4122 lines
105 KiB
JavaScript
4122 lines
105 KiB
JavaScript
// Scheme numbers.
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var __PLTNUMBERS_TOP__;
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if (typeof(exports) !== 'undefined') {
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__PLTNUMBERS_TOP__ = exports;
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} else {
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if (! this['jsnums']) {
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this['jsnums'] = {};
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}
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__PLTNUMBERS_TOP__ = this['jsnums'];
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}
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//var jsnums = {};
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// The numeric tower has the following levels:
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// integers
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// rationals
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// floats
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// complex numbers
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//
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// with the representations:
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// integers: fixnum or BigInteger [level=0]
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// rationals: Rational [level=1]
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// floats: FloatPoint [level=2]
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// complex numbers: Complex [level=3]
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// We try to stick with the unboxed fixnum representation for
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// integers, since that's what scheme programs commonly deal with, and
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// we want that common type to be lightweight.
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// A boxed-scheme-number is either BigInteger, Rational, FloatPoint, or Complex.
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// An integer-scheme-number is either fixnum or BigInteger.
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(function() {
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// Abbreviation
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var Numbers = __PLTNUMBERS_TOP__;
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//var Numbers = jsnums;
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// makeNumericBinop: (fixnum fixnum -> any) (scheme-number scheme-number -> any) -> (scheme-number scheme-number) X
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// Creates a binary function that works either on fixnums or boxnums.
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// Applies the appropriate binary function, ensuring that both scheme numbers are
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// lifted to the same level.
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var makeNumericBinop = function(onFixnums, onBoxednums, options) {
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options = options || {};
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return function(x, y) {
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if (options.isXSpecialCase && options.isXSpecialCase(x))
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return options.onXSpecialCase(x, y);
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if (options.isYSpecialCase && options.isYSpecialCase(y))
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return options.onYSpecialCase(x, y);
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if (typeof(x) === 'number' &&
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typeof(y) === 'number') {
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return onFixnums(x, y);
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}
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if (typeof(x) === 'number') {
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x = liftFixnumInteger(x, y);
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}
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if (typeof(y) === 'number') {
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y = liftFixnumInteger(y, x);
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}
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if (x.level < y.level) x = x.liftTo(y);
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if (y.level < x.level) y = y.liftTo(x);
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return onBoxednums(x, y);
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};
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}
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// fromFixnum: fixnum -> scheme-number
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var fromFixnum = function(x) {
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if (isNaN(x) || (! isFinite(x))) {
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return FloatPoint.makeInstance(x);
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}
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var nf = Math.floor(x);
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if (nf === x) {
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if (isOverflow(nf)) {
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return makeBignum(expandExponent(x+''));
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} else {
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return nf;
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}
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} else {
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return FloatPoint.makeInstance(x);
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}
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};
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var expandExponent = function(s) {
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var match = s.match(scientificPattern), mantissaChunks, exponent;
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if (match) {
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mantissaChunks = match[1].match(/^([^.]*)(.*)$/);
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exponent = Number(match[2]);
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if (mantissaChunks[2].length === 0) {
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return mantissaChunks[1] + zfill(exponent);
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}
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if (exponent >= mantissaChunks[2].length - 1) {
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return (mantissaChunks[1] +
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mantissaChunks[2].substring(1) +
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zfill(exponent - (mantissaChunks[2].length - 1)));
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} else {
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return (mantissaChunks[1] +
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mantissaChunks[2].substring(1, 1+exponent));
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}
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} else {
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return s;
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}
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};
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// zfill: integer -> string
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// builds a string of "0"'s of length n.
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var zfill = function(n) {
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var buffer = [];
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buffer.length = n;
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for (var i = 0; i < n; i++) {
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buffer[i] = '0';
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}
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return buffer.join('');
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};
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// liftFixnumInteger: fixnum-integer boxed-scheme-number -> boxed-scheme-number
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// Lifts up fixnum integers to a boxed type.
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var liftFixnumInteger = function(x, other) {
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switch(other.level) {
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case 0: // BigInteger
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return makeBignum(x);
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case 1: // Rational
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return new Rational(x, 1);
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case 2: // FloatPoint
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return new FloatPoint(x);
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case 3: // Complex
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return new Complex(x, 0);
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default:
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throwRuntimeError("IMPOSSIBLE: cannot lift fixnum integer to " + other.toString(), x, other);
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}
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};
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// throwRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
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// Throws a runtime error with the given message string.
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var throwRuntimeError = function(msg, x, y) {
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Numbers['onThrowRuntimeError'](msg, x, y);
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};
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// onThrowRuntimeError: string (scheme-number | undefined) (scheme-number | undefined) -> void
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// By default, will throw a new Error with the given message.
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// Override Numbers['onThrowRuntimeError'] if you need to do something special.
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var onThrowRuntimeError = function(msg, x, y) {
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throw new Error(msg);
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};
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// isSchemeNumber: any -> boolean
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// Returns true if the thing is a scheme number.
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var isSchemeNumber = function(thing) {
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return (typeof(thing) === 'number'
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|| (thing instanceof Rational ||
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thing instanceof FloatPoint ||
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thing instanceof Complex ||
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thing instanceof BigInteger));
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};
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// isRational: scheme-number -> boolean
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var isRational = function(n) {
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return (typeof(n) === 'number' ||
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(isSchemeNumber(n) && n.isRational()));
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};
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// isReal: scheme-number -> boolean
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var isReal = function(n) {
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return (typeof(n) === 'number' ||
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(isSchemeNumber(n) && n.isReal()));
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};
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// isExact: scheme-number -> boolean
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var isExact = function(n) {
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return (typeof(n) === 'number' ||
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(isSchemeNumber(n) && n.isExact()));
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};
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// isExact: scheme-number -> boolean
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var isInexact = function(n) {
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if (typeof(n) === 'number') {
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return false;
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} else {
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return (isSchemeNumber(n) && n.isInexact());
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}
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};
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// isInteger: scheme-number -> boolean
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var isInteger = function(n) {
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return (typeof(n) === 'number' ||
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(isSchemeNumber(n) && n.isInteger()));
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};
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// isExactInteger: scheme-number -> boolean
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var isExactInteger = function(n) {
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return (typeof(n) === 'number' ||
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(isSchemeNumber(n) &&
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n.isInteger() &&
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n.isExact()));
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}
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// toFixnum: scheme-number -> javascript-number
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var toFixnum = function(n) {
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if (typeof(n) === 'number')
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return n;
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return n.toFixnum();
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};
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// toExact: scheme-number -> scheme-number
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var toExact = function(n) {
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if (typeof(n) === 'number')
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return n;
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return n.toExact();
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};
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// toExact: scheme-number -> scheme-number
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var toInexact = function(n) {
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if (typeof(n) === 'number')
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return FloatPoint.makeInstance(n);
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return n.toInexact();
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};
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//////////////////////////////////////////////////////////////////////
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// add: scheme-number scheme-number -> scheme-number
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var add = function(x, y) {
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var sum;
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if (typeof(x) === 'number' && typeof(y) === 'number') {
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sum = x + y;
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if (isOverflow(sum)) {
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return (makeBignum(x)).add(makeBignum(y));
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}
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}
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if (x instanceof FloatPoint && y instanceof FloatPoint) {
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return x.add(y);
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}
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return addSlow(x, y);
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};
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var addSlow = makeNumericBinop(
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function(x, y) {
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var sum = x + y;
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if (isOverflow(sum)) {
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return (makeBignum(x)).add(makeBignum(y));
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} else {
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return sum;
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}
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},
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function(x, y) {
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return x.add(y);
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},
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{isXSpecialCase: function(x) {
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return isExactInteger(x) && _integerIsZero(x) },
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onXSpecialCase: function(x, y) { return y; },
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isYSpecialCase: function(y) {
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return isExactInteger(y) && _integerIsZero(y) },
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onYSpecialCase: function(x, y) { return x; }
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});
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// subtract: scheme-number scheme-number -> scheme-number
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var subtract = makeNumericBinop(
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function(x, y) {
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var diff = x - y;
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if (isOverflow(diff)) {
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return (makeBignum(x)).subtract(makeBignum(y));
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} else {
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return diff;
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}
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},
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function(x, y) {
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return x.subtract(y);
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},
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{isXSpecialCase: function(x) {
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return isExactInteger(x) && _integerIsZero(x) },
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onXSpecialCase: function(x, y) { return negate(y); },
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isYSpecialCase: function(y) {
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return isExactInteger(y) && _integerIsZero(y) },
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onYSpecialCase: function(x, y) { return x; }
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});
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// mulitply: scheme-number scheme-number -> scheme-number
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var multiply = function(x, y) {
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var prod;
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if (typeof(x) === 'number' && typeof(y) === 'number') {
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prod = x * y;
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if (isOverflow(prod)) {
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return (makeBignum(x)).multiply(makeBignum(y));
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} else {
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return prod;
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}
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}
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if (x instanceof FloatPoint && y instanceof FloatPoint) {
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return x.multiply(y);
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}
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return multiplySlow(x, y);
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};
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var multiplySlow = makeNumericBinop(
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function(x, y) {
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var prod = x * y;
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if (isOverflow(prod)) {
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return (makeBignum(x)).multiply(makeBignum(y));
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} else {
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return prod;
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}
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},
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function(x, y) {
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return x.multiply(y);
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},
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{isXSpecialCase: function(x) {
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return (isExactInteger(x) &&
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(_integerIsZero(x) || _integerIsOne(x) || _integerIsNegativeOne(x))) },
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onXSpecialCase: function(x, y) {
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if (_integerIsZero(x))
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return 0;
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if (_integerIsOne(x))
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return y;
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if (_integerIsNegativeOne(x))
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return negate(y);
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},
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isYSpecialCase: function(y) {
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return (isExactInteger(y) &&
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(_integerIsZero(y) || _integerIsOne(y) || _integerIsNegativeOne(y)))},
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onYSpecialCase: function(x, y) {
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if (_integerIsZero(y))
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return 0;
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if (_integerIsOne(y))
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return x;
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if (_integerIsNegativeOne(y))
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return negate(x);
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}
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});
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// divide: scheme-number scheme-number -> scheme-number
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var divide = makeNumericBinop(
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function(x, y) {
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if (_integerIsZero(y))
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throwRuntimeError("/: division by zero", x, y);
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var div = x / y;
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if (isOverflow(div)) {
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return (makeBignum(x)).divide(makeBignum(y));
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} else if (Math.floor(div) !== div) {
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return Rational.makeInstance(x, y);
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} else {
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return div;
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}
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},
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function(x, y) {
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return x.divide(y);
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},
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{ isXSpecialCase: function(x) {
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return (eqv(x, 0));
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},
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onXSpecialCase: function(x, y) {
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if (eqv(y, 0)) {
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throwRuntimeError("/: division by zero", x, y);
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}
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return 0;
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},
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isYSpecialCase: function(y) {
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return (eqv(y, 0)); },
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onYSpecialCase: function(x, y) {
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throwRuntimeError("/: division by zero", x, y);
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}
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});
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// equals: scheme-number scheme-number -> boolean
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var equals = makeNumericBinop(
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function(x, y) {
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return x === y;
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},
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function(x, y) {
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return x.equals(y);
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});
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// eqv: scheme-number scheme-number -> boolean
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var eqv = function(x, y) {
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if (x === y)
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return true;
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if (typeof(x) === 'number' && typeof(y) === 'number')
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return x === y;
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if (x === NEGATIVE_ZERO || y === NEGATIVE_ZERO)
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return x === y;
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if (x instanceof Complex || y instanceof Complex) {
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return (eqv(realPart(x), realPart(y)) &&
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eqv(imaginaryPart(x), imaginaryPart(y)));
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}
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var ex = isExact(x), ey = isExact(y);
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return (((ex && ey) || (!ex && !ey)) && equals(x, y));
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};
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// approxEqual: scheme-number scheme-number scheme-number -> boolean
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var approxEquals = function(x, y, delta) {
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return lessThan(abs(subtract(x, y)),
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delta);
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};
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// greaterThanOrEqual: scheme-number scheme-number -> boolean
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var greaterThanOrEqual = makeNumericBinop(
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function(x, y) {
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return x >= y;
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},
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function(x, y) {
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if (!(isReal(x) && isReal(y)))
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throwRuntimeError(
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">=: couldn't be applied to complex number", x, y);
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return x.greaterThanOrEqual(y);
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});
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// lessThanOrEqual: scheme-number scheme-number -> boolean
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var lessThanOrEqual = makeNumericBinop(
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function(x, y){
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return x <= y;
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},
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function(x, y) {
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if (!(isReal(x) && isReal(y)))
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throwRuntimeError("<=: couldn't be applied to complex number", x, y);
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return x.lessThanOrEqual(y);
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});
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// greaterThan: scheme-number scheme-number -> boolean
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var greaterThan = makeNumericBinop(
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function(x, y){
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return x > y;
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},
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function(x, y) {
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if (!(isReal(x) && isReal(y)))
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throwRuntimeError(">: couldn't be applied to complex number", x, y);
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return x.greaterThan(y);
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});
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// lessThan: scheme-number scheme-number -> boolean
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var lessThan = makeNumericBinop(
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function(x, y){
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return x < y;
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},
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function(x, y) {
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if (!(isReal(x) && isReal(y)))
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throwRuntimeError("<: couldn't be applied to complex number", x, y);
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return x.lessThan(y);
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});
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// expt: scheme-number scheme-number -> scheme-number
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var expt = (function() {
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var _expt = makeNumericBinop(
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function(x, y){
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var pow = Math.pow(x, y);
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if (isOverflow(pow)) {
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return (makeBignum(x)).expt(makeBignum(y));
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} else {
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return pow;
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}
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},
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function(x, y) {
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if (equals(y, 0)) {
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return add(y, 1);
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} else {
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return x.expt(y);
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}
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});
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return function(x, y) {
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if (equals(y, 0))
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return add(y, 1);
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if (isReal(y) && lessThan(y, 0)) {
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return _expt(divide(1, x), negate(y));
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}
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return _expt(x, y);
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};
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})();
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// exp: scheme-number -> scheme-number
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var exp = function(n) {
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if ( eqv(n, 0) ) {
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return 1;
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}
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if (typeof(n) === 'number') {
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return FloatPoint.makeInstance(Math.exp(n));
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}
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return n.exp();
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};
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// modulo: scheme-number scheme-number -> scheme-number
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var modulo = function(m, n) {
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if (! isInteger(m)) {
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throwRuntimeError('modulo: the first argument '
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+ m + " is not an integer.", m, n);
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}
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if (! isInteger(n)) {
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throwRuntimeError('modulo: the second argument '
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+ n + " is not an integer.", m, n);
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}
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var result;
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if (typeof(m) === 'number') {
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result = m % n;
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if (n < 0) {
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if (result <= 0)
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return result;
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else
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return result + n;
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} else {
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if (result < 0)
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return result + n;
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else
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return result;
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}
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}
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result = _integerModulo(floor(m), floor(n));
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// The sign of the result should match the sign of n.
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if (lessThan(n, 0)) {
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if (lessThanOrEqual(result, 0)) {
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return result;
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}
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return add(result, n);
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} else {
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if (lessThan(result, 0)) {
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return add(result, n);
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}
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return result;
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}
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};
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// numerator: scheme-number -> scheme-number
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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 (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));
|
|
};
|
|
|
|
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 fl;
|
|
}
|
|
else {
|
|
return ce;
|
|
}
|
|
} else {
|
|
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 (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+)$");
|
|
var complexRegexp = new RegExp("^([+-]?[\\d\\w/\\.]*)([+-])([\\d\\w/\\.]*)i$");
|
|
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(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 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
|
|
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; }
|
|
|
|
// (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 + ''; }
|
|
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;
|
|
|
|
})();
|