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Yet another class for arbitrary-precision integers in pure JavaScript. Small. Well tested.

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/* JavaScript BigInteger library version 0.9 http://silentmatt.com/biginteger/ Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com> Copyright (c) 2010,2011 by John Tobey <jtobey@john-edwin-tobey.org> Licensed under the MIT license. Support for arbitrary internal representation base was added by Vitaly Magerya. */ /* File: biginteger.js Exports: <BigInteger> */ /* Class: BigInteger An arbitrarily-large integer. <BigInteger> objects should be considered immutable. None of the "built-in" methods modify *this* or their arguments. All properties should be considered private. All the methods of <BigInteger> instances can be called "statically". The static versions are convenient if you don't already have a <BigInteger> object. As an example, these calls are equivalent. > BigInteger(4).multiply(5); // returns BigInteger(20); > BigInteger.multiply(4, 5); // returns BigInteger(20); > var a = 42; > var a = BigInteger.toJSValue("0b101010"); // Not completely useless... */ // IE doesn't support Array.prototype.map if (!Array.prototype.map) { Array.prototype.map = function(fun /*, thisp*/) { var len = this.length >>> 0; if (typeof fun !== "function") { throw new TypeError(); } var res = new Array(len); var thisp = arguments[1]; for (var i = 0; i < len; i++) { if (i in this) { res[i] = fun.call(thisp, this[i], i, this); } } return res; }; } /* Constructor: BigInteger() Convert a value to a <BigInteger>. Although <BigInteger()> is the constructor for <BigInteger> objects, it is best not to call it as a constructor. If *n* is a <BigInteger> object, it is simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse> without a radix argument. > var n0 = BigInteger(); // Same as <BigInteger.ZERO> > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123 > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123 > var n3 = BigInteger(n2); // Return n2, unchanged The constructor form only takes an array and a sign. *n* must be an array of numbers in little-endian order, where each digit is between 0 and BigInteger.base. The second parameter sets the sign: -1 for negative, +1 for positive, or 0 for zero. The array is *not copied and may be modified*. If the array contains only zeros, the sign parameter is ignored and is forced to zero. > new BigInteger([5], -1): create a new BigInteger with value -5 Parameters: n - Value to convert to a <BigInteger>. Returns: A <BigInteger> value. See Also: <parse>, <BigInteger> */ function BigInteger(n, s) { if (!(this instanceof BigInteger)) { if (n instanceof BigInteger) { return n; } else if (typeof n === "undefined") { return BigInteger.ZERO; } return BigInteger.parse(n); } n = n || []; // Provide the nullary constructor for subclasses. while (n.length && !n[n.length - 1]) { --n.length; } this._d = n; this._s = n.length ? (s || 1) : 0; } // Base-10 speedup hacks in parse, toString, exp10 and log functions // require base to be a power of 10. 10^7 is the largest such power // that won't cause a precision loss when digits are multiplied. BigInteger.base = 10000000; BigInteger.base_log10 = 7; BigInteger.init = function() { // Constant: ZERO // <BigInteger> 0. BigInteger.ZERO = new BigInteger([], 0); // Constant: ONE // <BigInteger> 1. BigInteger.ONE = new BigInteger([1], 1); // Constant: M_ONE // <BigInteger> -1. BigInteger.M_ONE = new BigInteger(BigInteger.ONE._d, -1); // Constant: _0 // Shortcut for <ZERO>. BigInteger._0 = BigInteger.ZERO; // Constant: _1 // Shortcut for <ONE>. BigInteger._1 = BigInteger.ONE; /* Constant: small Array of <BigIntegers> from 0 to 36. These are used internally for parsing, but useful when you need a "small" <BigInteger>. See Also: <ZERO>, <ONE>, <_0>, <_1> */ BigInteger.small = [ BigInteger.ZERO, BigInteger.ONE, /* Assuming BigInteger.base > 36 */ new BigInteger( [2], 1), new BigInteger( [3], 1), new BigInteger( [4], 1), new BigInteger( [5], 1), new BigInteger( [6], 1), new BigInteger( [7], 1), new BigInteger( [8], 1), new BigInteger( [9], 1), new BigInteger([10], 1), new BigInteger([11], 1), new BigInteger([12], 1), new BigInteger([13], 1), new BigInteger([14], 1), new BigInteger([15], 1), new BigInteger([16], 1), new BigInteger([17], 1), new BigInteger([18], 1), new BigInteger([19], 1), new BigInteger([20], 1), new BigInteger([21], 1), new BigInteger([22], 1), new BigInteger([23], 1), new BigInteger([24], 1), new BigInteger([25], 1), new BigInteger([26], 1), new BigInteger([27], 1), new BigInteger([28], 1), new BigInteger([29], 1), new BigInteger([30], 1), new BigInteger([31], 1), new BigInteger([32], 1), new BigInteger([33], 1), new BigInteger([34], 1), new BigInteger([35], 1), new BigInteger([36], 1) ]; } BigInteger.init(); // Used for parsing/radix conversion BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split(""); /* Method: toString Convert a <BigInteger> to a string. When *base* is greater than 10, letters are upper case. Parameters: base - Optional base to represent the number in (default is base 10). Must be between 2 and 36 inclusive, or an Error will be thrown. Returns: The string representation of the <BigInteger>. */ BigInteger.prototype.toString = function(base) { base = +base || 10; if (base < 2 || base > 36) { throw new Error("illegal radix " + base + "."); } if (this._s === 0) { return "0"; } if (base === 10) { var str = this._s < 0 ? "-" : ""; str += this._d[this._d.length - 1].toString(); for (var i = this._d.length - 2; i >= 0; i--) { var group = this._d[i].toString(); while (group.length < BigInteger.base_log10) group = '0' + group; str += group; } return str; } else { var numerals = BigInteger.digits; base = BigInteger.small[base]; var sign = this._s; var n = this.abs(); var digits = []; var digit; while (n._s !== 0) { var divmod = n.divRem(base); n = divmod[0]; digit = divmod[1]; // TODO: This could be changed to unshift instead of reversing at the end. // Benchmark both to compare speeds. digits.push(numerals[digit.valueOf()]); } return (sign < 0 ? "-" : "") + digits.reverse().join(""); } }; // Verify strings for parsing BigInteger.radixRegex = [ /^$/, /^$/, /^[01]*$/, /^[012]*$/, /^[0-3]*$/, /^[0-4]*$/, /^[0-5]*$/, /^[0-6]*$/, /^[0-7]*$/, /^[0-8]*$/, /^[0-9]*$/, /^[0-9aA]*$/, /^[0-9abAB]*$/, /^[0-9abcABC]*$/, /^[0-9a-dA-D]*$/, /^[0-9a-eA-E]*$/, /^[0-9a-fA-F]*$/, /^[0-9a-gA-G]*$/, /^[0-9a-hA-H]*$/, /^[0-9a-iA-I]*$/, /^[0-9a-jA-J]*$/, /^[0-9a-kA-K]*$/, /^[0-9a-lA-L]*$/, /^[0-9a-mA-M]*$/, /^[0-9a-nA-N]*$/, /^[0-9a-oA-O]*$/, /^[0-9a-pA-P]*$/, /^[0-9a-qA-Q]*$/, /^[0-9a-rA-R]*$/, /^[0-9a-sA-S]*$/, /^[0-9a-tA-T]*$/, /^[0-9a-uA-U]*$/, /^[0-9a-vA-V]*$/, /^[0-9a-wA-W]*$/, /^[0-9a-xA-X]*$/, /^[0-9a-yA-Y]*$/, /^[0-9a-zA-Z]*$/ ]; /* Function: parse Parse a string into a <BigInteger>. *base* is optional but, if provided, must be from 2 to 36 inclusive. If *base* is not provided, it will be guessed based on the leading characters of *s* as follows: - "0x" or "0X": *base* = 16 - "0c" or "0C": *base* = 8 - "0b" or "0B": *base* = 2 - else: *base* = 10 If no base is provided, or *base* is 10, the number can be in exponential form. For example, these are all valid: > BigInteger.parse("1e9"); // Same as "1000000000" > BigInteger.parse("1.234*10^3"); // Same as 1234 > BigInteger.parse("56789 * 10 ** -2"); // Same as 567 If any characters fall outside the range defined by the radix, an exception will be thrown. Parameters: s - The string to parse. base - Optional radix (default is to guess based on *s*). Returns: a <BigInteger> instance. */ BigInteger.parse = function(s, base) { // Expands a number in exponential form to decimal form. // expandExponential("-13.441*10^5") === "1344100"; // expandExponential("1.12300e-1") === "0.112300"; // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000"; function expandExponential(str) { str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e"); return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) { c = +c; var l = c < 0; var i = n.length + c; x = (l ? n : f).length; c = ((c = Math.abs(c)) >= x ? c - x + l : 0); var z = (new Array(c + 1)).join("0"); var r = n + f; return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : ""); }); } s = s.toString(); if (typeof base === "undefined" || +base === 10) { s = expandExponential(s); } var parts = /^([+\-]?)(0[xXcCbB])?([0-9A-Za-z]*)(?:\.\d*)?$/.exec(s); if (parts) { var sign = parts[1] || "+"; var baseSection = parts[2] || ""; var digits = parts[3] || ""; if (typeof base === "undefined") { // Guess base if (baseSection === "0x" || baseSection === "0X") { // Hex base = 16; } else if (baseSection === "0c" || baseSection === "0C") { // Octal base = 8; } else if (baseSection === "0b" || baseSection === "0B") { // Binary base = 2; } else { base = 10; } } else if (base < 2 || base > 36) { throw new Error("Illegal radix " + base + "."); } base = +base; // Check for digits outside the range if (!(BigInteger.radixRegex[base].test(digits))) { throw new Error("Bad digit for radix " + base); } // Strip leading zeros, and convert to array digits = digits.replace(/^0+/, "").split(""); if (digits.length === 0) { return BigInteger.ZERO; } // Get the sign (we know it's not zero) sign = (sign === "-") ? -1 : 1; // Optimize 10 if (base == 10) { var d = []; while (digits.length >= BigInteger.base_log10) { d.push(parseInt(digits.splice(-BigInteger.base_log10).join(''), 10)); } d.push(parseInt(digits.join(''), 10)); return new BigInteger(d, sign); } // Optimize base if (base === BigInteger.base) { return new BigInteger(digits.map(Number).reverse(), sign); } // Do the conversion var d = BigInteger.ZERO; base = BigInteger.small[base]; var small = BigInteger.small; for (var i = 0; i < digits.length; i++) { d = d.multiply(base).add(small[parseInt(digits[i], 36)]); } return new BigInteger(d._d, sign); } else { throw new Error("Invalid BigInteger format: " + s); } }; /* Function: add Add two <BigIntegers>. Parameters: n - The number to add to *this*. Will be converted to a <BigInteger>. Returns: The numbers added together. See Also: <subtract>, <multiply>, <quotient>, <next> */ BigInteger.prototype.add = function(n) { if (this._s === 0) { return BigInteger(n); } n = BigInteger(n); if (n._s === 0) { return this; } if (this._s !== n._s) { n = n.negate(); return this.subtract(n); } var a = this._d; var b = n._d; var al = a.length; var bl = b.length; var sum = new Array(Math.max(al, bl) + 1); var size = Math.min(al, bl); var carry = 0; var digit; for (var i = 0; i < size; i++) { digit = a[i] + b[i] + carry; sum[i] = digit % BigInteger.base; carry = (digit / BigInteger.base) | 0; } if (bl > al) { a = b; al = bl; } for (i = size; carry && i < al; i++) { digit = a[i] + carry; sum[i] = digit % BigInteger.base; carry = (digit / BigInteger.base) | 0; } if (carry) { sum[i] = carry; } for ( ; i < al; i++) { sum[i] = a[i]; } return new BigInteger(sum, this._s); }; /* Function: negate Get the additive inverse of a <BigInteger>. Returns: A <BigInteger> with the same magnatude, but with the opposite sign. See Also: <abs> */ BigInteger.prototype.negate = function() { return new BigInteger(this._d, -this._s); }; /* Function: abs Get the absolute value of a <BigInteger>. Returns: A <BigInteger> with the same magnatude, but always positive (or zero). See Also: <negate> */ BigInteger.prototype.abs = function() { return (this._s < 0) ? this.negate() : this; }; /* Function: subtract Subtract two <BigIntegers>. Parameters: n - The number to subtract from *this*. Will be converted to a <BigInteger>. Returns: The *n* subtracted from *this*. See Also: <add>, <multiply>, <quotient>, <prev> */ BigInteger.prototype.subtract = function(n) { if (this._s === 0) { return BigInteger(n).negate(); } n = BigInteger(n); if (n._s === 0) { return this; } if (this._s !== n._s) { n = n.negate(); return this.add(n); } var m = this; var t; // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a| if (this._s < 0) { t = m; m = new BigInteger(n._d, 1); n = new BigInteger(t._d, 1); } // Both are positive => a - b var sign = m.compareAbs(n); if (sign === 0) { return BigInteger.ZERO; } else if (sign < 0) { // swap m and n t = n; n = m; m = t; } // a > b var a = m._d; var b = n._d; var al = a.length; var bl = b.length; var diff = new Array(al); // al >= bl since a > b var borrow = 0; var i; var digit; for (i = 0; i < bl; i++) { digit = a[i] - borrow - b[i]; if (digit < 0) { digit += BigInteger.base; borrow = 1; } else { borrow = 0; } diff[i] = digit; } for (i = bl; i < al; i++) { digit = a[i] - borrow; if (digit < 0) { digit += BigInteger.base; } else { diff[i++] = digit; break; } diff[i] = digit; } for ( ; i < al; i++) { diff[i] = a[i]; } return new BigInteger(diff, sign); }; (function() { function addOne(n, sign) { var a = n._d; var sum = a.slice(); var carry = true; var i = 0; while (true) { var digit = (a[i] || 0) + 1; sum[i] = digit % BigInteger.base; if (digit <= BigInteger.base - 1) { break; } ++i; } return new BigInteger(sum, sign); } function subtractOne(n, sign) { var a = n._d; var sum = a.slice(); var borrow = true; var i = 0; while (true) { var digit = (a[i] || 0) - 1; if (digit < 0) { sum[i] = digit + BigInteger.base; } else { sum[i] = digit; break; } ++i; } return new BigInteger(sum, sign); } /* Function: next Get the next <BigInteger> (add one). Returns: *this* + 1. See Also: <add>, <prev> */ BigInteger.prototype.next = function() { switch (this._s) { case 0: return BigInteger.ONE; case -1: return subtractOne(this, -1); // case 1: default: return addOne(this, 1); } }; /* Function: prev Get the previous <BigInteger> (subtract one). Returns: *this* - 1. See Also: <next>, <subtract> */ BigInteger.prototype.prev = function() { switch (this._s) { case 0: return BigInteger.M_ONE; case -1: return addOne(this, -1); // case 1: default: return subtractOne(this, 1); } }; })(); /* Function: compareAbs Compare the absolute value of two <BigIntegers>. Calling <compareAbs> is faster than calling <abs> twice, then <compare>. Parameters: n - The number to compare to *this*. Will be converted to a <BigInteger>. Returns: -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*. See Also: <compare>, <abs> */ BigInteger.prototype.compareAbs = function(n) { if (this === n) { return 0; } if (!(n instanceof BigInteger)) { if (!isFinite(n)) { return(isNaN(n) ? n : -1); } n = BigInteger(n); } if (this._s === 0) { return (n._s !== 0) ? -1 : 0; } if (n._s === 0) { return 1; } var l = this._d.length; var nl = n._d.length; if (l < nl) { return -1; } else if (l > nl) { return 1; } var a = this._d; var b = n._d; for (var i = l-1; i >= 0; i--) { if (a[i] !== b[i]) { return a[i] < b[i] ? -1 : 1; } } return 0; }; /* Function: compare Compare two <BigIntegers>. Parameters: n - The number to compare to *this*. Will be converted to a <BigInteger>. Returns: -1, 0, or +1 if *this* is less than, equal to, or greater than *n*. See Also: <compareAbs>, <isPositive>, <isNegative>, <isUnit> */ BigInteger.prototype.compare = function(n) { if (this === n) { return 0; } n = BigInteger(n); if (this._s === 0) { return -n._s; } if (this._s === n._s) { // both positive or both negative var cmp = this.compareAbs(n); return cmp * this._s; } else { return this._s; } }; /* Function: isUnit Return true iff *this* is either 1 or -1. Returns: true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>. See Also: <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>, <BigInteger.ONE>, <BigInteger.M_ONE> */ BigInteger.prototype.isUnit = function() { return this === BigInteger.ONE || this === BigInteger.M_ONE || (this._d.length === 1 && this._d[0] === 1); }; /* Function: multiply Multiply two <BigIntegers>. Parameters: n - The number to multiply *this* by. Will be converted to a <BigInteger>. Returns: The numbers multiplied together. See Also: <add>, <subtract>, <quotient>, <square> */ BigInteger.prototype.multiply = function(n) { // TODO: Consider adding Karatsuba multiplication for large numbers if (this._s === 0) { return BigInteger.ZERO; } n = BigInteger(n); if (n._s === 0) { return BigInteger.ZERO; } if (this.isUnit()) { if (this._s < 0) { return n.negate(); } return n; } if (n.isUnit()) { if (n._s < 0) { return this.negate(); } return this; } if (this === n) { return this.square(); } var r = (this._d.length >= n._d.length); var a = (r ? this : n)._d; // a will be longer than b var b = (r ? n : this)._d; var al = a.length; var bl = b.length; var pl = al + bl; var partial = new Array(pl); var i; for (i = 0; i < pl; i++) { partial[i] = 0; } for (i = 0; i < bl; i++) { var carry = 0; var bi = b[i]; var jlimit = al + i; var digit; for (var j = i; j < jlimit; j++) { digit = partial[j] + bi * a[j - i] + carry; carry = (digit / BigInteger.base) | 0; partial[j] = (digit % BigInteger.base) | 0; } if (carry) { digit = partial[j] + carry; carry = (digit / BigInteger.base) | 0; partial[j] = digit % BigInteger.base; } } return new BigInteger(partial, this._s * n._s); }; // Multiply a BigInteger by a single-digit native number // Assumes that this and n are >= 0 // This is not really intended to be used outside the library itself BigInteger.prototype.multiplySingleDigit = function(n) { if (n === 0 || this._s === 0) { return BigInteger.ZERO; } if (n === 1) { return this; } var digit; if (this._d.length === 1) { digit = this._d[0] * n; if (digit >= BigInteger.base) { return new BigInteger([(digit % BigInteger.base)|0, (digit / BigInteger.base)|0], 1); } return new BigInteger([digit], 1); } if (n === 2) { return this.add(this); } if (this.isUnit()) { return new BigInteger([n], 1); } var a = this._d; var al = a.length; var pl = al + 1; var partial = new Array(pl); for (var i = 0; i < pl; i++) { partial[i] = 0; } var carry = 0; for (var j = 0; j < al; j++) { digit = n * a[j] + carry; carry = (digit / BigInteger.base) | 0; partial[j] = (digit % BigInteger.base) | 0; } if (carry) { digit = carry; carry = (digit / BigInteger.base) | 0; partial[j] = digit % BigInteger.base; } return new BigInteger(partial, 1); }; /* Function: square Multiply a <BigInteger> by itself. This is slightly faster than regular multiplication, since it removes the duplicated multiplcations. Returns: > this.multiply(this) See Also: <multiply> */ BigInteger.prototype.square = function() { // Normally, squaring a 10-digit number would take 100 multiplications. // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated. // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies). // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org if (this._s === 0) { return BigInteger.ZERO; } if (this.isUnit()) { return BigInteger.ONE; } var digits = this._d; var length = digits.length; var imult1 = new Array(length + length + 1); var product, carry, k; var i; // Calculate diagonal for (i = 0; i < length; i++) { k = i * 2; product = digits[i] * digits[i]; carry = (product / BigInteger.base) | 0; imult1[k] = product % BigInteger.base; imult1[k + 1] = carry; } // Calculate repeating part for (i = 0; i < length; i++) { carry = 0; k = i * 2 + 1; for (var j = i + 1; j < length; j++, k++) { product = digits[j] * digits[i] * 2 + imult1[k] + carry; carry = (product / BigInteger.base) | 0; imult1[k] = product % BigInteger.base; } k = length + i; var digit = carry + imult1[k]; carry = (digit / BigInteger.base) | 0; imult1[k] = digit % BigInteger.base; imult1[k + 1] += carry; } return new BigInteger(imult1, 1); }; /* Function: quotient Divide two <BigIntegers> and truncate towards zero. <quotient> throws an exception if *n* is zero. Parameters: n - The number to divide *this* by. Will be converted to a <BigInteger>. Returns: The *this* / *n*, truncated to an integer. See Also: <add>, <subtract>, <multiply>, <divRem>, <remainder> */ BigInteger.prototype.quotient = function(n) { return this.divRem(n)[0]; }; /* Function: divide Deprecated synonym for <quotient>. */ BigInteger.prototype.divide = BigInteger.prototype.quotient; /* Function: remainder Calculate the remainder of two <BigIntegers>. <remainder> throws an exception if *n* is zero. Parameters: n - The remainder after *this* is divided *this* by *n*. Will be converted to a <BigInteger>. Returns: *this* % *n*. See Also: <divRem>, <quotient> */ BigInteger.prototype.remainder = function(n) { return this.divRem(n)[1]; }; /* Function: divRem Calculate the integer quotient and remainder of two <BigIntegers>. <divRem> throws an exception if *n* is zero. Parameters: n - The number to divide *this* by. Will be converted to a <BigInteger>. Returns: A two-element array containing the quotient and the remainder. > a.divRem(b) is exactly equivalent to > [a.quotient(b), a.remainder(b)] except it is faster, because they are calculated at the same time. See Also: <quotient>, <remainder> */ BigInteger.prototype.divRem = function(n) { n = BigInteger(n); if (n._s === 0) { throw new Error("Divide by zero"); } if (this._s === 0) { return [BigInteger.ZERO, BigInteger.ZERO]; } if (n._d.length === 1) { return this.divRemSmall(n._s * n._d[0]); } // Test for easy cases -- |n1| <= |n2| switch (this.compareAbs(n)) { case 0: // n1 == n2 return [this._s === n._s ? BigInteger.ONE : BigInteger.M_ONE, BigInteger.ZERO]; case -1: // |n1| < |n2| return [BigInteger.ZERO, this]; } var sign = this._s * n._s; var a = n.abs(); var b_digits = this._d.slice(); var digits = n._d.length; var max = b_digits.length; var quot = []; var guess; var part = new BigInteger([], 1); part._s = 1; while (b_digits.length) { part._d.unshift(b_digits.pop()); part = new BigInteger(part._d, 1); if (part.compareAbs(n) < 0) { quot.push(0); continue; } if (part._s === 0) { guess = 0; } else { var xlen = part._d.length, ylen = a._d.length; var highx = part._d[xlen-1]*BigInteger.base + part._d[xlen-2]; var highy = a._d[ylen-1]*BigInteger.base + a._d[ylen-2]; if (part._d.length > a._d.length) { // The length of part._d can either match a._d length, // or exceed it by one. highx = (highx+1)*BigInteger.base; } guess = Math.ceil(highx/highy); } do { var check = a.multiplySingleDigit(guess); if (check.compareAbs(part) <= 0) { break; } guess--; } while (guess); quot.push(guess); if (!guess) { continue; } var diff = part.subtract(check); part._d = diff._d.slice(); } return [new BigInteger(quot.reverse(), sign), new BigInteger(part._d, this._s)]; }; // Throws an exception if n is outside of (-BigInteger.base, -1] or // [1, BigInteger.base). It's not necessary to call this, since the // other division functions will call it if they are able to. BigInteger.prototype.divRemSmall = function(n) { var r; n = +n; if (n === 0) { throw new Error("Divide by zero"); } var n_s = n < 0 ? -1 : 1; var sign = this._s * n_s; n = Math.abs(n); if (n < 1 || n >= BigInteger.base) { throw new Error("Argument out of range"); } if (this._s === 0) { return [BigInteger.ZERO, BigInteger.ZERO]; } if (n === 1 || n === -1) { return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign), BigInteger.ZERO]; } // 2 <= n < BigInteger.base // divide a single digit by a single digit if (this._d.length === 1) { var q = new BigInteger([(this._d[0] / n) | 0], 1); r = new BigInteger([(this._d[0] % n) | 0], 1); if (sign < 0) { q = q.negate(); } if (this._s < 0) { r = r.negate(); } return [q, r]; } var digits = this._d.slice(); var quot = new Array(digits.length); var part = 0; var diff = 0; var i = 0; var guess; while (digits.length) { part = part * BigInteger.base + digits[digits.length - 1]; if (part < n) { quot[i++] = 0; digits.pop(); diff = BigInteger.base * diff + part; continue; } if (part === 0) { guess = 0; } else { guess = (part / n) | 0; } var check = n * guess; diff = part - check; quot[i++] = guess; if (!guess) { digits.pop(); continue; } digits.pop(); part = diff; } r = new BigInteger([diff], 1); if (this._s < 0) { r = r.negate(); } return [new BigInteger(quot.reverse(), sign), r]; }; /* Function: isEven Return true iff *this* is divisible by two. Note that <BigInteger.ZERO> is even. Returns: true if *this* is even, false otherwise. See Also: <isOdd> */ BigInteger.prototype.isEven = function() { var digits = this._d; return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0; }; /* Function: isOdd Return true iff *this* is not divisible by two. Returns: true if *this* is odd, false otherwise. See Also: <isEven> */ BigInteger.prototype.isOdd = function() { return !this.isEven(); }; /* Function: sign Get the sign of a <BigInteger>. Returns: * -1 if *this* < 0 * 0 if *this* == 0 * +1 if *this* > 0 See Also: <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO> */ BigInteger.prototype.sign = function() { return this._s; }; /* Function: isPositive Return true iff *this* > 0. Returns: true if *this*.compare(<BigInteger.ZERO>) == 1. See Also: <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO> */ BigInteger.prototype.isPositive = function() { return this._s > 0; }; /* Function: isNegative Return true iff *this* < 0. Returns: true if *this*.compare(<BigInteger.ZERO>) == -1. See Also: <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO> */ BigInteger.prototype.isNegative = function() { return this._s < 0; }; /* Function: isZero Return true iff *this* == 0. Returns: true if *this*.compare(<BigInteger.ZERO>) == 0. See Also: <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO> */ BigInteger.prototype.isZero = function() { return this._s === 0; }; /* Function: exp10 Multiply a <BigInteger> by a power of 10. This is equivalent to, but faster than > if (n >= 0) { > return this.multiply(BigInteger("1e" + n)); > } > else { // n <= 0 > return this.quotient(BigInteger("1e" + -n)); > } Parameters: n - The power of 10 to multiply *this* by. *n* is converted to a javascipt number and must be no greater than <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown. Returns: *this* * (10 ** *n*), truncated to an integer if necessary. See Also: <pow>, <multiply> */ BigInteger.prototype.exp10 = function(n) { n = +n; if (n === 0) { return this; } if (Math.abs(n) > Number(BigInteger.MAX_EXP)) { throw new Error("exponent too large in BigInteger.exp10"); } if (n > 0) { var k = new BigInteger(this._d.slice(), this._s); for (; n >= BigInteger.base_log10; n -= BigInteger.base_log10) { k._d.unshift(0); } if (n == 0) return k; k._s = 1; k = k.multiplySingleDigit(Math.pow(10, n)); return (this._s < 0 ? k.negate() : k); } else if (-n >= this._d.length*BigInteger.base_log10) { return BigInteger.ZERO; } else { var k = new BigInteger(this._d.slice(), this._s); for (n = -n; n >= BigInteger.base_log10; n -= BigInteger.base_log10) { k._d.shift(); } return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0]; } }; /* Function: pow Raise a <BigInteger> to a power. In this implementation, 0**0 is 1. Parameters: n - The exponent to raise *this* by. *n* must be no greater than <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown. Returns: *this* raised to the *nth* power. See Also: <modPow> */ BigInteger.prototype.pow = function(n) { if (this.isUnit()) { if (this._s > 0) { return this; } else { return BigInteger(n).isOdd() ? this : this.negate(); } } n = BigInteger(n); if (n._s === 0) { return BigInteger.ONE; } else if (n._s < 0) { if (this._s === 0) { throw new Error("Divide by zero"); } else { return BigInteger.ZERO; } } if (this._s === 0) { return BigInteger.ZERO; } if (n.isUnit()) { return this; } if (n.compareAbs(BigInteger.MAX_EXP) > 0) { throw new Error("exponent too large in BigInteger.pow"); } var x = this; var aux = BigInteger.ONE; var two = BigInteger.small[2]; while (n.isPositive()) { if (n.isOdd()) { aux = aux.multiply(x); if (n.isUnit()) { return aux; } } x = x.square(); n = n.quotient(two); } return aux; }; /* Function: modPow Raise a <BigInteger> to a power (mod m). Because it is reduced by a modulus, <modPow> is not limited by <BigInteger.MAX_EXP> like <pow>. Parameters: exponent - The exponent to raise *this* by. Must be positive. modulus - The modulus. Returns: *this* ^ *exponent* (mod *modulus*). See Also: <pow>, <mod> */ BigInteger.prototype.modPow = function(exponent, modulus) { var result = BigInteger.ONE; var base = this; while (exponent.isPositive()) { if (exponent.isOdd()) { result = result.multiply(base).remainder(modulus); } exponent = exponent.quotient(BigInteger.small[2]); if (exponent.isPositive()) { base = base.square().remainder(modulus); } } return result; }; /* Function: log Get the natural logarithm of a <BigInteger> as a native JavaScript number. This is equivalent to > Math.log(this.toJSValue()) but handles values outside of the native number range. Returns: log( *this* ) See Also: <toJSValue> */ BigInteger.prototype.log = function() { switch (this._s) { case 0: return -Infinity; case -1: return NaN; default: // Fall through. } var l = this._d.length; if (l*BigInteger.base_log10 < 30) { return Math.log(this.valueOf()); } var N = Math.ceil(30/BigInteger.base_log10); var firstNdigits = this._d.slice(l - N); return Math.log((new BigInteger(firstNdigits, 1)).valueOf()) + (l - N) * Math.log(BigInteger.base); }; /* Function: valueOf Convert a <BigInteger> to a native JavaScript integer. This is called automatically by JavaScipt to convert a <BigInteger> to a native value. Returns: > parseInt(this.toString(), 10) See Also: <toString>, <toJSValue> */ BigInteger.prototype.valueOf = function() { return parseInt(this.toString(), 10); }; /* Function: toJSValue Convert a <BigInteger> to a native JavaScript integer. This is the same as valueOf, but more explicitly named. Returns: > parseInt(this.toString(), 10) See Also: <toString>, <valueOf> */ BigInteger.prototype.toJSValue = function() { return parseInt(this.toString(), 10); }; // Constant: MAX_EXP // The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647). BigInteger.MAX_EXP = BigInteger(0x7FFFFFFF); (function() { function makeUnary(fn) { return function(a) { return fn.call(BigInteger(a)); }; } function makeBinary(fn) { return function(a, b) { return fn.call(BigInteger(a), BigInteger(b)); }; } function makeTrinary(fn) { return function(a, b, c) { return fn.call(BigInteger(a), BigInteger(b), BigInteger(c)); }; } (function() { var i, fn; var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(","); var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(","); var trinary = ["modPow"]; for (i = 0; i < unary.length; i++) { fn = unary[i]; BigInteger[fn] = makeUnary(BigInteger.prototype[fn]); } for (i = 0; i < binary.length; i++) { fn = binary[i]; BigInteger[fn] = makeBinary(BigInteger.prototype[fn]); } for (i = 0; i < trinary.length; i++) { fn = trinary[i]; BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]); } BigInteger.exp10 = function(x, n) { return BigInteger(x).exp10(n); }; })(); })(); if (typeof exports !== 'undefined') { exports.BigInteger = BigInteger; } // Scheme numerical tower in JavaScript. // Copyright (c) 2011,2012 by John Tobey <jtobey@john-edwin-tobey.org> /* File: schemeNumber.js Exports: <SchemeNumber> Depends: <biginteger.js> for <BigInteger> */ /* Class: SchemeNumber A number object as <defined by the Scheme language at http://www.r6rs.org/>. Scheme supports *exact* arithmetic and mixing exact with standard (*inexact*) numbers. Several basic operations, including addition, subtraction, multiplication, and division, when given only exact arguments, must return an exact, numerically correct result. These operations are allowed to fail due to running out of memory, but they are not allowed to return approximations the way ECMAScript operators may, unless given one or more inexact arguments. For example, adding exact *1/100* to exact *0* one hundred times produces exactly *1*, not 1.0000000000000007 as in JavaScript. Raising exact *2* to the power of exact *1024* returns a 308-digit integer with complete precision, not *Infinity* as in ECMAScript. This implementation provides all functions listed in the <R6RS Scheme specification at http://www.r6rs.org/>, Section 11.7, along with <eqv?> from Section 11.5. (<eqv?> uses JavaScript's *===* to compare non-numbers.) Exact numbers support the standard ECMA Number formatting methods (toFixed, toExponential, and toPrecision) without a fixed upper limit to precision. The schemeNumber.js file exports an object <SchemeNumber>. It contains a property <fn>, which in turn contains the functions implementing the numeric types. The <SchemeNumber> object is in fact a function that converts its argument to a Scheme number: similar to a constructor, but it may not always return an object, let alone a unique object. Parameters: obj - Object to be converted to a Scheme number. *obj* may have any of the following types: Scheme number - returned unchanged. String - converted as if by *string->number*. Native ECMAScript number - treated as an inexact real. Returns: A Scheme number. Exceptions: If *obj* can not be parsed, <SchemeNumber> will <raise> an exception with condition type *&assertion*. See Also: <fn>, <raise>, <R6RS Chapter 3: Numbers at http://www.r6rs.org/final/html/r6rs/r6rs-Z-H-6.html#node_chap_3> */ var SchemeNumber = (function() { // // Multiple dispatch support. // var DispatchJs = (function() { "use strict"; /* Multiple dispatch for JavaScript functions of fixed arity. Example: // B and C inherit from A. D inherits from C. var A = disp.defClass("A", {ctor: function(x) { this.x = x }}); var B = disp.defClass("B", {base: "A"}); var C = disp.defClass("C", {base: "A"}); // Classes may be defined after their superclass methods. //var D = disp.defClass("D", {base: "C"}); // Or you can declare existing classes: //var disp = DispatchJs; //function A(){} A.prototype = {}; //disp.defClass("A", {ctor: A}); //function B(){} B.prototype = new A(); //disp.defClass("B", {ctor: B, base "A"}); //function C(){} C.prototype = new A(); //disp.defClass("C", {ctor: C, base "A"}); //function D(){} D.prototype = new C(); //disp.defClass("D", {ctor: D, base "C"}); // This creates a function of 2 arguments: var frob = disp.defGeneric("frob", 2); // Define methods. Methods receive frob's first argument as "this" and // the rest as method arguments. frob.def("A", "A", function(a1) { return "A A" }); frob.def("A", "B", function(a1) { return "A B" }); frob.def("B", "A", function(a1) { return "B A" }); frob.def("B", "B", function(a1) { return "B B" }); frob.def("A", "C", function(a1) { return "A C" }); var D = disp.defClass("D", function(x) { this.x = x }, "C"); frob.def("D", "D", function(a1) { return "D D" }); // Create some arguments: var a = new A(); var b = new B(); var c = new C(); var d = new D(); // Call the function: frob(a,a); // "A A" frob(a,b); // "A B" frob(a,c); // "A C" frob(a,d); // "A C" frob(b,a); // "B A" frob(b,b); // "B B" frob(b,c); // "B A" or "A C" frob(b,d); // "B A" or "A C" frob(c,a); // "A A" frob(c,b); // "A B" frob(c,c); // "A C" frob(c,d); // "A C" frob(d,a); // "A A" frob(d,b); // "A B" frob(d,c); // "A C" frob(d,d); // "D D" Ambiguous calls such as frob(b,c) and frob(b,d) above use whichever of the best candidates was defined first: the method for types B,A or the one for A,C. */ function short_fn(f) { return String(f).replace(/(?:.|\n)*(function .*?\(.*?\))(?:.|\n)*/, "$1"); } var Formals = []; function makeContext(opts) { var g = opts.globals; var _Function = (g ? g.Function : Function); var uncurry = _Function.prototype.bind.bind(_Function.prototype.call); var _Object = (g ? g.Object : Object); var _String = (g ? g.String : String); var _Array = (g ? g.Array : Array); var _Error = (g ? g.Error : Error); var _apply = uncurry(_Function.prototype.apply); var _slice = uncurry(_Array.prototype.slice); var _join = uncurry(_Array.prototype.join); var _push = uncurry(_Array.prototype.push); var _unshift = uncurry(_Array.prototype.unshift); var _forEach = uncurry(_Array.prototype.forEach); var _concat = uncurry(_Array.prototype.concat); var _replace = uncurry(_String.prototype.replace); var _split = uncurry(_String.prototype.split); var _create = _Object.create; var _hasOwnProperty = uncurry(_Object.prototype.hasOwnProperty); var String_indexOf = uncurry(_String.prototype.indexOf); var Array_indexOf = uncurry(_Array.prototype.indexOf); var prefix = opts.methodNamePrefix || "_jsmd"; var ePrefix = _replace(prefix, /([\"\\])/g, "\\$1"); var sep = opts.methodNameSeparator || " "; var classes = _create(null); function classToName(cl) { if (cl != null) { var name = cl[prefix]; if (typeof name === "string") if (classes[name] && classes[name].ctor === cl) return name; else for (name in classes) if (classes[name] && classes[name].ctor === cl) return name; } } function assertClassToName(cl) { if ("string" === typeof cl) return cl; var ret = classToName(cl); if (ret) return ret; throw _Error("Class not defined: " + cl); } function pureVirtual() { var msg = "Abstract method not overridden for "; try { msg += this; } catch (e) { try { msg += _Object.prototype.toString.call(this); } catch (e) { msg += "object"; } } throw new _Error(msg); } var ret = { getConstructor: function(name) { return classes[name] && classes[name].ctor; }, defClass: function(name, opts) { var ctor, base; var bctor, proto, key, sub, sepBase, cname, c; var ometh, meth, func, array, doit, i, indices; opts.debug && console.log("defClass: ", name); if (opts) { ctor = opts.ctor; if (opts.base) base = assertClassToName(opts.base); } if (typeof base === "undefined" && ctor && ctor.prototype != null) { base = classToName(ctor.prototype.constructor); } //opts.debug && console.log("base:", base); if (typeof base !== "undefined") { bctor = classes[base].ctor; } ctor = ctor || function(){} if (typeof name !== "string") { throw _Error("Usage: defClass(NAME, [OPTS])"); } if (classes[name]) { if (classes[name].ctor !== ctor || classes[name].base !== base) { throw _Error("Can't redefine class " + name); } return ctor; } if (String_indexOf(name, sep) != -1) { throw _Error((sep == " " ? "Space" : "Separator") + " in class name: " + name); } if (typeof (ctor[prefix]) !== "undefined") { if (ctor[prefix] !== name) throw _Error("Cannot define constructor as " + name + ", it was previously defined as " + ctor[prefix]); } else { ctor[prefix] = name; } //opts.debug && console.log("checking prototype constructor"); if (ctor.prototype) { if (_hasOwnProperty(ctor.prototype, "constructor")) { if (ctor.prototype.constructor !== ctor) throw _Error("ctor.prototype.constructor is not ctor"); } else { ctor.prototype.constructor = ctor; } } //opts.debug && console.log("ok") if (!ctor.prototype || (bctor && !(ctor.prototype instanceof bctor))) { proto = (bctor ? new bctor() : _create(null)); //opts.debug && console.log("proto.constructor[prefix]", proto.constructor[prefix]); if (ctor.prototype) { // XXX Used for BigInteger; too hacky? for (key in ctor.prototype) { proto[key] = ctor.prototype[key]; } } proto.constructor = ctor; ctor.prototype = proto; } classes[name] = { ctor: ctor, base: base, sub: [], ename: _replace(sep + name, /([\"\\])/g, "\\$1") }; //opts.debug && console.log("defClass:", name, "base:", base); if (typeof base !== "undefined") { sub = classes[base].sub; if (Array_indexOf(sub, name) === -1) _push(sub, name); sepBase = sep + base; for (cname in classes) { proto = classes[cname].ctor.prototype; for (ometh in proto) { if (!_hasOwnProperty(proto, ometh)) continue; if (!String_indexOf(ometh, sepBase)) continue; array = _split(ometh, sep); if (array[0] !== prefix) continue; func = proto[ometh]; indices = []; for (i = Array_indexOf(array, base, 2); i !== -1; i = Array_indexOf(array, base, i + 1)) { _push(indices, i); } doit = function(i) { if (i === indices.length) { meth = _join(array, sep); if (meth !== ometh) { opts.debug && console.log(cname + '["'+meth+'"] propagated -> ' + short_fn(func)); proto[meth] = func; } return; } array[indices[i]] = base; doit(i + 1); array[indices[i]] = name; doit(i + 1); } doit(0); } } } return ctor; }, defGeneric: function (fnName, ndisp, nargs) { if (String_indexOf(fnName, sep) != -1) throw _Error((sep == " " ? "Space" : "Separator") + " in function name: " + fnName); nargs = nargs || ndisp; if (fnName == "" || ndisp < 1 || ndisp != (ndisp | 0) || nargs < 1 || nargs != (nargs | 0)) throw Error("Usage: defGeneric(NAME, NDISP [, NARGS])"); var eName = _replace(sep + fnName, /([\"\\])/g, "\\$1"); var eTopMethod = ePrefix + eName; for (var i = Formals.length; i < nargs; i++) Formals[i] = "a" + i; var array = _slice(Formals, 0, nargs); // e.g., function(a0,a1,a2,a3){return a3["_jsmd frob"](a0,a1,a2)} _push(array, "return " + Formals[ndisp-1] + '["' + eTopMethod + '"](' + _join(_concat(_slice(array, 0, ndisp-1), _slice(array, ndisp, nargs)), ",") + ')') var ret = _apply(_Function, null, array); var func_cache = _create(null); function get_func(i, etypes) { var suffix = _join(_slice(etypes, i), ""); if (!func_cache[suffix]) { var method = ePrefix + eName + suffix; var array = _concat(_slice(Formals, 0,i), _slice(Formals, i+1, nargs)); _push(array, "return " + Formals[i-1] + '["' + method + '"](' + _join(_concat(_slice(Formals, 0, i-1), "this", _slice(Formals, i+1, nargs)), ",") + ')'); func_cache[suffix] = _apply(_Function, null, array); } return func_cache[suffix]; } // For error message. function usageArgs() { switch (ndisp) { case 1: return "TYPE"; case 2: return "TYPE1, TYPE2"; case 3: return "TYPE1, TYPE2, TYPE3"; default: return "TYPE1, ..., TYPE" + ndisp; } } // def(TYPE1, ..., TYPEn, FUNCTION) // Defines FUNCTION as this method's specialization for the // given types. Each TYPEi must have been passed as the // NAME argument in a successful call to defClass. function def() { var fn = arguments[ndisp] || pureVirtual; if (typeof fn !== "function") { throw _Error("Not a function. Usage: " + fnName + ".def(" + usageArgs() + ", FUNCTION)"); } var types = _slice(arguments, 0, ndisp); //opts.debug && console.log("def", fnName, types, short_fn(fn)); for (i = 0; i < ndisp; i++) { // Throw error if not registered. // XXX Could add def() arguments to a list to be // defined during defClass. types[i] = assertClassToName(types[i]); } //opts.debug && console.log("def"); do_def(types, fn, _create(null)); } function do_def(types, fn, inherited) { var cs = new _Array(ndisp); var eTypes = new _Array(ndisp); var i, suffix, oldm, newm; for (i = 0; i < ndisp; i++) { cs[i] = classes[types[i]]; //opts.debug && console.log("cs[" + i + "]=classes[", types[i], "]"); eTypes[i] = cs[i].ename; } opts.debug && console.log("do_def", fnName, eTypes); oldm = new Array(ndisp); for (i = ndisp-1, suffix = ""; ; i--) { oldm[i] = cs[i].ctor.prototype[ prefix + sep + fnName + suffix]; //opts.debug && console.log("oldm[" + i + "]" + oldm[i]); if (i === 0) break; suffix = eTypes[i] + suffix; } newm = new _Array(ndisp); newm[0] = fn; for (i=1; i<ndisp; i++) newm[i] = get_func(i, eTypes); function doit(i, method) { var key; var proto = cs[i].ctor.prototype; if (proto[method]