,z);
}
// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;
// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
// Copyright (c) 2005-2009 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
// (public)
function bnClone() { var r = nbi(); this.copyTo(r); return r; }
// (public) return value as integer
function bnIntValue() {
if(this.s < 0) {
if(this.t == 1) return this[0]-this.DV;
else if(this.t == 0) return -1;
}
else if(this.t == 1) return this[0];
else if(this.t == 0) return 0;
// assumes 16 < DB < 32
return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
}
// (public) return value as byte
function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
// (public) return value as short (assumes DB>=16)
function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
if(this.s < 0) return -1;
else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
else return 1;
}
// (protected) convert to radix string
function bnpToRadix(b) {
if(b == null) b = 10;
if(this.signum() == 0 || b < 2 || b > 36) return "0";
var cs = this.chunkSize(b);
var a = Math.pow(b,cs);
var d = nbv(a), y = nbi(), z = nbi(), r = "";
this.divRemTo(d,y,z);
while(y.signum() > 0) {
r = (a+z.intValue()).toString(b).substr(1) + r;
y.divRemTo(d,y,z);
}
return z.intValue().toString(b) + r;
}
// (protected) convert from radix string
function bnpFromRadix(s,b) {
this.fromInt(0);
if(b == null) b = 10;
var cs = this.chunkSize(b);
var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
for(var i = 0; i < s.length; ++i) {
var x = intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
continue;
}
w = b*w+x;
if(++j >= cs) {
this.dMultiply(d);
this.dAddOffset(w,0);
j = 0;
w = 0;
}
}
if(j > 0) {
this.dMultiply(Math.pow(b,j));
this.dAddOffset(w,0);
}
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) alternate constructor
function bnpFromNumber(a,b,c) {
if("number" == typeof b) {
// new BigInteger(int,int,RNG)
if(a < 2) this.fromInt(1);
else {
this.fromNumber(a,c);
if(!this.testBit(a-1)) // force MSB set
this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
if(this.isEven()) this.dAddOffset(1,0); // force odd
while(!this.isProbablePrime(b)) {
this.dAddOffset(2,0);
if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
}
}
}
else {
// new BigInteger(int,RNG)
var x = [], t = a&7;
x.length = (a>>3)+1;
b.nextBytes(x);
if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
this.fromString(x,256);
}
}
// (public) convert to bigendian byte array
function bnToByteArray() {
var i = this.t, r = [];
r[0] = this.s;
var p = this.DB-(i*this.DB)%8, d, k = 0;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
r[k++] = d|(this.s<<(this.DB-p));
while(i >= 0) {
if(p < 8) {
d = (this[i]&((1<<p)-1))<<(8-p);
d |= this[--i]>>(p+=this.DB-8);
}
else {
d = (this[i]>>(p-=8))&0xff;
if(p <= 0) { p += this.DB; --i; }
}
if((d&0x80) != 0) d |= -256;
if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
if(k > 0 || d != this.s) r[k++] = d;
}
}
return r;
}
function bnEquals(a) { return(this.compareTo(a)==0); }
function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a,op,r) {
var i, f, m = Math.min(a.t,this.t);
for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
if(a.t < this.t) {
f = a.s&this.DM;
for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
r.t = this.t;
}
else {
f = this.s&this.DM;
for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
r.t = a.t;
}
r.s = op(this.s,a.s);
r.clamp();
}
// (public) this & a
function op_and(x,y) { return x&y; }
function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
// (public) this | a
function op_or(x,y) { return x|y; }
function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
|
dyoo/js-numbers
|
8658df7dcd8b84a636420877ab969b880b19aef1
|
updating test cases; complex numbers have consistent inexactness
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index d02d84f..35a356a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,2652 +1,2682 @@
// Scheme numbers.
+
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
+//var jsnums = {};
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
+ //var Numbers = jsnums;
+
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isExact: scheme-number -> boolean
var isInexact = function(n) {
if (typeof(n) === 'number') {
return false;
} else {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
+ if ( eqv(n, 0) ) {
+ return 1;
+ }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
+ if ( eqv(n, 1) ) {
+ return 0;
+ }
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.isInexact = function() {
return false;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
- var fracPart = this.n - Math.floor(this.n);
- var intPart = this.n - fracPart;
- return add(intPart,
- Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
+
+ var stringRep = this.n.toString();
+ var match = stringRep.match(/^(.*)\.(.*)$/);
+ if (match) {
+ var intPart = parseInt(match[1]);
+ var fracPart = parseInt(match[2]);
+ var tenToDecimalPlaces = Math.pow(10, match[2].length);
+ return Rational.makeInstance(Math.round(this.n * tenToDecimalPlaces),
+ tenToDecimalPlaces);
+ }
+ else {
+ return this.n;
+ }
};
FloatPoint.prototype.toInexact = function() {
return this;
};
FloatPoint.prototype.isInexact = function() {
return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
- if (this.n === 0)
- return "0.0";
- return this.n.toString();
+ var partialResult = this.n.toString();
+ if (! partialResult.match('\\.')) {
+ return partialResult + ".0";
+ } else {
+ return partialResult;
+ }
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
- return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
+ var afterDecimal = parseInt(match[2]);
+ var factorToInt = Math.pow(10, match[2].length);
+ var extraFactor = _integerGcd(factorToInt, afterDecimal);
+ var multFactor = factorToInt / extraFactor;
+ return FloatPoint.makeInstance( Math.round(this.n * multFactor) );
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
- return FloatPoint.makeInstance(Math.pow(10, match[2].length));
+ var afterDecimal = parseInt(match[2]);
+ var factorToInt = Math.pow(10, match[2].length);
+ var extraFactor = _integerGcd(factorToInt, afterDecimal);
+ return FloatPoint.makeInstance( Math.round(factorToInt/extraFactor) );
} else {
- return FloatPoint.makeInstance(1.0);
+ return FloatPoint.makeInstance(1);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
+ if (isInexact(r) || isInexact(i)) {
+ r = toInexact(r);
+ i = toInexact(i);
+ }
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
- if (! this.isReal()) {
- throwRuntimeError("inexact->exact: expects argument of type real number", this);
- }
- return toExact(this.r);
+ return Complex.makeInstance( toExact(this.r), toExact(this.i) );
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.isInexact = function() {
return isInexact(this.r) || isInexact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
- var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
+ var i = divide(this.i, sqrt(multiply(r_plus_x, 2)));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
diff --git a/test/tests.js b/test/tests.js
index 9dabbd7..6b96a56 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -65,1434 +65,1435 @@ describe('rational constructions', {
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
// FIXME: add tests for polar construction
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
+ // If any component of a complex is inexact, both
+ // the real and imaginary parts get turned into
+ // inexact quantities.
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
- makeFloat(1.1)))).should_be_false();
+ makeFloat(1.1)))).should_be_true();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
assertTrue(isReal(makeBignum("1e1000")));
assertTrue(isReal(makeBignum("-1e1000")));
assertTrue(isReal(makeBignum("1e23784")));
assertTrue(isReal(makeBignum("-7.241e23784")));
},
'rationals': function() {
assertTrue(isReal(makeRational(0, 1)));
assertTrue(isReal(makeRational(0, 12342)));
assertTrue(isReal(makeRational(-2324, 12342)));
assertTrue(isReal(makeRational(1, 2)));
},
'floats': function() {
assertTrue(isReal(makeFloat(1.0)));
assertTrue(isReal(makeFloat(25.0)));
assertTrue(isReal(e));
assertTrue(isReal(pi));
assertTrue(isReal(inf));
assertTrue(isReal(negative_inf));
assertTrue(isReal(nan));
},
'complex': function() {
assertTrue(isReal(makeComplex(0, 0)));
assertTrue(isReal(makeComplex(e, 0)));
assertTrue(isReal(makeComplex(pi, 0)));
assertTrue(isReal(makeComplex(nan, 0)));
assertTrue(isReal(makeComplex(inf, 0)));
assertTrue(isReal(makeComplex(negative_inf, 0)));
assertFalse(isReal(makeComplex(0, 1)));
assertFalse(isReal(makeComplex(0, negative_inf)));
assertFalse(isReal(makeComplex(pi, inf)));
assertFalse(isReal(makeComplex(234, nan)));
},
'others': function() {
assertFalse(isReal("0"));
assertFalse(isReal("hello"));
assertFalse(isReal([]));
assertFalse(isReal({}));
assertFalse(isReal(false));
}
});
describe('isExact', {
'fixnums': function() {
assertTrue(isExact(19));
assertTrue(isExact(0));
assertTrue(isExact(-1));
assertTrue(isExact(1));
},
'bignums': function() {
assertTrue(isExact(makeBignum("0")));
assertTrue(isExact(makeBignum("1")));
assertTrue(isExact(makeBignum("-1")));
assertTrue(isExact(makeBignum("23497842398287924789232439723")));
assertTrue(isExact(makeBignum("1e1000")));
assertTrue(isExact(makeBignum("-1e1000")));
assertTrue(isExact(makeBignum("12342357892297851728921374891327893")));
assertTrue(isExact(makeBignum("4.1321e200")));
assertTrue(isExact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertTrue(isExact(makeRational(19)));
assertTrue(isExact(makeRational(0)));
assertTrue(isExact(makeRational(-1)));
assertTrue(isExact(makeRational(1)));
assertTrue(isExact(makeRational(1, 2)));
assertTrue(isExact(makeRational(1, 29291)));
},
'floats': function() {
assertFalse(isExact(e));
assertFalse(isExact(pi));
assertFalse(isExact(inf));
assertFalse(isExact(negative_inf));
assertFalse(isExact(nan));
assertFalse(isExact(makeFloat(0)));
assertFalse(isExact(makeFloat(1111.1)));
},
'complex': function() {
assertTrue(isExact(makeComplex(0, 0)));
assertTrue(isExact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertFalse(isExact(makeComplex(e,
makeRational(1, 17))));
assertFalse(isExact(makeComplex(makeRational(1,2),
pi)));
assertFalse(isExact(makeComplex(makeRational(1,2),
nan)));
assertFalse(isExact(makeComplex(negative_inf,
nan)));
}
});
describe('isInexact', {
'fixnums': function() {
assertFalse(isInexact(19));
assertFalse(isInexact(0));
assertFalse(isInexact(-1));
assertFalse(isInexact(1));
},
'bignums': function() {
assertFalse(isInexact(makeBignum("0")));
assertFalse(isInexact(makeBignum("1")));
assertFalse(isInexact(makeBignum("-1")));
assertFalse(isInexact(makeBignum("23497842398287924789232439723")));
assertFalse(isInexact(makeBignum("1e1000")));
assertFalse(isInexact(makeBignum("-1e1000")));
assertFalse(isInexact(makeBignum("12342357892297851728921374891327893")));
assertFalse(isInexact(makeBignum("4.1321e200")));
assertFalse(isInexact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertFalse(isInexact(makeRational(19)));
assertFalse(isInexact(makeRational(0)));
assertFalse(isInexact(makeRational(-1)));
assertFalse(isInexact(makeRational(1)));
assertFalse(isInexact(makeRational(1, 2)));
assertFalse(isInexact(makeRational(1, 29291)));
},
'floats': function() {
assertTrue(isInexact(e));
assertTrue(isInexact(pi));
assertTrue(isInexact(inf));
assertTrue(isInexact(negative_inf));
assertTrue(isInexact(nan));
assertTrue(isInexact(makeFloat(0)));
assertTrue(isInexact(makeFloat(1111.1)));
},
'complex': function() {
assertFalse(isInexact(makeComplex(0, 0)));
assertFalse(isInexact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(e,
makeRational(1, 17))));
assertTrue(isInexact(makeComplex(makeRational(1,2),
pi)));
assertTrue(isInexact(makeComplex(makeRational(1,2),
nan)));
assertTrue(isInexact(makeComplex(negative_inf,
nan)));
}
});
describe('isInteger', {
'fixnums': function() {
assertTrue(isInteger(1));
assertTrue(isInteger(-1));
},
'bignums': function() {
assertTrue(isInteger(makeBignum("2983473189472187414789132743928148151617364")));
assertTrue(isInteger(makeBignum("-99999999999999999999999999999999999999")));
},
'rationals': function() {
assertTrue(isInteger(makeRational(1, 1)));
assertFalse(isInteger(makeRational(1, 2)));
assertFalse(isInteger(makeRational(9999, 10000)));
assertFalse(isInteger(makeRational(9999, 1000)));
},
'floats': function() {
assertFalse(isInteger(makeFloat(2.3)));
assertTrue(isInteger(makeFloat(4.0)));
assertFalse(isInteger(inf));
assertFalse(isInteger(negative_inf));
assertFalse(isInteger(nan));
},
'complex': function() {
assertTrue(isInteger(makeComplex(42, 0)));
assertFalse(isInteger(makeComplex(42, 42)));
assertFalse(isInteger(i));
assertFalse(isInteger(negative_i));
},
'others': function() {
assertFalse(isInteger("hello"));
assertFalse(isInteger("0"));
}
});
describe('toFixnum', {
'fixnums': function() {
assertEquals(42, toFixnum(42));
assertEquals(-20, toFixnum(-20));
assertEquals(0, toFixnum(0));
},
'bignums': function() {
assertEquals(123456789, toFixnum(makeBignum("123456789")));
assertEquals(0, toFixnum(makeBignum("0")));
assertEquals(-123, toFixnum(makeBignum("-123")));
assertEquals(123456, toFixnum(makeBignum("123456")));
// We're dealing with big numbers, where the numerical error
// makes it difficult to compare for equality. We just go for
// percentage and see that it is ok.
assertTrue(diffPercent(1e200, toFixnum(makeBignum("1e200")))
< 1e-10);
assertTrue(diffPercent(-1e200, toFixnum(makeBignum("-1e200")))
< 1e-10);
},
'rationals': function() {
assertEquals(0, toFixnum(zero));
assertEquals(17/2, toFixnum(makeRational(17, 2)));
assertEquals(1926/3, toFixnum(makeRational(1926, 3)));
assertEquals(-11150/17, toFixnum(makeRational(-11150, 17)));
},
'floats': function() {
assertEquals(12345.6789, toFixnum(makeFloat(12345.6789)));
assertEquals(Math.PI, toFixnum(pi));
assertEquals(Math.E, toFixnum(e));
assertEquals(Number.POSITIVE_INFINITY, toFixnum(inf));
assertEquals(Number.NEGATIVE_INFINITY, toFixnum(negative_inf));
assertTrue(isNaN(toFixnum(nan)));
},
'complex': function() {
assertFails(function() { toFixnum(makeComplex(2, 1)); });
assertFails(function() { toFixnum(i); });
assertFails(function() { toFixnum(negative_i); });
assertEquals(2, toFixnum(makeComplex(2, 0)));
assertEquals(1/2, toFixnum(makeComplex(makeRational(1, 2),
0)));
assertEquals(Number.POSITIVE_INFINITY,
toFixnum(makeComplex(inf, 0)));
assertEquals(Number.NEGATIVE_INFINITY,
toFixnum(makeComplex(negative_inf, 0)));
assertTrue(isNaN(toFixnum(makeComplex(nan, 0))));
}
});
describe('toExact', {
'fixnums': function() {
assertEquals(1792, toExact(1792));
assertEquals(0, toExact(0));
assertEquals(-1, toExact(-1));
},
'bignums': function() {
assertEquals(makeBignum("4.2e100"),
toExact(makeBignum("4.2e100")));
assertEquals(makeBignum("0"),
toExact(makeBignum("0")));
assertEquals(makeBignum("1"),
toExact(makeBignum("1")));
assertEquals(makeBignum("-1"),
toExact(makeBignum("-1")));
assertEquals(makeBignum("-12345"),
toExact(makeBignum("-12345")));
assertEquals(makeBignum("-1.723e500"),
toExact(makeBignum("-1.723e500")));
},
'rationals': function() {
assertEquals(makeRational(1, 2), toExact(makeRational(1, 2)));
assertEquals(makeRational(1, 9999), toExact(makeRational(1, 9999)));
assertEquals(makeRational(0, 1), toExact(makeRational(0, 9999)));
assertEquals(makeRational(-290, 1), toExact(makeRational(-290, 1)));
},
'floats': function() {
assertEquals(makeRational(1, 2), toExact(makeFloat(0.5)));
assertEquals(makeRational(1, 10), toExact(makeFloat(0.1)));
assertEquals(makeRational(9, 10), toExact(makeFloat(0.9)));
assertTrue(isExact(toExact(makeFloat(10234.7))));
assertTrue(diffPercent(makeRational(102347, 10),
toExact(makeFloat(10234.7))) < 1);
assertEquals(-1, toExact(makeFloat(-1)));
assertEquals(0, toExact(makeFloat(0)));
assertEquals(1024, toExact(makeFloat(1024)));
assertFails(function() { toExact(nan); });
assertFails(function() { toExact(inf); });
assertFails(function() { toExact(negative_inf); });
},
'complex': function() {
assertEquals(0, toExact(makeComplex(0, 0)));
assertEquals(99, toExact(makeComplex(99, 0)));
assertEquals(makeRational(-1, 2),
toExact(makeComplex(makeRational(-1, 2), 0)));
- assertEquals(makeRational(1, 4),
- toExact(makeComplex(.25, 0)));
- assertFails(function() { toExact(makeComplex(nan, 0)); });
- assertFails(function() { toExact(makeComplex(inf, 0)); });
- assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
- assertFails(function() { toExact(makeComplex(0, 1)); });
- assertFails(function() { toExact(makeComplex(0, pi)); });
- assertFails(function() { toExact(makeComplex(0, e)); });
- assertFails(function() { toExact(makeComplex(0, nan)); });
+ assertEquals(makeRational(1, 4),
+ toExact(makeComplex(makeFloat(.25), 0)));
+ assertFails(function() { toExact(makeComplex(nan, 0)); });
+ assertFails(function() { toExact(makeComplex(inf, 0)); });
+ assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
+ assertTrue(eqv(toExact(makeComplex(0, 1)), makeComplex(0, 1)));
+ assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = subtract(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("-1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(subtract(1, makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532868")));
assertTrue(eqv(subtract(-1,
makeBignum("3219789841236123678239865237892936825367953267523689352968869532869")),
makeBignum("-3219789841236123678239865237892936825367953267523689352968869532870")));
},
'bignum / bignum' : function() {
assertTrue(eqv(subtract(makeBignum("10e500"),
makeBignum("10e500")),
0));
assertFalse(eqv(subtract(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(subtract(makeBignum("0"),
makeBignum("-1")),
1));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("532679532692536916785915689")),
makeBignum("235336853156840152606903617000")));
assertTrue(eqv(subtract(makeBignum("235869532689532689523689532689"),
makeBignum("-532679532692536916785915689")),
makeBignum("236402212222225226440475448378")));
assertTrue(eqv(subtract(makeBignum("1e500"),
makeBignum("1e400")),
makeBignum("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")));
},
'bignum / rational': function() {
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(1, 2)),
makeRational(makeBignum("24685078656847578479654737"),
2)));
assertTrue(eqv(subtract(makeBignum("12342539328423789239827369"),
makeRational(makeBignum("32658963528962385326953269"),
makeBignum("653289953253269"))),
makeRational(makeBignum("8063256940892578770775763336720167965992"),
makeBignum("653289953253269"))));
},
'bignum / float' : function() {
assertTrue(eqv(subtract(makeBignum("1e50"),
makeFloat(1)),
makeFloat(1e50-1)));
assertFalse(eqv(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(equals(subtract(makeBignum("1e50"),
makeFloat(1e-50)),
makeBignum("1e50")));
assertTrue(eqv(subtract(makeBignum("0"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("0")),
inf));
assertTrue(eqv(subtract(makeBignum("1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("1e500")),
inf));
assertTrue(eqv(subtract(makeBignum("-1e500"),
inf),
negative_inf));
assertTrue(eqv(subtract(inf,
makeBignum("-1e500")),
inf));
},
'bignum / complex' : function() {
assertTrue(eqv(0, subtract(makeBignum("42"),
makeComplex(42, 0))));
assertTrue(eqv(makeComplex(-1, -4567),
subtract(makeBignum("1233"),
makeComplex(1234, 4567))));
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
@@ -2636,1169 +2637,1169 @@ describe('tan', {
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
- assertEquals('-1', makeFloat(-1).toString());
+ assertEquals('-1.0', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
- assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
- assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
+ assertEquals("1.0+0.0i", makeComplex(1, makeFloat(0)).toString());
+ assertEquals("-1.0+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
- assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
+ assertEquals("0.0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
assertTrue(isRational(makeRational(42)));
assertTrue(isRational(makeFloat(3.1415)));
assertTrue(isRational(pi));
assertFalse(isRational(nan));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
assertTrue(isSchemeNumber(makeRational(42)));
assertTrue(isSchemeNumber(42));
assertFalse(isSchemeNumber(false));
assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
assertTrue("1" === (1).toString());
- assertEquals("5+0.0i",
+ assertEquals("5.0+0.0i",
(makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
(makeComplex(5, 1)).toString());
assertEquals("4-2i",
(makeComplex(4, -2)).toString());
},
testQuotient : function(){
assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
makeFloat(3)));
assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, modulo(n1, n2));
assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(isReal(pi));
assertTrue(isReal(1));
assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!isReal("hi"));
},
testRound : function(){
assertTrue(equals(round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(round(makeRational(3)),
makeRational(3)));
assertTrue(equals(round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(round(makeRational(-17, 4)),
makeRational(-4)));
},
// testSgn : function(){
// assertTrue(equals(sgn(makeFloat(4)), 1));
// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
// assertTrue(equals(sgn(0), 0));
// },
// testZero_question_ : function(){
// assertTrue(Kernel.zero_question_(0));
// assertTrue(!Kernel.zero_question_(1));
// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
// }
});
|
dyoo/js-numbers
|
a8356b226a10508e725045d9d0f8412ad87b7243
|
either repaired or commented tests from the old moby test suite; the ones that are commented are those that test functions that js-numbers no longer does directly.
|
diff --git a/test/tests.js b/test/tests.js
index b0169a9..9dabbd7 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -3156,649 +3156,649 @@ describe('toString', {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(toExact(makeFloat(3)),
makeRational(3)));
assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! isExact(makeFloat(3.0)));
},
// testOdd_question_ : function(){
// assertTrue(Kernel.odd_question_(1));
// assertTrue(! Kernel.odd_question_(0));
// assertTrue(Kernel.odd_question_(makeFloat(1)));
// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
// testEven_question_ : function(){
// assertTrue(Kernel.even_question_(0));
// assertTrue(! Kernel.even_question_(1));
// assertTrue(Kernel.even_question_(makeFloat(2)));
// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
// },
// testPositive_question_ : function(){
// assertTrue(Kernel.positive_question_(1));
// assertTrue(!Kernel.positive_question_(0));
// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
// },
// testNegative_question_ : function(){
// assertTrue(Kernel.negative_question_(makeRational(-5)));
// assertTrue(!Kernel.negative_question_(1));
// assertTrue(!Kernel.negative_question_(0));
// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
// },
testCeiling : function(){
assertTrue(equals(ceiling(1), 1));
assertTrue(equals(ceiling(pi), makeFloat(4)));
assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(floor(1), 1));
assertTrue(equals(floor(pi), makeFloat(3)));
assertTrue(equals(floor(makeComplex(makeFloat(3.1),
makeRational(0))),
makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(imaginaryPart(1), 0));
assertTrue(equals(imaginaryPart(pi), 0));
assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
makeRational(1))),
1));
},
testReal_dash_part : function(){
assertTrue(equals(realPart(1), 1));
assertTrue(equals(realPart(pi), pi));
assertTrue(equals(realPart(makeComplex(makeRational(0),
makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(isInteger(1));
assertTrue(isInteger(makeFloat(3.0)));
assertTrue(!isInteger(makeFloat(3.1)));
assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
// testMake_dash_rectangular: function(){
// assertTrue(equals(makeComplex(1, 1),
// makeComplex(makeRational(1),makeRational(1))));
// },
// testMaxAndMin : function(){
// var n1 = makeFloat(-1);
// var n2 = 0;
// var n3 = 1;
// var n4 = makeComplex(makeRational(4),makeRational(0));
// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
// var n5 = makeFloat(1.1);
// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
// },
testLcm : function () {
assertTrue(equals(makeRational(12),
lcm(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
gcd(makeRational(1),
[makeRational(2),
makeRational(3),
makeRational(4)])));
assertTrue(equals(makeRational(5),
gcd(makeRational(100),
[makeRational(5),
makeRational(10),
makeRational(25)])));
},
testIsRational : function() {
- assertTrue(Kernel.rational_question_(makeRational(42)));
- assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
- assertTrue(! Kernel.rational_question_("blah"));
+ assertTrue(isRational(makeRational(42)));
+ assertTrue(isRational(makeFloat(3.1415)));
+ assertTrue(isRational(pi));
+ assertFalse(isRational(nan));
+ assertFalse(isRational(inf));
+ assertFalse(isRational(negative_inf));
+ assertTrue(! isRational("blah"));
},
testNumberQuestion : function() {
- assertTrue(Kernel.number_question_(makeRational(42)));
- assertTrue(Kernel.number_question_(42) == false);
+ assertTrue(isSchemeNumber(makeRational(42)));
+ assertTrue(isSchemeNumber(42));
+ assertFalse(isSchemeNumber(false));
+ assertFalse(isSchemeNumber("blah again"));
},
testNumber_dash__greaterthan_string : function(){
- assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
- assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
-
- assertEquals("5+0i",
- Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
-
+ assertTrue("1" === (1).toString());
+ assertEquals("5+0.0i",
+ (makeComplex(5, makeFloat(0))).toString());
assertEquals("5+1i",
- Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
-
+ (makeComplex(5, 1)).toString());
assertEquals("4-2i",
- Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
-
+ (makeComplex(4, -2)).toString());
},
testQuotient : function(){
- assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
- assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
+ assertTrue(equals(quotient(makeFloat(3), makeFloat(4)), 0));
+ assertTrue(equals(quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
- Kernel.quotient(makeRational(-36),
- makeRational(7)),
+ quotient(makeRational(-36),
+ makeRational(7)),
makeRational(-5)));
assertTrue(equals(
- Kernel.quotient(makeRational(-36),
- makeRational(-7)),
+ quotient(makeRational(-36),
+ makeRational(-7)),
makeRational(5)));
-
+
assertTrue(equals(
- Kernel.quotient(makeRational(36),
- makeRational(-7)),
+ quotient(makeRational(36),
+ makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
- Kernel.quotient(makeRational(36),
- makeRational(7)),
+ quotient(makeRational(36),
+ makeRational(7)),
makeRational(5)));
-
-
-
},
+
testRemainder : function(){
- assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
- assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
+ assertTrue(equals(remainder(makeFloat(3), makeFloat(4)),
+ makeFloat(3)));
+ assertTrue(equals(remainder(makeFloat(4), makeFloat(3)),
+ makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
- assertEquals(n3, Kernel.modulo(n1, n2));
- assertEquals(n2, Kernel.modulo(n2, n1));
+ assertEquals(n3, modulo(n1, n2));
+ assertEquals(n2, modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
- Kernel.modulo(makeRational(13),
- makeRational(-4))));
+ modulo(makeRational(13),
+ makeRational(-4))));
assertTrue(equals(
makeRational(3),
- Kernel.modulo(makeRational(-13),
- makeRational(4))));
+ modulo(makeRational(-13),
+ makeRational(4))));
assertTrue(equals(
makeRational(-1),
- Kernel.modulo(makeRational(-13),
- makeRational(-4))));
+ modulo(makeRational(-13),
+ makeRational(-4))));
assertTrue(equals(
makeRational(0),
- Kernel.modulo(makeRational(4),
- makeRational(-2))));
-
+ modulo(makeRational(4),
+ makeRational(-2))));
},
testReal_question_ : function(){
- assertTrue(Kernel.real_question_(pi));
- assertTrue(Kernel.real_question_(1));
- assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
- assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
- assertTrue(!Kernel.real_question_("hi"));
+ assertTrue(isReal(pi));
+ assertTrue(isReal(1));
+ assertTrue(!isReal(makeComplex(makeRational(0),makeRational(1))));
+ assertTrue(isReal(makeComplex(makeRational(1),makeRational(0))));
+ assertTrue(!isReal("hi"));
},
testRound : function(){
- assertTrue(equals(Kernel.round(makeFloat(3.499999)),
+ assertTrue(equals(round(makeFloat(3.499999)),
makeFloat(3)));
- assertTrue(equals(Kernel.round(makeFloat(3.5)),
+ assertTrue(equals(round(makeFloat(3.5)),
makeFloat(4)));
- assertTrue(equals(Kernel.round(makeFloat(3.51)),
+ assertTrue(equals(round(makeFloat(3.51)),
makeFloat(4)));
- assertTrue(equals(Kernel.round(makeRational(3)),
+ assertTrue(equals(round(makeRational(3)),
makeRational(3)));
- assertTrue(equals(Kernel.round(makeRational(17, 4)),
+ assertTrue(equals(round(makeRational(17, 4)),
makeRational(4)));
- assertTrue(equals(Kernel.round(makeRational(-17, 4)),
+ assertTrue(equals(round(makeRational(-17, 4)),
makeRational(-4)));
},
- testSgn : function(){
- assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
- assertTrue(equals(Kernel.sgn(makeFloat(-4)), makeRational(-1)));
- assertTrue(equals(Kernel.sgn(0), 0));
- },
+// testSgn : function(){
+// assertTrue(equals(sgn(makeFloat(4)), 1));
+// assertTrue(equals(sgn(makeFloat(-4)), makeRational(-1)));
+// assertTrue(equals(sgn(0), 0));
+// },
- testZero_question_ : function(){
- assertTrue(Kernel.zero_question_(0));
- assertTrue(!Kernel.zero_question_(1));
- assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
- }
+// testZero_question_ : function(){
+// assertTrue(Kernel.zero_question_(0));
+// assertTrue(!Kernel.zero_question_(1));
+// assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
+// }
});
|
dyoo/js-numbers
|
cd6bd8a9da799388619e9eb3a15d6cdf3f002048
|
fixing gcd, lcm
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 06aae8a..d02d84f 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -157,1044 +157,1044 @@ if (typeof(exports) !== 'undefined') {
return (isSchemeNumber(n) && n.isInexact());
}
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
- b = integerModulo(t, b);
+ b = _integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
- var divisor = gcd(result, rest[i]);
+ var divisor = _integerGcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('remainder: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('remainder: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
diff --git a/test/tests.js b/test/tests.js
index 2d5d50a..b0169a9 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -3031,761 +3031,774 @@ describe('integerSqrt', {
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(eqv(toInexact(makeRational(3)),
makeFloat(3.0)));
assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
- assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
- makeRational(3)
- ));
- assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
+ assertTrue(equals(toExact(makeFloat(3)),
+ makeRational(3)));
+ assertTrue(isExact(toExact(makeFloat(3))));
},
testFloatsAreInexact: function() {
- assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
+ assertTrue(! isExact(makeFloat(3.0)));
},
- testOdd_question_ : function(){
- assertTrue(Kernel.odd_question_(1));
- assertTrue(! Kernel.odd_question_(0));
- assertTrue(Kernel.odd_question_(makeFloat(1)));
- assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
- assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
- },
+// testOdd_question_ : function(){
+// assertTrue(Kernel.odd_question_(1));
+// assertTrue(! Kernel.odd_question_(0));
+// assertTrue(Kernel.odd_question_(makeFloat(1)));
+// assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
+// assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
+// },
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
- testEven_question_ : function(){
- assertTrue(Kernel.even_question_(0));
- assertTrue(! Kernel.even_question_(1));
- assertTrue(Kernel.even_question_(makeFloat(2)));
- assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
- },
+// testEven_question_ : function(){
+// assertTrue(Kernel.even_question_(0));
+// assertTrue(! Kernel.even_question_(1));
+// assertTrue(Kernel.even_question_(makeFloat(2)));
+// assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
+// },
- testPositive_question_ : function(){
- assertTrue(Kernel.positive_question_(1));
- assertTrue(!Kernel.positive_question_(0));
- assertTrue(Kernel.positive_question_(makeFloat(1.1)));
- assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
- },
+// testPositive_question_ : function(){
+// assertTrue(Kernel.positive_question_(1));
+// assertTrue(!Kernel.positive_question_(0));
+// assertTrue(Kernel.positive_question_(makeFloat(1.1)));
+// assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
+// },
- testNegative_question_ : function(){
- assertTrue(Kernel.negative_question_(makeRational(-5)));
- assertTrue(!Kernel.negative_question_(1));
- assertTrue(!Kernel.negative_question_(0));
- assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
- assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
- },
+// testNegative_question_ : function(){
+// assertTrue(Kernel.negative_question_(makeRational(-5)));
+// assertTrue(!Kernel.negative_question_(1));
+// assertTrue(!Kernel.negative_question_(0));
+// assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
+// assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
+// },
testCeiling : function(){
- assertTrue(equals(Kernel.ceiling(1), 1));
- assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
- assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
+ assertTrue(equals(ceiling(1), 1));
+ assertTrue(equals(ceiling(pi), makeFloat(4)));
+ assertTrue(equals(ceiling(makeComplex(makeFloat(3.1),
+ makeRational(0))),
+ makeFloat(4)));
},
testFloor : function(){
- assertTrue(equals(Kernel.floor(1), 1));
- assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
- assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
+ assertTrue(equals(floor(1), 1));
+ assertTrue(equals(floor(pi), makeFloat(3)));
+ assertTrue(equals(floor(makeComplex(makeFloat(3.1),
+ makeRational(0))),
+ makeFloat(3)));
},
testImag_dash_part : function(){
- assertTrue(equals(Kernel.imag_dash_part(1), 0));
- assertTrue(equals(Kernel.imag_dash_part(pi), 0));
- assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
+ assertTrue(equals(imaginaryPart(1), 0));
+ assertTrue(equals(imaginaryPart(pi), 0));
+ assertTrue(equals(imaginaryPart(makeComplex(makeRational(0),
+ makeRational(1))),
+ 1));
},
testReal_dash_part : function(){
- assertTrue(equals(Kernel.real_dash_part(1), 1));
- assertTrue(equals(Kernel.real_dash_part(pi), pi));
- assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
+ assertTrue(equals(realPart(1), 1));
+ assertTrue(equals(realPart(pi), pi));
+ assertTrue(equals(realPart(makeComplex(makeRational(0),
+ makeRational(1))), 0));
},
testInteger_question_ : function(){
- assertTrue(Kernel.integer_question_(1));
- assertTrue(Kernel.integer_question_(makeFloat(3.0)));
- assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
- assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
- assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
+ assertTrue(isInteger(1));
+ assertTrue(isInteger(makeFloat(3.0)));
+ assertTrue(!isInteger(makeFloat(3.1)));
+ assertTrue(isInteger(makeComplex(makeRational(3),makeRational(0))));
+ assertTrue(!isInteger(makeComplex(makeFloat(3.1),makeRational(0))));
},
- testMake_dash_rectangular: function(){
- assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
- },
+// testMake_dash_rectangular: function(){
+// assertTrue(equals(makeComplex(1, 1),
+// makeComplex(makeRational(1),makeRational(1))));
+// },
- testMaxAndMin : function(){
- var n1 = makeFloat(-1);
- var n2 = 0;
- var n3 = 1;
- var n4 = makeComplex(makeRational(4),makeRational(0));
- assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
- assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
-
- var n5 = makeFloat(1.1);
- assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
- assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
- },
+// testMaxAndMin : function(){
+// var n1 = makeFloat(-1);
+// var n2 = 0;
+// var n3 = 1;
+// var n4 = makeComplex(makeRational(4),makeRational(0));
+// assertTrue(equals(n4, max(n1, [n2,n3,n4])));
+// assertTrue(equals(n1, min(n1, [n2,n3,n4])));
+
+// var n5 = makeFloat(1.1);
+// assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
+// assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
+// },
testLcm : function () {
assertTrue(equals(makeRational(12),
- Kernel.lcm(makeRational(1),
- [makeRational(2), makeRational(3), makeRational(4)])));
+ lcm(makeRational(1),
+ [makeRational(2),
+ makeRational(3),
+ makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
- Kernel.gcd(makeRational(1),
- [makeRational(2), makeRational(3), makeRational(4)])));
-
+ gcd(makeRational(1),
+ [makeRational(2),
+ makeRational(3),
+ makeRational(4)])));
+
assertTrue(equals(makeRational(5),
- Kernel.gcd(makeRational(100),
- [makeRational(5), makeRational(10), makeRational(25)])));
+ gcd(makeRational(100),
+ [makeRational(5),
+ makeRational(10),
+ makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(pi));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_("hi"));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), makeRational(-1)));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
5af38c639b61acbf6cb64c19f46bca02a1e4d059
|
added isInexact, isExact
|
diff --git a/README b/README
index bc21914..f5bd228 100644
--- a/README
+++ b/README
@@ -1,300 +1,306 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a toplevel namespace called
jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
+isInexact: scheme-number -> boolean
+ Produces true if the number is inexact.
+
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
+toInexact: scheme-number -> scheme-number
+ Converts the number to an inexact scheme-number.
+
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
quotient: scheme-number scheme-number -> scheme-number
Produces the quotient. Both inputs must be integers.
remainder: scheme-number scheme-number -> scheme-number
Produces the remainder. Both inputs must be integers.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
June 2010: got implementation of integer-sqrt from Ugur Cekmez;
brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 47564c1..06aae8a 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,663 +1,672 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
+ // isExact: scheme-number -> boolean
+ var isInexact = function(n) {
+ if (typeof(n) === 'number') {
+ return false;
+ } else {
+ return (isSchemeNumber(n) && n.isInexact());
+ }
+ };
+
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
// toExact: scheme-number -> scheme-number
var toInexact = function(n) {
if (typeof(n) === 'number')
return FloatPoint.makeInstance(n);
return n.toInexact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
@@ -772,1692 +781,1709 @@ if (typeof(exports) !== 'undefined') {
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
Rational.prototype.isExact = function() {
return true;
};
+ Rational.prototype.isInexact = function() {
+ return false;
+ };
+
+
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
+ FloatPoint.prototype.isExact = function() {
+ return false;
+ };
+
+ FloatPoint.prototype.isInexact = function() {
+ return true;
+ };
+
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.toInexact = function() {
return this;
};
- FloatPoint.prototype.isExact = function() {
- return false;
+ FloatPoint.prototype.isInexact = function() {
+ return true;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.toInexact = function() {
return Complex.makeInstance(toInexact(this.r),
toInexact(this.i));
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
+ Complex.prototype.isInexact = function() {
+ return isInexact(this.r) || isInexact(this.i);
+ };
+
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
@@ -3096,760 +3122,765 @@ if (typeof(exports) !== 'undefined') {
var r = 0, x = this.s&this.DM;
for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
return r;
}
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this.DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this.DB)))!=0);
}
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
var r = BigInteger.ONE.shiftLeft(n);
this.bitwiseTo(r,op,r);
return r;
}
// (public) this | (1<<n)
function bnSetBit(n) { return this.changeBit(n,op_or); }
// (public) this & ~(1<<n)
function bnClearBit(n) { return this.changeBit(n,op_andnot); }
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this.changeBit(n,op_xor); }
// (protected) r = this + a
function bnpAddTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]+a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this.DV+c;
r.t = i;
r.clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
+ BigInteger.prototype.isInexact = function() {
+ return false;
+ };
+
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toInexact = function() {
return FloatPoint.makeInstance(this.toFixnum());
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess, floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
+ Numbers['isInexact'] = isInexact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
})();
diff --git a/test/tests.js b/test/tests.js
index b4d4e1c..2d5d50a 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -255,1024 +255,1090 @@ describe('equals', {
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_false();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
assertTrue(isRational(0));
assertTrue(isRational(1));
assertTrue(isRational(238977428));
assertTrue(isRational(-2371));
},
'bignums': function() {
assertTrue(isRational(makeBignum("324987329848724791")));
assertTrue(isRational(makeBignum("0")));
assertTrue(isRational(makeBignum("-1239847210")));
},
'rationals': function() {
assertTrue(isRational(makeRational(0, 1)));
assertTrue(isRational(makeRational(1, 100)));
assertTrue(isRational(makeRational(9999, 10000)));
assertTrue(isRational(makeRational(1, 4232)));
},
'floats': function() {
assertTrue(isRational(makeFloat(1.0)));
assertTrue(isRational(makeFloat(25.0)));
assertTrue(isRational(e));
assertTrue(isRational(pi));
assertFalse(isRational(inf));
assertFalse(isRational(negative_inf));
assertFalse(isRational(nan));
},
'complex': function() {
assertTrue(isRational(makeComplex(0, 0)));
assertTrue(isRational(makeComplex(e, 0)));
assertTrue(isRational(makeComplex(pi, 0)));
assertFalse(isRational(makeComplex(nan, 0)));
assertFalse(isRational(makeComplex(0, 1)));
assertFalse(isRational(makeComplex(0, negative_inf)));
},
'others': function() {
assertFalse(isRational("0"));
assertFalse(isRational("hello"));
assertFalse(isRational({}));
assertFalse(isRational([]));
assertFalse(isRational(false));
},
});
describe('isReal', {
'fixnums': function() {
assertTrue(isReal(237489));
assertTrue(isReal(0));
assertTrue(isReal(-12345));
},
'bignums': function() {
assertTrue(isReal(makeBignum("0")));
assertTrue(isReal(makeBignum("1")));
assertTrue(isReal(makeBignum("-1")));
assertTrue(isReal(makeBignum("23497842398287924789232439723")));
assertTrue(isReal(makeBignum("1e1000")));
assertTrue(isReal(makeBignum("-1e1000")));
assertTrue(isReal(makeBignum("1e23784")));
assertTrue(isReal(makeBignum("-7.241e23784")));
},
'rationals': function() {
assertTrue(isReal(makeRational(0, 1)));
assertTrue(isReal(makeRational(0, 12342)));
assertTrue(isReal(makeRational(-2324, 12342)));
assertTrue(isReal(makeRational(1, 2)));
},
'floats': function() {
assertTrue(isReal(makeFloat(1.0)));
assertTrue(isReal(makeFloat(25.0)));
assertTrue(isReal(e));
assertTrue(isReal(pi));
assertTrue(isReal(inf));
assertTrue(isReal(negative_inf));
assertTrue(isReal(nan));
},
'complex': function() {
assertTrue(isReal(makeComplex(0, 0)));
assertTrue(isReal(makeComplex(e, 0)));
assertTrue(isReal(makeComplex(pi, 0)));
assertTrue(isReal(makeComplex(nan, 0)));
assertTrue(isReal(makeComplex(inf, 0)));
assertTrue(isReal(makeComplex(negative_inf, 0)));
assertFalse(isReal(makeComplex(0, 1)));
assertFalse(isReal(makeComplex(0, negative_inf)));
assertFalse(isReal(makeComplex(pi, inf)));
assertFalse(isReal(makeComplex(234, nan)));
},
'others': function() {
assertFalse(isReal("0"));
assertFalse(isReal("hello"));
assertFalse(isReal([]));
assertFalse(isReal({}));
assertFalse(isReal(false));
}
});
describe('isExact', {
'fixnums': function() {
assertTrue(isExact(19));
assertTrue(isExact(0));
assertTrue(isExact(-1));
assertTrue(isExact(1));
},
'bignums': function() {
assertTrue(isExact(makeBignum("0")));
assertTrue(isExact(makeBignum("1")));
assertTrue(isExact(makeBignum("-1")));
assertTrue(isExact(makeBignum("23497842398287924789232439723")));
assertTrue(isExact(makeBignum("1e1000")));
assertTrue(isExact(makeBignum("-1e1000")));
assertTrue(isExact(makeBignum("12342357892297851728921374891327893")));
assertTrue(isExact(makeBignum("4.1321e200")));
assertTrue(isExact(makeBignum("-4.1321e200")));
},
'rationals': function() {
assertTrue(isExact(makeRational(19)));
assertTrue(isExact(makeRational(0)));
assertTrue(isExact(makeRational(-1)));
assertTrue(isExact(makeRational(1)));
assertTrue(isExact(makeRational(1, 2)));
assertTrue(isExact(makeRational(1, 29291)));
},
'floats': function() {
assertFalse(isExact(e));
assertFalse(isExact(pi));
assertFalse(isExact(inf));
assertFalse(isExact(negative_inf));
assertFalse(isExact(nan));
assertFalse(isExact(makeFloat(0)));
assertFalse(isExact(makeFloat(1111.1)));
},
'complex': function() {
assertTrue(isExact(makeComplex(0, 0)));
assertTrue(isExact(makeComplex(makeRational(1,2),
makeRational(1, 17))));
assertFalse(isExact(makeComplex(e,
makeRational(1, 17))));
assertFalse(isExact(makeComplex(makeRational(1,2),
pi)));
assertFalse(isExact(makeComplex(makeRational(1,2),
nan)));
assertFalse(isExact(makeComplex(negative_inf,
nan)));
}
});
+
+
+
+
+describe('isInexact', {
+ 'fixnums': function() {
+ assertFalse(isInexact(19));
+ assertFalse(isInexact(0));
+ assertFalse(isInexact(-1));
+ assertFalse(isInexact(1));
+ },
+
+ 'bignums': function() {
+ assertFalse(isInexact(makeBignum("0")));
+ assertFalse(isInexact(makeBignum("1")));
+ assertFalse(isInexact(makeBignum("-1")));
+ assertFalse(isInexact(makeBignum("23497842398287924789232439723")));
+ assertFalse(isInexact(makeBignum("1e1000")));
+ assertFalse(isInexact(makeBignum("-1e1000")));
+ assertFalse(isInexact(makeBignum("12342357892297851728921374891327893")));
+ assertFalse(isInexact(makeBignum("4.1321e200")));
+ assertFalse(isInexact(makeBignum("-4.1321e200")));
+ },
+
+ 'rationals': function() {
+ assertFalse(isInexact(makeRational(19)));
+ assertFalse(isInexact(makeRational(0)));
+ assertFalse(isInexact(makeRational(-1)));
+ assertFalse(isInexact(makeRational(1)));
+ assertFalse(isInexact(makeRational(1, 2)));
+ assertFalse(isInexact(makeRational(1, 29291)));
+ },
+
+ 'floats': function() {
+ assertTrue(isInexact(e));
+ assertTrue(isInexact(pi));
+ assertTrue(isInexact(inf));
+ assertTrue(isInexact(negative_inf));
+ assertTrue(isInexact(nan));
+ assertTrue(isInexact(makeFloat(0)));
+ assertTrue(isInexact(makeFloat(1111.1)));
+ },
+
+ 'complex': function() {
+ assertFalse(isInexact(makeComplex(0, 0)));
+ assertFalse(isInexact(makeComplex(makeRational(1,2),
+ makeRational(1, 17))));
+ assertTrue(isInexact(makeComplex(e,
+ makeRational(1, 17))));
+ assertTrue(isInexact(makeComplex(makeRational(1,2),
+ pi)));
+ assertTrue(isInexact(makeComplex(makeRational(1,2),
+ nan)));
+
+ assertTrue(isInexact(makeComplex(negative_inf,
+ nan)));
+ }
+});
+
+
+
+
+
+
+
+
describe('isInteger', {
'fixnums': function() {
assertTrue(isInteger(1));
assertTrue(isInteger(-1));
},
'bignums': function() {
assertTrue(isInteger(makeBignum("2983473189472187414789132743928148151617364")));
assertTrue(isInteger(makeBignum("-99999999999999999999999999999999999999")));
},
'rationals': function() {
assertTrue(isInteger(makeRational(1, 1)));
assertFalse(isInteger(makeRational(1, 2)));
assertFalse(isInteger(makeRational(9999, 10000)));
assertFalse(isInteger(makeRational(9999, 1000)));
},
'floats': function() {
assertFalse(isInteger(makeFloat(2.3)));
assertTrue(isInteger(makeFloat(4.0)));
assertFalse(isInteger(inf));
assertFalse(isInteger(negative_inf));
assertFalse(isInteger(nan));
},
'complex': function() {
assertTrue(isInteger(makeComplex(42, 0)));
assertFalse(isInteger(makeComplex(42, 42)));
assertFalse(isInteger(i));
assertFalse(isInteger(negative_i));
},
'others': function() {
assertFalse(isInteger("hello"));
assertFalse(isInteger("0"));
}
});
describe('toFixnum', {
'fixnums': function() {
assertEquals(42, toFixnum(42));
assertEquals(-20, toFixnum(-20));
assertEquals(0, toFixnum(0));
},
'bignums': function() {
assertEquals(123456789, toFixnum(makeBignum("123456789")));
assertEquals(0, toFixnum(makeBignum("0")));
assertEquals(-123, toFixnum(makeBignum("-123")));
assertEquals(123456, toFixnum(makeBignum("123456")));
// We're dealing with big numbers, where the numerical error
// makes it difficult to compare for equality. We just go for
// percentage and see that it is ok.
assertTrue(diffPercent(1e200, toFixnum(makeBignum("1e200")))
< 1e-10);
assertTrue(diffPercent(-1e200, toFixnum(makeBignum("-1e200")))
< 1e-10);
},
'rationals': function() {
assertEquals(0, toFixnum(zero));
assertEquals(17/2, toFixnum(makeRational(17, 2)));
assertEquals(1926/3, toFixnum(makeRational(1926, 3)));
assertEquals(-11150/17, toFixnum(makeRational(-11150, 17)));
},
'floats': function() {
assertEquals(12345.6789, toFixnum(makeFloat(12345.6789)));
assertEquals(Math.PI, toFixnum(pi));
assertEquals(Math.E, toFixnum(e));
assertEquals(Number.POSITIVE_INFINITY, toFixnum(inf));
assertEquals(Number.NEGATIVE_INFINITY, toFixnum(negative_inf));
assertTrue(isNaN(toFixnum(nan)));
},
'complex': function() {
assertFails(function() { toFixnum(makeComplex(2, 1)); });
assertFails(function() { toFixnum(i); });
assertFails(function() { toFixnum(negative_i); });
assertEquals(2, toFixnum(makeComplex(2, 0)));
assertEquals(1/2, toFixnum(makeComplex(makeRational(1, 2),
0)));
assertEquals(Number.POSITIVE_INFINITY,
toFixnum(makeComplex(inf, 0)));
assertEquals(Number.NEGATIVE_INFINITY,
toFixnum(makeComplex(negative_inf, 0)));
assertTrue(isNaN(toFixnum(makeComplex(nan, 0))));
}
});
describe('toExact', {
'fixnums': function() {
assertEquals(1792, toExact(1792));
assertEquals(0, toExact(0));
assertEquals(-1, toExact(-1));
},
'bignums': function() {
assertEquals(makeBignum("4.2e100"),
toExact(makeBignum("4.2e100")));
assertEquals(makeBignum("0"),
toExact(makeBignum("0")));
assertEquals(makeBignum("1"),
toExact(makeBignum("1")));
assertEquals(makeBignum("-1"),
toExact(makeBignum("-1")));
assertEquals(makeBignum("-12345"),
toExact(makeBignum("-12345")));
assertEquals(makeBignum("-1.723e500"),
toExact(makeBignum("-1.723e500")));
},
'rationals': function() {
assertEquals(makeRational(1, 2), toExact(makeRational(1, 2)));
assertEquals(makeRational(1, 9999), toExact(makeRational(1, 9999)));
assertEquals(makeRational(0, 1), toExact(makeRational(0, 9999)));
assertEquals(makeRational(-290, 1), toExact(makeRational(-290, 1)));
},
'floats': function() {
assertEquals(makeRational(1, 2), toExact(makeFloat(0.5)));
assertEquals(makeRational(1, 10), toExact(makeFloat(0.1)));
assertEquals(makeRational(9, 10), toExact(makeFloat(0.9)));
assertTrue(isExact(toExact(makeFloat(10234.7))));
assertTrue(diffPercent(makeRational(102347, 10),
toExact(makeFloat(10234.7))) < 1);
assertEquals(-1, toExact(makeFloat(-1)));
assertEquals(0, toExact(makeFloat(0)));
assertEquals(1024, toExact(makeFloat(1024)));
assertFails(function() { toExact(nan); });
assertFails(function() { toExact(inf); });
assertFails(function() { toExact(negative_inf); });
},
'complex': function() {
assertEquals(0, toExact(makeComplex(0, 0)));
assertEquals(99, toExact(makeComplex(99, 0)));
assertEquals(makeRational(-1, 2),
toExact(makeComplex(makeRational(-1, 2), 0)));
assertEquals(makeRational(1, 4),
toExact(makeComplex(.25, 0)));
assertFails(function() { toExact(makeComplex(nan, 0)); });
assertFails(function() { toExact(makeComplex(inf, 0)); });
assertFails(function() { toExact(makeComplex(negative_inf, 0)); });
assertFails(function() { toExact(makeComplex(0, 1)); });
assertFails(function() { toExact(makeComplex(0, pi)); });
assertFails(function() { toExact(makeComplex(0, e)); });
assertFails(function() { toExact(makeComplex(0, nan)); });
}
});
describe('toInexact', {
'fixnum' : function() {
assertTrue(eqv(toInexact(5), makeFloat(5)));
assertTrue(eqv(toInexact(0), makeFloat(0)));
assertTrue(eqv(toInexact(-167), makeFloat(-167)));
},
'bignum': function() {
assertTrue(eqv(toInexact(makeBignum('5')), makeFloat(5)));
assertTrue(eqv(toInexact(makeBignum('0')), makeFloat(0)));
assertTrue(eqv(toInexact(makeBignum('-167')), makeFloat(-167)));
assertTrue(eqv(toInexact(expt(2, 10000)),
inf));
assertTrue(eqv(toInexact(subtract(0, expt(2, 10000))),
negative_inf));
},
'rational': function() {
assertTrue(eqv(toInexact(makeRational(1, 2)),
makeFloat(0.5)));
assertTrue(eqv(toInexact(makeRational(12362534, 237)),
makeFloat(52162.59071729958)));
},
'float': function() {
assertTrue(eqv(toInexact(makeFloat(0)),
toInexact(makeFloat(0))));
assertTrue(eqv(toInexact(makeFloat(123.4)),
toInexact(makeFloat(123.4))));
assertTrue(eqv(toInexact(makeFloat(-42)),
toInexact(makeFloat(-42))));
assertTrue(eqv(toInexact(inf),
inf));
assertTrue(eqv(toInexact(negative_inf),
negative_inf));
assertTrue(eqv(toInexact(negative_zero),
negative_zero));
},
'complex': function() {
assertTrue(eqv(toInexact(makeComplex(1, 2)),
makeComplex(makeFloat(1), makeFloat(2))));
assertTrue(eqv(toInexact(makeComplex(makeRational(1, 2),
2)),
makeComplex(makeFloat(0.5), makeFloat(2))));
}});
describe('add', {
'fixnum / fixnum' : function() {
assertEquals(0, add(0, 0));
assertEquals(1025, add(1024, 1));
assertEquals(-84, add(-42, -42));
assertEquals(982, add(1024, -42));
},
'finum overflows to bignum' : function() {
var aNumber = 0;
for (var i = 0 ; i < 1000; i++) {
aNumber = add(aNumber, fromFixnum(1e20));
}
assertTrue(eqv(makeBignum("1e23"), aNumber));
},
'fixnum / bignum': function() {
assertTrue(eqv(2, add(1, makeBignum("1"))));
assertTrue(eqv(makeBignum("1234298352389543294732947983"),
add(1, makeBignum("1234298352389543294732947982"))));
assertFalse(eqv(makeBignum("1234298352389543294732947982"),
add(1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947982"),
add(0, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("1234298352389543294732947981"),
add(-1, makeBignum("1234298352389543294732947982"))));
assertTrue(eqv(makeBignum("999999999999999999999999999999"),
add(-1, makeBignum("1000000000000000000000000000000"))));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("1999999999999999999999999999999"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(1,
add(makeBignum("-999999999999999999999999999999"),
makeBignum("1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1999999999999999999999999999999"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertTrue(eqv(makeBignum("-1"),
add(makeBignum("999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
assertFalse(eqv(makeBignum("-20000000000000000000000000000"),
add(makeBignum("-999999999999999999999999999999"),
makeBignum("-1000000000000000000000000000000"))));
},
'bignum / rational': function() {
assertFalse(eqv(makeBignum("1234"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1236"),
add(makeBignum("1234"),
makeRational(2))));
assertTrue(eqv(makeBignum("1e500"),
add(makeBignum("1e500"),
makeRational(0))));
assertTrue(eqv(makeRational(add(makeBignum("1e500"), 1),
makeBignum("1e500")),
add(1, makeRational(1, makeBignum("1e500")))));
assertTrue(eqv(fromString("461489806479620935470974478730/23987523567"),
add(makeBignum("19238743223768948327"),
fromString("1732914256756321/23987523567"))));
assertTrue(eqv(fromString("-77100525133482588244247/239875239"),
add(fromString("-321419273847891"),
fromString("-13284973298/239875239"))));
},
'bignum / float' : function() {
assertTrue(diffPercent(add(makeBignum("42"),
makeFloat(17.5)),
makeFloat(59.5))
< 2e-10);
assertTrue(diffPercent(add(makeBignum("-42"),
makeFloat(17.5)),
makeFloat(-24.5))
< 2e-10);
assertTrue(eqv(nan,
add(makeBignum("0"), nan)));
assertTrue(eqv(nan,
add(makeBignum("10e500"), nan)));
assertTrue(eqv(nan,
add(makeBignum("-10e500"), nan)));
assertTrue(eqv(inf,
add(makeBignum("0"), inf)));
assertTrue(eqv(negative_inf,
add(makeBignum("0"), negative_inf)));
},
'huge bignum and infinity': function() {
// NOTE: this case is tricky, because 1e1000 will be naively coersed
// to inf by toFixnum. We need to somehow distinguished coersed
// values that are too large to represent with fixnums, but are yet
// finite, so that addition with infinite quantities does the right
// thing, at least with respect to adding bignums to inexact floats.
assertTrue(eqv(negative_inf,
add(makeBignum("1e1000"), negative_inf)));
assertTrue(eqv(inf,
add(makeBignum("-1e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("2e1000"), inf)));
assertTrue(eqv(inf, add(makeBignum("-2e1000"), inf)));
assertTrue(eqv(negative_inf, add(makeBignum("2e1000"), negative_inf)));
assertTrue(eqv(negative_inf, add(makeBignum("-2e1000"), negative_inf)));
},
'bignum / complex' : function() {
assertTrue(eqv(add(makeBignum("12345"),
makeComplex(1, 1)),
makeComplex(makeBignum("12346"),
1)));
assertTrue(eqv(add(makeBignum("10e500"),
makeComplex(makeBignum("10e500"),
makeBignum("124529478"))),
makeComplex(makeBignum("20e500"),
makeBignum("124529478"))));
},
'fixnum / rational' : function() {
assertEquals(0, add(0, makeRational(0)));
assertEquals(12347, add(12345, makeRational(2)));
assertEquals(makeRational(33, 2), add(16, makeRational(1, 2)));
assertEquals(makeRational(-1, 2), add(0, makeRational(-1, 2)));
assertEquals(makeRational(-1, 7), add(0, makeRational(-1, 7)));
assertEquals(makeRational(6, 7), add(1, makeRational(-1, 7)));
},
'fixnum / floating' : function() {
assertTrue(equals(0, add(0, makeFloat(0))));
assertEquals(makeFloat(1.5), add(1, makeFloat(.5)));
assertEquals(makeFloat(1233.5), add(1234, makeFloat(-.5)));
assertEquals(makeFloat(-1233.5), add(-1234, makeFloat(.5)));
assertEquals(inf, add(1234, inf));
assertEquals(negative_inf, add(1234, negative_inf));
assertEquals(nan, add(1234, nan));
},
'fixnum / complex' : function() {
assertTrue(equals(0, add(0, makeComplex(0, 0))));
assertTrue(equals(1040, add(16, makeComplex(1024, 0))));
assertEquals(makeComplex(1040, 17), add(16, makeComplex(1024, 17)));
assertEquals(makeComplex(1040, -17), add(16, makeComplex(1024, -17)));
assertEquals(makeComplex(1040, pi), add(16, makeComplex(1024, pi)));
},
'rational / rational' : function() {
assertEquals(1, add(makeRational(1, 2),
makeRational(1, 2)));
assertEquals(0, add(makeRational(1, 2),
makeRational(-1, 2)));
assertEquals(makeRational(155, 21),
add(makeRational(17, 3), makeRational(12, 7)));
assertEquals(makeRational(-1199068363, 9758),
add(makeRational(-29384289, 238), makeRational(23897, 41)));
assertEquals(makeRational(-1, 99990000),
add(makeRational(1, 10000), makeRational(-1, 9999)));
},
'rational / floating' : function() {
assertEquals(makeFloat(0.2), add(makeRational(0), makeFloat(0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(0.8), add(makeRational(1), makeFloat(-0.2)));
assertEquals(makeFloat(1.1), add(makeRational(1, 2), makeFloat(0.6)));
assertEquals(inf, add(makeRational(1, 2), inf));
assertEquals(negative_inf, add(makeRational(1, 2), negative_inf));
assertEquals(nan, add(makeRational(1, 2), nan));
},
'rational / complex' : function() {
assertEquals(makeComplex(makeRational(-324, 23), 1),
add(makeRational(-324, 23), makeComplex(0, 1)));
assertEquals(makeComplex(0, -234),
add(makeRational(-324, 23),
makeComplex(makeRational(324, 23),
-234)));
},
'floating / floating' : function() {
assertEquals(makeFloat(12345.678),
add(makeFloat(12345), makeFloat(.678)));
assertEquals(makeFloat(-12344.322),
add(makeFloat(-12345), makeFloat(.678)));
assertEquals(makeFloat(Math.PI + Math.E),
add(pi, e));
assertEquals(inf, add(inf, inf));
assertEquals(nan, add(inf, negative_inf));
assertEquals(nan, add(inf, nan));
assertEquals(nan, add(negative_inf, inf));
assertEquals(negative_inf, add(negative_inf, negative_inf));
assertEquals(nan, add(negative_inf, nan));
assertEquals(nan, add(nan, inf));
assertEquals(nan, add(nan, negative_inf));
assertEquals(nan, add(nan, nan));
},
'floating / complex' : function() {
assertEquals(makeComplex(inf, 1), add(inf, makeComplex(inf, 1)));
assertEquals(makeComplex(nan, 2), add(inf, makeComplex(negative_inf, 2)));
assertEquals(makeComplex(nan, 3), add(inf, makeComplex(nan, 3)));
assertEquals(makeComplex(nan, 4), add(negative_inf, makeComplex(inf, 4)));
assertEquals(makeComplex(negative_inf, 5),
add(negative_inf, makeComplex(negative_inf, 5)));
assertEquals(makeComplex(nan, 6), add(negative_inf, makeComplex(nan, 6)));
assertEquals(makeComplex(nan, 7), add(nan, makeComplex(inf, 7)));
assertEquals(makeComplex(nan, 8), add(nan, makeComplex(negative_inf, 8)));
assertEquals(makeComplex(nan, 9), add(nan, makeComplex(nan, 9)));
},
'complex / complex' : function() {
assertEquals(makeComplex(4, 6), add(makeComplex(1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(2, 6), add(makeComplex(-1, 2),
makeComplex(3, 4)));
assertEquals(makeComplex(4, -2), add(makeComplex(1, 2),
makeComplex(3, -4)));
assertEquals(makeComplex(pi, e), add(makeComplex(pi, 0),
makeComplex(0, e)));
assertEquals(makeComplex(add(pi, makeRational(-1,4)),
add(makeRational(1, 2), e)),
add(makeComplex(pi, makeRational(1, 2)),
makeComplex(makeRational(-1, 4), e)));
},
'negative zero': function() {
assertTrue(eqv(negative_zero,
add(negative_zero, negative_zero)));
assertFalse(eqv(negative_zero,
add(makeFloat(0), negative_zero)));
assertTrue(eqv(makeFloat(0),
add(makeFloat(0), negative_zero)));
assertFalse(eqv(negative_zero,
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeFloat(0),
add(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(0, makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(makeFloat(0), makeFloat(0)),
add(makeFloat(0), makeComplex(negative_zero, makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, makeFloat(0)),
add(negative_zero, makeComplex(negative_zero, makeFloat(0)))));
},
'0 acts as the identity': function() {
assertTrue(eqv(add(0, 42),
42));
assertTrue(eqv(add(0, -42),
-42));
assertTrue(eqv(add(0, makeBignum("129834789213412345678910")),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(0, makeFloat(0.12345)),
makeFloat(0.12345)));
assertTrue(eqv(add(0, nan),
nan));
assertTrue(eqv(add(0, inf),
inf));
assertTrue(eqv(add(0, negative_inf),
negative_inf));
assertTrue(eqv(add(42, 0),
42));
assertTrue(eqv(add(-42, 0),
-42));
assertTrue(eqv(add(makeBignum("129834789213412345678910"), 0),
makeBignum("129834789213412345678910")));
assertTrue(eqv(add(makeFloat(0.12345), 0),
makeFloat(0.12345)));
assertTrue(eqv(add(nan, 0),
nan));
assertTrue(eqv(add(inf, 0),
inf));
assertTrue(eqv(add(negative_inf, 0),
negative_inf));
}
});
describe('subtract', {
'fixnum / fixnum' : function() {
assertTrue(eqv(subtract(fromFixnum(32768),
fromFixnum(32768)),
fromFixnum(0)));
assertTrue(eqv(subtract(10, 1), 9));
assertTrue(eqv(subtract(1, 10), -9));
assertTrue(eqv(subtract(13274, 1659),
11615));
assertTrue(eqv(subtract(-13274, 1659),
-14933));
@@ -2958,769 +3024,768 @@ describe('integerSqrt', {
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
- assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
- makeFloat(3.0)
- ));
- assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
+ assertTrue(eqv(toInexact(makeRational(3)),
+ makeFloat(3.0)));
+ assertTrue(isInexact(toInexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(pi));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_("hi"));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), makeRational(-1)));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
b3b7c4fe6befcbd2785a92282756534cb3cd7f3a
|
implemented toInexact
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 9b6c61f..47564c1 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,694 +1,703 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['jsnums']) {
this['jsnums'] = {};
}
__PLTNUMBERS_TOP__ = this['jsnums'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
+ // toExact: scheme-number -> scheme-number
+ var toInexact = function(n) {
+ if (typeof(n) === 'number')
+ return FloatPoint.makeInstance(n);
+ return n.toInexact();
+ };
+
+
+
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (Complex.makeInstance(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
throwRuntimeError('quotient: the first argument ' + x.toString() +
" is not an integer.", x);
}
if (! isInteger(y)) {
throwRuntimeError('quotient: the second argument ' + y.toString() +
" is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
@@ -754,1681 +763,1696 @@ if (typeof(exports) !== 'undefined') {
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
+ Rational.prototype.toInexact = function() {
+ return FloatPoint.makeInstance(this.toFixnum());
+ };
+
+
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
+ FloatPoint.prototype.toInexact = function() {
+ return this;
+ };
+
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
+ Complex.prototype.toInexact = function() {
+ return Complex.makeInstance(toInexact(this.r),
+ toInexact(this.i));
+ };
+
+
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return Rational.makeInstance(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return Complex.makeInstance(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
@@ -3076,752 +3100,756 @@ if (typeof(exports) !== 'undefined') {
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this.DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this.DB)))!=0);
}
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
var r = BigInteger.ONE.shiftLeft(n);
this.bitwiseTo(r,op,r);
return r;
}
// (public) this | (1<<n)
function bnSetBit(n) { return this.changeBit(n,op_or); }
// (public) this & ~(1<<n)
function bnClearBit(n) { return this.changeBit(n,op_andnot); }
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this.changeBit(n,op_xor); }
// (protected) r = this + a
function bnpAddTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]+a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this.DV+c;
r.t = i;
r.clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.toExact = function() {
return this;
};
+ BigInteger.prototype.toInexact = function() {
+ return FloatPoint.makeInstance(this.toFixnum());
+ };
+
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess, floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
return Complex.makeInstance(0,
searchIter(tmpThis, tmpThis));
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['toInexact'] = toInexact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['quotient'] = quotient;
Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
})();
|
dyoo/js-numbers
|
fd0b4bf450133cd6cd4c90ea7900d38445fbf841
|
renaming to jsnums, for easier integration with mzscheme-vm
|
diff --git a/README b/README
index 72d6fd6..bc21914 100644
--- a/README
+++ b/README
@@ -1,311 +1,300 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
-Contributors: I want to express my thanks to the following people:
+Contributors: I want to thank the following people:
Zhe Zhang
Ethan Cecchetti
Ugur Cekmez
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
-Loading js-numbers.js will define a namespace called
+Loading js-numbers.js will define a toplevel namespace called
- plt.lib.Numbers
+ jsnums
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
-
-
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
+quotient: scheme-number scheme-number -> scheme-number
+ Produces the quotient. Both inputs must be integers.
+
+remainder: scheme-number scheme-number -> scheme-number
+ Produces the remainder. Both inputs must be integers.
+
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
- atan2, cosh, sinh, makePolar, makeRectangular, quotient, remainder,
- sgn
+ atan2, cosh, sinh, sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
-* Integrate bignums.
-
- - There are two bignum libraries to look into:
-
- jbsn: http://www-cs-students.stanford.edu/~tjw/jsbn/
- BigInteger: http://silentmatt.com/biginteger/
-We're going to use jsbn: it looks more mature, given that it's been around
-for a longer time than the BigInteger package.
-
-
-* Find out: what is the implementation mentioned in:
-
-Deniz A. Gursel, Ugur Cekmez, R. Emre Basar. "Implementation of
-Scheme Numeric System for JavaScript"
-http://ab.org.tr/ab10/bildiri/161.pdf
-
-I suspect it's worldwithweb, but it's hard to find.
======================================================================
History
-February 2010: initial refactoring from the moby-scheme source tree.
\ No newline at end of file
+February 2010: initial refactoring from the moby-scheme source tree.
+
+June 2010: got implementation of integer-sqrt from Ugur Cekmez;
+brought in some fixes from Ethan Cecchetti.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index c4ed3c1..4950928 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,1212 +1,1212 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
- if (! this['plt']) {
- this['plt'] = {};
+ if (! this['jsnums']) {
+ this['jsnums'] = {};
}
-
- if (! this['plt']['lib']) {
- this['plt']['lib'] = {};
- }
-
- if (! this['plt']['lib']['Numbers']) {
- this['plt']['lib']['Numbers'] = {};
- }
- __PLTNUMBERS_TOP__ = this['plt']['lib']['Numbers'];
+ __PLTNUMBERS_TOP__ = this['jsnums'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeComplex(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
+ throwRuntimeError('quotient: the first argument ' + x.toString() +
+ " is not an integer.", x);
}
if (! isInteger(y)) {
+ throwRuntimeError('quotient: the second argument ' + y.toString() +
+ " is not an integer.", y);
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
+ throwRuntimeError('remainder: the first argument ' + x.toString() +
+ " is not an integer.", x);
}
if (! isInteger(y)) {
+ throwRuntimeError('remainder: the second argument ' + y.toString() +
+ " is not an integer.", y);
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
diff --git a/test/tests.js b/test/tests.js
index 4fb6c95..9b7b701 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,515 +1,515 @@
// Let's open up plt.lib.Numbers to make it easy to test.
-var N = plt.lib.Numbers;
+var N = jsnums;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal).should_be_false();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
describe('complex construction', {
'polar' : function() {
// FIXME: add tests for polar construction
},
'non-real inputs should raise errors' : function() {
// FIXME: add tests for polar construction
}});
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
@@ -1515,1034 +1515,1035 @@ describe('multiply', {
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
assertTrue(eqv(sqrt(4), 2));
assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
-
assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
assertTrue(eqv(sqrt(-297354289),
makeComplex(0,
makeFloat(17243.963842458033))));
},
+
'bignums': function() {
// FIXME: we're missing this
},
+
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
@@ -3027,644 +3028,642 @@ describe('toString', {
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0)
));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
- assertTrue(Kernel.number_question_(plt.types.makeRational(42)));
+ assertTrue(Kernel.number_question_(makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(pi));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
- assertTrue(!Kernel.real_question_(plt.types.Empty.EMPTY));
- assertTrue(!Kernel.real_question_(String.makeInstance("hi")));
- assertTrue(!Kernel.real_question_(Symbol.makeInstance('h')));
+ assertTrue(!Kernel.real_question_("hi"));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
- assertTrue(equals(Kernel.sgn(makeFloat(-4)), Rational.NEGATIVE_ONE));
+ assertTrue(equals(Kernel.sgn(makeFloat(-4)), makeRational(-1)));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
11d6c99bf2ce8078bd581d9a0fcf7e83ae37d509
|
making sure sqrt -1 is complex
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 23994f9..c4ed3c1 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,1817 +1,1817 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['plt']) {
this['plt'] = {};
}
if (! this['plt']['lib']) {
this['plt']['lib'] = {};
}
if (! this['plt']['lib']['Numbers']) {
this['plt']['lib']['Numbers'] = {};
}
__PLTNUMBERS_TOP__ = this['plt']['lib']['Numbers'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
if (isReal(y) && lessThan(y, 0)) {
return _expt(divide(1, x), negate(y));
}
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
- return (makeBignum(n)).sqrt();
+ return (makeComplex(0, sqrt(-n)));
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
- var result = sqrt(x);
+ var result = sqrt(this);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
diff --git a/test/tests.js b/test/tests.js
index f49c466..4fb6c95 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1513,1035 +1513,1045 @@ describe('multiply', {
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
assertTrue(eqv(expt(2, 1), 2));
assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
assertTrue(eqv(expt(2, -1),
makeRational(1,2)));
assertTrue(eqv(expt(2, -2),
makeRational(1,4)));
assertTrue(eqv(expt(2, -100),
makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
1));
assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
1));
},
'bignum / bignum' : function() {
assertTrue(eqv(expt(makeBignum("0"),
makeBignum("0")),
1));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("999")),
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("1")),
-2));
assertTrue(eqv(expt(makeBignum("-2"),
makeBignum("2")),
4));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-1")),
makeRational(1, 2)));
assertTrue(eqv(expt(makeBignum("2"),
makeBignum("-999")),
makeRational(1,
makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
- // FIXME: we're missing this
+ assertTrue(eqv(sqrt(4), 2));
+ assertTrue(eqv(sqrt(-4), makeComplex(0, 2)));
+
+ assertTrue(eqv(sqrt(-1), makeComplex(0, 1)));
+ assertTrue(eqv(sqrt(297354289), makeFloat(17243.963842458033)));
+ assertTrue(eqv(sqrt(-297354289),
+ makeComplex(0,
+ makeFloat(17243.963842458033))));
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
+
'floats': function() {
- // FIXME: we're missing this
+ assertTrue(eqv(sqrt(makeFloat(-4)), makeComplex(0, makeFloat(2))));
+ assertTrue(eqv(sqrt(makeFloat(4)), makeFloat(2)));
},
+
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
28438118b3bb9ab3f55698562d904f7eb6f6ed1e
|
changing the logic of expt
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 656ed8d..23994f9 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,916 +1,914 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['plt']) {
this['plt'] = {};
}
if (! this['plt']['lib']) {
this['plt']['lib'] = {};
}
if (! this['plt']['lib']['Numbers']) {
this['plt']['lib']['Numbers'] = {};
}
__PLTNUMBERS_TOP__ = this['plt']['lib']['Numbers'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
- if (y > 0) {
- var pow = Math.pow(x, y);
- if (isOverflow(pow)) {
- return (makeBignum(x)).expt(makeBignum(y));
- } else {
- return pow;
- }
+ var pow = Math.pow(x, y);
+ if (isOverflow(pow)) {
+ return (makeBignum(x)).expt(makeBignum(y));
} else {
- return expt(makeRational(1, x),
- negate(y));
+ return pow;
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
+ if (isReal(y) && lessThan(y, 0)) {
+ return _expt(divide(1, x), negate(y));
+ }
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
@@ -942,1061 +940,1048 @@ if (typeof(exports) !== 'undefined') {
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
var _integerRemainder = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnRemainder.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
- var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
- // _rationalCache = {};
- // (function() {
- // var i;
- // for(i = -500; i < 500; i++) {
- // _rationalCache[i] = new Rational(i, 1);
- // }
- // })();
- // Rational.NEGATIVE_ONE = new Rational(-1, 1);
- // Rational.ZERO = new Rational(0, 1);
- // Rational.ONE = new Rational(1, 1);
- // Rational.TWO = new Rational(2, 1);
-
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
|
dyoo/js-numbers
|
744363e563bb37e9988e4a5d6cd187b278abdf9d
|
Isolating another problem with expt and negative numbers.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 9843b94..656ed8d 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,910 +1,911 @@
// Scheme numbers.
var __PLTNUMBERS_TOP__;
if (typeof(exports) !== 'undefined') {
__PLTNUMBERS_TOP__ = exports;
} else {
if (! this['plt']) {
this['plt'] = {};
}
if (! this['plt']['lib']) {
this['plt']['lib'] = {};
}
if (! this['plt']['lib']['Numbers']) {
this['plt']['lib']['Numbers'] = {};
}
__PLTNUMBERS_TOP__ = this['plt']['lib']['Numbers'];
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
if (y > 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
- return (makeBignum(x)).expt(makeBignum(y));
+ return expt(makeRational(1, x),
+ negate(y));
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
- return x.expt(y);
+ return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
var quotient = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerQuotient(x, y);
};
var remainder = function(x, y) {
if (! isInteger(x)) {
}
if (! isInteger(y)) {
}
return _integerRemainder(x, y);
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return Complex.makeInstance(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
diff --git a/test/tests.js b/test/tests.js
index 6d2e1dc..f49c466 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1319,1048 +1319,1075 @@ describe('subtract', {
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
assertTrue(eqv(expt(2, 0), 1));
- assertTrue(eqv(expt(2, 1), 2));
- assertTrue(eqv(expt(2, 100), makeBignum("1125899906842624")));
- assertTrue(eqv(expt(2, -1),
- makeRational(1,2)));
- assertTrue(eqv(expt(2, -2),
- makeRational(1,4)));
- assertTrue(eqv(expt(2, -100),
- makeRational(1, makeBignum("1267650600228229401496703205376"))));
- // FIXME: add test case where value needs to become a bignum.
+ assertTrue(eqv(expt(2, 1), 2));
+ assertTrue(eqv(expt(2, 100), makeBignum("1267650600228229401496703205376")));
+ assertTrue(eqv(expt(2, -1),
+ makeRational(1,2)));
+ assertTrue(eqv(expt(2, -2),
+ makeRational(1,4)));
+ assertTrue(eqv(expt(2, -100),
+ makeRational(1, makeBignum("1267650600228229401496703205376"))));
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
- // FIXME: we're missing this
+ assertTrue(eqv(expt(1, makeBignum("123689321689125689")),
+ 1));
+
+ assertTrue(eqv(expt(1, makeBignum("-123689321689125689")),
+ 1));
},
'bignum / bignum' : function() {
- // FIXME: we're missing this
- },
+ assertTrue(eqv(expt(makeBignum("0"),
+ makeBignum("0")),
+ 1));
+ assertTrue(eqv(expt(makeBignum("2"),
+ makeBignum("999")),
+ makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688")));
+
+
+ assertTrue(eqv(expt(makeBignum("-2"),
+ makeBignum("1")),
+ -2));
+
+ assertTrue(eqv(expt(makeBignum("-2"),
+ makeBignum("2")),
+ 4));
+
+ assertTrue(eqv(expt(makeBignum("2"),
+ makeBignum("-1")),
+ makeRational(1, 2)));
+
+ assertTrue(eqv(expt(makeBignum("2"),
+ makeBignum("-999")),
+ makeRational(1,
+ makeBignum("5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688"))));
+ },
+
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
c6c56b5a17e369e93d42e46ad3a941532da50bce
|
adding tests that show something messed up with expt
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index d55c7c0..9843b94 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -175,1300 +175,1326 @@ if (typeof(exports) !== 'undefined') {
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = (function() {
var _expt = makeNumericBinop(
function(x, y){
if (y > 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
if (equals(y, 0)) {
return add(y, 1);
} else {
return x.expt(y);
}
});
return function(x, y) {
if (equals(y, 0))
return add(y, 1);
return _expt(x, y);
};
})();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
+
+
+ var quotient = function(x, y) {
+ if (! isInteger(x)) {
+ }
+ if (! isInteger(y)) {
+ }
+ return _integerQuotient(x, y);
+ };
+
+
+ var remainder = function(x, y) {
+ if (! isInteger(x)) {
+ }
+ if (! isInteger(y)) {
+ }
+ return _integerRemainder(x, y);
+ };
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
- return makeComplex(multiply(r, cos(theta)),
- multiply(r, sin(theta)));
+ return Complex.makeInstance(multiply(r, cos(theta)),
+ multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
+ var _integerRemainder = makeIntegerBinop(
+ function(m, n) {
+ return m % n;
+ },
+ function(m, n) {
+ return bnRemainder.call(m, n);
+ });
+
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// _rationalCache = {};
// (function() {
// var i;
// for(i = -500; i < 500; i++) {
// _rationalCache[i] = new Rational(i, 1);
// }
// })();
// Rational.NEGATIVE_ONE = new Rational(-1, 1);
// Rational.ZERO = new Rational(0, 1);
// Rational.ONE = new Rational(1, 1);
// Rational.TWO = new Rational(2, 1);
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
@@ -1722,1032 +1748,1032 @@ if (typeof(exports) !== 'undefined') {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
- return makeRational(fromString(aMatch[1]),
- fromString(aMatch[2]));
+ return Rational.makeInstance(fromString(aMatch[1]),
+ fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
- return makeComplex(fromString(cMatch[1] || "0"),
- fromString(cMatch[2] + (cMatch[3] || "1")));
+ return Complex.makeInstance(fromString(cMatch[1] || "0"),
+ fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
@@ -3144,670 +3170,671 @@ if (typeof(exports) !== 'undefined') {
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
(function() {
// Classic implementation of Newton-Ralphson square-root search,
// adapted for integer-sqrt.
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
var searchIter = function(n, guess) {
while(!(goodEnough(n, guess))) {
guess = average(guess, floor(divide(n, guess)));
}
return guess;
};
var average = function (x,y) {
return floor(divide(add(x,y), 2));
};
var goodEnough = function(n, guess) {
return (lessThanOrEqual(sqr(guess),n) &&
lessThan(n,sqr(add(guess, 1))));
};
// integerSqrt: -> scheme-number
BigInteger.prototype.integerSqrt = function() {
if(this.s == 0) {
return searchIter(this, this);
} else {
var tmpThis = multiply(this, -1);
- return makeComplex(0,
- searchIter(tmpThis, tmpThis));
+ return Complex.makeInstance(0,
+ searchIter(tmpThis, tmpThis));
}
};
})();
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
BigInteger.prototype.expt = function(n) {
return bnPow.call(this, n);
};
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
+ Numbers['quotient'] = quotient;
+ Numbers['remainder'] = remainder;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
-
})();
diff --git a/test/tests.js b/test/tests.js
index 418f883..6d2e1dc 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1318,1024 +1318,1033 @@ describe('subtract', {
assertTrue(eqv(makeComplex(-1, 4567),
subtract(makeBignum("1233"),
makeComplex(1234, -4567))));
},
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
+ assertTrue(eqv(expt(2, 0), 1));
+ assertTrue(eqv(expt(2, 1), 2));
+ assertTrue(eqv(expt(2, 100), makeBignum("1125899906842624")));
+ assertTrue(eqv(expt(2, -1),
+ makeRational(1,2)));
+ assertTrue(eqv(expt(2, -2),
+ makeRational(1,4)));
+ assertTrue(eqv(expt(2, -100),
+ makeRational(1, makeBignum("1267650600228229401496703205376"))));
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
assertTrue(eqv(expt(2, 1000),
makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"),
ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"),
ceiling(makeRational(0, -1))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeRational(1, 1))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-1"),
ceiling(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("2"),
ceiling(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333334"),
ceiling(makeRational(100000001, 3))));
assertTrue(eqv(makeBignum("99481699535421"),
ceiling(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
e84668bd1502b7c72104d6914a707eaa91cca49e
|
Adding reference to Ugur
|
diff --git a/README b/README
index 1a8744e..72d6fd6 100644
--- a/README
+++ b/README
@@ -1,308 +1,311 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
-Contributors:
+Contributors: I want to express my thanks to the following people:
+
Zhe Zhang
Ethan Cecchetti
+ Ugur Cekmez
+
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a namespace called
plt.lib.Numbers
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
makeComplexPolar: scheme-number scheme-number -> scheme-number
Constructs a complex number; the radius and theta must be basic
scheme numbers (i.e. not complex).
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
cosh: scheme-number -> scheme-number
Produces the hyperbolic cosine.
sinh: scheme-number -> scheme-number
Produces the hyperbolic sine.
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, makePolar, makeRectangular, quotient, remainder,
sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
* Integrate bignums.
- There are two bignum libraries to look into:
jbsn: http://www-cs-students.stanford.edu/~tjw/jsbn/
BigInteger: http://silentmatt.com/biginteger/
We're going to use jsbn: it looks more mature, given that it's been around
for a longer time than the BigInteger package.
* Find out: what is the implementation mentioned in:
Deniz A. Gursel, Ugur Cekmez, R. Emre Basar. "Implementation of
Scheme Numeric System for JavaScript"
http://ab.org.tr/ab10/bildiri/161.pdf
I suspect it's worldwithweb, but it's hard to find.
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
\ No newline at end of file
|
dyoo/js-numbers
|
4210e3374fc58b116b92f608458bf8208f7fdf45
|
Implementation of expt for bignums
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index f769856..013b765 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,902 +1,912 @@
// Scheme numbers.
if (! this['plt']) {
this['plt'] = {};
}
if (! this['plt']['lib']) {
this['plt']['lib'] = {};
}
if (! this['plt']['lib']['Numbers']) {
this['plt']['lib']['Numbers'] = {};
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = plt.lib.Numbers;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
- var expt = makeNumericBinop(
- function(x, y){
- if (y >= 0) {
- var pow = Math.pow(x, y);
- if (isOverflow(pow)) {
+ var expt = (function() {
+ var _expt = makeNumericBinop(
+ function(x, y){
+ if (y > 0) {
+ var pow = Math.pow(x, y);
+ if (isOverflow(pow)) {
+ return (makeBignum(x)).expt(makeBignum(y));
+ } else {
+ return pow;
+ }
+ } else {
return (makeBignum(x)).expt(makeBignum(y));
+ }
+ },
+ function(x, y) {
+ if (equals(y, 0)) {
+ return add(y, 1);
} else {
- return pow;
+ return x.expt(y);
}
- } else {
- return (makeBignum(x)).expt(makeBignum(y));
- }
- },
- function(x, y) {
- return x.expt(y);
- });
-
+ });
+ return function(x, y) {
+ if (equals(y, 0))
+ return add(y, 1);
+ return _expt(x, y);
+ };
+ })();
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
return Math.floor(Math.sqrt(x));
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return makeComplex(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
@@ -3118,617 +3128,623 @@ if (! this['plt']['lib']['Numbers']) {
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
// integerSqrt: -> scheme-number
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
+
// expt: scheme-number -> scheme-number
// Produce the power to the input.
+ BigInteger.prototype.expt = function(n) {
+ return bnPow.call(this, n);
+ };
+
+
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
})();
\ No newline at end of file
diff --git a/test/tests.js b/test/tests.js
index 0a06d69..49c2c48 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1322,1025 +1322,1026 @@ describe('subtract', {
'fixnum / rational' : function() {
assertTrue(eqv(makeRational(1, 2),
subtract(1, makeRational(1, 2))));
assertTrue(eqv(makeRational(-1, 2),
subtract(1, makeRational(3, 2))));
assertTrue(eqv(makeRational(341, 20),
subtract(17, makeRational(-1, 20))));
},
'fixnum / floating' : function() {
assertTrue(eqv(makeFloat(0),
subtract(1, makeFloat(1.0))));
assertTrue(eqv(makeFloat(-22998.1),
subtract(2398, makeFloat(25396.1))));
},
'fixnum / complex' : function() {
assertTrue(eqv(makeComplex(0, -1),
subtract(0, makeComplex(0, 1))));
assertTrue(eqv(makeComplex(0, makeFloat(-1.1234)),
subtract(0, makeComplex(0, makeFloat(1.1234)))));
assertTrue(eqv(makeComplex(0, makeFloat(1.1234)),
subtract(0, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(234, makeFloat(1.1234)),
subtract(234, makeComplex(0, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(200, makeFloat(1.1234)),
subtract(234, makeComplex(34, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(-24, makeFloat(1.1234)),
subtract(0, makeComplex(24, makeFloat(-1.1234)))));
assertTrue(eqv(makeComplex(makeRational(16, 17),
makeFloat(1.1234)),
subtract(1, makeComplex(makeRational(1, 17),
makeFloat(-1.1234)))));
},
'rational / rational' : function() {
value_of(subtract(makeRational(1, 3), makeRational(1, 2))
).should_be(makeRational(-1, 6));
value_of(subtract(makeRational(6, 3), makeRational(0, 1))
).should_be(makeRational(2, 1));
value_of(subtract(makeRational(6, -3), makeRational(0, 1))
).should_be(makeRational(-2, 1));
value_of(subtract(makeRational(-1, 3), makeRational(1, -2))
).should_be(makeRational(1, 6));
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
- // FIXME
+ assertTrue(eqv(expt(2, 1000),
+ makeBignum("10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376")));
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('ceiling', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
|
dyoo/js-numbers
|
ff832782e4dc947dcdbfee9e88e1cea3d18ac361
|
compatibility with node.js
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 35b418d..bd0d6de 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,552 +1,558 @@
// Scheme numbers.
+var __PLTNUMBERS_TOP__;
+if (typeof(exports) !== 'undefined') {
+ __PLTNUMBERS_TOP__ = exports;
+} else {
if (! this['plt']) {
this['plt'] = {};
}
-
-if (! this['plt']['lib']) {
- this['plt']['lib'] = {};
+
+ if (! this['plt']['lib']) {
+ this['plt']['lib'] = {};
+ }
+
+ if (! this['plt']['lib']['Numbers']) {
+ this['plt']['lib']['Numbers'] = {};
+ }
+ __PLTNUMBERS_TOP__ = this['plt']['lib']['Numbers'];
}
-if (! this['plt']['lib']['Numbers']) {
- this['plt']['lib']['Numbers'] = {};
-}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
- var Numbers = plt.lib.Numbers;
-
+ var Numbers = __PLTNUMBERS_TOP__;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
@@ -1818,1029 +1824,1029 @@ if (! this['plt']['lib']['Numbers']) {
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
if (isInteger(this)) {
return integerSqrt(this.r);
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(2, atan(divide(this,
add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return makeRational(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return makeComplex(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
- if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
+ if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
- else if(j_lm && (navigator.appName != "Netscape")) {
+ else if(j_lm && (typeof(navigator) !== 'undefined' && navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
// use am to combine the multiply-shift-add into one call
j = i+this.m.t;
x[j] += this.m.am(0,u0,x,i,0,this.m.t);
// propagate carry
while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
}
x.clamp();
x.drShiftTo(this.m.t,x);
if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = "x^2/R mod m"; x != r
function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = "xy/R mod m"; x,y != r
function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;
// (protected) true iff this is even
function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e,z) {
if(e > 0xffffffff || e < 1) return BigInteger.ONE;
var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
g.copyTo(r);
while(--i >= 0) {
z.sqrTo(r,r2);
if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
else { var t = r; r = r2; r2 = t; }
}
return z.revert(r);
}
// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e,m) {
var z;
if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
return this.exp(e,z);
}
// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;
// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
// Copyright (c) 2005-2009 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
// (public)
function bnClone() { var r = nbi(); this.copyTo(r); return r; }
// (public) return value as integer
function bnIntValue() {
if(this.s < 0) {
if(this.t == 1) return this[0]-this.DV;
else if(this.t == 0) return -1;
}
else if(this.t == 1) return this[0];
else if(this.t == 0) return 0;
// assumes 16 < DB < 32
return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
}
// (public) return value as byte
function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
|
dyoo/js-numbers
|
d486a9cc5b70e500ccfbbaaf4a8ed62e3f0a89f9
|
fixing the implemementation of BigInteger.integerSqrt so it doesn't introduce the inexact zero. Also moved off the helper methods as helper functions, locally scoped for safety.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 85845e2..35b418d 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -2900,891 +2900,892 @@ if (! this['plt']['lib']['Numbers']) {
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) alternate constructor
function bnpFromNumber(a,b,c) {
if("number" == typeof b) {
// new BigInteger(int,int,RNG)
if(a < 2) this.fromInt(1);
else {
this.fromNumber(a,c);
if(!this.testBit(a-1)) // force MSB set
this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
if(this.isEven()) this.dAddOffset(1,0); // force odd
while(!this.isProbablePrime(b)) {
this.dAddOffset(2,0);
if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
}
}
}
else {
// new BigInteger(int,RNG)
var x = [], t = a&7;
x.length = (a>>3)+1;
b.nextBytes(x);
if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
this.fromString(x,256);
}
}
// (public) convert to bigendian byte array
function bnToByteArray() {
var i = this.t, r = [];
r[0] = this.s;
var p = this.DB-(i*this.DB)%8, d, k = 0;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
r[k++] = d|(this.s<<(this.DB-p));
while(i >= 0) {
if(p < 8) {
d = (this[i]&((1<<p)-1))<<(8-p);
d |= this[--i]>>(p+=this.DB-8);
}
else {
d = (this[i]>>(p-=8))&0xff;
if(p <= 0) { p += this.DB; --i; }
}
if((d&0x80) != 0) d |= -256;
if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
if(k > 0 || d != this.s) r[k++] = d;
}
}
return r;
}
function bnEquals(a) { return(this.compareTo(a)==0); }
function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a,op,r) {
var i, f, m = Math.min(a.t,this.t);
for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
if(a.t < this.t) {
f = a.s&this.DM;
for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
r.t = this.t;
}
else {
f = this.s&this.DM;
for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
r.t = a.t;
}
r.s = op(this.s,a.s);
r.clamp();
}
// (public) this & a
function op_and(x,y) { return x&y; }
function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
// (public) this | a
function op_or(x,y) { return x|y; }
function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
// (public) ~this
function bnNot() {
var r = nbi();
for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
r.t = this.t;
r.s = ~this.s;
return r;
}
// (public) this << n
function bnShiftLeft(n) {
var r = nbi();
if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
return r;
}
// (public) this >> n
function bnShiftRight(n) {
var r = nbi();
if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
return r;
}
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if(x == 0) return -1;
var r = 0;
if((x&0xffff) == 0) { x >>= 16; r += 16; }
if((x&0xff) == 0) { x >>= 8; r += 8; }
if((x&0xf) == 0) { x >>= 4; r += 4; }
if((x&3) == 0) { x >>= 2; r += 2; }
if((x&1) == 0) ++r;
return r;
}
// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
for(var i = 0; i < this.t; ++i)
if(this[i] != 0) return i*this.DB+lbit(this[i]);
if(this.s < 0) return this.t*this.DB;
return -1;
}
// return number of 1 bits in x
function cbit(x) {
var r = 0;
while(x != 0) { x &= x-1; ++r; }
return r;
}
// (public) return number of set bits
function bnBitCount() {
var r = 0, x = this.s&this.DM;
for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
return r;
}
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this.DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this.DB)))!=0);
}
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
var r = BigInteger.ONE.shiftLeft(n);
this.bitwiseTo(r,op,r);
return r;
}
// (public) this | (1<<n)
function bnSetBit(n) { return this.changeBit(n,op_or); }
// (public) this & ~(1<<n)
function bnClearBit(n) { return this.changeBit(n,op_andnot); }
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this.changeBit(n,op_xor); }
// (protected) r = this + a
function bnpAddTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]+a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this.DV+c;
r.t = i;
r.clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return [q,r];
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
if(n == 0) return;
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
- // (protected)
- function bnpSearchIter(guess) {
- while(!(this.goodEnough(guess))) {
- guess = this.improve(guess);
- }
- return guess;
- }
-
- // (protected)
- function bnpImprove(guess) {
- return this.average(guess, floor(divide(this,guess)));
- }
-
- // (protected)
- function bnpAverage(x,y) {
- return floor(divide(add(x,y), makeBignum("2")))
- }
-
- // (protected)
- function bnpGoodEnough(guess) {
- return lessThanOrEqual(sqr(guess),this) && lessThan(this,sqr(add(guess, makeBignum("1"))));
- }
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
- BigInteger.prototype.searchIter = bnpSearchIter
- BigInteger.prototype.improve = bnpImprove
- BigInteger.prototype.average = bnpAverage
- BigInteger.prototype.goodEnough = bnpGoodEnough
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
- // integerSqrt: -> scheme-number
- BigInteger.prototype.integerSqrt = function() {
- if(this.s == 0) {
- return this.searchIter(this);
- }else {
- tmpThis = multiply(this,makeBignum("-1"));
- return makeComplex(makeFloat(0), tmpThis.searchIter(tmpThis));
- }
- }
+
+ (function() {
+ // Classic implementation of Newton-Ralphson square-root search,
+ // adapted for integer-sqrt.
+ // http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
+ var searchIter = function(n, guess) {
+ while(!(goodEnough(n, guess))) {
+ guess = average(guess, floor(divide(n, guess)));
+ }
+ return guess;
+ };
+
+ var average = function (x,y) {
+ return floor(divide(add(x,y), 2));
+ };
+
+ var goodEnough = function(n, guess) {
+ return (lessThanOrEqual(sqr(guess),n) &&
+ lessThan(n,sqr(add(guess, 1))));
+ };
+
+ // integerSqrt: -> scheme-number
+ BigInteger.prototype.integerSqrt = function() {
+ if(this.s == 0) {
+ return searchIter(this, this);
+ } else {
+ var tmpThis = multiply(this, -1);
+ return makeComplex(0,
+ searchIter(tmpThis, tmpThis));
+ }
+ };
+ })();
+
+
+
+
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
BigInteger.prototype.floor = function() {
return this;
}
// ceiling: -> scheme-number
// Produce the ceiling.
BigInteger.prototype.ceiling = function() {
return this;
}
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
Numbers['cosh'] = cosh;
Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
})();
diff --git a/test/tests.js b/test/tests.js
index 61a3720..e8e3432 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2426,1025 +2426,1025 @@ describe('atan', {
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
'bignums': function() {
assertTrue(eqv(makeComplex(0, makeBignum("1")),
integerSqrt(makeBignum("-1"))));
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeBignum("1"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("4"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("5"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("6"))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeBignum("7"))));
assertTrue(eqv(makeBignum("8"),
integerSqrt(makeBignum("70"))));
assertTrue(eqv(makeBignum("26"),
integerSqrt(makeBignum("700"))));
assertTrue(eqv(makeBignum("92113"),
integerSqrt(makeBignum("8484848484"))));
assertTrue(eqv(makeBignum("35136418"),
integerSqrt(makeBignum("1234567891234567"))));
assertTrue(eqv(makeBignum("50000000000"),
integerSqrt(makeBignum("2500000000050000000000"))));
assertTrue(eqv(makeBignum("999999999949999"),
integerSqrt(makeBignum("999999999900000000000000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("92113")),
integerSqrt(makeBignum("-8484848484"))));
assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
integerSqrt(makeBignum("-1234567891234567"))));
assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
integerSqrt(makeBignum("-2500000000050000000000"))));
assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
'rationals': function() {
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
assertTrue(eqv(makeBignum("0"),
integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("2"),
integerSqrt(makeRational(makeBignum("55555555555"),
makeBignum("11111111111")))));
assertTrue(eqv(makeBignum("5000000000"),
integerSqrt(makeRational(makeBignum("25000000005000000000"),
makeBignum("1")))));
assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
integerSqrt(makeRational(makeBignum("-25000000005000000000"),
makeBignum("1")))));
},
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
assertTrue(eqv(makeFloat(0.0),
integerSqrt(makeFloat(0.0))));
assertTrue(eqv(makeFloat(1.0),
integerSqrt(makeFloat(1.0))));
assertTrue(eqv(makeFloat(111.0),
integerSqrt(makeFloat(12345.0))));
assertTrue(eqv(makeComplex(0, makeFloat(111)),
integerSqrt(makeFloat(-12345.0))));
},
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
assertFails(function() { integerSqrt(makeComplex(negative_inf,
negative_inf))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
makeBignum("2")))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))});
assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
makeBignum("200")))});
assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
makeRational(3,2)))});
assertTrue(eqv(makeComplex(0,makeBignum("1")),
integerSqrt(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
integerSqrt(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeComplex(0, makeBignum("2")),
integerSqrt(makeComplex(makeBignum("-7"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("351"),
integerSqrt(makeComplex(makeBignum("123456"),
makeBignum("0")))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("351")),
+ assertTrue(eqv(makeComplex(0,makeBignum("351")),
integerSqrt(makeComplex(makeBignum("-123456"),
makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0)
));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
|
dyoo/js-numbers
|
a5848321dec1d80a163261edf845ddce0f3bb071
|
establishing test cases to make sure we're not sensitive to the representation of integers.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 6f68902..85845e2 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -429,1413 +429,1408 @@ if (! this['plt']['lib']['Numbers']) {
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
return Complex.makeInstance(0,
Math.floor(Math.sqrt(-x)))
} else {
return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return makeComplex(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
- return (m / n - m % n / n);
+ return ((m / n) - ((m % n) / n));
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return subtract(quotient, 1);
} else {
return quotient;
}
};
Rational.prototype.ceiling = function() {
var quotient = _integerQuotient(this.n, this.d);
if (_integerLessThan(this.n, 0)) {
return quotient;
} else {
return add(quotient, 1);
}
- // if(this.n.s == -1 && this.d.s == -1 || this.n.s == 0 && this.d.s == 0) {
- // return add(_integerQuotient(this.n,this.d),makeBignum("1"));
- // }else {
- // return _integerQuotient(this.n,this.d);
- // }
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// _rationalCache = {};
// (function() {
// var i;
// for(i = -500; i < 500; i++) {
// _rationalCache[i] = new Rational(i, 1);
// }
// })();
// Rational.NEGATIVE_ONE = new Rational(-1, 1);
// Rational.ZERO = new Rational(0, 1);
// Rational.ONE = new Rational(1, 1);
// Rational.TWO = new Rational(2, 1);
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
diff --git a/test/tests.js b/test/tests.js
index f9bac76..61a3720 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1706,1037 +1706,1073 @@ describe('lessThanOrEqual', {
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
makeBignum("-1")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
makeBignum("1")))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("-3"),
makeBignum("2")))));
assertTrue(eqv(makeBignum("-2"),
floor(makeRational(makeBignum("3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"),
floor(makeRational(makeBignum("-3"),
makeBignum("-2")))));
assertTrue(eqv(makeBignum("0"),
floor(makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959689"),
floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
makeBignum("93485783475983475983")))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
assertTrue(eqv(makeBignum("33333333"),
floor(makeRational(makeBignum("100000001"),
3))));
assertTrue(eqv(makeBignum("99481699535420"),
floor(makeRational(makeBignum("123456789123456789"),
1241))));
},
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
+
'rationals': function() {
- assertTrue(eqv(makeBignum("0"), ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
- assertTrue(eqv(makeBignum("0"), ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
- assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
- assertTrue(eqv(makeBignum("2"), ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("-1"), ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("2"), ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
- assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
- assertTrue(eqv(makeBignum("33333334"), ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
- assertTrue(eqv(makeBignum("99481699535421"), ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
- assertTrue(eqv(makeBignum("88104168679280445959690"), ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),makeBignum("93485783475983475983")))));
+ assertTrue(eqv(makeBignum("0"),
+ ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
+ assertTrue(eqv(makeBignum("0"),
+ ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
+ assertTrue(eqv(makeBignum("1"),
+ ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
+ assertTrue(eqv(makeBignum("1"),
+ ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
+ assertTrue(eqv(makeBignum("2"),
+ ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
+ assertTrue(eqv(makeBignum("-1"),
+ ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
+ assertTrue(eqv(makeBignum("2"),
+ ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
+ assertTrue(eqv(makeBignum("1"),
+ ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
+ assertTrue(eqv(makeBignum("33333334"),
+ ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
+ assertTrue(eqv(makeBignum("99481699535421"),
+ ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
+ assertTrue(eqv(makeBignum("88104168679280445959690"),
+ ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
+ makeBignum("93485783475983475983")))));
+
+
+ assertTrue(eqv(makeBignum("0"),
+ ceiling(makeRational(0, 1))));
+ assertTrue(eqv(makeBignum("0"),
+ ceiling(makeRational(0, -1))));
+ assertTrue(eqv(makeBignum("1"),
+ ceiling(makeRational(1, 2))));
+ assertTrue(eqv(makeBignum("1"),
+ ceiling(makeRational(1, 1))));
+ assertTrue(eqv(makeBignum("2"),
+ ceiling(makeRational(3, 2))));
+ assertTrue(eqv(makeBignum("-1"),
+ ceiling(makeRational(-3, 2))));
+ assertTrue(eqv(makeBignum("2"),
+ ceiling(makeRational(-3, -2))));
+ assertTrue(eqv(makeBignum("33333334"),
+ ceiling(makeRational(100000001, 3))));
+ assertTrue(eqv(makeBignum("99481699535421"),
+ ceiling(makeRational(makeBignum("123456789123456789"),
+ 1241))));
},
+
+
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
|
dyoo/js-numbers
|
a6a9334bdda715a2d7d1d8059bf76a04cde3b1de
|
repairing definition of Rational.floor, which must not assume that the numerator and denominator are of bignum type.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 8284521..6f68902 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -105,1730 +105,1737 @@ if (! this['plt']['lib']['Numbers']) {
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
if(x < 0) {
- return Complex.makeInstance(0,Math.floor(Math.sqrt(-x)))
- }else {
- return Math.floor(Math.sqrt(x));
+ return Complex.makeInstance(0,
+ Math.floor(Math.sqrt(-x)))
+ } else {
+ return Math.floor(Math.sqrt(x));
}
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
// Implementation of the hyperbolic functions
// http://en.wikipedia.org/wiki/Hyperbolic_cosine
var cosh = function(x) {
return divide(add(exp(x), exp(negate(x))),
2);
};
var sinh = function(x) {
return divide(subtract(exp(x), exp(negate(x))),
2);
};
var makeComplexPolar = function(r, theta) {
// special case: if theta is zero, just return
// the scalar.
if (equals(theta, 0)) {
return r;
}
return makeComplex(multiply(r, cos(theta)),
multiply(r, sin(theta)));
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
- return m / n;
+ return (m / n - m % n / n);
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
- if(this.n.s == -1 && this.d.s == -1 || this.n.s == 0 && this.d.s == 0) {
- return _integerQuotient(this.n,this.d);
- }else {
- return subtract(_integerQuotient(this.n,this.d),makeBignum("1"));
- }
+ var quotient = _integerQuotient(this.n, this.d);
+ if (_integerLessThan(this.n, 0)) {
+ return subtract(quotient, 1);
+ } else {
+ return quotient;
+ }
};
Rational.prototype.ceiling = function() {
- if(this.n.s == -1 && this.d.s == -1 || this.n.s == 0 && this.d.s == 0) {
- return add(_integerQuotient(this.n,this.d),makeBignum("1"));
- }else {
- return _integerQuotient(this.n,this.d);
- }
-
+ var quotient = _integerQuotient(this.n, this.d);
+ if (_integerLessThan(this.n, 0)) {
+ return quotient;
+ } else {
+ return add(quotient, 1);
+ }
+ // if(this.n.s == -1 && this.d.s == -1 || this.n.s == 0 && this.d.s == 0) {
+ // return add(_integerQuotient(this.n,this.d),makeBignum("1"));
+ // }else {
+ // return _integerQuotient(this.n,this.d);
+ // }
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
return fastExpt(this, a);
}
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// _rationalCache = {};
// (function() {
// var i;
// for(i = -500; i < 500; i++) {
// _rationalCache[i] = new Rational(i, 1);
// }
// })();
// Rational.NEGATIVE_ONE = new Rational(-1, 1);
// Rational.ZERO = new Rational(0, 1);
// Rational.ONE = new Rational(1, 1);
// Rational.TWO = new Rational(2, 1);
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
if (isInteger(this)) {
if(this.n >= 0) {
return FloatPoint.makeInstance(floor(sqrt(this.n)));
}else {
return Complex.makeInstance(0,
FloatPoint.makeInstance(floor(sqrt(-this.n))))
}
} else {
throwRuntimeError("integerSqrt: can only be applied to an integer", this);
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
diff --git a/test/tests.js b/test/tests.js
index c5a360a..f9bac76 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1567,1038 +1567,1075 @@ describe('divide', {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
assertEquals(0, floor(0));
assertEquals(1, floor(1));
assertEquals(-1, floor(-1));
assertEquals(1, floor(makeFloat(1.2)));
assertEquals(-2, floor(makeFloat(-1.2)));
assertEquals(123123123, floor(makeFloat(123123123.9)));
assertEquals(-1000000000, floor(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), floor(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), floor(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), floor(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), floor(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), floor(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), floor(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), floor(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), floor(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), floor(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
- assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),makeBignum("1")))));
- assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),makeBignum("-1")))));
- assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),makeBignum("1")))));
- assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("-2"), floor(makeRational(makeBignum("-3"),makeBignum("2")))));
- assertTrue(eqv(makeBignum("-2"), floor(makeRational(makeBignum("3"),makeBignum("-2")))));
-
- assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("-3"),makeBignum("-2")))));
- assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
- assertTrue(eqv(makeBignum("33333333"), floor(makeRational(makeBignum("100000001"),makeBignum("3")))));
- assertTrue(eqv(makeBignum("99481699535420"), floor(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
- assertTrue(eqv(makeBignum("88104168679280445959689"), floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),makeBignum("93485783475983475983")))));
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
+ makeBignum("1")))));
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("0"),
+ makeBignum("-1")))));
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(makeBignum("1"),
+ makeBignum("2")))));
+ assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("1"),
+ makeBignum("1")))));
+ assertTrue(eqv(makeBignum("1"), floor(makeRational(makeBignum("3"),
+ makeBignum("2")))));
+ assertTrue(eqv(makeBignum("-2"),
+ floor(makeRational(makeBignum("-3"),
+ makeBignum("2")))));
+ assertTrue(eqv(makeBignum("-2"),
+ floor(makeRational(makeBignum("3"),
+ makeBignum("-2")))));
+
+ assertTrue(eqv(makeBignum("1"),
+ floor(makeRational(makeBignum("-3"),
+ makeBignum("-2")))));
+ assertTrue(eqv(makeBignum("0"),
+ floor(makeRational(makeBignum("100000000000000000000"),
+ makeBignum("200000000000000000000")))));
+ assertTrue(eqv(makeBignum("33333333"),
+ floor(makeRational(makeBignum("100000001"),
+ makeBignum("3")))));
+ assertTrue(eqv(makeBignum("99481699535420"),
+ floor(makeRational(makeBignum("123456789123456789"),
+ makeBignum("1241")))));
+ assertTrue(eqv(makeBignum("88104168679280445959689"),
+ floor(makeRational(makeBignum("8236487236482736823687236826582365827652875"),
+ makeBignum("93485783475983475983")))));
+
+
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(0, 1))));
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(0, -1))));
+ assertTrue(eqv(makeBignum("0"), floor(makeRational(1, 2))));
+ assertTrue(eqv(makeBignum("1"), floor(makeRational(1, 1))));
+ assertTrue(eqv(makeBignum("1"), floor(makeRational(3, 2))));
+ assertTrue(eqv(makeBignum("-2"), floor(makeRational(-3, 2))));
+ assertTrue(eqv(makeBignum("-2"), floor(makeRational(3, -2))));
+ assertTrue(eqv(makeBignum("1"), floor(makeRational(-3, -2))));
+ assertTrue(eqv(makeBignum("33333333"),
+ floor(makeRational(makeBignum("100000001"),
+ 3))));
+ assertTrue(eqv(makeBignum("99481699535420"),
+ floor(makeRational(makeBignum("123456789123456789"),
+ 1241))));
},
+
+
'floats': function() {
assertEquals(makeBignum("0"), floor(makeFloat(0.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.0)));
assertEquals(makeBignum("-1"), floor(makeFloat(-1.0)));
assertEquals(makeBignum("1"), floor(makeFloat(1.1)));
assertEquals(makeBignum("1"), floor(makeFloat(1.999)));
assertEquals(makeBignum("-2"), floor(makeFloat(-1.999)));
assertEquals(makeBignum("123456"), floor(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234567"), floor(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234568"), floor(makeFloat(-1234567891234567.8)));
assertEquals(nan, floor(nan));
assertEquals(inf, floor(inf));
assertEquals(negative_inf, floor(negative_inf));
assertEquals(negative_zero, floor(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, floor(makeComplex(nan, 0))));
assertFails(function() { floor(makeComplex(0, nan))});
assertFails(function() { floor(makeComplex(nan, 1))});
assertFails(function() { floor(makeComplex(1, nan))});
assertFails(function() { floor(makeComplex(nan, inf))});
assertFails(function() { floor(makeComplex(inf, nan))});
assertFails(function() { floor(makeComplex(negative_zero, nan))});
assertFails(function() { floor(makeComplex(nan, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { floor(makeComplex(inf,inf))});
assertFails(function() { floor(makeComplex(0,inf))});
assertTrue(eqv(inf, floor(makeComplex(inf,0))));
assertFails(function() { floor(makeComplex(negative_inf,negative_inf))});
assertFails(function() { floor(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { floor(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1102,
floor(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { floor(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { floor(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), floor(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), floor(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), floor(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("0"),
floor(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-2"), floor(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234567"),
floor(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('ceiling', {
'fixnums': function() {
assertEquals(0, ceiling(0));
assertEquals(1, ceiling(1));
assertEquals(-1, ceiling(-1));
assertEquals(2, ceiling(makeFloat(1.2)));
assertEquals(-1, ceiling(makeFloat(-1.2)));
assertEquals(123123124, ceiling(makeFloat(123123123.9)));
assertEquals(-999999999, ceiling(makeFloat(-999999999.9)));
},
'bignums': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeBignum("0"))));
assertTrue(eqv(makeBignum("1"), ceiling(makeBignum("1"))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeBignum("-1"))));
assertTrue(eqv(makeBignum("100"), ceiling(makeBignum("100"))));
assertTrue(eqv(makeBignum("-100"), ceiling(makeBignum("-100"))));
assertTrue(eqv(makeBignum("10000000000"), ceiling(makeBignum("10000000000"))));
assertTrue(eqv(makeBignum("-10000000000"), ceiling(makeBignum("-10000000000"))));
assertTrue(eqv(makeBignum("100000000000000000000"), ceiling(makeBignum("100000000000000000000"))));
assertTrue(eqv(makeBignum("-100000009000000800000"), ceiling(makeBignum("-100000009000000800000"))));
},
'rationals': function() {
assertTrue(eqv(makeBignum("0"), ceiling(makeRational(makeBignum("0"),makeBignum("1")))));
assertTrue(eqv(makeBignum("0"), ceiling(makeRational(makeBignum("0"),makeBignum("-1")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("1"),makeBignum("2")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("1"),makeBignum("1")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeRational(makeBignum("3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeRational(makeBignum("-3"),makeBignum("2")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeRational(makeBignum("-3"),makeBignum("-2")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeRational(makeBignum("100000000000000000000"),makeBignum("200000000000000000000")))));
assertTrue(eqv(makeBignum("33333334"), ceiling(makeRational(makeBignum("100000001"),makeBignum("3")))));
assertTrue(eqv(makeBignum("99481699535421"), ceiling(makeRational(makeBignum("123456789123456789"),makeBignum("1241")))));
assertTrue(eqv(makeBignum("88104168679280445959690"), ceiling(makeRational(makeBignum("8236487236482736823687236826582365827652875"),makeBignum("93485783475983475983")))));
},
'floats': function() {
assertEquals(makeBignum("0"), ceiling(makeFloat(0.0)));
assertEquals(makeBignum("1"), ceiling(makeFloat(1.0)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.0)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.1)));
assertEquals(makeBignum("2"), ceiling(makeFloat(1.999)));
assertEquals(makeBignum("-1"), ceiling(makeFloat(-1.999)));
assertEquals(makeBignum("123457"), ceiling(makeFloat(123456.789)));
assertEquals(makeBignum("1234567891234568"), ceiling(makeFloat(1234567891234567.8)));
assertEquals(makeBignum("-1234567891234567"), ceiling(makeFloat(-1234567891234567.8)));
assertEquals(nan, ceiling(nan));
assertEquals(inf, ceiling(inf));
assertEquals(negative_inf, ceiling(negative_inf));
assertEquals(negative_zero, ceiling(negative_zero));
},
'complex': function() {
assertTrue(eqv(nan, ceiling(makeComplex(nan, 0))));
assertFails(function() { ceiling(makeComplex(0, nan))});
assertFails(function() { ceiling(makeComplex(nan, 1))});
assertFails(function() { ceiling(makeComplex(1, nan))});
assertFails(function() { ceiling(makeComplex(nan, inf))});
assertFails(function() { ceiling(makeComplex(inf, nan))});
assertEquals(nan,floor(makeComplex(nan, negative_zero)));
assertFails(function() { ceiling(makeComplex(negative_zero, nan))});
assertFails(function() { ceiling(makeComplex(nan, nan))});
assertFails(function() { ceiling(makeComplex(inf,inf))});
assertFails(function() { ceiling(makeComplex(0,inf))});
assertTrue(eqv(inf, ceiling(makeComplex(inf,0))));
assertFails(function() { ceiling(makeComplex(negative_inf,negative_inf))});
assertFails(function() { ceiling(makeComplex(makeBignum("0"),makeBignum("2")))});
assertFails(function() { ceiling(makeComplex(makeBignum("1"),makeBignum("2")))});
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
|
dyoo/js-numbers
|
66f7902890ea0a61a4945a48f66c17c9693c1a38
|
fixing bugs in the tests for integer-sqrt. Exposing issues with the implementation.
|
diff --git a/test/tests.js b/test/tests.js
index d3618f3..c5a360a 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2226,1104 +2226,1154 @@ describe('ceiling', {
assertTrue(eqv(1103,
ceiling(makeComplex(makeRational(makeBignum("9919"),
makeBignum("9")),
0))));
assertFails(function() { ceiling(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
assertFails(function() { ceiling(makeComplex(makeFloat(4.25), makeRational(3,2)))});
assertTrue(eqv(makeBignum("0"), ceiling(makeComplex(makeBignum("0"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeBignum("-1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeBignum("1"),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"), ceiling(makeComplex(makeRational(makeBignum("1")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("2"), ceiling(makeComplex(makeRational(makeBignum("3"),
makeBignum("2")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1"),
ceiling(makeComplex(
makeRational(makeBignum("100000000000000000000"),
makeBignum("200000000000000000000")),
makeBignum("0")))));
assertTrue(eqv(makeBignum("-1"), ceiling(makeComplex(makeFloat(-1.999),
makeBignum("0")))));
assertTrue(eqv(makeBignum("1234567891234568"),
ceiling(makeComplex(makeFloat(1234567891234567.8),
makeBignum("0")))));
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cosh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sinh', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
+ assertEquals(0, integerSqrt(0));
assertEquals(makeComplex(0,1), integerSqrt(-1));
assertEquals(makeComplex(0,11096), integerSqrt(-123123123));
assertEquals(0, integerSqrt(-0));
assertEquals(0, integerSqrt(0));
assertEquals(1, integerSqrt(1));
assertEquals(2, integerSqrt(4));
assertEquals(2, integerSqrt(5));
assertEquals(14, integerSqrt(200));
assertEquals(5000000000, integerSqrt(25000000005000000000));
},
- 'bignums': function() {
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("1")), integerSqrt(makeBignum("-1"))));
- assertTrue(eqv(makeBignum("0"), integerSqrt(makeBignum("0"))));
- assertTrue(eqv(makeBignum("1"), integerSqrt(makeBignum("1"))));
- assertTrue(eqv(makeBignum("2"), integerSqrt(makeBignum("4"))));
- assertTrue(eqv(makeBignum("2"), integerSqrt(makeBignum("5"))));
- assertTrue(eqv(makeBignum("2"), integerSqrt(makeBignum("6"))));
- assertTrue(eqv(makeBignum("2"), integerSqrt(makeBignum("7"))));
- assertTrue(eqv(makeBignum("8"), integerSqrt(makeBignum("70"))));
- assertTrue(eqv(makeBignum("26"), integerSqrt(makeBignum("700"))));
- assertTrue(eqv(makeBignum("92113"), integerSqrt(makeBignum("8484848484"))));
- assertTrue(eqv(makeBignum("35136418"), integerSqrt(makeBignum("1234567891234567"))));
- assertTrue(eqv(makeBignum("50000000000"), integerSqrt(makeBignum("2500000000050000000000"))));
- assertTrue(eqv(makeBignum("999999999949999"), integerSqrt(makeBignum("999999999900000000000000000000"))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("92113")), integerSqrt(makeBignum("-8484848484"))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("35136418")), integerSqrt(makeBignum("-1234567891234567"))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("50000000000")), integerSqrt(makeBignum("-2500000000050000000000"))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("999999999949999")), integerSqrt(makeBignum("-999999999900000000000000000000"))));
+ 'bignums': function() {
+ assertTrue(eqv(makeComplex(0, makeBignum("1")),
+ integerSqrt(makeBignum("-1"))));
+ assertTrue(eqv(makeBignum("0"),
+ integerSqrt(makeBignum("0"))));
+ assertTrue(eqv(makeBignum("1"),
+ integerSqrt(makeBignum("1"))));
+ assertTrue(eqv(makeBignum("2"),
+ integerSqrt(makeBignum("4"))));
+ assertTrue(eqv(makeBignum("2"),
+ integerSqrt(makeBignum("5"))));
+ assertTrue(eqv(makeBignum("2"),
+ integerSqrt(makeBignum("6"))));
+ assertTrue(eqv(makeBignum("2"),
+ integerSqrt(makeBignum("7"))));
+ assertTrue(eqv(makeBignum("8"),
+ integerSqrt(makeBignum("70"))));
+ assertTrue(eqv(makeBignum("26"),
+ integerSqrt(makeBignum("700"))));
+ assertTrue(eqv(makeBignum("92113"),
+ integerSqrt(makeBignum("8484848484"))));
+ assertTrue(eqv(makeBignum("35136418"),
+ integerSqrt(makeBignum("1234567891234567"))));
+ assertTrue(eqv(makeBignum("50000000000"),
+ integerSqrt(makeBignum("2500000000050000000000"))));
+ assertTrue(eqv(makeBignum("999999999949999"),
+ integerSqrt(makeBignum("999999999900000000000000000000"))));
+ assertTrue(eqv(makeComplex(0, makeBignum("92113")),
+ integerSqrt(makeBignum("-8484848484"))));
+ assertTrue(eqv(makeComplex(0, makeBignum("35136418")),
+ integerSqrt(makeBignum("-1234567891234567"))));
+ assertTrue(eqv(makeComplex(0, makeBignum("50000000000")),
+ integerSqrt(makeBignum("-2500000000050000000000"))));
+ assertTrue(eqv(makeComplex(0, makeBignum("999999999949999")),
+ integerSqrt(makeBignum("-999999999900000000000000000000"))));
},
+
'rationals': function() {
- assertFails(function() {integerSqrt(makeRational(makeBignum("1"),makeBignum("4")))});
- assertFails(function() {integerSqrt(makeRational(makeBignum("1"),makeBignum("5")))});
- assertFails(function() {integerSqrt(makeRational(makeBignum("5"),makeBignum("2")))});
+ assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("4"))) });
+ assertFails(function() { integerSqrt(makeRational(makeBignum("1"),makeBignum("5"))) });
+ assertFails(function() { integerSqrt(makeRational(makeBignum("5"),makeBignum("2"))) });
- assertTrue(eqv(makeBignum("0"), integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
- assertTrue(eqv(makeBignum("2"), integerSqrt(makeRational(makeBignum("55555555555"),makeBignum("11111111111")))));
- assertTrue(eqv(makeBignum("5000000000"), integerSqrt(makeRational(makeBignum("25000000005000000000"),makeBignum("1")))));
+ assertTrue(eqv(makeBignum("0"),
+ integerSqrt(makeRational(makeBignum("0"),makeBignum("-1")))));
+ assertTrue(eqv(makeBignum("2"),
+ integerSqrt(makeRational(makeBignum("55555555555"),
+ makeBignum("11111111111")))));
+ assertTrue(eqv(makeBignum("5000000000"),
+ integerSqrt(makeRational(makeBignum("25000000005000000000"),
+ makeBignum("1")))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("5000000000")), integerSqrt(makeRational(makeBignum("-25000000005000000000"),makeBignum("1")))));
+ assertTrue(eqv(makeComplex(0, makeBignum("5000000000")),
+ integerSqrt(makeRational(makeBignum("-25000000005000000000"),
+ makeBignum("1")))));
},
+
'floats': function() {
assertFails(function() { integerSqrt(nan) });
assertFails(function() { integerSqrt(inf) });
assertFails(function() { integerSqrt(negative_inf) });
assertFails(function() { integerSqrt(makeFloat(0.1))});
assertFails(function() { integerSqrt(makeFloat(-0.1))});
assertFails(function() { integerSqrt(makeFloat(9999999999.000001))});
assertFails(function() { integerSqrt(makeFloat(negative_zero))});
- assertTrue(eqv(makeFloat(0.0), integerSqrt(makeFloat(0.0))));
- assertTrue(eqv(makeFloat(1.0), integerSqrt(makeFloat(1.0))));
- assertTrue(eqv(makeFloat(111.0), integerSqrt(makeFloat(12345.0))));
- assertTrue(eqv(makeComplex(0, makeFloat(111)), integerSqrt(makeFloat(-12345.0))));
+ assertTrue(eqv(makeFloat(0.0),
+ integerSqrt(makeFloat(0.0))));
+ assertTrue(eqv(makeFloat(1.0),
+ integerSqrt(makeFloat(1.0))));
+ assertTrue(eqv(makeFloat(111.0),
+ integerSqrt(makeFloat(12345.0))));
+ assertTrue(eqv(makeComplex(0, makeFloat(111)),
+ integerSqrt(makeFloat(-12345.0))));
},
+
'complex': function() {
assertFails(function() { integerSqrt(makeComplex(nan, 0))});
assertFails(function() { integerSqrt(makeComplex(0, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, 1))});
assertFails(function() { integerSqrt(makeComplex(1, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, inf))});
assertFails(function() { integerSqrt(makeComplex(inf, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, negative_zero))});
assertFails(function() { integerSqrt(makeComplex(negative_zero, nan))});
assertFails(function() { integerSqrt(makeComplex(nan, nan))});
assertFails(function() { integerSqrt(makeComplex(inf,inf))});
assertFails(function() { integerSqrt(makeComplex(0,inf))});
assertFails(function() { integerSqrt(makeComplex(inf,0))});
- assertFails(function() { integerSqrt(makeComplex(negative_inf,negative_inf))});
- assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),makeBignum("2")))});
- assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),makeBignum("2")))});
- assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),0))});
- assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),makeBignum("9")),makeBignum("200")))});
- assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25), makeRational(3,2)))});
+ assertFails(function() { integerSqrt(makeComplex(negative_inf,
+ negative_inf))});
+ assertFails(function() { integerSqrt(makeComplex(makeBignum("0"),
+ makeBignum("2")))});
+ assertFails(function() { integerSqrt(makeComplex(makeBignum("1"),
+ makeBignum("2")))});
+ assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
+ makeBignum("9")),
+ 0))});
+ assertFails(function() { integerSqrt(makeComplex(makeRational(makeBignum("9919"),
+ makeBignum("9")),
+ makeBignum("200")))});
+ assertFails(function() { integerSqrt(makeComplex(makeFloat(4.25),
+ makeRational(3,2)))});
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("1")), integerSqrt(makeComplex(makeBignum("-1"),makeBignum("0")))));
- assertTrue(eqv(makeBignum("1"), integerSqrt(makeComplex(makeBignum("1"),makeBignum("0")))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("2")), integerSqrt(makeComplex(makeBignum("-7"),makeBignum("0")))));
- assertTrue(eqv(makeBignum("351"), integerSqrt(makeComplex(makeBignum("123456"),makeBignum("0")))));
- assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("351")), integerSqrt(makeComplex(makeBignum("-123456"),makeBignum("0")))));
+ assertTrue(eqv(makeComplex(0,makeBignum("1")),
+ integerSqrt(makeComplex(makeBignum("-1"),
+ makeBignum("0")))));
+ assertTrue(eqv(makeBignum("1"),
+ integerSqrt(makeComplex(makeBignum("1"),
+ makeBignum("0")))));
+ assertTrue(eqv(makeComplex(0, makeBignum("2")),
+ integerSqrt(makeComplex(makeBignum("-7"),
+ makeBignum("0")))));
+ assertTrue(eqv(makeBignum("351"),
+ integerSqrt(makeComplex(makeBignum("123456"),
+ makeBignum("0")))));
+ assertTrue(eqv(makeComplex(makeFloat(0.0),makeBignum("351")),
+ integerSqrt(makeComplex(makeBignum("-123456"),
+ makeBignum("0")))));
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(makeComplexPolar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),
makeRational(0))));
var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(imaginaryPart(n),
makeRational(0),
delta));
assertTrue(approxEquals(realPart(n),
makeRational(-5),
delta));
},
testCosh : function(){
assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(denominator(makeRational(7,2)),
makeRational(2,1)));
assertTrue(equals(denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(numerator(makeRational(7,2)),
makeRational(7,1)));
assertTrue(equals(numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(isExact(makeRational(3)));
assertTrue(! isExact(makeFloat(3.0)));
assertTrue(! isExact(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0)
));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
|
dyoo/js-numbers
|
d3b446357584ac7a6b2d2dae4b005c3fb2b3a005
|
continuing to re-instate test cases.
|
diff --git a/README b/README
index dc91666..1a8744e 100644
--- a/README
+++ b/README
@@ -1,297 +1,308 @@
js-numbers: a Javascript implementation of Scheme's numeric tower
Developer:
Danny Yoo (dyoo@cs.wpi.edu)
License:
BSD
Summary: js-numbers implements the "numeric tower" commonly associated
with the Scheme language. The operations in this package
automatically coerse between fixnums, bignums, rationals, floating
point, and complex numbers.
Contributors:
Zhe Zhang
Ethan Cecchetti
Other sources:
The bignum implementation (content from jsbn.js and jsbn2.js) used
in js-numbers comes from Tom Wu's JSBN library at:
http://www-cs-students.stanford.edu/~tjw/jsbn/
======================================================================
WARNING WARNING
This package is currently being factored out of an existing project,
Moby-Scheme. As such, the code here is in major flux, and this is
nowhere near ready from public consumption yet. We're still in the
middle of migrating over the test cases from Moby-Scheme over to this
package, and furthermore, I'm taking the time to redo some of the
implementation. So this is going to be buggy for a bit. Use at your
own risk.
======================================================================
Examples
[fill me in]
======================================================================
API
Loading js-numbers.js will define a namespace called
plt.lib.Numbers
which contains following constants and functions:
pi: scheme-number
e: scheme-number
nan: scheme-number
Not-A-Number
inf: scheme-number
infinity
negative_inf: scheme-number
negative infinity
negative_zero: scheme-number
The value -0.0.
zero: scheme-number
one: scheme-number
negative_one: scheme-number
i: scheme-number
The square root of -1.
negative_i: scheme-number
The negative of i.
fromString: string -> (scheme-number | false)
Convert from a string to a scheme-number. If we find the number is malformed,
returns false.
fromFixnum: javascript-number -> scheme-number
Convert from a javascript number to a scheme-number.
makeRational: javascript-number javascript-number? -> scheme-number
Low level constructor: Constructs a rational with the given
numerator and denominator. If only one argument is given, assumes
the denominator is 1.
makeFloat: javascript-number -> scheme-number
Low level constructor: constructs a floating-point number.
makeBignum: string -> scheme-number
Low level constructor: constructs a bignum.
makeComplex: scheme-number scheme-number? -> scheme-number
Constructs a complex number; the real and imaginary parts of the
input must be basic scheme numbers (i.e. not complex). If only one
argument is given, assumes the imaginary part is 0.
+makeComplexPolar: scheme-number scheme-number -> scheme-number
+ Constructs a complex number; the radius and theta must be basic
+ scheme numbers (i.e. not complex).
+
+
isSchemeNumber: any -> boolean
Produces true if the thing is a scheme number.
isRational: scheme-number -> boolean
Produces true if the number is rational.
isReal: scheme-number -> boolean
Produces true if the number is a real.
isExact: scheme-number -> boolean
Produces true if the number is being represented exactly.
isInteger: scheme-number -> boolean
Produces true if the number is an integer.
toFixnum: scheme-number -> javascript-number
Produces the javascript number closest in interpretation to the
given scheme-number.
toExact: scheme-number -> scheme-number
Converts the number to an exact scheme-number.
add: scheme-number scheme-number -> scheme-number
Adds the two numbers together.
subtract: scheme-number scheme-number -> scheme-number
Subtracts the first number from the second.
mulitply: scheme-number scheme-number -> scheme-number
Multiplies the two numbers together.
divide: scheme-number scheme-number -> scheme-number
Divides the first number by the second.
equals: scheme-number scheme-number -> boolean
Produces true if the two numbers are equal.
eqv: scheme-number scheme-number -> boolean
Produces true if the two numbers are equivalent.
approxEquals: scheme-number scheme-number scheme-number -> boolean
Produces true if the two numbers are approximately equal, within the
bounds of the third argument.
greaterThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is greater than or equal to the second.
lessThanOrEqual: scheme-number scheme-number -> boolean
Produces true if the first number is less than or equal to the second.
greaterThan: scheme-number scheme-number -> boolean
Produces true if the first number is greater than the second.
lessThan: scheme-number scheme-number -> boolean
Produces true if the first number is less than the second.
expt: scheme-number scheme-number -> scheme-number
Produces the first number exponentiated to the second number.
exp: scheme-number -> scheme-number
Produces e exponentiated to the given number.
modulo: scheme-number scheme-number -> scheme-number
Produces the modulo of the two numbers.
numerator: scheme-number -> scheme-number
Produces the numerator of the rational number.
denominator: scheme-number -> scheme-number
Produces the denominator of the rational number.
sqrt: scheme-number -> scheme-number
Produces the square root.
abs: scheme-number -> scheme-number
Produces the absolute value.
floor: scheme-number -> scheme-number
Produces the floor.
round: scheme-number -> scheme-number
Produces the number rounded to the nearest integer.
ceiling: scheme-number -> scheme-number
Produces the ceiling.
conjugate: scheme-number -> scheme-number
Produces the complex conjugate.
magnitude: scheme-number -> scheme-number
Produces the complex magnitude.
log: scheme-number -> scheme-number
Produces the natural log (base e) of the given number.
angle: scheme-number -> scheme-number
Produces the complex angle.
cos: scheme-number -> scheme-number
Produces the cosine.
sin: scheme-number -> scheme-number
Produces the sin.
tan: scheme-number -> scheme-number
Produces the tangent.
asin: scheme-number -> scheme-number
- Produces the arc sine;
+ Produces the arc sine.
acos: scheme-number -> scheme-number
Produces the arc cosine.
atan: scheme-number -> scheme-number
Produces the arc tangent.
+cosh: scheme-number -> scheme-number
+ Produces the hyperbolic cosine.
+
+sinh: scheme-number -> scheme-number
+ Produces the hyperbolic sine.
+
realPart: scheme-number -> scheme-number
Produces the real part of the complex number.
imaginaryPart: scheme-number -> scheme-number
Produces the imaginary part of the complex number.
sqr: scheme-number -> scheme-number
Produces the square.
integerSqrt: scheme-number -> scheme-number
Produces the integer square root.
gcd: scheme-number [scheme-number ...] -> scheme-number
Produces the greatest common divisor.
lcm: scheme-number [scheme-number ...] -> scheme-number
Produces the least common mulitple.
======================================================================
Test suite
Open tests/index.html, which should run our test suite over all the
public functions in js-numbers.
If you notice a good test case is missing, please let the developer
know, and we'll be happy to add it in.
======================================================================
TODO
* Absorb implementations of:
atan2, cosh, sinh, makePolar, makeRectangular, quotient, remainder,
sgn
* Bring over the numeric test cases from Moby.
* Add real documentation.
* Integrate bignums.
- There are two bignum libraries to look into:
jbsn: http://www-cs-students.stanford.edu/~tjw/jsbn/
BigInteger: http://silentmatt.com/biginteger/
We're going to use jsbn: it looks more mature, given that it's been around
for a longer time than the BigInteger package.
* Find out: what is the implementation mentioned in:
Deniz A. Gursel, Ugur Cekmez, R. Emre Basar. "Implementation of
Scheme Numeric System for JavaScript"
http://ab.org.tr/ab10/bildiri/161.pdf
I suspect it's worldwithweb, but it's hard to find.
======================================================================
History
February 2010: initial refactoring from the moby-scheme source tree.
\ No newline at end of file
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 1f260b2..f769856 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -156,1024 +156,1049 @@ if (! this['plt']['lib']['Numbers']) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
return Math.floor(Math.sqrt(x));
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
+ // Implementation of the hyperbolic functions
+ // http://en.wikipedia.org/wiki/Hyperbolic_cosine
+ var cosh = function(x) {
+ return divide(add(exp(x), exp(negate(x))),
+ 2);
+ };
+
+ var sinh = function(x) {
+ return divide(subtract(exp(x), exp(negate(x))),
+ 2);
+ };
+
+
+
+ var makeComplexPolar = function(r, theta) {
+ // special case: if theta is zero, just return
+ // the scalar.
+ if (equals(theta, 0)) {
+ return r;
+ }
+ return makeComplex(multiply(r, cos(theta)),
+ multiply(r, sin(theta)));
+ };
+
+
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (n instanceof Rational) {
n = numerator(n);
}else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (m instanceof Rational) {
m = numerator(m);
} else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
@@ -3131,576 +3156,579 @@ if (! this['plt']['lib']['Numbers']) {
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = [], n = 3, k1 = k-1, km = (1<<k)-1;
g[1] = z.convert(this);
if(k > 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1<<i)) == 0) {
z.sqrTo(r,r2); t = r; r = r2; r2 = t;
if(--i < 0) { i = this.DB-1; --j; }
}
}
return z.revert(r);
}
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s<0)?this.negate():this.clone();
var y = (a.s<0)?a.negate():a.clone();
if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if(g < 0) return x;
if(i < g) g = i;
if(g > 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// END OF copy-and-paste of jsbn.
BigInteger.NEGATIVE_ONE = BigInteger.ONE.negate();
// Other methods we need to add for compatibilty with js-numbers numeric tower.
// add is implemented above.
// subtract is implemented above.
// multiply is implemented above.
// equals is implemented above.
// abs is implemented above.
// negate is defined above.
// makeBignum: string -> BigInteger
var makeBignum = function(s) {
if (typeof(s) === 'number') { s = s + ''; }
var match = s.match(bignumScientificPattern);
if (match) {
return new BigInteger(match[1]+match[2] +
zerostring(Number(match[3]) - match[2].length),
10);
} else {
return new BigInteger(s, 10);
}
};
var zerostring = function(n) {
var buf = [];
for (var i = 0; i < n; i++) {
buf.push('0');
}
return buf.join('');
};
BigInteger.prototype.level = 0;
BigInteger.prototype.liftTo = function(target) {
if (target.level === 1) {
return new Rational(this, 1);
}
if (target.level === 2) {
var fixrep = this.toFixnum();
if (fixrep === Number.POSITIVE_INFINITY)
return TOO_POSITIVE_TO_REPRESENT;
if (fixrep === Number.NEGATIVE_INFINITY)
return TOO_NEGATIVE_TO_REPRESENT;
return new FloatPoint(fixrep);
}
if (target.level === 3) {
return new Complex(this, 0);
}
return throwRuntimeError("invalid level for BigInteger lift", this, target);
};
BigInteger.prototype.isFinite = function() {
return true;
};
BigInteger.prototype.isInteger = function() {
return true;
};
BigInteger.prototype.isRational = function() {
return true;
};
BigInteger.prototype.isReal = function() {
return true;
};
BigInteger.prototype.isExact = function() {
return true;
};
BigInteger.prototype.toExact = function() {
return this;
};
BigInteger.prototype.toFixnum = function() {
var result = 0, str = this.toString(), i;
if (str[0] === '-') {
for (i=1; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return -result;
} else {
for (i=0; i < str.length; i++) {
result = result * 10 + Number(str[i]);
}
return result;
}
};
BigInteger.prototype.greaterThan = function(other) {
return this.compareTo(other) > 0;
};
BigInteger.prototype.greaterThanOrEqual = function(other) {
return this.compareTo(other) >= 0;
};
BigInteger.prototype.lessThan = function(other) {
return this.compareTo(other) < 0;
};
BigInteger.prototype.lessThanOrEqual = function(other) {
return this.compareTo(other) <= 0;
};
// divide: scheme-number -> scheme-number
// WARNING NOTE: we override the old version of divide.
BigInteger.prototype.divide = function(other) {
var quotientAndRemainder = bnDivideAndRemainder.call(this, other);
if (quotientAndRemainder[1].compareTo(BigInteger.ZERO) === 0) {
return quotientAndRemainder[0];
} else {
var result = add(quotientAndRemainder[0],
Rational.makeInstance(quotientAndRemainder[1], other));
return result;
}
};
BigInteger.prototype.numerator = function() {
return this;
};
BigInteger.prototype.denominator = function() {
return 1;
};
// integerSqrt: -> scheme-number
// sqrt: -> scheme-number
// http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// Produce the square root.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
BigInteger.prototype.imaginaryPart = function() {
return 0;
}
BigInteger.prototype.realPart = function() {
return this;
}
// round: -> scheme-number
// Round to the nearest integer.
// External interface of js-numbers:
Numbers['fromFixnum'] = fromFixnum;
Numbers['fromString'] = fromString;
Numbers['makeBignum'] = makeBignum;
Numbers['makeRational'] = Rational.makeInstance;
Numbers['makeFloat'] = FloatPoint.makeInstance;
Numbers['makeComplex'] = Complex.makeInstance;
+ Numbers['makeComplexPolar'] = makeComplexPolar;
Numbers['pi'] = FloatPoint.pi;
Numbers['e'] = FloatPoint.e;
Numbers['nan'] = FloatPoint.nan;
Numbers['negative_inf'] = FloatPoint.neginf;
Numbers['inf'] = FloatPoint.inf;
Numbers['negative_one'] = -1; // Rational.NEGATIVE_ONE;
Numbers['zero'] = 0; // Rational.ZERO;
Numbers['one'] = 1; // Rational.ONE;
Numbers['i'] = plusI;
Numbers['negative_i'] = minusI;
Numbers['negative_zero'] = NEGATIVE_ZERO;
Numbers['onThrowRuntimeError'] = onThrowRuntimeError;
Numbers['isSchemeNumber'] = isSchemeNumber;
Numbers['isRational'] = isRational;
Numbers['isReal'] = isReal;
Numbers['isExact'] = isExact;
Numbers['isInteger'] = isInteger;
Numbers['toFixnum'] = toFixnum;
Numbers['toExact'] = toExact;
Numbers['add'] = add;
Numbers['subtract'] = subtract;
Numbers['multiply'] = multiply;
Numbers['divide'] = divide;
Numbers['equals'] = equals;
Numbers['eqv'] = eqv;
Numbers['approxEquals'] = approxEquals;
Numbers['greaterThanOrEqual'] = greaterThanOrEqual;
Numbers['lessThanOrEqual'] = lessThanOrEqual;
Numbers['greaterThan'] = greaterThan;
Numbers['lessThan'] = lessThan;
Numbers['expt'] = expt;
Numbers['exp'] = exp;
Numbers['modulo'] = modulo;
Numbers['numerator'] = numerator;
Numbers['denominator'] = denominator;
Numbers['integerSqrt'] = integerSqrt;
Numbers['sqrt'] = sqrt;
Numbers['abs'] = abs;
Numbers['floor'] = floor;
Numbers['ceiling'] = ceiling;
Numbers['conjugate'] = conjugate;
Numbers['magnitude'] = magnitude;
Numbers['log'] = log;
Numbers['angle'] = angle;
Numbers['tan'] = tan;
Numbers['atan'] = atan;
Numbers['cos'] = cos;
Numbers['sin'] = sin;
Numbers['tan'] = tan;
Numbers['acos'] = acos;
Numbers['asin'] = asin;
+ Numbers['cosh'] = cosh;
+ Numbers['sinh'] = sinh;
Numbers['imaginaryPart'] = imaginaryPart;
Numbers['realPart'] = realPart;
Numbers['round'] = round;
Numbers['sqr'] = sqr;
Numbers['gcd'] = gcd;
Numbers['lcm'] = lcm;
})();
\ No newline at end of file
diff --git a/test/tests.js b/test/tests.js
index 740d28f..0a06d69 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1,594 +1,604 @@
// Let's open up plt.lib.Numbers to make it easy to test.
var N = plt.lib.Numbers;
for (val in N) {
if (N.hasOwnProperty(val)) {
this[val] = N[val];
}
}
var diffPercent = function(x, y) {
if (typeof(x) === 'number') {
x = fromFixnum(x);
}
if (typeof(y) === 'number') {
y = fromFixnum(y);
}
return Math.abs(toFixnum(divide(subtract(x, y), y)));
};
var assertTrue = function(aVal) {
value_of(aVal).should_be_true();
};
var assertFalse = function(aVal) {
value_of(aVal).should_be_false();
};
var assertEquals = function(expected, aVal) {
value_of(aVal).should_be(expected);
};
var assertFails = function(thunk) {
var isFailed = false;
try {
thunk();
} catch (e) {
isFailed = true;
}
value_of(isFailed).should_be_true();
};
-
describe('rational constructions', {
'constructions' : function() {
value_of(isSchemeNumber(makeRational(42)))
.should_be_true();
value_of(isSchemeNumber(makeRational(21, 2)))
.should_be_true();
value_of(isSchemeNumber(makeRational(2, 1)))
.should_be_true();
value_of(isSchemeNumber(makeRational(-17, -171)))
.should_be_true();
value_of(isSchemeNumber(makeRational(17, -171)))
.should_be_true();
},
'reductions' : function() {
value_of(equals(makeRational(1, 2),
makeRational(5, 10)))
.should_be_true();
value_of(equals(makeRational(1, 2),
makeRational(6, 10)));
value_of(equals(makeRational(1, 2),
makeRational(-1, -2)))
.should_be_true();
}
});
+
+describe('complex construction', {
+ 'polar' : function() {
+ // FIXME: add tests for polar construction
+ },
+ 'non-real inputs should raise errors' : function() {
+ // FIXME: add tests for polar construction
+ }});
+
+
+
describe('built-in constants', {
'pi': function() {
value_of(isSchemeNumber(pi)).should_be_true(); },
'e': function() {
value_of(isSchemeNumber(e)).should_be_true(); },
'nan' : function() {
value_of(isSchemeNumber(nan)).should_be_true(); },
'negative_inf' : function() {
value_of(isSchemeNumber(negative_inf)).should_be_true(); },
'inf' : function() {
value_of(isSchemeNumber(inf)).should_be_true(); },
'negative_one' : function() {
value_of(isSchemeNumber(negative_one)).should_be_true(); },
'zero' : function() {
value_of(isSchemeNumber(zero)).should_be_true(); },
'one' : function() {
value_of(isSchemeNumber(one)).should_be_true(); },
'i' : function() {
value_of(isSchemeNumber(i)).should_be_true(); },
'negative_i' : function() {
value_of(isSchemeNumber(negative_i)).should_be_true(); }
});
describe('fromString', {
'fixnums': function() {
assertEquals(43, fromString("43"));
assertEquals(43, fromString("+43"));
assertEquals(-43, fromString("-43"));
},
'bignums': function() {
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("123456789012345678901234567890"));
assertEquals(makeBignum("123456789012345678901234567890"),
fromString("+123456789012345678901234567890"));
assertEquals(makeBignum("-123456789012345678901234567890"),
fromString("-123456789012345678901234567890"));
},
'rationals': function() {
assertEquals(makeRational(1, 2),
fromString("1/2"));
assertEquals(makeRational(23,34),
fromString("+23/34"));
assertEquals(makeRational(-1, 2),
fromString("-1/2"));
assertEquals(makeRational(1234, 5678910),
fromString("1234/5678910"));
assertEquals(makeRational(makeBignum("99999999999999999999"),
5678910),
fromString("99999999999999999999/5678910"));
assertEquals(makeRational(makeBignum("-13284973298"),
makeBignum("239875239")),
fromString("-13284973298/239875239"));
},
'floats': function() {
assertEquals(makeFloat(42.1), fromString("42.1"));
assertEquals(makeFloat(0.1), fromString(".1"));
assertEquals(makeFloat(0.23), fromString("0.23"));
assertEquals(makeFloat(0.1), fromString("+.1"));
assertEquals(makeFloat(-0.1), fromString("-.1"));
assertEquals(makeFloat(-0.123423), fromString("-.123423"));
assertEquals(makeFloat(123.45), fromString("123.45"));
assertEquals(makeFloat(4123.423), fromString("4.123423e3"));
},
'complex': function() {
assertEquals(makeComplex(0, 1), fromString("0+i"));
assertEquals(makeComplex(0, 1), fromString("0+1i"));
assertEquals(makeComplex(0, makeRational(23, 45)), fromString("0+23/45i"));
assertEquals(makeComplex(0, makeFloat(2.5)), fromString("0+2.5i"));
assertEquals(makeComplex(0, -1), fromString("0-i"));
assertEquals(makeComplex(0, -1), fromString("0-1i"));
assertEquals(makeComplex(0, makeRational(-29, 42)), fromString("0-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(1, makeRational(-29, 42)), fromString("1-29/42i"));
assertEquals(makeComplex(makeFloat(100.5),
makeRational(-29, 42)), fromString("100.5-29/42i"));
assertEquals(makeComplex(0, makeFloat(-3.7)), fromString("0-3.7i"));
assertEquals(makeComplex(inf, makeFloat(-3.7)), fromString("+inf.0-3.7i"));
assertEquals(makeComplex(nan, makeFloat(-3.7)), fromString("+nan.0-3.7i"));
assertEquals(makeComplex(negative_inf, makeFloat(-3.7)),
fromString("-inf.0-3.7i"));
assertEquals(makeComplex(negative_inf, negative_inf),
fromString("-inf.0-inf.0i"));
assertEquals(makeComplex(nan, nan),
fromString("+nan.0+nan.0i"));
assertEquals(makeComplex(-42, -43),
fromString("-42-43i"));
},
'special constants' : function() {
assertEquals(nan, fromString("+nan.0"));
assertEquals(nan, fromString("-nan.0"));
assertEquals(inf, fromString("+inf.0"));
assertEquals(negative_inf, fromString("-inf.0"));
assertTrue(fromString("-0.0") === negative_zero);
},
'malformed': function() {
assertFalse(fromString(""));
assertFalse(fromString(" "));
assertFalse(fromString("sdkfjls"));
assertFalse(fromString("1+1k"));
assertFalse(fromString("1.2.3"));
assertFalse(fromString("1.2/3"));
assertFalse(fromString("--1/3"));
assertFalse(fromString("-1/-3"));
}});
describe('fromFixnum', {
'fixnums': function() {
value_of(equals(fromFixnum(42),
makeRational(42))).should_be_true();
value_of(equals(fromFixnum(43),
makeRational(43))).should_be_true();
value_of(equals(fromFixnum(42),
makeRational(43))).should_be_false();
},
'bignums': function() {
assertEquals(makeBignum("100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e100));
assertEquals(makeBignum("1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
fromFixnum(10e200));
},
'floats': function() {
value_of(equals(fromFixnum(42.1),
makeFloat(42.1))).should_be_true();
}
});
describe('equals', {
'nan': function() {
value_of(equals(nan, nan)).should_be_false();
value_of(equals(nan, 3)).should_be_false();
value_of(equals(nan, makeFloat(239843))).should_be_false();
value_of(equals(nan, makeComplex(239843, 2))).should_be_false();
},
'-0.0': function() {
assertTrue(equals(negative_zero, makeFloat(0)));
assertTrue(equals(negative_zero, 0));
assertTrue(equals(negative_zero, negative_zero));
assertTrue(equals(negative_zero, makeRational(0)));
assertTrue(equals(negative_zero, makeRational(makeBignum("0"))));
assertFalse(equals(negative_zero, 1));
},
'fixnum / fixnum': function() {
value_of(equals(42, 42)).should_be_true();
value_of(equals(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(equals(42, makeBignum("42")));
assertTrue(equals(-42, makeBignum("-42")));
assertTrue(equals(0, makeBignum("0")));
assertFalse(equals(1, makeBignum("0")));
},
'bignum / bignum' : function() {
assertTrue(equals(makeBignum("31415926"),
makeBignum("31415926")));
assertFalse(equals(makeBignum("31415926"),
makeBignum("271818296")));
},
'bignum / rational': function() {
assertTrue(equals(makeBignum("0"),
makeRational(0)));
assertTrue(equals(makeBignum("12345"),
makeRational(12345)));
assertTrue(equals(makeBignum("-12345"),
makeRational(-12345)));
assertFalse(equals(makeBignum("1"),
makeRational(0)));
},
'bignum / float' : function() {
assertTrue(equals(makeBignum("12345"),
makeFloat(12345.0)));
assertTrue(equals(makeBignum("-12345"),
makeFloat(-12345.0)));
assertTrue(equals(fromString("7e40"),
makeFloat(7e40)));
assertTrue(equals(fromString("-7e40"),
makeFloat(-7e40)));
},
'bignum / complex' : function() {
assertTrue(equals(makeBignum("1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertFalse(equals(makeBignum("1.1e2000"),
makeComplex(makeBignum("1e2000"),
0)));
assertTrue(equals(makeBignum("0"),
makeComplex(0, 0)));
assertTrue(equals(makeBignum("91326"),
makeComplex(makeBignum("91326"))));
assertFalse(equals(makeBignum("00000"),
makeComplex(makeBignum("91326"))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210))));
assertTrue(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0))));
assertFalse(equals(makeBignum("90210"),
makeComplex(makeFloat(90210), makeFloat(0.1))));
},
'fixnum / rational': function() {
value_of(equals(0, zero)).should_be_true();
value_of(equals(42, makeRational(84, 2))).should_be_true();
value_of(equals(42, makeRational(84, 3))).should_be_false();
value_of(equals(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(equals(1024, makeFloat(1024))).should_be_true();
value_of(equals(1024, makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex ': function() {
value_of(equals(31337, makeComplex(31337))).should_be_true();
value_of(equals(31337, makeComplex(31337, 1))).should_be_false();
},
'rational / rational ' : function() {
value_of(equals(makeRational(23849),
makeRational(23849))).should_be_true();
value_of(equals(makeRational(23849),
makeRational(23489))).should_be_false();
},
'rational / float': function() {
value_of(equals(makeRational(2),
makeFloat(2))).should_be_true();
value_of(equals(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(equals(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(equals(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(equals(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(equals(pi, pi)).should_be_true();
value_of(equals(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(equals(pi, makeComplex(pi, 0))).should_be_true();
value_of(equals(pi, makeComplex(e, 0))).should_be_false();
},
'complex / complex': function() {
value_of(equals(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(equals(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(equals(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_true();
value_of(equals(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(equals(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
}
});
describe('eqv', {
'nan' : function() {
value_of(eqv(nan,
makeFloat(Number.NaN))).should_be_true();
},
'-0.0' : function() {
assertFalse(eqv(negative_zero, makeFloat(0)));
assertFalse(eqv(negative_zero, 0));
assertTrue(eqv(negative_zero, negative_zero));
assertFalse(eqv(negative_zero, makeRational(0)));
assertFalse(eqv(negative_zero, makeRational(makeBignum("0"))));
assertFalse(eqv(negative_zero, 1));
},
'inf' : function() {
value_of(eqv(inf, inf)).should_be_true();
value_of(eqv(negative_inf, negative_inf)).should_be_true();
assertFalse(eqv(inf, negative_inf));
assertFalse(eqv(inf,
makeBignum("1e3000")));
assertFalse(eqv(negative_inf,
makeBignum("-1e3000")));
},
'fixnum / fixnum': function() {
value_of(eqv(42, 42)).should_be_true();
value_of(eqv(42, 43)).should_be_false();
},
'fixnum / bignum': function() {
assertTrue(eqv(0, makeBignum("0")));
assertTrue(eqv(-1, makeBignum("-1")));
assertTrue(eqv(42, makeBignum("42")));
assertTrue(eqv(123456789, makeBignum("123456789")));
assertTrue(eqv(-123456789, makeBignum("-123456789")));
assertFalse(eqv(-123456788, makeBignum("-123456789")));
},
'bignum / bignum' : function() {
assertTrue(eqv(makeBignum("0"),
makeBignum("0")));
assertTrue(eqv(makeBignum("-1"),
makeBignum("-1")));
assertTrue(eqv(makeBignum("7.3241e324"),
makeBignum("7.3241e324")));
assertFalse(eqv(makeBignum("7.3240e324"),
makeBignum("7.3241e324")));
assertTrue(eqv(makeBignum("-13241e324"),
makeBignum("-13241e324")));
assertTrue(eqv(makeBignum("3"),
makeBignum("3")));
assertFalse(eqv(makeBignum("12345"),
makeBignum("12344")));
},
'bignum / rational': function() {
assertTrue(eqv(makeBignum("0"),
makeRational(0, 1)));
assertTrue(eqv(makeBignum("0"),
makeRational(makeBignum("0"), 1)));
assertTrue(eqv(makeBignum("24"),
makeRational(makeBignum("24"), 1)));
assertTrue(eqv(makeBignum("-1"),
makeRational(-1, 1)));
assertFalse(eqv(makeBignum("0"),
makeRational(-1, 1)));
assertTrue(eqv(makeBignum("3"),
makeRational(makeBignum("3"))));
assertTrue(eqv(makeBignum("27"),
makeRational(27)));
},
'bignum / float' : function() {
assertFalse(eqv(makeBignum("27"),
makeFloat(27.0)));
assertFalse(eqv(makeBignum("0"),
makeFloat(0)));
assertFalse(eqv(makeBignum("1e100"),
makeFloat(1e100)));
assertFalse(eqv(makeBignum("-1e100"),
makeFloat(-1e100)));
},
'bignum / complex' : function() {
assertTrue(eqv(makeBignum("71"),
makeComplex(71)));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeBignum("71"))));
assertTrue(eqv(makeBignum("71"),
makeComplex(makeRational(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71))));
assertFalse(eqv(makeBignum("71"),
makeComplex(70)));
assertFalse(eqv(makeBignum("66"),
makeComplex(makeBignum("42"))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeRational(71, 17))));
assertFalse(eqv(makeBignum("71"),
makeComplex(makeFloat(71), 2)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
0)));
assertTrue(eqv(makeBignum("5e23"),
makeComplex(makeRational(makeBignum("5e23")),
0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeFloat(5e23), 0)));
assertFalse(eqv(makeBignum("5e23"),
makeComplex(makeBignum("5e23"),
1)));
},
'fixnum / rational': function() {
value_of(eqv(42, makeRational(84, 2))).should_be_true();
value_of(eqv(42, makeRational(84, 3))).should_be_false();
value_of(eqv(28, makeRational(84, 3))).should_be_true();
},
'fixnum / float ' : function() {
value_of(eqv(fromFixnum(1024), makeFloat(1024))).should_be_false();
value_of(eqv(fromFixnum(1024), makeFloat(1024.0001))).should_be_false();
},
'fixnum / complex' : function() {
value_of(eqv(10, makeComplex(10))).should_be_true();
value_of(eqv(10, makeComplex(0))).should_be_false();
},
'rational / rational': function() {
value_of(eqv(makeRational(2, 3),
makeRational(2, 3))).should_be_true();
value_of(eqv(makeRational(3, 2),
makeRational(2, 3))).should_be_false();
},
'rational / float': function() {
value_of(eqv(makeRational(2),
makeFloat(2))).should_be_false();
value_of(eqv(makeRational(2),
makeFloat(2.1))).should_be_false();
},
'rational / complex': function() {
value_of(eqv(makeRational(2),
makeComplex(2, 0))).should_be_true();
value_of(eqv(makeRational(2),
makeComplex(2, 1))).should_be_false();
value_of(eqv(makeRational(2),
makeComplex(0, 0))).should_be_false();
},
'float / float': function() {
value_of(eqv(pi, pi)).should_be_true();
value_of(eqv(e, e)).should_be_true();
value_of(eqv(pi, e)).should_be_false();
},
'float / complex': function() {
value_of(eqv(pi, makeComplex(pi))).should_be_true();
value_of(eqv(3, makeComplex(makeFloat(3)))).should_be_false();
value_of(eqv(pi, makeComplex(pi, 1))).should_be_false();
},
'complex / complex': function() {
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 2))).should_be_true();
value_of(eqv(makeComplex(17, 2),
makeComplex(2, 17))).should_be_false();
value_of(eqv(makeComplex(17, 2),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(2, 17),
makeComplex(17, 17))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeFloat(100), 0))).should_be_true();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100.1), 0),
makeComplex(makeRational(100), 0))).should_be_false();
value_of(eqv(makeComplex(makeFloat(100), 0),
makeComplex(makeRational(100), 1))).should_be_false();
},
'tricky case with complex': function() {
value_of(eqv(makeComplex(0,
makeFloat(1.1)),
makeComplex(makeFloat(0.0),
makeFloat(1.1)))).should_be_false();
}
});
describe('isSchemeNumber', {
'strings': function() {
value_of(isSchemeNumber("42")).should_be_false();
value_of(isSchemeNumber(42)).should_be_true();
assertTrue(isSchemeNumber(makeBignum("298747328418794387941798324789421978")));
value_of(isSchemeNumber(makeRational(42, 42))).should_be_true();
value_of(isSchemeNumber(makeFloat(42.2))).should_be_true();
value_of(isSchemeNumber(makeComplex(17))).should_be_true();
value_of(isSchemeNumber(makeComplex(17, 1))).should_be_true();
value_of(isSchemeNumber(makeComplex(makeFloat(17), 1))).should_be_true();
value_of(isSchemeNumber(undefined)).should_be_false();
value_of(isSchemeNumber(null)).should_be_false();
value_of(isSchemeNumber(false)).should_be_false();
}
});
describe('isRational', {
'fixnums': function() {
@@ -1763,1475 +1773,1498 @@ describe('greaterThan', {
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'expt of anything to zero is 1' : function() {
assertTrue(eqv(1, expt(nan, 0)));
assertTrue(eqv(1, expt(inf, 0)));
assertTrue(eqv(1, expt(negative_inf, 0)));
assertTrue(eqv(1, expt(negative_zero, 0)));
assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('ceiling', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
+describe('cosh', {
+ 'fixnums': function() {
+ // FIXME: we're missing this
+ },
+ 'bignums': function() {
+ // FIXME: we're missing this
+ },
+ 'rationals': function() {
+ // FIXME: we're missing this
+ },
+ 'floats': function() {
+ // FIXME: we're missing this
+ },
+ 'complex': function() {
+ // FIXME: we're missing this
+ }
+});
+
+
+describe('sinh', {
+ 'fixnums': function() {
+ // FIXME: we're missing this
+ },
+ 'bignums': function() {
+ // FIXME: we're missing this
+ },
+ 'rationals': function() {
+ // FIXME: we're missing this
+ },
+ 'floats': function() {
+ // FIXME: we're missing this
+ },
+ 'complex': function() {
+ // FIXME: we're missing this
+ }
+});
+
+
+
+
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, integerSqrt(n1));
assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(acos(1), 0));
assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
assertTrue(equals(asin(0),
0));
assertTrue(equals(asin(-1),
multiply(pi, makeRational(-1, 2))));
assertTrue(equals(asin(1),
divide(pi, 2)));
assertTrue(equals(asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(asin(makeComplex(1, 5)),
makeComplex(makeFloat(0.1937931365549321),
makeFloat(2.3309746530493123))));
},
testTan : function(){
assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(isSchemeNumber(pi));
assertTrue(isSchemeNumber(1));
assertTrue(isSchemeNumber(makeFloat(2.718)));
assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
- assertTrue(equals(Kernel.make_dash_polar(makeRational(5),
- makeRational(0)),
- makeComplex(makeRational(5),makeRational( 0))));
- var n = Kernel.make_dash_polar(makeRational(5),
+ assertTrue(equals(makeComplexPolar(makeRational(5),
+ makeRational(0)),
+ makeComplex(makeRational(5),
+ makeRational(0))));
+ var n = makeComplexPolar(makeRational(5),
pi);
var delta = makeFloat(0.0000001);
- assertTrue(approxEquals(Kernel.imag_dash_part(n),
- makeRational(0),
- delta));
- assertTrue(approxEquals(Kernel.real_dash_part(n),
- makeRational(-5),
- delta));
+ assertTrue(approxEquals(imaginaryPart(n),
+ makeRational(0),
+ delta));
+ assertTrue(approxEquals(realPart(n),
+ makeRational(-5),
+ delta));
},
-
- testMakeRectangular: function() {
- assertTrue(equals(Kernel.make_dash_rectangular
- (makeRational(4),
- makeRational(3)),
- makeComplex(makeRational(4),makeRational( 3))));
- assertTrue(equals(Kernel.make_dash_rectangular
- (makeRational(5),
- makeRational(4)),
- makeComplex(makeRational(5),makeRational( 4))));
- },
-
-
testCosh : function(){
- assertTrue(equals(Kernel.cosh(0), 1));
+ assertTrue(equals(cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
- assertTrue(equals(Kernel.denominator(makeRational(7,2)), makeRational(2,1)));
- assertTrue(equals(Kernel.denominator(makeFloat(3)),
- makeFloat(1)));
+ assertTrue(equals(denominator(makeRational(7,2)),
+ makeRational(2,1)));
+ assertTrue(equals(denominator(makeFloat(3)),
+ makeFloat(1)));
},
testNumerator : function(){
- assertTrue(equals(Kernel.numerator(makeRational(7,2)), makeRational(7,1)));
- assertTrue(equals(Kernel.numerator(makeFloat(3)),
- makeFloat(3)));
+ assertTrue(equals(numerator(makeRational(7,2)),
+ makeRational(7,1)));
+ assertTrue(equals(numerator(makeFloat(3)),
+ makeFloat(3)));
},
testIsExact : function() {
- assertTrue(Kernel.exact_question_(makeRational(3)));
- assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
- assertTrue(! Kernel.exact_question_(makeFloat(3.5)));
+ assertTrue(isExact(makeRational(3)));
+ assertTrue(! isExact(makeFloat(3.0)));
+ assertTrue(! isExact(makeFloat(3.5)));
},
- testIsInexact : function() {
- assertTrue(! Kernel.inexact_question_(makeRational(3)));
- assertTrue(Kernel.inexact_question_(makeFloat(3.0)));
- assertTrue(Kernel.inexact_question_(makeFloat(3.5)));
- },
-
-
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0)
));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(plt.types.makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(pi));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.real_question_(String.makeInstance("hi")));
assertTrue(!Kernel.real_question_(Symbol.makeInstance('h')));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), Rational.NEGATIVE_ONE));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
44cfec9a7e86b3085df091581e3f17eee0da9f1d
|
more tests passing.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index c216b16..1f260b2 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -242,1062 +242,1069 @@ if (! this['plt']['lib']['Numbers']) {
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
return Math.floor(Math.sqrt(x));
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
// fastExpt: computes n^k by squaring.
// n^k = (n^2)^(k/2)
// Assumes k is non-negative integer.
var fastExpt = function(n, k) {
var acc = 1;
while (true) {
if (_integerIsZero(k)) {
return acc;
}
if (equals(modulo(k, 2), 0)) {
n = multiply(n, n);
k = divide(k, 2);
} else {
acc = multiply(acc, n);
k = subtract(k, 1);
}
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
- if (m instanceof Complex) {
+ if (m instanceof Rational) {
+ m = numerator(m);
+ } else if (m instanceof Complex) {
m = realPart(m);
}
- if (n instanceof Complex) {
+
+ if (n instanceof Rational) {
+ n = numerator(n);
+ }else if (n instanceof Complex) {
n = realPart(n);
}
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
- if (m instanceof Complex) {
+ if (m instanceof Rational) {
+ m = numerator(m);
+ } else if (m instanceof Complex) {
m = realPart(m);
}
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
return fromFixnum(Math.floor(this.n / this.d));
};
Rational.prototype.ceiling = function() {
return fromFixnum(Math.ceil(this.n / this.d));
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
@@ -1578,1075 +1585,1068 @@ if (! this['plt']['lib']['Numbers']) {
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
- var z2 = Complex.makeInstance(0, Rational.TWO);
+ var z2 = Complex.makeInstance(0, 2);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt = function(y){
if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
return fastExpt(this, y);
}
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
- subtract(
- 1,
- sqr(this));
+ subtract(1, sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
- return multiply(
- Rational.TWO,
- atan(divide(
- this,
- add(
- 1,
- sqrtOneNegateThisSq))));
+ return multiply(2, atan(divide(this,
+ add(1, sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return makeRational(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return makeComplex(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
diff --git a/test/tests.js b/test/tests.js
index a625b00..740d28f 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -1360,1877 +1360,1878 @@ describe('subtract', {
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0.0),
subtract(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0.0),
subtract(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
subtract(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
subtract(0, makeComplex(makeFloat(0), makeFloat(0)))));
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negation': function() {
assertTrue(eqv(subtract(0, 42),
-42));
assertTrue(eqv(subtract(0, -42),
42));
assertTrue(eqv(subtract(0, makeBignum("129834789213412345678910")),
makeBignum("-129834789213412345678910")));
assertTrue(eqv(subtract(0, makeFloat(0.12345)),
makeFloat(-0.12345)));
assertTrue(eqv(subtract(0, makeFloat(0)),
negative_zero));
assertTrue(eqv(subtract(0, negative_zero),
makeFloat(0)));
assertTrue(eqv(subtract(0, nan),
nan));
assertTrue(eqv(subtract(0, inf),
negative_inf));
assertTrue(eqv(subtract(0, negative_inf),
inf));
}
});
describe('multiply', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'negative zero': function() {
assertTrue(eqv(makeFloat(0),
multiply(negative_zero, negative_zero)));
assertTrue(eqv(makeFloat(0),
multiply(makeFloat(0), negative_zero)));
assertTrue(eqv(negative_zero,
multiply(negative_zero, makeFloat(0))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(0, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(-1, makeComplex(makeFloat(0), makeFloat(0)))));
assertTrue(eqv(makeComplex(negative_zero, negative_zero),
multiply(makeComplex(makeFloat(0), makeFloat(0)), -1)));
},
'1 acts as the identity': function() {
assertTrue(eqv(0,
multiply(1, 0)));
assertTrue(eqv(1,
multiply(1, 1)));
assertTrue(eqv(-1,
multiply(1, -1)));
assertTrue(eqv(1234,
multiply(1, 1234)));
assertTrue(eqv(makeBignum("1929365432165895132685321689"),
multiply(1, makeBignum("1929365432165895132685321689"))));
assertTrue(eqv(makeBignum("-1929365432165895132685321689"),
multiply(1, makeBignum("-1929365432165895132685321689"))));
assertTrue(eqv(makeRational(1, 24),
multiply(1, makeRational(1, 24))));
assertTrue(eqv(makeRational(-21, 24),
multiply(1, makeRational(-21, 24))));
assertTrue(eqv(makeFloat(123.45),
multiply(1, makeFloat(123.45))));
assertTrue(eqv(makeFloat(0),
multiply(1, makeFloat(0))));
assertTrue(eqv(nan,
multiply(1, nan)));
assertTrue(eqv(inf,
multiply(1, inf)));
assertTrue(eqv(negative_inf,
multiply(1, negative_inf)));
assertTrue(eqv(negative_zero,
multiply(1, negative_zero)));
}
});
describe('divide', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
},
'division by zeros' : function() {
assertFails(function() {divide(1, 0);});
assertFails(function() {divide(makeRational(1, 2), 0);});
assertFails(function() {divide(makeComplex(1, 2), 0);});
assertTrue(eqv(inf, divide(1, makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(1, negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(-42), makeFloat(0.0))));
assertTrue(eqv(negative_inf, divide(makeFloat(42), negative_zero)));
assertTrue(eqv(inf, divide(makeFloat(-42), negative_zero)));
assertTrue(eqv(inf, divide(makeRational(1, 2), makeFloat(0.0))));
assertTrue(eqv(makeComplex(inf, inf), divide(makeComplex(1, 2), makeFloat(0.0))));
},
'division 0 by 0': function() {
assertFails(function() { divide(0, 0); });
assertFails(function() { divide(makeFloat(0), 0); });
assertTrue(eqv(negative_zero,
divide(makeFloat(0), makeFloat(0))));
assertTrue(eqv(0,
divide(0, makeFloat(0))));
}
});
describe('greaterThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThanOrEqual', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('greaterThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lessThan', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('expt', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum overflows to bignum': function() {
// FIXME
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
+ },
+ 'expt of anything to zero is 1' : function() {
+ assertTrue(eqv(1, expt(nan, 0)));
+ assertTrue(eqv(1, expt(inf, 0)));
+ assertTrue(eqv(1, expt(negative_inf, 0)));
+ assertTrue(eqv(1, expt(negative_zero, 0)));
+ assertTrue(eqv(1, expt(0, 0)));
}
});
describe('modulo', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('numerator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('denominator', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('abs', {
'fixnums': function() {
assertEquals(0, abs(0));
assertEquals(42, abs(42));
assertEquals(42, abs(-42));
assertEquals(1, abs(-1));
},
'bignums': function() {
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("23569236859962835638935268952936825689536829253968"))));
assertTrue(eqv(makeBignum("23569236859962835638935268952936825689536829253968"),
abs(makeBignum("-23569236859962835638935268952936825689536829253968"))));
assertEquals(makeBignum("1"),
abs(makeBignum("-1")));
assertEquals(makeBignum("1"),
abs(makeBignum("1")));
assertEquals(makeBignum("0"),
abs(makeBignum("0")));
},
'rationals': function() {
assertEquals(makeRational(2, 1),
abs(makeRational(-2, 1)));
assertEquals(makeRational(2, 1),
abs(makeRational(2, 1)));
assertEquals(makeRational(0, 1),
abs(makeRational(0, 1)));
assertEquals(makeRational(3298, 28),
abs(makeRational(3298, 28)));
assertEquals(makeRational(3298, 28),
abs(makeRational(-3298, 28)));
},
'floats': function() {
assertEquals(makeFloat(0.0),
abs(makeFloat(0.0)));
assertTrue(eqv(makeFloat(0.0),
abs(negative_zero)));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(1342.7))));
assertTrue(eqv(makeFloat(1342.7),
abs(makeFloat(-1342.7))));
},
'complex': function() {
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(-2, 0))));
assertTrue(eqv(makeComplex(2, 0),
abs(makeComplex(2, 0))));
}
});
describe('floor', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('ceiling', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('conjugate', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('magnitude', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('log', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('angle', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('atan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('cos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(exp(0), 1));
assertTrue(equals(exp(1),
e));
assertTrue(approxEquals(exp(makeRational(2)),
sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
expt(i, i),
exp(multiply(pi, makeRational(-1, 2)))));
assertTrue(equals(
expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(expt(makeComplex(makeRational(3,4),
makeRational(7,8)),
makeRational(2)),
makeComplex(makeRational(-13, 64),
makeRational(21, 16))));
},
testSin : function(){
- assertTrue(equals(Kernel.sin(divide(PI, makeFloat(2))), 1));
+ assertTrue(equals(sin(divide(pi, makeFloat(2))), 1));
},
testCos : function(){
- assertTrue(equals(Kernel.cos(0), 1));
+ assertTrue(equals(cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
- assertEquals(1764, sqr(n1).toFixnum());
+ assertEquals(1764, toFixnum(sqr(n1)));
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
- assertEquals(n2, Kernel.integer_dash_sqrt(n1));
- assertFails(function() { Kernel.integer_dash_sqrt(makeFloat(3.5)); });
+ assertEquals(n2, integerSqrt(n1));
+ assertFails(function() { integerSqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
- assertTrue(equals(Kernel.acos(1), 0));
- assertTrue(equals(Kernel.acos(makeFloat(-1)), PI));
+ assertTrue(equals(acos(1), 0));
+ assertTrue(equals(acos(makeFloat(-1)), pi));
},
testAsin : function(){
- assertTrue(equals(
- Kernel.asin(0), 0));
- assertTrue(equals(Kernel.asin(-1), PI.half().minus()));
- assertTrue(equals(
- Kernel.asin(1), PI.half()));
-
- assertTrue(equals(
- Kernel.asin(makeRational(1, 4)),
- makeFloat(0.25268025514207865)));
-
- assertTrue(equals(
- Kernel.asin(makeComplex(1, 5)),
- makeComplex(0.1937931365549321,
- 2.3309746530493123)));
+ assertTrue(equals(asin(0),
+ 0));
+ assertTrue(equals(asin(-1),
+ multiply(pi, makeRational(-1, 2))));
+ assertTrue(equals(asin(1),
+ divide(pi, 2)));
+ assertTrue(equals(asin(makeRational(1, 4)),
+ makeFloat(0.25268025514207865)));
+ assertTrue(equals(asin(makeComplex(1, 5)),
+ makeComplex(makeFloat(0.1937931365549321),
+ makeFloat(2.3309746530493123))));
},
testTan : function(){
- assertTrue(equals(Kernel.tan(0), 0));
+ assertTrue(equals(tan(0), 0));
},
testComplex_question_ : function(){
- assertTrue(Kernel.complex_question_(PI));
- assertTrue(Kernel.complex_question_(1));
- assertTrue(Kernel.complex_question_(makeFloat(2.718)));
- assertTrue(Kernel.complex_question_(makeComplex(0,1)));
- assertTrue(!Kernel.complex_question_(plt.types.Empty.EMPTY));
- assertTrue(!Kernel.complex_question_(String.makeInstance("hi")));
- assertTrue(!Kernel.complex_question_(Symbol.makeInstance('h')));
+ assertTrue(isSchemeNumber(pi));
+ assertTrue(isSchemeNumber(1));
+ assertTrue(isSchemeNumber(makeFloat(2.718)));
+ assertTrue(isSchemeNumber(makeComplex(0,1)));
},
testMakePolar : function() {
assertTrue(equals(Kernel.make_dash_polar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),makeRational( 0))));
var n = Kernel.make_dash_polar(makeRational(5),
- PI);
+ pi);
var delta = makeFloat(0.0000001);
assertTrue(approxEquals(Kernel.imag_dash_part(n),
makeRational(0),
delta));
assertTrue(approxEquals(Kernel.real_dash_part(n),
makeRational(-5),
delta));
},
testMakeRectangular: function() {
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(4),
makeRational(3)),
makeComplex(makeRational(4),makeRational( 3))));
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(5),
makeRational(4)),
makeComplex(makeRational(5),makeRational( 4))));
},
testCosh : function(){
assertTrue(equals(Kernel.cosh(0), 1));
},
testSinh : function(){
- assertTrue(equals(Kernel.sinh(0), 0));
+ assertTrue(equals(sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(Kernel.denominator(makeRational(7,2)), makeRational(2,1)));
assertTrue(equals(Kernel.denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(Kernel.numerator(makeRational(7,2)), makeRational(7,1)));
assertTrue(equals(Kernel.numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(Kernel.exact_question_(makeRational(3)));
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
assertTrue(! Kernel.exact_question_(makeFloat(3.5)));
},
testIsInexact : function() {
assertTrue(! Kernel.inexact_question_(makeRational(3)));
assertTrue(Kernel.inexact_question_(makeFloat(3.0)));
assertTrue(Kernel.inexact_question_(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0)
));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3)
));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
- assertTrue(equals(Kernel.ceiling(PI), makeFloat(4)));
+ assertTrue(equals(Kernel.ceiling(pi), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
- assertTrue(equals(Kernel.floor(PI), makeFloat(3)));
+ assertTrue(equals(Kernel.floor(pi), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
- assertTrue(equals(Kernel.imag_dash_part(PI), 0));
+ assertTrue(equals(Kernel.imag_dash_part(pi), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
- assertTrue(equals(Kernel.real_dash_part(PI), PI));
+ assertTrue(equals(Kernel.real_dash_part(pi), pi));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(plt.types.makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
- assertTrue(Kernel.real_question_(PI));
+ assertTrue(Kernel.real_question_(pi));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.real_question_(String.makeInstance("hi")));
assertTrue(!Kernel.real_question_(Symbol.makeInstance('h')));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), Rational.NEGATIVE_ONE));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
d8d7334dab4fcacc69840da993a7884013ebcefd
|
Implementing expt
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 4d1a86e..c216b16 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -205,2372 +205,2408 @@ if (! this['plt']['lib']['Numbers']) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
return Math.floor(Math.sqrt(x));
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
+ // fastExpt: computes n^k by squaring.
+ // n^k = (n^2)^(k/2)
+ // Assumes k is non-negative integer.
+ var fastExpt = function(n, k) {
+ var acc = 1;
+ while (true) {
+ if (_integerIsZero(k)) {
+ return acc;
+ }
+ if (equals(modulo(k, 2), 0)) {
+ n = multiply(n, n);
+ k = divide(k, 2);
+ } else {
+ acc = multiply(acc, n);
+ k = subtract(k, 1);
+ }
+ }
+ };
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
+ if (m instanceof Complex) {
+ m = realPart(m);
+ }
+ if (n instanceof Complex) {
+ n = realPart(n);
+ }
+
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
+ if (m instanceof Complex) {
+ m = realPart(m);
+ }
+
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
// log: -> scheme-number
// Produce the log.
// angle: -> scheme-number
// Produce the angle.
// atan: -> scheme-number
// Produce the arc tangent.
// cos: -> scheme-number
// Produce the cosine.
// sin: -> scheme-number
// Produce the sine.
// expt: scheme-number -> scheme-number
// Produce the power to the input.
// exp: -> scheme-number
// Produce e raised to the given power.
// acos: -> scheme-number
// Produce the arc cosine.
// asin: -> scheme-number
// Produce the arc sine.
// imaginaryPart: -> scheme-number
// Produce the imaginary part
// realPart: -> scheme-number
// Produce the real part.
// round: -> scheme-number
// Round to the nearest integer.
// equals: scheme-number -> boolean
// Produce true if the given number of the same type is equal.
//////////////////////////////////////////////////////////////////////
// Rationals
var Rational = function(n, d) {
this.n = n;
this.d = d;
};
Rational.prototype.toString = function() {
if (_integerIsOne(this.d)) {
return this.n.toString() + "";
} else {
return this.n.toString() + "/" + this.d.toString();
}
};
Rational.prototype.level = 1;
Rational.prototype.liftTo = function(target) {
if (target.level === 2)
return new FloatPoint(
_integerDivideToFixnum(this.n, this.d));
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
Rational.prototype.isFinite = function() {
return true;
};
Rational.prototype.equals = function(other) {
return (other instanceof Rational &&
_integerEquals(this.n, other.n) &&
_integerEquals(this.d, other.d));
};
Rational.prototype.isInteger = function() {
return _integerIsOne(this.d);
};
Rational.prototype.isRational = function() {
return true;
};
Rational.prototype.isReal = function() {
return true;
};
Rational.prototype.add = function(other) {
return Rational.makeInstance(_integerAdd(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.subtract = function(other) {
return Rational.makeInstance(_integerSubtract(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n)),
_integerMultiply(this.d, other.d));
};
Rational.prototype.negate = function() {
return Rational.makeInstance(-this.n, d)
};
Rational.prototype.multiply = function(other) {
return Rational.makeInstance(_integerMultiply(this.n, other.n),
_integerMultiply(this.d, other.d));
};
Rational.prototype.divide = function(other) {
if (_integerIsZero(this.d) || _integerIsZero(other.n)) {
throwRuntimeError("division by zero", this, other);
}
return Rational.makeInstance(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.toExact = function() {
return this;
};
Rational.prototype.isExact = function() {
return true;
};
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
return fromFixnum(Math.floor(this.n / this.d));
};
Rational.prototype.ceiling = function() {
return fromFixnum(Math.ceil(this.n / this.d));
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
+ if (isExactInteger(a) && greaterThanOrEqual(a, 0)) {
+ return fastExpt(this, a);
+ }
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// _rationalCache = {};
// (function() {
// var i;
// for(i = -500; i < 500; i++) {
// _rationalCache[i] = new Rational(i, 1);
// }
// })();
// Rational.NEGATIVE_ONE = new Rational(-1, 1);
// Rational.ZERO = new Rational(0, 1);
// Rational.ONE = new Rational(1, 1);
// Rational.TWO = new Rational(2, 1);
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, Rational.TWO);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
- Complex.prototype.expt= function(y){
+
+ Complex.prototype.expt = function(y){
+ if (isExactInteger(y) && greaterThanOrEqual(y, 0)) {
+ return fastExpt(this, y);
+ }
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(
1,
sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(
Rational.TWO,
atan(divide(
this,
add(
1,
sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return makeRational(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return makeComplex(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Basic JavaScript BN library - subset useful for RSA encryption.
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
// (public) Constructor
function BigInteger(a,b,c) {
if(a != null)
if("number" == typeof a) this.fromNumber(a,b,c);
else if(b == null && "string" != typeof a) this.fromString(a,256);
else this.fromString(a,b);
}
// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
while(--n >= 0) {
var v = x*this[i++]+w[j]+c;
c = Math.floor(v/0x4000000);
w[j++] = v&0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
var xl = x&0x7fff, xh = x>>15;
while(--n >= 0) {
var l = this[i]&0x7fff;
var h = this[i++]>>15;
var m = xh*l+h*xl;
l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
w[j++] = l&0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
var xl = x&0x3fff, xh = x>>14;
while(--n >= 0) {
var l = this[i]&0x3fff;
var h = this[i++]>>14;
var m = xh*l+h*xl;
l = xl*l+((m&0x3fff)<<14)+w[j]+c;
c = (l>>28)+(m>>14)+xh*h;
w[j++] = l&0xfffffff;
}
return c;
}
if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
BigInteger.prototype.am = am2;
dbits = 30;
}
else if(j_lm && (navigator.appName != "Netscape")) {
BigInteger.prototype.am = am1;
dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
BigInteger.prototype.am = am3;
dbits = 28;
}
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = [];
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = [], i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r.push(int2char(d)); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r.push(int2char(d));
}
}
return m?r.join(""):"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<cbs)-1;
var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
for(i = this.t-1; i >= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<<bs;
}
for(i = ds-1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<<bs)-1;
r[0] = this[ds]>>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<<cbs;
r[i-ds] = this[i]>>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
r.t = this.t-ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a,r) {
var i = 0, c = 0, m = Math.min(a.t,this.t);
while(i < m) {
c += this[i]-a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
var i = r.t, j = i-ys, t = (q==null)?nbi():q;
y.dlShiftTo(j,t);
if(r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
diff --git a/test/tests.js b/test/tests.js
index f92c42d..a625b00 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2306,938 +2306,931 @@ describe('realPart', {
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, conjugate(n1)));
assertTrue(equals(n2, conjugate(n2)));
assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
assertTrue(equals(n1, magnitude(n1)));
assertTrue(equals(n2, magnitude(n2)));
assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
assertTrue(greaterThan(makeRational(2,1),
makeRational(1,1)));
assertTrue(greaterThan(makeFloat(2.1),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeFloat(2.0),
makeRational(2,1)));
assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
makeRational(2,1)));
assertTrue(lessThan(makeRational(2),
makeRational(3)));
assertTrue(! lessThan(makeRational(3),
makeRational(2)));
},
testComparisonMore: function() {
assertTrue(! greaterThan(makeRational(2),
makeRational(3)));
assertTrue(greaterThan(makeRational(3),
makeRational(2)));
assertTrue(! greaterThan(makeRational(3),
makeRational(3)));
assertTrue(lessThanOrEqual(makeRational(17),
makeRational(17)));
assertTrue(lessThanOrEqual(makeRational(16),
makeRational(17)));
assertTrue(!lessThanOrEqual(makeRational(16),
makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
assertTrue(lessThan(makeRational(5, 1),
upper));
assertTrue(lessThan(makeRational(6, 1),
upper));
assertTrue(lessThan(makeRational(7, 1),
upper));
assertTrue(lessThan(makeRational(8, 1),
upper));
assertTrue(lessThan(makeRational(9, 1),
upper));
for (var i = 0; i < 60; i++) {
assertTrue(lessThan
(num, upper));
num = add(num, 1);
}
},
testAtan : function(){
assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
assertTrue(equals(log(1), 0));
assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
assertTrue(equals(angle(makeFloat(-1)), pi));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
multiply(pi, makeFloat(0.75))));
assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
multiply(pi, makeFloat(-0.75))));
assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
- assertTrue(equals(Kernel.exp(0), 1, []));
- assertTrue(equals(Kernel.exp(1),
- Kernel.e, []));
- assertTrue(equals_tilde_(Kernel.exp(makeRational(2)),
- Kernel.sqr(Kernel.e),
+ assertTrue(equals(exp(0), 1));
+ assertTrue(equals(exp(1),
+ e));
+ assertTrue(approxEquals(exp(makeRational(2)),
+ sqr(e),
makeFloat(0.0001)));
},
testExpt : function(){
- var i = plt.types.makeComplex(
+ var i = makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
- Kernel.expt(i, i),
- Kernel.exp(PI.half().minus())));
+ expt(i, i),
+ exp(multiply(pi, makeRational(-1, 2)))));
- assertTrue(equals(
- Kernel.expt(makeFloat(2),
- makeFloat(3)),
- makeFloat(8)));
+ assertTrue(equals(
+ expt(makeFloat(2),
+ makeFloat(3)),
+ makeFloat(8)));
- assertTrue(equals(
- Kernel.expt(makeComplex(
- makeRational(3,4),
- makeRational(7,8)),
- makeRational(2))),
- makeComplex(makeRational(-13, 64),
- makeRational(21, 16)));
+ assertTrue(equals(expt(makeComplex(makeRational(3,4),
+ makeRational(7,8)),
+ makeRational(2)),
+ makeComplex(makeRational(-13, 64),
+ makeRational(21, 16))));
},
testSin : function(){
assertTrue(equals(Kernel.sin(divide(PI, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(Kernel.cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
- assertEquals(1764, Kernel.sqr(n1).toFixnum());
- assertFails(isTypeMismatch,
- function() { Kernel.sqr("42"); });
+ assertEquals(1764, sqr(n1).toFixnum());
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, Kernel.integer_dash_sqrt(n1));
assertFails(function() { Kernel.integer_dash_sqrt(makeFloat(3.5)); });
},
testSqrt : function(){
- assertTrue(equals(Kernel.sqrt(makeFloat(4)), makeFloat(2)));
- assertTrue(equals(Kernel.sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
+ assertTrue(equals(sqrt(makeFloat(4)), makeFloat(2)));
+ assertTrue(equals(sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(Kernel.acos(1), 0));
assertTrue(equals(Kernel.acos(makeFloat(-1)), PI));
},
testAsin : function(){
assertTrue(equals(
Kernel.asin(0), 0));
assertTrue(equals(Kernel.asin(-1), PI.half().minus()));
assertTrue(equals(
Kernel.asin(1), PI.half()));
assertTrue(equals(
Kernel.asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(
Kernel.asin(makeComplex(1, 5)),
makeComplex(0.1937931365549321,
2.3309746530493123)));
},
testTan : function(){
assertTrue(equals(Kernel.tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(Kernel.complex_question_(PI));
assertTrue(Kernel.complex_question_(1));
assertTrue(Kernel.complex_question_(makeFloat(2.718)));
assertTrue(Kernel.complex_question_(makeComplex(0,1)));
assertTrue(!Kernel.complex_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.complex_question_(String.makeInstance("hi")));
assertTrue(!Kernel.complex_question_(Symbol.makeInstance('h')));
},
testMakePolar : function() {
assertTrue(equals(Kernel.make_dash_polar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),makeRational( 0))));
var n = Kernel.make_dash_polar(makeRational(5),
PI);
var delta = makeFloat(0.0000001);
- assertTrue(equals_tilde_(Kernel.imag_dash_part(n),
+ assertTrue(approxEquals(Kernel.imag_dash_part(n),
makeRational(0),
delta));
- assertTrue(equals_tilde_(Kernel.real_dash_part(n),
+ assertTrue(approxEquals(Kernel.real_dash_part(n),
makeRational(-5),
delta));
},
testMakeRectangular: function() {
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(4),
makeRational(3)),
makeComplex(makeRational(4),makeRational( 3))));
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(5),
makeRational(4)),
makeComplex(makeRational(5),makeRational( 4))));
},
testCosh : function(){
assertTrue(equals(Kernel.cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(Kernel.sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(Kernel.denominator(makeRational(7,2)), makeRational(2,1)));
assertTrue(equals(Kernel.denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(Kernel.numerator(makeRational(7,2)), makeRational(7,1)));
assertTrue(equals(Kernel.numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(Kernel.exact_question_(makeRational(3)));
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
assertTrue(! Kernel.exact_question_(makeFloat(3.5)));
},
testIsInexact : function() {
assertTrue(! Kernel.inexact_question_(makeRational(3)));
assertTrue(Kernel.inexact_question_(makeFloat(3.0)));
assertTrue(Kernel.inexact_question_(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
- makeFloat(3.0),
- []));
+ makeFloat(3.0)
+ ));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
- makeRational(3),
- []));
+ makeRational(3)
+ ));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
- assertTrue(equals(0,
- multiply([0,
- inf]),
- []));
+ assertTrue(equals(0, multiply(0, inf)));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(PI), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(PI), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(PI), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(PI), PI));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(plt.types.makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(PI));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.real_question_(String.makeInstance("hi")));
assertTrue(!Kernel.real_question_(Symbol.makeInstance('h')));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), Rational.NEGATIVE_ONE));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
dyoo/js-numbers
|
fde4fc6ac5dddff612adfff3e1cbe933dbdef7dd
|
up to angle.
|
diff --git a/src/js-numbers.js b/src/js-numbers.js
index 430f631..4d1a86e 100644
--- a/src/js-numbers.js
+++ b/src/js-numbers.js
@@ -1,1024 +1,1025 @@
// Scheme numbers.
if (! this['plt']) {
this['plt'] = {};
}
if (! this['plt']['lib']) {
this['plt']['lib'] = {};
}
if (! this['plt']['lib']['Numbers']) {
this['plt']['lib']['Numbers'] = {};
}
// The numeric tower has the following levels:
// integers
// rationals
// floats
// complex numbers
//
// with the representations:
// integers: fixnum or BigInteger [level=0]
// rationals: Rational [level=1]
// floats: FloatPoint [level=2]
// complex numbers: Complex [level=3]
// We try to stick with the unboxed fixnum representation for
// integers, since that's what scheme programs commonly deal with, and
// we want that common type to be lightweight.
// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
// An integer-scheme-number is either fixnum or BigInteger.
(function() {
// Abbreviation
var Numbers = plt.lib.Numbers;
// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
// Creates a binary function that works either on fixnums or boxnums.
// Applies the appropriate binary function, ensuring that both scheme numbers are
// lifted to the same level.
var makeNumericBinop = function(onFixnums, onBoxednums, options) {
options = options || {};
return function(x, y) {
if (options.isXSpecialCase && options.isXSpecialCase(x))
return options.onXSpecialCase(x, y);
if (options.isYSpecialCase && options.isYSpecialCase(y))
return options.onYSpecialCase(x, y);
if (typeof(x) === 'number' &&
typeof(y) === 'number') {
return onFixnums(x, y);
}
if (typeof(x) === 'number') {
x = liftFixnumInteger(x, y);
}
if (typeof(y) === 'number') {
y = liftFixnumInteger(y, x);
}
if (x.level < y.level) x = x.liftTo(y);
if (y.level < x.level) y = y.liftTo(x);
return onBoxednums(x, y);
};
}
// fromFixnum: fixnum -> scheme-number
var fromFixnum = function(x) {
if (isNaN(x) || (! isFinite(x))) {
return FloatPoint.makeInstance(x);
}
var nf = Math.floor(x);
if (nf === x) {
if (isOverflow(nf)) {
return makeBignum(x);
} else {
return nf;
}
} else {
return FloatPoint.makeInstance(x);
}
};
// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
// Lifts up fixnum integers to a boxed type.
var liftFixnumInteger = function(x, other) {
switch(other.level) {
case 0: // BigInteger
return makeBignum(x);
case 1: // Rational
return new Rational(x, 1);
case 2: // FloatPoint
return new FloatPoint(x);
case 3: // Complex
return new Complex(x, 0);
default:
return throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
}
};
// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// Throws a runtime error with the given message string.
var throwRuntimeError = function(msg, x, y) {
Numbers['onThrowRuntimeError'](msg, x, y);
};
// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
// By default, will throw a new Error with the given message.
// Override Numbers['onThrowRuntimeError'] if you need to do something special.
var onThrowRuntimeError = function(msg, x, y) {
throw new Error(msg);
};
// isSchemeNumber: any -> boolean
// Returns true if the thing is a scheme number.
var isSchemeNumber = function(thing) {
return (typeof(thing) === 'number'
|| (thing instanceof Rational ||
thing instanceof FloatPoint ||
thing instanceof Complex ||
thing instanceof BigInteger));
};
// isRational: scheme-number -> boolean
var isRational = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isRational()));
};
// isReal: scheme-number -> boolean
var isReal = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isReal()));
};
// isExact: scheme-number -> boolean
var isExact = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isExact()));
};
// isInteger: scheme-number -> boolean
var isInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) && n.isInteger()));
};
// isExactInteger: scheme-number -> boolean
var isExactInteger = function(n) {
return (typeof(n) === 'number' ||
(isSchemeNumber(n) &&
n.isInteger() &&
n.isExact()));
}
// toFixnum: scheme-number -> javascript-number
var toFixnum = function(n) {
if (typeof(n) === 'number')
return n;
return n.toFixnum();
};
// toExact: scheme-number -> scheme-number
var toExact = function(n) {
if (typeof(n) === 'number')
return n;
return n.toExact();
};
//////////////////////////////////////////////////////////////////////
// add: scheme-number scheme-number -> scheme-number
var add = makeNumericBinop(
function(x, y) {
var sum = x + y;
if (isOverflow(sum)) {
return (makeBignum(x)).add(makeBignum(y));
} else {
return sum;
}
},
function(x, y) {
return x.add(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return y; },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// subtract: scheme-number scheme-number -> scheme-number
var subtract = makeNumericBinop(
function(x, y) {
var diff = x - y;
if (isOverflow(diff)) {
return (makeBignum(x)).subtract(makeBignum(y));
} else {
return diff;
}
},
function(x, y) {
return x.subtract(y);
},
{isXSpecialCase: function(x) {
return isExactInteger(x) && _integerIsZero(x) },
onXSpecialCase: function(x, y) { return negate(y); },
isYSpecialCase: function(y) {
return isExactInteger(y) && _integerIsZero(y) },
onYSpecialCase: function(x, y) { return x; }
});
// mulitply: scheme-number scheme-number -> scheme-number
var multiply = makeNumericBinop(
function(x, y) {
var prod = x * y;
if (isOverflow(prod)) {
return (makeBignum(x)).multiply(makeBignum(y));
} else {
return prod;
}
},
function(x, y) {
return x.multiply(y);
},
{isXSpecialCase: function(x) {
return (isExactInteger(x) &&
(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
onXSpecialCase: function(x, y) {
if (_integerIsZero(x))
return 0;
if (_integerIsOne(x))
return y;
if (_integerIsNegativeOne(x))
return negate(y);
},
isYSpecialCase: function(y) {
return (isExactInteger(y) &&
(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
onYSpecialCase: function(x, y) {
if (_integerIsZero(y))
return 0;
if (_integerIsOne(y))
return x;
if (_integerIsNegativeOne(y))
return negate(x);
}
});
// divide: scheme-number scheme-number -> scheme-number
var divide = makeNumericBinop(
function(x, y) {
if (_integerIsZero(y))
throwRuntimeError("division by zero", x, y);
var div = x / y;
if (isOverflow(div)) {
return (makeBignum(x)).divide(makeBignum(y));
} else if (Math.floor(div) !== div) {
return Rational.makeInstance(x, y);
} else {
return div;
}
},
function(x, y) {
return x.divide(y);
});
// equals: scheme-number scheme-number -> boolean
var equals = makeNumericBinop(
function(x, y) {
return x === y;
},
function(x, y) {
return x.equals(y);
});
// eqv: scheme-number scheme-number -> boolean
var eqv = function(x, y) {
if (x === y)
return true;
if (typeof(x) === 'number' && typeof(y) === 'number')
return x === y;
if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
return x === y;
if (x instanceof Complex || y instanceof Complex) {
return (eqv(realPart(x), realPart(y)) &&
eqv(imaginaryPart(x), imaginaryPart(y)));
}
var ex = isExact(x), ey = isExact(y);
return (((ex && ey) || (!ex && !ey)) && equals(x, y));
};
// approxEqual: scheme-number scheme-number scheme-number -> boolean
var approxEquals = function(x, y, delta) {
return lessThan(abs(subtract(x, y)),
delta);
};
// greaterThanOrEqual: scheme-number scheme-number -> boolean
var greaterThanOrEqual = makeNumericBinop(
function(x, y) {
return x >= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError(
"greaterThanOrEqual: couldn't be applied to complex number", x, y);
return x.greaterThanOrEqual(y);
});
// lessThanOrEqual: scheme-number scheme-number -> boolean
var lessThanOrEqual = makeNumericBinop(
function(x, y){
return x <= y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThanOrEqual: couldn't be applied to complex number", x, y);
return x.lessThanOrEqual(y);
});
// greaterThan: scheme-number scheme-number -> boolean
var greaterThan = makeNumericBinop(
function(x, y){
return x > y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("greaterThan: couldn't be applied to complex number", x, y);
return x.greaterThan(y);
});
// lessThan: scheme-number scheme-number -> boolean
var lessThan = makeNumericBinop(
function(x, y){
return x < y;
},
function(x, y) {
if (!(isReal(x) && isReal(y)))
throwRuntimeError("lessThan: couldn't be applied to complex number", x, y);
return x.lessThan(y);
});
// expt: scheme-number scheme-number -> scheme-number
var expt = makeNumericBinop(
function(x, y){
if (y >= 0) {
var pow = Math.pow(x, y);
if (isOverflow(pow)) {
return (makeBignum(x)).expt(makeBignum(y));
} else {
return pow;
}
} else {
return (makeBignum(x)).expt(makeBignum(y));
}
},
function(x, y) {
return x.expt(y);
});
// exp: scheme-number -> scheme-number
var exp = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.exp(n));
}
return n.exp();
};
// modulo: scheme-number scheme-number -> scheme-number
var modulo = function(m, n) {
if (! isInteger(m)) {
throwRuntimeError('modulo: the first argument '
+ m + " is not an integer.", m, n);
}
if (! isInteger(n)) {
throwRuntimeError('modulo: the second argument '
+ n + " is not an integer.", m, n);
}
var result;
if (typeof(m) === 'number') {
result = m % n;
if (n < 0) {
if (result <= 0)
return result;
else
return result + n;
} else {
if (result < 0)
return result + n;
else
return result;
}
}
result = _integerModulo(floor(m), floor(n));
// The sign of the result should match the sign of n.
if (lessThan(n, 0)) {
if (lessThanOrEqual(result, 0)) {
return result;
}
return add(result, n);
} else {
if (lessThan(result, 0)) {
return add(result, n);
}
return result;
}
};
// numerator: scheme-number -> scheme-number
var numerator = function(n) {
if (typeof(n) === 'number')
return n;
return n.numerator();
};
// denominator: scheme-number -> scheme-number
var denominator = function(n) {
if (typeof(n) === 'number')
return 1;
return n.denominator();
};
// sqrt: scheme-number -> scheme-number
var sqrt = function(n) {
if (typeof(n) === 'number') {
if (n >= 0) {
var result = Math.sqrt(n);
if (Math.floor(result) === result) {
return result;
} else {
return FloatPoint.makeInstance(result);
}
} else {
return (makeBignum(n)).sqrt();
}
}
return n.sqrt();
};
// abs: scheme-number -> scheme-number
var abs = function(n) {
if (typeof(n) === 'number') {
return Math.abs(n);
}
return n.abs();
};
// floor: scheme-number -> scheme-number
var floor = function(n) {
if (typeof(n) === 'number')
return n;
return n.floor();
};
// ceiling: scheme-number -> scheme-number
var ceiling = function(n) {
if (typeof(n) === 'number')
return n;
return n.ceiling();
};
// conjugate: scheme-number -> scheme-number
var conjugate = function(n) {
if (typeof(n) === 'number')
return n;
return n.conjugate();
};
// magnitude: scheme-number -> scheme-number
var magnitude = function(n) {
if (typeof(n) === 'number')
return Math.abs(n);
return n.magnitude();
};
+
// log: scheme-number -> scheme-number
var log = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.log(n));
}
return n.log();
};
// angle: scheme-number -> scheme-number
var angle = function(n) {
if (typeof(n) === 'number') {
if (n > 0)
return 0;
else
return FloatPoint.pi;
}
return n.angle();
};
// tan: scheme-number -> scheme-number
var tan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.tan(n));
}
return n.tan();
};
// atan: scheme-number -> scheme-number
var atan = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.atan(n));
}
return n.atan();
};
// cos: scheme-number -> scheme-number
var cos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.cos(n));
}
return n.cos();
};
// sin: scheme-number -> scheme-number
var sin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.sin(n));
}
return n.sin();
};
// acos: scheme-number -> scheme-number
var acos = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.acos(n));
}
return n.acos();
};
// asin: scheme-number -> scheme-number
var asin = function(n) {
if (typeof(n) === 'number') {
return FloatPoint.makeInstance(Math.asin(n));
}
return n.asin();
};
// imaginaryPart: scheme-number -> scheme-number
var imaginaryPart = function(n) {
if (typeof(n) === 'number') {
return 0;
}
return n.imaginaryPart();
};
// realPart: scheme-number -> scheme-number
var realPart = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.realPart();
};
// round: scheme-number -> scheme-number
var round = function(n) {
if (typeof(n) === 'number') {
return n;
}
return n.round();
};
// sqr: scheme-number -> scheme-number
var sqr = function(x) {
return multiply(x, x);
};
// integerSqrt: scheme-number -> scheme-number
var integerSqrt = function(x) {
if (typeof (x) === 'number') {
return Math.floor(Math.sqrt(x));
}
return x.integerSqrt();
};
// gcd: scheme-number [scheme-number ...] -> scheme-number
var gcd = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('gcd: the argument ' + first.toString() +
" is not an integer.", first);
}
var a = abs(first), t, b;
for(var i = 0; i < rest.length; i++) {
b = abs(rest[i]);
if (! isInteger(b)) {
throwRuntimeError('gcd: the argument ' + b.toString() +
" is not an integer.", b);
}
while (! _integerIsZero(b)) {
t = a;
a = b;
b = integerModulo(t, b);
}
}
return a;
};
// lcm: scheme-number [scheme-number ...] -> scheme-number
var lcm = function(first, rest) {
if (! isInteger(first)) {
throwRuntimeError('lcm: the argument ' + first.toString() +
" is not an integer.", first);
}
var result = abs(first);
if (_integerIsZero(result)) { return 0; }
for (var i = 0; i < rest.length; i++) {
if (! isInteger(rest[i])) {
throwRuntimeError('lcm: the argument ' + rest[i].toString() +
" is not an integer.", rest[i]);
}
var divisor = gcd(result, rest[i]);
if (_integerIsZero(divisor)) {
return 0;
}
result = divide(multiply(result, rest[i]), divisor);
}
return result;
};
//////////////////////////////////////////////////////////////////////
// Helpers
// IsFinite: scheme-number -> boolean
// Returns true if the scheme number is finite or not.
var isSchemeNumberFinite = function(n) {
if (typeof(n) === 'number') {
return isFinite(n);
} else {
return n.isFinite();
}
};
// isOverflow: javascript-number -> boolean
// Returns true if we consider the number an overflow.
var MIN_FIXNUM = -(9e15);
var MAX_FIXNUM = (9e15);
var isOverflow = function(n) {
return (n < MIN_FIXNUM || MAX_FIXNUM < n);
};
// negate: scheme-number -> scheme-number
// multiplies a number times -1.
var negate = function(n) {
if (typeof(n) === 'number') {
return -n;
}
return n.negate();
};
// halve: scheme-number -> scheme-number
// Divide a number by 2.
var halve = function(n) {
return divide(n, 2);
};
// timesI: scheme-number scheme-number
// multiplies a number times i.
var timesI = function(x) {
return multiply(x, plusI);
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Integer operations
// Integers are either represented as fixnums or as BigIntegers.
// makeIntegerBinop: (fixnum fixnum -> X) (BigInteger BigInteger -> X) -> X
// Helper to collect the common logic for coersing integer fixnums or bignums to a
// common type before doing an operation.
var makeIntegerBinop = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m, n) {
if (typeof(m) === 'number' && typeof(n) === 'number') {
var result = onFixnums(m, n);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint || n instanceof FloatPoint) {
if (options.doNotCoerseToFloating) {
return onFixnums(toFixnum(m), toFixnum(n));
}
else {
return FloatPoint.makeInstance(
onFixnums(toFixnum(m), toFixnum(n)));
}
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
if (typeof(n) === 'number') {
n = makeBignum(n);
}
return onBignums(m, n);
});
};
var makeIntegerUnOp = function(onFixnums, onBignums, options) {
options = options || {};
return (function(m) {
if (typeof(m) === 'number') {
var result = onFixnums(m);
if (! isOverflow(result) ||
(options.ignoreOverflow)) {
return result;
}
}
if (m instanceof FloatPoint) {
return onFixnums(toFixnum(m));
}
if (typeof(m) === 'number') {
m = makeBignum(m);
}
return onBignums(m);
});
};
// _integerModulo: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerModulo = makeIntegerBinop(
function(m, n) {
return m % n;
},
function(m, n) {
return bnMod.call(m, n);
});
// _integerGcd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerGcd = makeIntegerBinop(
function(a, b) {
var t;
while (b !== 0) {
t = a;
a = b;
b = t % b;
}
return a;
},
function(m, n) {
return bnGCD.call(m, n);
});
// _integerIsZero: integer-scheme-number -> boolean
// Returns true if the number is zero.
var _integerIsZero = makeIntegerUnOp(
function(n){
return n === 0;
},
function(n) {
return bnEquals.call(n, BigInteger.ZERO);
}
);
// _integerIsOne: integer-scheme-number -> boolean
var _integerIsOne = makeIntegerUnOp(
function(n) {
return n === 1;
},
function(n) {
return bnEquals.call(n, BigInteger.ONE);
});
// _integerIsNegativeOne: integer-scheme-number -> boolean
var _integerIsNegativeOne = makeIntegerUnOp(
function(n) {
return n === -1;
},
function(n) {
return bnEquals.call(n, BigInteger.NEGATIVE_ONE);
});
// _integerAdd: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerAdd = makeIntegerBinop(
function(m, n) {
return m + n;
},
function(m, n) {
return bnAdd.call(m, n);
});
// _integerSubtract: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerSubtract = makeIntegerBinop(
function(m, n) {
return m - n;
},
function(m, n) {
return bnSubtract.call(m, n);
});
// _integerMultiply: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerMultiply = makeIntegerBinop(
function(m, n) {
return m * n;
},
function(m, n) {
return bnMultiply.call(m, n);
});
//_integerQuotient: integer-scheme-number integer-scheme-number -> integer-scheme-number
var _integerQuotient = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return bnDivide.call(m, n);
});
// _integerDivideToFixnum: integer-scheme-number integer-scheme-number -> fixnum
var _integerDivideToFixnum = makeIntegerBinop(
function(m, n) {
return m / n;
},
function(m, n) {
return toFixnum(m) / toFixnum(n);
},
{ignoreOverflow: true,
doNotCoerseToFloating: true});
// _integerEquals: integer-scheme-number integer-scheme-number -> boolean
var _integerEquals = makeIntegerBinop(
function(m, n) {
return m === n;
},
function(m, n) {
return bnEquals.call(m, n);
},
{doNotCoerseToFloating: true});
// _integerGreaterThan: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThan = makeIntegerBinop(
function(m, n) {
return m > n;
},
function(m, n) {
return bnCompareTo.call(m, n) > 0;
},
{doNotCoerseToFloating: true});
// _integerLessThan: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThan = makeIntegerBinop(
function(m, n) {
return m < n;
},
function(m, n) {
return bnCompareTo.call(m, n) < 0;
},
{doNotCoerseToFloating: true});
// _integerGreaterThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerGreaterThanOrEqual = makeIntegerBinop(
function(m, n) {
return m >= n;
},
function(m, n) {
return bnCompareTo.call(m, n) >= 0;
},
{doNotCoerseToFloating: true});
// _integerLessThanOrEqual: integer-scheme-number integer-scheme-number -> boolean
var _integerLessThanOrEqual = makeIntegerBinop(
function(m, n) {
return m <= n;
},
function(m, n) {
return bnCompareTo.call(m, n) <= 0;
},
{doNotCoerseToFloating: true});
//////////////////////////////////////////////////////////////////////
// The boxed number types are expected to implement the following
// interface.
//
// toString: -> string
// level: number
// liftTo: scheme-number -> scheme-number
// isFinite: -> boolean
// isInteger: -> boolean
// Produce true if this number can be coersed into an integer.
// isRational: -> boolean
// Produce true if the number is rational.
// isReal: -> boolean
// Produce true if the number is real.
// isExact: -> boolean
// Produce true if the number is exact
// toExact: -> scheme-number
// Produce an exact number.
// toFixnum: -> javascript-number
// Produce a javascript number.
// greaterThan: scheme-number -> boolean
// Compare against instance of the same type.
// greaterThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// lessThan: scheme-number -> boolean
// Compare against instance of the same type.
// lessThanOrEqual: scheme-number -> boolean
// Compare against instance of the same type.
// add: scheme-number -> scheme-number
// Add with an instance of the same type.
// subtract: scheme-number -> scheme-number
// Subtract with an instance of the same type.
// multiply: scheme-number -> scheme-number
// Multiply with an instance of the same type.
// divide: scheme-number -> scheme-number
// Divide with an instance of the same type.
// numerator: -> scheme-number
// Return the numerator.
// denominator: -> scheme-number
// Return the denominator.
// integerSqrt: -> scheme-number
// Produce the integer square root.
// sqrt: -> scheme-number
// Produce the square root.
// abs: -> scheme-number
// Produce the absolute value.
// floor: -> scheme-number
// Produce the floor.
// ceiling: -> scheme-number
// Produce the ceiling.
// conjugate: -> scheme-number
// Produce the conjugate.
// magnitude: -> scheme-number
// Produce the magnitude.
@@ -1161,1025 +1162,1025 @@ if (! this['plt']['lib']['Numbers']) {
Rational.prototype.toFixnum = function() {
return _integerDivideToFixnum(this.n, this.d);
};
Rational.prototype.numerator = function() {
return this.n;
};
Rational.prototype.denominator = function() {
return this.d;
};
// FIXME: up to this point I've modified Rational to use the _integer functions.
// I need to fix up the rest of Rational.
Rational.prototype.greaterThan = function(other) {
return _integerGreaterThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.greaterThanOrEqual = function(other) {
return _integerGreaterThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThan = function(other) {
return _integerLessThan(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.lessThanOrEqual = function(other) {
return _integerLessThanOrEqual(_integerMultiply(this.n, other.d),
_integerMultiply(this.d, other.n));
};
Rational.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Rational.prototype.sqrt = function() {
if (_integerGreaterThanOrEqual(this.n, 0)) {
var newN = sqrt(this.n);
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Rational.makeInstance(newN, newD);
} else {
return FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD));
}
} else {
var newN = sqrt(negate(this.n));
var newD = sqrt(this.d);
if (equals(floor(newN), newN) &&
equals(floor(newD), newD)) {
return Complex.makeInstance(
0,
Rational.makeInstance(newN, newD));
} else {
return Complex.makeInstance(
0,
FloatPoint.makeInstance(_integerDivideToFixnum(newN, newD)));
}
}
};
Rational.prototype.abs = function() {
return Rational.makeInstance(abs(this.n),
this.d);
};
Rational.prototype.floor = function() {
return fromFixnum(Math.floor(this.n / this.d));
};
Rational.prototype.ceiling = function() {
return fromFixnum(Math.ceil(this.n / this.d));
};
Rational.prototype.conjugate = function() {
return this;
};
Rational.prototype.magnitude = Rational.prototype.abs;
Rational.prototype.log = function(){
return FloatPoint.makeInstance(Math.log(this.n / this.d));
};
Rational.prototype.angle = function(){
if (_integerIsZero(this.n))
return 0;
if (_integerGreaterThan(this.n, 0))
return 0;
else
return FloatPoint.pi;
};
Rational.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.expt = function(a){
return FloatPoint.makeInstance(Math.pow(_integerDivideToFixnum(this.n, this.d),
_integerDivideToFixnum(a.n, a.d)));
};
Rational.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(_integerDivideToFixnum(this.n, this.d)));
};
Rational.prototype.imaginaryPart = function(){
return 0;
};
Rational.prototype.realPart = function(){
return this;
};
Rational.prototype.round = function() {
// FIXME: not correct when values are bignums
if (equals(this.d, 2)) {
// Round to even if it's a n/2
var v = _integerDivideToFixnum(this.n, this.d);
var fl = Math.floor(v);
var ce = Math.ceil(v);
if (_integerIsZero(fl % 2)) {
return fromFixnum(fl);
}
else {
return fromFixnum(ce);
}
} else {
return fromFixnum(Math.round(this.n / this.d));
}
};
var _rationalCache = {};
Rational.makeInstance = function(n, d) {
if (n === undefined)
throwRuntimeError("n undefined", n, d);
if (d === undefined) { d = 1; }
if (_integerLessThan(d, 0)) {
n = negate(n);
d = negate(d);
}
var divisor = _integerGcd(abs(n), abs(d));
n = _integerQuotient(n, divisor);
d = _integerQuotient(d, divisor);
// Optimization: if we can get around construction the rational
// in favor of just returning n, do it:
if (_integerIsOne(d) || _integerIsZero(n)) {
return n;
}
return new Rational(n, d);
};
// _rationalCache = {};
// (function() {
// var i;
// for(i = -500; i < 500; i++) {
// _rationalCache[i] = new Rational(i, 1);
// }
// })();
// Rational.NEGATIVE_ONE = new Rational(-1, 1);
// Rational.ZERO = new Rational(0, 1);
// Rational.ONE = new Rational(1, 1);
// Rational.TWO = new Rational(2, 1);
// Floating Point numbers
var FloatPoint = function(n) {
this.n = n;
};
FloatPoint = FloatPoint;
var NaN = new FloatPoint(Number.NaN);
var inf = new FloatPoint(Number.POSITIVE_INFINITY);
var neginf = new FloatPoint(Number.NEGATIVE_INFINITY);
// We use these two constants to represent the floating-point coersion
// of bignums that can't be represented with fidelity.
var TOO_POSITIVE_TO_REPRESENT = new FloatPoint(Number.POSITIVE_INFINITY);
var TOO_NEGATIVE_TO_REPRESENT = new FloatPoint(Number.NEGATIVE_INFINITY);
// Negative zero is a distinguished value representing -0.0.
// There should only be one instance for -0.0.
var NEGATIVE_ZERO = new FloatPoint(0);
FloatPoint.pi = new FloatPoint(Math.PI);
FloatPoint.e = new FloatPoint(Math.E);
FloatPoint.nan = NaN;
FloatPoint.inf = inf;
FloatPoint.neginf = neginf;
FloatPoint.makeInstance = function(n) {
if (isNaN(n)) {
return FloatPoint.nan;
} else if (n === Number.POSITIVE_INFINITY) {
return FloatPoint.inf;
} else if (n === Number.NEGATIVE_INFINITY) {
return FloatPoint.neginf;
}
return new FloatPoint(n);
};
FloatPoint.prototype.isFinite = function() {
return (isFinite(this.n) ||
this === TOO_POSITIVE_TO_REPRESENT ||
this === TOO_NEGATIVE_TO_REPRESENT);
};
FloatPoint.prototype.toExact = function() {
// The precision of ieee is about 16 decimal digits, which we use here.
if (! isFinite(this.n) || isNaN(this.n)) {
throwRuntimeError("toExact: no exact representation for " + this, this);
}
var fracPart = this.n - Math.floor(this.n);
var intPart = this.n - fracPart;
return add(intPart,
Rational.makeInstance(Math.floor(fracPart * 10e16), 10e16));
};
FloatPoint.prototype.isExact = function() {
return false;
};
FloatPoint.prototype.level = 2;
FloatPoint.prototype.liftTo = function(target) {
if (target.level === 3)
return new Complex(this, 0);
return throwRuntimeError("invalid level of Number", this, target);
};
FloatPoint.prototype.toString = function() {
if (isNaN(this.n))
return "+nan.0";
if (this.n === Number.POSITIVE_INFINITY)
return "+inf.0";
if (this.n === Number.NEGATIVE_INFINITY)
return "-inf.0";
if (this === NEGATIVE_ZERO)
return "-0.0";
if (this.n === 0)
return "0.0";
return this.n.toString();
};
FloatPoint.prototype.equals = function(other, aUnionFind) {
return ((other instanceof FloatPoint) &&
((this.n === other.n)));
};
FloatPoint.prototype.isRational = function() {
return this.isFinite();
};
FloatPoint.prototype.isInteger = function() {
return this.isFinite() && this.n === Math.floor(this.n);
};
FloatPoint.prototype.isReal = function() {
return true;
};
// sign: Number -> {-1, 0, 1}
var sign = function(n) {
if (lessThan(n, 0)) {
return -1;
} else if (greaterThan(n, 0)) {
return 1;
} else if (n === NEGATIVE_ZERO) {
return -1;
} else {
return 0;
}
};
FloatPoint.prototype.add = function(other) {
if (this.isFinite() && other.isFinite()) {
if (this === NEGATIVE_ZERO && other === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(this.n + other.n);
} else {
if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (this.isFinite() && ! other.isFinite()) {
return other;
} else if (!this.isFinite() && other.isFinite()) {
return this;
} else {
return ((sign(this) * sign(other) === 1) ?
this : NaN);
};
}
};
FloatPoint.prototype.subtract = function(other) {
if (this.isFinite() && other.isFinite()) {
var result = this.n - other.n;
if (result === 0.0) {
if (other.n === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(result);
}
else if (this.n === NEGATIVE_ZERO) {
return NEGATIVE_ZERO;
}
}
return FloatPoint.makeInstance(result);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && ! other.isFinite()) {
if (sign(this) === sign(other)) {
return NaN;
} else {
return this;
}
} else if (this.isFinite()) {
return multiply(other, -1);
} else { // other.isFinite()
return this;
}
};
FloatPoint.prototype.negate = function() {
if (this === NEGATIVE_ZERO) {
return FloatPoint.makeInstance(0);
} else if (this.n === 0) {
return NEGATIVE_ZERO;
}
return FloatPoint.makeInstance(-this.n);
};
FloatPoint.prototype.multiply = function(other) {
if (this.n === 0 || other.n === 0) { return FloatPoint.makeInstance(0.0); }
if (this.isFinite() && other.isFinite()) {
var product = this.n * other.n;
if (product !== 0) {
return FloatPoint.makeInstance(product);
}
return sign(this) * sign(other) == 1 ?
FloatPoint.makeInstance(0) : NEGATIVE_ZERO;
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
}
};
FloatPoint.prototype.divide = function(other) {
if (this.isFinite() && other.isFinite()) {
if (other.n === 0) {
return throwRuntimeError("division by zero", this, other);
}
return FloatPoint.makeInstance(this.n / other.n);
} else if (isNaN(this.n) || isNaN(other.n)) {
return NaN;
} else if (! this.isFinite() && !other.isFinite()) {
return NaN;
} else if (this.isFinite() && !other.isFinite()) {
return FloatPoint.makeInstance(0.0);
} else if (! this.isFinite() && other.isFinite()) {
return ((sign(this) * sign(other) === 1) ? inf : neginf);
} else {
return throwRuntimeError("impossible", this, other);
}
};
FloatPoint.prototype.toFixnum = function() {
return this.n;
};
FloatPoint.prototype.numerator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(parseFloat(match[1] + match[2]));
} else {
return this;
}
};
FloatPoint.prototype.denominator = function() {
var stringRep = this.n.toString();
var match = stringRep.match(/^(.*)\.(.*)$/);
if (match) {
return FloatPoint.makeInstance(Math.pow(10, match[2].length));
} else {
return FloatPoint.makeInstance(1.0);
}
};
FloatPoint.prototype.floor = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.floor(this.n));
};
FloatPoint.prototype.ceiling = function() {
if (! isFinite(this.n)) {
return this;
}
return fromFixnum(Math.ceil(this.n));
};
FloatPoint.prototype.greaterThan = function(other) {
return this.n > other.n;
};
FloatPoint.prototype.greaterThanOrEqual = function(other) {
return this.n >= other.n;
};
FloatPoint.prototype.lessThan = function(other) {
return this.n < other.n;
};
FloatPoint.prototype.lessThanOrEqual = function(other) {
return this.n <= other.n;
};
FloatPoint.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
FloatPoint.prototype.sqrt = function() {
if (this.n < 0) {
var result = Complex.makeInstance(
0,
FloatPoint.makeInstance(Math.sqrt(-this.n)));
return result;
} else {
return FloatPoint.makeInstance(Math.sqrt(this.n));
}
};
FloatPoint.prototype.abs = function() {
return FloatPoint.makeInstance(Math.abs(this.n));
};
FloatPoint.prototype.log = function(){
if (this.n < 0)
- return log(Complex.makeInstance(this, 0));
+ return (new Complex(this, 0)).log();
else
return FloatPoint.makeInstance(Math.log(this.n));
};
FloatPoint.prototype.angle = function(){
if (0 === this.n)
return 0;
if (this.n > 0)
return 0;
else
return FloatPoint.pi;
};
FloatPoint.prototype.tan = function(){
return FloatPoint.makeInstance(Math.tan(this.n));
};
FloatPoint.prototype.atan = function(){
return FloatPoint.makeInstance(Math.atan(this.n));
};
FloatPoint.prototype.cos = function(){
return FloatPoint.makeInstance(Math.cos(this.n));
};
FloatPoint.prototype.sin = function(){
return FloatPoint.makeInstance(Math.sin(this.n));
};
FloatPoint.prototype.expt = function(a){
if (this.n === 1) {
if (a.isFinite()) {
return this;
} else if (isNaN(a.n)){
return this;
} else {
return this;
}
} else {
return FloatPoint.makeInstance(Math.pow(this.n, a.n));
}
};
FloatPoint.prototype.exp = function(){
return FloatPoint.makeInstance(Math.exp(this.n));
};
FloatPoint.prototype.acos = function(){
return FloatPoint.makeInstance(Math.acos(this.n));
};
FloatPoint.prototype.asin = function(){
return FloatPoint.makeInstance(Math.asin(this.n));
};
FloatPoint.prototype.imaginaryPart = function(){
return 0;
};
FloatPoint.prototype.realPart = function(){
return this;
};
FloatPoint.prototype.round = function(){
if (isFinite(this.n)) {
if (Math.abs(Math.floor(this.n) - this.n) === 0.5) {
if (Math.floor(this.n) % 2 === 0)
return fromFixnum(Math.floor(this.n));
return fromFixnum(Math.ceil(this.n));
} else {
return fromFixnum(Math.round(this.n));
}
} else {
return this;
}
};
FloatPoint.prototype.conjugate = function() {
return this;
};
FloatPoint.prototype.magnitude = FloatPoint.prototype.abs;
//////////////////////////////////////////////////////////////////////
// Complex numbers
//////////////////////////////////////////////////////////////////////
var Complex = function(r, i){
this.r = r;
this.i = i;
};
// Constructs a complex number from two basic number r and i. r and i can
// either be plt.type.Rational or plt.type.FloatPoint.
Complex.makeInstance = function(r, i){
if (i === undefined) { i = 0; }
if (typeof(r) === 'number') { r = fromFixnum(r); }
if (typeof(i) === 'number') { i = fromFixnum(i); }
if (isExact(i) && isInteger(i) && _integerIsZero(i)) {
return r;
}
return new Complex(r, i);
};
Complex.prototype.toString = function() {
var realPart = this.r.toString(), imagPart = this.i.toString();
if (imagPart[0] === '-' || imagPart[0] === '+') {
return realPart + imagPart + 'i';
} else {
return realPart + "+" + imagPart + 'i';
}
};
Complex.prototype.isFinite = function() {
return isSchemeNumberFinite(this.r) && isSchemeNumberFinite(this.i);
};
Complex.prototype.isRational = function() {
return isRational(this.r) && equals(this.i, 0);
};
Complex.prototype.isInteger = function() {
return (isInteger(this.r) &&
equals(this.i, 0));
};
Complex.prototype.toExact = function() {
if (! this.isReal()) {
throwRuntimeError("inexact->exact: expects argument of type real number", this);
}
return toExact(this.r);
};
Complex.prototype.isExact = function() {
return isExact(this.r) && isExact(this.i);
};
Complex.prototype.level = 3;
Complex.prototype.liftTo = function(target){
throwRuntimeError("Don't know how to lift Complex number", this, target);
};
Complex.prototype.equals = function(other) {
var result = ((other instanceof Complex) &&
(equals(this.r, other.r)) &&
(equals(this.i, other.i)));
return result;
};
Complex.prototype.greaterThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">: expects argument of type real number", this, other);
}
return greaterThan(this.r, other.r);
};
Complex.prototype.greaterThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError(">=: expects argument of type real number", this, other);
}
return greaterThanOrEqual(this.r, other.r);
};
Complex.prototype.lessThan = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<: expects argument of type real number", this, other);
}
return lessThan(this.r, other.r);
};
Complex.prototype.lessThanOrEqual = function(other) {
if (! this.isReal() || ! other.isReal()) {
throwRuntimeError("<=: expects argument of type real number", this, other);
}
return lessThanOrEqual(this.r, other.r);
};
Complex.prototype.abs = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("abs: expects argument of type real number", this);
return abs(this.r);
};
Complex.prototype.toFixnum = function(){
if (!equals(this.i, 0).valueOf())
throwRuntimeError("toFixnum: expects argument of type real number", this);
return toFixnum(this.r);
};
Complex.prototype.numerator = function() {
if (!this.isReal())
throwRuntimeError("numerator: can only be applied to real number", this);
return numerator(this.n);
};
Complex.prototype.denominator = function() {
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return denominator(this.n);
};
Complex.prototype.add = function(other){
return Complex.makeInstance(
add(this.r, other.r),
add(this.i, other.i));
};
Complex.prototype.subtract = function(other){
return Complex.makeInstance(
subtract(this.r, other.r),
subtract(this.i, other.i));
};
Complex.prototype.negate = function() {
return Complex.makeInstance(negate(this.r),
negate(this.i));
};
Complex.prototype.multiply = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
multiply(this.r, other.r),
multiply(this.i, other.r));
}
var r = subtract(
multiply(this.r, other.r),
multiply(this.i, other.i));
var i = add(
multiply(this.r, other.i),
multiply(this.i, other.r));
return Complex.makeInstance(r, i);
};
Complex.prototype.divide = function(other){
// If the other value is real, just do primitive division
if (other.isReal()) {
return Complex.makeInstance(
divide(this.r, other.r),
divide(this.i, other.r));
}
var con = conjugate(other);
var up = multiply(this, con);
// Down is guaranteed to be real by this point.
var down = multiply(other, con);
var result = Complex.makeInstance(
divide(realPart(up), down),
divide(imaginaryPart(up), down));
return result;
};
Complex.prototype.conjugate = function(){
var result = Complex.makeInstance(
this.r,
subtract(0,
this.i));
return result;
};
Complex.prototype.magnitude = function(){
var sum = add(
multiply(this.r, this.r),
multiply(this.i, this.i));
return sqrt(sum);
};
Complex.prototype.isReal = function(){
return equals(this.i, 0);
};
Complex.prototype.integerSqrt = function() {
var result = sqrt(x);
if (isRational(result)) {
return toExact(floor(result));
} else if (isReal(result)) {
return toExact(floor(result));
} else {
return Complex.makeInstance(toExact(floor(realPart(result))),
toExact(floor(imaginaryPart(result))));
}
};
Complex.prototype.sqrt = function(){
if (this.isReal())
return sqrt(this.r);
// http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers
var r_plus_x = add(this.magnitude(), this.r);
var r = sqrt(halve(r_plus_x));
var i = divide(this.i, sqrt(multiply(r_plus_x, FloatPoint.makeInstance(2))));
return Complex.makeInstance(r, i);
};
Complex.prototype.log = function(){
var m = this.magnitude();
var theta = this.angle();
var result = add(
log(m),
timesI(theta));
return result;
};
Complex.prototype.angle = function(){
if (this.isReal()) {
return angle(this.r);
}
if (equals(0, this.r)) {
var tmp = halve(FloatPoint.pi);
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
var tmp = atan(divide(abs(this.i), abs(this.r)));
if (greaterThan(this.r, 0)) {
return greaterThan(this.i, 0) ?
tmp : negate(tmp);
} else {
return greaterThan(this.i, 0) ?
subtract(FloatPoint.pi, tmp) : subtract(tmp, FloatPoint.pi);
}
}
};
var plusI = Complex.makeInstance(0, 1);
var minusI = Complex.makeInstance(0, -1);
Complex.prototype.tan = function() {
return divide(this.sin(), this.cos());
};
Complex.prototype.atan = function(){
if (equals(this, plusI) ||
equals(this, minusI)) {
return neginf;
}
return multiply(
plusI,
multiply(
FloatPoint.makeInstance(0.5),
log(divide(
add(plusI, this),
add(
plusI,
subtract(0, this))))));
};
Complex.prototype.cos = function(){
if (this.isReal())
return cos(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
return halve(add(exp(iz), exp(iz_negate)));
};
Complex.prototype.sin = function(){
if (this.isReal())
return sin(this.r);
var iz = timesI(this);
var iz_negate = negate(iz);
var z2 = Complex.makeInstance(0, Rational.TWO);
var exp_negate = subtract(exp(iz), exp(iz_negate));
var result = divide(exp_negate, z2);
return result;
};
Complex.prototype.expt= function(y){
var expo = multiply(y, this.log());
return exp(expo);
};
Complex.prototype.exp = function(){
var r = exp(this.r);
var cos_a = cos(this.i);
var sin_a = sin(this.i);
return multiply(
r,
add(cos_a, timesI(sin_a)));
};
Complex.prototype.acos = function(){
if (this.isReal())
return acos(this.r);
var pi_half = halve(FloatPoint.pi);
var iz = timesI(this);
var root = sqrt(subtract(1, sqr(this)));
var l = timesI(log(add(iz, root)));
return add(pi_half, l);
};
Complex.prototype.asin = function(){
if (this.isReal())
return asin(this.r);
var oneNegateThisSq =
subtract(
1,
sqr(this));
var sqrtOneNegateThisSq = sqrt(oneNegateThisSq);
return multiply(
Rational.TWO,
atan(divide(
this,
add(
1,
sqrtOneNegateThisSq))));
};
Complex.prototype.ceiling = function(){
if (!this.isReal())
throwRuntimeError("ceiling: can only be applied to real number", this);
return ceiling(this.r);
};
Complex.prototype.floor = function(){
if (!this.isReal())
throwRuntimeError("floor: can only be applied to real number", this);
return floor(this.r);
};
Complex.prototype.imaginaryPart = function(){
return this.i;
};
Complex.prototype.realPart = function(){
return this.r;
};
Complex.prototype.round = function(){
if (!this.isReal())
throwRuntimeError("round: can only be applied to real number", this);
return round(this.r);
};
var rationalRegexp = new RegExp("^([+-]?\\d+)/(\\d+)$");
var bignumScientificPattern = new RegExp("^([+-]?\\d*)\\.?(\\d*)[Ee](\\+?\\d+)$");
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
var flonumRegexp = new RegExp("^([+-]?\\d*)\\.?(\\d*)$");
// fromString: string -> (scheme-number | false)
var fromString = function(x) {
var aMatch = x.match(rationalRegexp);
if (aMatch) {
return makeRational(fromString(aMatch[1]),
fromString(aMatch[2]));
}
var cMatch = x.match(complexRegexp);
if (cMatch) {
return makeComplex(fromString(cMatch[1] || "0"),
fromString(cMatch[2] + (cMatch[3] || "1")));
}
if (x === '+nan.0' || x === '-nan.0')
return FloatPoint.nan;
if (x === '+inf.0')
return FloatPoint.inf;
if (x === '-inf.0')
return FloatPoint.neginf;
if (x === "-0.0") {
return NEGATIVE_ZERO;
}
if (x.match(flonumRegexp) || x.match(bignumScientificPattern)) {
var n = Number(x);
if (isOverflow(n)) {
return makeBignum(x);
} else {
return fromFixnum(n);
}
} else {
return false;
}
};
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// The code below comes from Tom Wu's BigInteger implementation:
diff --git a/test/tests.js b/test/tests.js
index 494371c..f92c42d 100644
--- a/test/tests.js
+++ b/test/tests.js
@@ -2207,1048 +2207,1037 @@ describe('sin', {
// FIXME: we're missing this
}
});
describe('tan', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('acos', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('asin', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('imaginaryPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('realPart', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('round', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('exp', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('sqr', {
'fixnums': function() {
// FIXME: add test case where value needs to become a bignum.
assertTrue(eqv(sqr(42), 1764));
assertTrue(eqv(sqr(0), 0));
assertTrue(eqv(sqr(1), 1));
assertTrue(eqv(sqr(2), 4));
assertTrue(eqv(sqr(-1), 1));
assertTrue(eqv(sqr(-2), 4));
assertTrue(eqv(sqr(-12349), 152497801));
},
'fixnum overflows to bignum': function() {
var x = fromFixnum(2);
for(var i = 0; i < 10; i++) {
x = sqr(x);
}
// Basically, computing (expt 2 (expt 2 10))
assertTrue(eqv(x, makeBignum("179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216")));
},
'bignums': function() {
assertTrue(eqv(sqr(makeBignum("1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
assertTrue(eqv(sqr(makeBignum("-1297684398542133568912839")),
makeBignum("1683984798219658952314406790914015952992379039921")));
},
'rationals': function() {
assertTrue(eqv(sqr(makeRational(1, 2)),
makeRational(1, 4)));
assertTrue(eqv(sqr(makeRational(-1, 7)),
makeRational(1, 49)));
assertTrue(eqv(sqr(makeRational(makeBignum("-1297684398542133568912839"),
5)),
makeRational(makeBignum("1683984798219658952314406790914015952992379039921"),
25)));
},
'floats': function() {
assertTrue(eqv(sqr(makeFloat(0.0)),
makeFloat(0.0)));
assertTrue(eqv(sqr(makeFloat(.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(makeFloat(-.25)),
makeFloat(0.0625)));
assertTrue(eqv(sqr(nan), nan));
assertTrue(eqv(sqr(inf), inf));
assertTrue(eqv(sqr(negative_inf), inf));
assertTrue(eqv(sqr(negative_zero), makeFloat(0.0)));
},
'complex': function() {
assertTrue(eqv(sqr(negative_i),
-1));
assertTrue(eqv(sqr(i),
-1));
}
});
describe('gcd', {
'fixnum / fixnum' : function() {
// FIXME: we're missing this
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('lcm', {
'fixnum / fixnum' : function() {
// FIXME: add test case where value needs to become a bignum.
},
'fixnum / bignum': function() {
// FIXME: we're missing this
},
'bignum / bignum' : function() {
// FIXME: we're missing this
},
'bignum / rational': function() {
// FIXME: we're missing this
},
'bignum / float' : function() {
// FIXME: we're missing this
},
'bignum / complex' : function() {
// FIXME: we're missing this
},
'fixnum / rational' : function() {
// FIXME: we're missing this
},
'fixnum / floating' : function() {
// FIXME: we're missing this
},
'fixnum / complex' : function() {
// FIXME: we're missing this
},
'rational / rational' : function() {
// FIXME: we're missing this
},
'rational / floating' : function() {
// FIXME: we're missing this
},
'rational / complex' : function() {
// FIXME: we're missing this
},
'floating / floating' : function() {
// FIXME: we're missing this
},
'floating / complex' : function() {
// FIXME: we're missing this
},
'complex / complex' : function() {
// FIXME: we're missing this
}
});
describe('integerSqrt', {
'fixnums': function() {
// FIXME: we're missing this
},
'bignums': function() {
// FIXME: we're missing this
},
'rationals': function() {
// FIXME: we're missing this
},
'floats': function() {
// FIXME: we're missing this
},
'complex': function() {
// FIXME: we're missing this
}
});
describe('toString', {
'fixnums': function() {
assertEquals("-123456789012345678901234567890",
makeBignum("-123456789012345678901234567890").toString());
assertEquals("123456789012345678901234567890",
makeBignum("123456789012345678901234567890").toString());
},
'bignums': function() {
assertEquals("0",
makeBignum("0").toString());
assertEquals("-236579329853268932967423894623849289323568268954",
makeBignum("-236579329853268932967423894623849289323568268954").toString());
assertEquals("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612",
makeBignum("312981532653268913529653216935216851268932416843269129356216894159681236850432163527231684321782317892513672317605612").toString());
},
'rationals': function() {
assertEquals("1/2",
makeRational(1, 2));
assertEquals("2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("2398742368955236823956823968"),
makeBignum("239856325892398441")));
assertEquals("-2398742368955236823956823968/239856325892398441",
makeRational(makeBignum("-2398742368955236823956823968"),
makeBignum("239856325892398441")));
},
'floats': function() {
assertEquals('0.0', makeFloat(0).toString());
assertEquals('0.25', makeFloat(0.25).toString());
assertEquals('1.2354e+200', makeFloat(1.2354e200).toString());
assertEquals('1.2354e-200', makeFloat(1.2354e-200).toString());
assertEquals('-1.2354e-200', makeFloat(-1.2354e-200).toString());
assertEquals('-1', makeFloat(-1).toString());
assertEquals("+nan.0", nan.toString());
assertEquals("+inf.0", inf.toString());
assertEquals("-inf.0", negative_inf.toString());
assertEquals("-0.0", negative_zero.toString());
},
'complex': function() {
assertEquals("1+0.0i", makeComplex(1, makeFloat(0)).toString());
assertEquals("-1+0.0i", makeComplex(-1, makeFloat(0)).toString());
assertEquals("0+1i", makeComplex(0, 1).toString());
assertEquals("0-1i", makeComplex(0, -1).toString());
assertEquals("0-0.0i", makeComplex(0, negative_zero).toString());
assertEquals("3/4+5/6i", makeComplex(makeRational(3, 4),
makeRational(5, 6)).toString());
assertEquals("3/4-5/6i", makeComplex(makeRational(3, 4),
makeRational(-5, 6)).toString());
assertEquals("0.1-inf.0i", makeComplex(makeFloat(0.1),
negative_inf).toString());
assertEquals("+nan.0+inf.0i", makeComplex(nan, inf).toString());
assertEquals("+nan.0+nan.0i", makeComplex(nan, nan).toString());
assertEquals("-inf.0-inf.0i", makeComplex(negative_inf, negative_inf).toString());
}
});
describe('old tests from Moby Scheme', {
testRationalReduction: function() {
var n1 = makeRational(1,2);
var n2 = makeRational(5, 10);
var n3 = makeRational(5, 12);
assertTrue(equals(n1, n2));
assertTrue(! equals(n2, n3));
},
testEqv: function() {
assertTrue(eqv(nan, nan));
assertTrue(false == eqv(makeFloat(42),
makeRational(42)));
assertTrue(eqv(inf, inf));
assertTrue(eqv(negative_inf, negative_inf));
},
testEqual: function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.0);
assertTrue(equals(n1, n2));
var n3 = makeComplex(makeRational(2),makeRational(0));
var n4 = makeComplex(makeRational(2),makeRational(1));
assertTrue(equals(n1, n3));
assertTrue(!equals(n3, n4));
assertTrue(equals(makeRational(1, 2), makeRational(2, 4)));
assertTrue(false == equals(makeRational(1, 2),
makeRational(2, 5)));
assertTrue(false === equals(nan, nan));
assertTrue(false === equals(nan, makeRational(3)));
assertTrue(false === equals(makeRational(3), nan));
},
testAbs : function(){
var n1 = makeRational(-2,1);
var n2 = makeRational(4, 2);
var n3 = makeComplex(makeRational(2),
makeRational(0));
assertTrue(equals(abs(n1), n2));
assertTrue(equals(abs(n3), n2));
},
testAdd : function(){
assertTrue(equals(add(makeRational(2,1), makeRational(3,1)),
makeRational(5,1)));
assertTrue(equals(add(makeRational(2,1), makeFloat(2.1)), makeFloat(4.1)));
assertTrue(equals(add(makeRational(2,1),
makeComplex(makeRational(2), makeRational(2))),
makeComplex(makeRational(4),makeRational(2))));
assertTrue(equals(add(makeFloat(3.1), makeComplex(makeRational(2),makeRational(2))),
makeComplex(makeFloat(5.1), makeRational(2))));
assertTrue(equals(add(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(5),makeRational( 4))));
},
testDivisionByZero: function() {
divide(1, 1);
assertFails(function() {
divide(1, 0);
});
assertFails(function() { divide(makeFloat(1), 0); });
assertFails(function() { divide(makeFloat(1),makeFloat(0)); });
},
testAddFloats: function() {
assertEquals(0.1, add(makeRational(0),
makeFloat(0.1)).toFixnum());
},
testSubtract : function(){
assertTrue(equals(subtract(subtract(0, makeRational(2,1)),
makeRational(3,1)),
makeRational(-5,1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeFloat(2.1)),
makeFloat(-4.1)));
assertTrue(equals(subtract(subtract(0, makeRational(2,1)), makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeRational(-4),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeFloat(2.1)),
makeComplex(makeRational(2),makeRational( 2))),
makeComplex(makeFloat(-4.1),makeRational( -2))));
assertTrue(equals(subtract(subtract(0, makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(3),makeRational( 2))),
makeComplex(makeRational(-5),makeRational( -4))));
},
testMultiply : function(){
assertTrue(equals(multiply(makeRational(2,1), makeRational(3,1)), makeRational(6,1)));
assertTrue(equals(multiply(makeRational(2,1), makeFloat(2.1)), makeFloat(4.2)));
assertTrue(equals(multiply(makeRational(2,1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeRational(4),makeRational(4))));
assertTrue(equals(multiply(makeFloat(2.1), makeComplex(makeRational(2),makeRational( 2))), makeComplex(makeFloat(4.2),makeFloat( 4.2))));
assertTrue(equals(multiply(makeComplex(makeRational(2),makeRational( 2)), makeComplex(makeRational(3),makeRational( 2))), makeComplex(makeRational(2),makeRational( 10))));
},
testDivide : function(){
var six = makeRational(6, 1);
assertTrue(equals(divide(divide(six, makeRational(2,1)), makeRational(3,1)), 1));
assertTrue(equals(divide(divide(six, makeFloat(1.5)), makeFloat(4.0)), 1));
assertTrue(equals(divide(divide(makeFloat(150),
makeComplex(makeRational(3),makeRational( 4))),
makeComplex(makeRational(3),makeRational( -4))),
six));
assertTrue(equals(divide(1, six),
makeRational(1, 6)));
},
testConjugate : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
- assertTrue(equals(n1, Kernel.conjugate(n1)));
- assertTrue(equals(n2, Kernel.conjugate(n2)));
- assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), Kernel.conjugate(makeComplex(makeRational(1),makeRational( -2)))));
+ assertTrue(equals(n1, conjugate(n1)));
+ assertTrue(equals(n2, conjugate(n2)));
+ assertTrue(equals(makeComplex(makeRational(1),makeRational( 2)), conjugate(makeComplex(makeRational(1),makeRational( -2)))));
},
testMagnitude : function(){
var n1 = makeRational(2,1);
var n2 = makeFloat(2.1);
- assertTrue(equals(n1, Kernel.magnitude(n1)));
- assertTrue(equals(n2, Kernel.magnitude(n2)));
- assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), Kernel.magnitude(makeComplex(makeRational(3),makeRational( -4)))));
+ assertTrue(equals(n1, magnitude(n1)));
+ assertTrue(equals(n2, magnitude(n2)));
+ assertTrue(equals(makeComplex(makeRational(5),makeRational( 0)), magnitude(makeComplex(makeRational(3),makeRational( -4)))));
},
testComparison : function(){
- assertTrue(Kernel._greaterthan_(makeRational(2,1),
- makeRational(1,1),
- []));
- assertTrue(Kernel._greaterthan_(makeFloat(2.1),
- makeRational(2,1), []));
- assertTrue(Kernel._greaterthan__equal_(makeFloat(2.0),
- makeRational(2,1),
- []));
- assertTrue(Kernel._greaterthan__equal_(makeComplex(makeFloat(2.0),makeRational( 0)),
- makeRational(2,1),
- []));
+ assertTrue(greaterThan(makeRational(2,1),
+ makeRational(1,1)));
+ assertTrue(greaterThan(makeFloat(2.1),
+ makeRational(2,1)));
+ assertTrue(greaterThanOrEqual(makeFloat(2.0),
+ makeRational(2,1)));
+ assertTrue(greaterThanOrEqual(makeComplex(makeFloat(2.0),makeRational( 0)),
+ makeRational(2,1)));
- assertTrue(Kernel._lessthan_(makeRational(2),
- makeRational(3), []));
+ assertTrue(lessThan(makeRational(2),
+ makeRational(3)));
- assertTrue(! Kernel._lessthan_(makeRational(3),
- makeRational(2), []));
+ assertTrue(! lessThan(makeRational(3),
+ makeRational(2)));
},
- testComparisonTypes : function() {
- assertFails(isTypeMismatch,
- function() {
- Kernel._lessthan_(2, 3, [])});
- assertFails(isTypeMismatch,
- function() {
- Kernel._greaterthan_("2", "3", [])});
- },
testComparisonMore: function() {
- assertTrue(! Kernel._greaterthan_(makeRational(2),
- makeRational(3), []));
+ assertTrue(! greaterThan(makeRational(2),
+ makeRational(3)));
- assertTrue(Kernel._greaterthan_(makeRational(3),
- makeRational(2), []));
+ assertTrue(greaterThan(makeRational(3),
+ makeRational(2)));
- assertTrue(! Kernel._greaterthan_(makeRational(3),
- makeRational(3), []));
+ assertTrue(! greaterThan(makeRational(3),
+ makeRational(3)));
- assertTrue(Kernel._lessthan__equal_(makeRational(17),
- makeRational(17), []));
+ assertTrue(lessThanOrEqual(makeRational(17),
+ makeRational(17)));
- assertTrue(Kernel._lessthan__equal_(makeRational(16),
- makeRational(17), []));
+ assertTrue(lessThanOrEqual(makeRational(16),
+ makeRational(17)));
- assertTrue(!Kernel._lessthan__equal_(makeRational(16),
- makeRational(15), []));
- assertFails(isTypeMismatch,
- function() {
- Kernel._lessthan__equal_("2", "3", [])});
+ assertTrue(!lessThanOrEqual(makeRational(16),
+ makeRational(15)));
},
testComparison2 : function () {
var num = makeRational(0, 1);
var upper = makeRational(480, 1);
- assertTrue(Kernel._lessthan_(makeRational(5, 1),
- upper, []));
- assertTrue(Kernel._lessthan_(makeRational(6, 1),
- upper, []));
- assertTrue(Kernel._lessthan_(makeRational(7, 1),
- upper, []));
- assertTrue(Kernel._lessthan_(makeRational(8, 1),
- upper, []));
- assertTrue(Kernel._lessthan_(makeRational(9, 1),
- upper, []));
+ assertTrue(lessThan(makeRational(5, 1),
+ upper));
+ assertTrue(lessThan(makeRational(6, 1),
+ upper));
+ assertTrue(lessThan(makeRational(7, 1),
+ upper));
+ assertTrue(lessThan(makeRational(8, 1),
+ upper));
+ assertTrue(lessThan(makeRational(9, 1),
+ upper));
for (var i = 0; i < 60; i++) {
- assertTrue(Kernel._lessthan_
- (num, upper, []));
- num = add([num, 1]);
+ assertTrue(lessThan
+ (num, upper));
+ num = add(num, 1);
}
},
testAtan : function(){
- assertTrue(equals(Kernel.atan(1, []), plt.Kernel.pi.half().half()));
+ assertTrue(equals(atan(1), divide(pi, 4)));
},
testLog : function(){
- assertTrue(equals(Kernel.log(1), 0));
- assertTrue(equals(Kernel.log(makeComplex(makeRational(0),makeRational(1))), plt.Kernel.pi.toComplex().timesI().half()));
- assertTrue(equals(Kernel.log(makeFloat(-1)), plt.Kernel.pi.toComplex().timesI()));
+ assertTrue(equals(log(1), 0));
+ assertTrue(equals(log(makeComplex(makeRational(0),makeRational(1))), divide(multiply(pi, i), 2)));
+ assertTrue(equals(log(makeFloat(-1)), multiply(pi, i)));
},
testAngle : function(){
- assertTrue(equals(Kernel.angle(makeComplex(makeRational(0),makeRational(1))), PI.half()));
- assertTrue(equals(Kernel.angle(makeComplex(makeRational(1),makeRational(1))), PI.half().half()));
- assertTrue(equals(Kernel.angle(makeFloat(-1)), PI));
- assertTrue(equals(Kernel.angle(makeComplex(makeRational(-1),makeRational( 1))), PI.multiply(makeFloat(0.75))));
- assertTrue(equals(Kernel.angle(makeComplex(makeRational(-1),makeRational( -1))), PI.multiply(makeFloat(-0.75))));
- assertTrue(equals(Kernel.angle(makeComplex(makeRational(1),makeRational( -1))), PI.half().half().minus()));
+ assertTrue(equals(angle(makeComplex(makeRational(0),makeRational(1))), divide(pi, 2)));
+ assertTrue(equals(angle(makeComplex(makeRational(1),makeRational(1))), divide(pi, 4)));
+ assertTrue(equals(angle(makeFloat(-1)), pi));
+ assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( 1))),
+ multiply(pi, makeFloat(0.75))));
+ assertTrue(equals(angle(makeComplex(makeRational(-1),makeRational( -1))),
+ multiply(pi, makeFloat(-0.75))));
+ assertTrue(equals(angle(makeComplex(makeRational(1),makeRational( -1))),
+ multiply(pi, makeRational(-1, 4))));
},
testExp : function(){
assertTrue(equals(Kernel.exp(0), 1, []));
assertTrue(equals(Kernel.exp(1),
Kernel.e, []));
assertTrue(equals_tilde_(Kernel.exp(makeRational(2)),
Kernel.sqr(Kernel.e),
makeFloat(0.0001)));
},
testExpt : function(){
var i = plt.types.makeComplex(
makeRational(0),makeRational( 1));
assertTrue(equals(
Kernel.expt(i, i),
Kernel.exp(PI.half().minus())));
assertTrue(equals(
Kernel.expt(makeFloat(2),
makeFloat(3)),
makeFloat(8)));
assertTrue(equals(
Kernel.expt(makeComplex(
makeRational(3,4),
makeRational(7,8)),
makeRational(2))),
makeComplex(makeRational(-13, 64),
makeRational(21, 16)));
},
testSin : function(){
assertTrue(equals(Kernel.sin(divide(PI, makeFloat(2))), 1));
},
testCos : function(){
assertTrue(equals(Kernel.cos(0), 1));
},
testSqr: function() {
var n1 = makeRational(42);
assertEquals(1764, Kernel.sqr(n1).toFixnum());
assertFails(isTypeMismatch,
function() { Kernel.sqr("42"); });
},
testIntegerSqrt: function() {
var n1 = makeRational(36);
var n2 = makeRational(6);
assertEquals(n2, Kernel.integer_dash_sqrt(n1));
assertFails(function() { Kernel.integer_dash_sqrt(makeFloat(3.5)); });
},
testSqrt : function(){
assertTrue(equals(Kernel.sqrt(makeFloat(4)), makeFloat(2)));
assertTrue(equals(Kernel.sqrt(makeFloat(-1)), makeComplex(makeRational(0),makeRational(1))));
},
testAcos : function(){
assertTrue(equals(Kernel.acos(1), 0));
assertTrue(equals(Kernel.acos(makeFloat(-1)), PI));
},
testAsin : function(){
assertTrue(equals(
Kernel.asin(0), 0));
assertTrue(equals(Kernel.asin(-1), PI.half().minus()));
assertTrue(equals(
Kernel.asin(1), PI.half()));
assertTrue(equals(
Kernel.asin(makeRational(1, 4)),
makeFloat(0.25268025514207865)));
assertTrue(equals(
Kernel.asin(makeComplex(1, 5)),
makeComplex(0.1937931365549321,
2.3309746530493123)));
},
testTan : function(){
assertTrue(equals(Kernel.tan(0), 0));
},
testComplex_question_ : function(){
assertTrue(Kernel.complex_question_(PI));
assertTrue(Kernel.complex_question_(1));
assertTrue(Kernel.complex_question_(makeFloat(2.718)));
assertTrue(Kernel.complex_question_(makeComplex(0,1)));
assertTrue(!Kernel.complex_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.complex_question_(String.makeInstance("hi")));
assertTrue(!Kernel.complex_question_(Symbol.makeInstance('h')));
},
testMakePolar : function() {
assertTrue(equals(Kernel.make_dash_polar(makeRational(5),
makeRational(0)),
makeComplex(makeRational(5),makeRational( 0))));
var n = Kernel.make_dash_polar(makeRational(5),
PI);
var delta = makeFloat(0.0000001);
assertTrue(equals_tilde_(Kernel.imag_dash_part(n),
makeRational(0),
delta));
assertTrue(equals_tilde_(Kernel.real_dash_part(n),
makeRational(-5),
delta));
},
testMakeRectangular: function() {
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(4),
makeRational(3)),
makeComplex(makeRational(4),makeRational( 3))));
assertTrue(equals(Kernel.make_dash_rectangular
(makeRational(5),
makeRational(4)),
makeComplex(makeRational(5),makeRational( 4))));
},
testCosh : function(){
assertTrue(equals(Kernel.cosh(0), 1));
},
testSinh : function(){
assertTrue(equals(Kernel.sinh(0), 0));
},
testDenominator : function(){
assertTrue(equals(Kernel.denominator(makeRational(7,2)), makeRational(2,1)));
assertTrue(equals(Kernel.denominator(makeFloat(3)),
makeFloat(1)));
},
testNumerator : function(){
assertTrue(equals(Kernel.numerator(makeRational(7,2)), makeRational(7,1)));
assertTrue(equals(Kernel.numerator(makeFloat(3)),
makeFloat(3)));
},
testIsExact : function() {
assertTrue(Kernel.exact_question_(makeRational(3)));
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
assertTrue(! Kernel.exact_question_(makeFloat(3.5)));
},
testIsInexact : function() {
assertTrue(! Kernel.inexact_question_(makeRational(3)));
assertTrue(Kernel.inexact_question_(makeFloat(3.0)));
assertTrue(Kernel.inexact_question_(makeFloat(3.5)));
},
testExactToInexact : function() {
assertTrue(equals(Kernel.exact_dash__greaterthan_inexact(makeRational(3)),
makeFloat(3.0),
[]));
assertTrue(Kernel.inexact_question_(Kernel.exact_dash__greaterthan_inexact(makeRational(3))));
},
testInexactToExact : function() {
assertTrue(equals(Kernel.inexact_dash__greaterthan_exact(makeFloat(3)),
makeRational(3),
[]));
assertTrue(Kernel.exact_question_(Kernel.inexact_dash__greaterthan_exact(makeFloat(3))));
},
testFloatsAreInexact: function() {
assertTrue(! Kernel.exact_question_(makeFloat(3.0)));
},
testOdd_question_ : function(){
assertTrue(Kernel.odd_question_(1));
assertTrue(! Kernel.odd_question_(0));
assertTrue(Kernel.odd_question_(makeFloat(1)));
assertTrue(Kernel.odd_question_(makeComplex(makeRational(1),makeRational( 0))));
assertTrue(Kernel.odd_question_(makeRational(-1, 1)));
},
testInfinityComputations : function() {
assertTrue(equals(0,
multiply([0,
inf]),
[]));
},
testEven_question_ : function(){
assertTrue(Kernel.even_question_(0));
assertTrue(! Kernel.even_question_(1));
assertTrue(Kernel.even_question_(makeFloat(2)));
assertTrue(Kernel.even_question_(makeComplex(makeRational(2),makeRational( 0))));
},
testPositive_question_ : function(){
assertTrue(Kernel.positive_question_(1));
assertTrue(!Kernel.positive_question_(0));
assertTrue(Kernel.positive_question_(makeFloat(1.1)));
assertTrue(Kernel.positive_question_(makeComplex(makeRational(1),makeRational(0))));
},
testNegative_question_ : function(){
assertTrue(Kernel.negative_question_(makeRational(-5)));
assertTrue(!Kernel.negative_question_(1));
assertTrue(!Kernel.negative_question_(0));
assertTrue(!Kernel.negative_question_(makeFloat(1.1)));
assertTrue(!Kernel.negative_question_(makeComplex(makeRational(1),makeRational(0))));
},
testCeiling : function(){
assertTrue(equals(Kernel.ceiling(1), 1));
assertTrue(equals(Kernel.ceiling(PI), makeFloat(4)));
assertTrue(equals(Kernel.ceiling(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(4)));
},
testFloor : function(){
assertTrue(equals(Kernel.floor(1), 1));
assertTrue(equals(Kernel.floor(PI), makeFloat(3)));
assertTrue(equals(Kernel.floor(makeComplex(makeFloat(3.1),makeRational(0))), makeFloat(3)));
},
testImag_dash_part : function(){
assertTrue(equals(Kernel.imag_dash_part(1), 0));
assertTrue(equals(Kernel.imag_dash_part(PI), 0));
assertTrue(equals(Kernel.imag_dash_part(makeComplex(makeRational(0),makeRational(1))), 1));
},
testReal_dash_part : function(){
assertTrue(equals(Kernel.real_dash_part(1), 1));
assertTrue(equals(Kernel.real_dash_part(PI), PI));
assertTrue(equals(Kernel.real_dash_part(makeComplex(makeRational(0),makeRational(1))), 0));
},
testInteger_question_ : function(){
assertTrue(Kernel.integer_question_(1));
assertTrue(Kernel.integer_question_(makeFloat(3.0)));
assertTrue(!Kernel.integer_question_(makeFloat(3.1)));
assertTrue(Kernel.integer_question_(makeComplex(makeRational(3),makeRational(0))));
assertTrue(!Kernel.integer_question_(makeComplex(makeFloat(3.1),makeRational(0))));
},
testMake_dash_rectangular: function(){
assertTrue(equals(Kernel.make_dash_rectangular(1, 1), makeComplex(makeRational(1),makeRational(1))));
},
testMaxAndMin : function(){
var n1 = makeFloat(-1);
var n2 = 0;
var n3 = 1;
var n4 = makeComplex(makeRational(4),makeRational(0));
assertTrue(equals(n4, Kernel.max(n1, [n2,n3,n4])));
assertTrue(equals(n1, Kernel.min(n1, [n2,n3,n4])));
var n5 = makeFloat(1.1);
assertEquals(n5, Kernel.max(n1, [n2, n3, n5]));
assertEquals(n1, Kernel.min(n2, [n3, n4, n5, n1]));
},
testLcm : function () {
assertTrue(equals(makeRational(12),
Kernel.lcm(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
},
testGcd : function () {
assertTrue(equals(makeRational(1),
Kernel.gcd(makeRational(1),
[makeRational(2), makeRational(3), makeRational(4)])));
assertTrue(equals(makeRational(5),
Kernel.gcd(makeRational(100),
[makeRational(5), makeRational(10), makeRational(25)])));
},
testIsRational : function() {
assertTrue(Kernel.rational_question_(makeRational(42)));
assertTrue(! Kernel.rational_question_(makeFloat(3.1415)));
assertTrue(! Kernel.rational_question_("blah"));
},
testNumberQuestion : function() {
assertTrue(Kernel.number_question_(plt.types.makeRational(42)));
assertTrue(Kernel.number_question_(42) == false);
},
testNumber_dash__greaterthan_string : function(){
assertTrue(Kernel.string_equal__question_(String.makeInstance("1"), Kernel.number_dash__greaterthan_string(1),[]));
assertTrue(!Kernel.string_equal__question_(String.makeInstance("2"), Kernel.number_dash__greaterthan_string(1),[]));
assertEquals("5+0i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 0)));
assertEquals("5+1i",
Kernel.number_dash__greaterthan_string(makeComplex(5, 1)));
assertEquals("4-2i",
Kernel.number_dash__greaterthan_string(makeComplex(4, -2)));
},
testQuotient : function(){
assertTrue(equals(Kernel.quotient(makeFloat(3), makeFloat(4)), 0));
assertTrue(equals(Kernel.quotient(makeFloat(4), makeFloat(3)), 1));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(-36),
makeRational(-7)),
makeRational(5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(-7)),
makeRational(-5)));
assertTrue(equals(
Kernel.quotient(makeRational(36),
makeRational(7)),
makeRational(5)));
},
testRemainder : function(){
assertTrue(equals(Kernel.remainder(makeFloat(3), makeFloat(4)), makeFloat(3)));
assertTrue(equals(Kernel.remainder(makeFloat(4), makeFloat(3)), makeFloat(1)));
},
testModulo : function() {
var n1 = makeRational(17);
var n2 = makeRational(3);
var n3 = makeRational(2);
assertEquals(n3, Kernel.modulo(n1, n2));
assertEquals(n2, Kernel.modulo(n2, n1));
assertTrue(equals(
makeRational(-3),
Kernel.modulo(makeRational(13),
makeRational(-4))));
assertTrue(equals(
makeRational(3),
Kernel.modulo(makeRational(-13),
makeRational(4))));
assertTrue(equals(
makeRational(-1),
Kernel.modulo(makeRational(-13),
makeRational(-4))));
assertTrue(equals(
makeRational(0),
Kernel.modulo(makeRational(4),
makeRational(-2))));
},
testReal_question_ : function(){
assertTrue(Kernel.real_question_(PI));
assertTrue(Kernel.real_question_(1));
assertTrue(!Kernel.real_question_(makeComplex(makeRational(0),makeRational(1))));
assertTrue(Kernel.real_question_(makeComplex(makeRational(1),makeRational(0))));
assertTrue(!Kernel.real_question_(plt.types.Empty.EMPTY));
assertTrue(!Kernel.real_question_(String.makeInstance("hi")));
assertTrue(!Kernel.real_question_(Symbol.makeInstance('h')));
},
testRound : function(){
assertTrue(equals(Kernel.round(makeFloat(3.499999)),
makeFloat(3)));
assertTrue(equals(Kernel.round(makeFloat(3.5)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeFloat(3.51)),
makeFloat(4)));
assertTrue(equals(Kernel.round(makeRational(3)),
makeRational(3)));
assertTrue(equals(Kernel.round(makeRational(17, 4)),
makeRational(4)));
assertTrue(equals(Kernel.round(makeRational(-17, 4)),
makeRational(-4)));
},
testSgn : function(){
assertTrue(equals(Kernel.sgn(makeFloat(4)), 1));
assertTrue(equals(Kernel.sgn(makeFloat(-4)), Rational.NEGATIVE_ONE));
assertTrue(equals(Kernel.sgn(0), 0));
},
testZero_question_ : function(){
assertTrue(Kernel.zero_question_(0));
assertTrue(!Kernel.zero_question_(1));
assertTrue(Kernel.zero_question_(makeComplex(makeRational(0),makeRational(0))));
}
});
|
bryanwoods/portfolio
|
a954842f3d1d469779ae499636425603d7a041a1
|
Adding new screenshot
|
diff --git a/screenshots/invitedtoourwedding/backend.png b/screenshots/invitedtoourwedding/backend.png
index 3219e1b..40c1586 100644
Binary files a/screenshots/invitedtoourwedding/backend.png and b/screenshots/invitedtoourwedding/backend.png differ
diff --git a/screenshots/invitedtoourwedding/screenshot.png b/screenshots/invitedtoourwedding/screenshot.png
deleted file mode 100644
index dac4618..0000000
Binary files a/screenshots/invitedtoourwedding/screenshot.png and /dev/null differ
|
bryanwoods/portfolio
|
70de1b2483c833197842d4c58eca29c5f18cf17a
|
Updating screenshots
|
diff --git a/screenshots/invitedtoourwedding/backend.png b/screenshots/invitedtoourwedding/backend.png
new file mode 100644
index 0000000..3219e1b
Binary files /dev/null and b/screenshots/invitedtoourwedding/backend.png differ
diff --git a/screenshots/invitedtoourwedding/frontend.png b/screenshots/invitedtoourwedding/frontend.png
new file mode 100644
index 0000000..95b60bc
Binary files /dev/null and b/screenshots/invitedtoourwedding/frontend.png differ
diff --git a/screenshots/whothefrank/screenshot.png b/screenshots/whothefrank/screenshot.png
index 2d5667b..9cd2d17 100644
Binary files a/screenshots/whothefrank/screenshot.png and b/screenshots/whothefrank/screenshot.png differ
diff --git a/screenshots/wilsoncolab.com/screenshot.png b/screenshots/wilsoncolab.com/screenshot.png
new file mode 100644
index 0000000..8425777
Binary files /dev/null and b/screenshots/wilsoncolab.com/screenshot.png differ
|
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