1621 lines
33 KiB
JavaScript
1621 lines
33 KiB
JavaScript
/*
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JavaScript BigInteger library version 0.9.1
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http://silentmatt.com/biginteger/
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Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
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Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
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Licensed under the MIT license.
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Support for arbitrary internal representation base was added by
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Vitaly Magerya.
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*/
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/*
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File: biginteger.js
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Exports:
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<BigInteger>
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*/
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(function(exports) {
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"use strict";
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/*
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Class: BigInteger
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An arbitrarily-large integer.
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<BigInteger> objects should be considered immutable. None of the "built-in"
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methods modify *this* or their arguments. All properties should be
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considered private.
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All the methods of <BigInteger> instances can be called "statically". The
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static versions are convenient if you don't already have a <BigInteger>
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object.
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As an example, these calls are equivalent.
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> BigInteger(4).multiply(5); // returns BigInteger(20);
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> BigInteger.multiply(4, 5); // returns BigInteger(20);
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> var a = 42;
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> var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
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*/
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var CONSTRUCT = {}; // Unique token to call "private" version of constructor
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/*
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Constructor: BigInteger()
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Convert a value to a <BigInteger>.
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Although <BigInteger()> is the constructor for <BigInteger> objects, it is
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best not to call it as a constructor. If *n* is a <BigInteger> object, it is
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simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
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without a radix argument.
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> var n0 = BigInteger(); // Same as <BigInteger.ZERO>
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> var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
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> var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
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> var n3 = BigInteger(n2); // Return n2, unchanged
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The constructor form only takes an array and a sign. *n* must be an
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array of numbers in little-endian order, where each digit is between 0
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and BigInteger.base. The second parameter sets the sign: -1 for
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negative, +1 for positive, or 0 for zero. The array is *not copied and
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may be modified*. If the array contains only zeros, the sign parameter
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is ignored and is forced to zero.
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> new BigInteger([5], -1): create a new BigInteger with value -5
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Parameters:
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n - Value to convert to a <BigInteger>.
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Returns:
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A <BigInteger> value.
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See Also:
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<parse>, <BigInteger>
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*/
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function BigInteger(n, s, token) {
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if (token !== CONSTRUCT) {
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if (n instanceof BigInteger) {
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return n;
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}
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else if (typeof n === "undefined") {
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return ZERO;
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}
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return BigInteger.parse(n);
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}
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n = n || []; // Provide the nullary constructor for subclasses.
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while (n.length && !n[n.length - 1]) {
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--n.length;
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}
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this._d = n;
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this._s = n.length ? (s || 1) : 0;
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}
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BigInteger._construct = function(n, s) {
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return new BigInteger(n, s, CONSTRUCT);
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};
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// Base-10 speedup hacks in parse, toString, exp10 and log functions
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// require base to be a power of 10. 10^7 is the largest such power
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// that won't cause a precision loss when digits are multiplied.
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var BigInteger_base = 10000000;
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var BigInteger_base_log10 = 7;
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BigInteger.base = BigInteger_base;
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BigInteger.base_log10 = BigInteger_base_log10;
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var ZERO = new BigInteger([], 0, CONSTRUCT);
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// Constant: ZERO
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// <BigInteger> 0.
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BigInteger.ZERO = ZERO;
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var ONE = new BigInteger([1], 1, CONSTRUCT);
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// Constant: ONE
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// <BigInteger> 1.
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BigInteger.ONE = ONE;
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var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT);
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// Constant: M_ONE
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// <BigInteger> -1.
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BigInteger.M_ONE = M_ONE;
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// Constant: _0
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// Shortcut for <ZERO>.
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BigInteger._0 = ZERO;
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// Constant: _1
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// Shortcut for <ONE>.
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BigInteger._1 = ONE;
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/*
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Constant: small
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Array of <BigIntegers> from 0 to 36.
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These are used internally for parsing, but useful when you need a "small"
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<BigInteger>.
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See Also:
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<ZERO>, <ONE>, <_0>, <_1>
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*/
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BigInteger.small = [
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ZERO,
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ONE,
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/* Assuming BigInteger_base > 36 */
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new BigInteger( [2], 1, CONSTRUCT),
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new BigInteger( [3], 1, CONSTRUCT),
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new BigInteger( [4], 1, CONSTRUCT),
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new BigInteger( [5], 1, CONSTRUCT),
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new BigInteger( [6], 1, CONSTRUCT),
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new BigInteger( [7], 1, CONSTRUCT),
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new BigInteger( [8], 1, CONSTRUCT),
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new BigInteger( [9], 1, CONSTRUCT),
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new BigInteger([10], 1, CONSTRUCT),
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new BigInteger([11], 1, CONSTRUCT),
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new BigInteger([12], 1, CONSTRUCT),
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new BigInteger([13], 1, CONSTRUCT),
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new BigInteger([14], 1, CONSTRUCT),
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new BigInteger([15], 1, CONSTRUCT),
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new BigInteger([16], 1, CONSTRUCT),
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new BigInteger([17], 1, CONSTRUCT),
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new BigInteger([18], 1, CONSTRUCT),
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new BigInteger([19], 1, CONSTRUCT),
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new BigInteger([20], 1, CONSTRUCT),
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new BigInteger([21], 1, CONSTRUCT),
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new BigInteger([22], 1, CONSTRUCT),
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new BigInteger([23], 1, CONSTRUCT),
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new BigInteger([24], 1, CONSTRUCT),
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new BigInteger([25], 1, CONSTRUCT),
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new BigInteger([26], 1, CONSTRUCT),
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new BigInteger([27], 1, CONSTRUCT),
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new BigInteger([28], 1, CONSTRUCT),
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new BigInteger([29], 1, CONSTRUCT),
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new BigInteger([30], 1, CONSTRUCT),
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new BigInteger([31], 1, CONSTRUCT),
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new BigInteger([32], 1, CONSTRUCT),
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new BigInteger([33], 1, CONSTRUCT),
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new BigInteger([34], 1, CONSTRUCT),
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new BigInteger([35], 1, CONSTRUCT),
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new BigInteger([36], 1, CONSTRUCT)
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];
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// Used for parsing/radix conversion
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BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
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/*
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Method: toString
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Convert a <BigInteger> to a string.
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When *base* is greater than 10, letters are upper case.
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Parameters:
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base - Optional base to represent the number in (default is base 10).
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Must be between 2 and 36 inclusive, or an Error will be thrown.
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Returns:
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The string representation of the <BigInteger>.
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*/
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BigInteger.prototype.toString = function(base) {
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base = +base || 10;
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if (base < 2 || base > 36) {
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throw new Error("illegal radix " + base + ".");
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}
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if (this._s === 0) {
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return "0";
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}
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if (base === 10) {
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var str = this._s < 0 ? "-" : "";
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str += this._d[this._d.length - 1].toString();
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for (var i = this._d.length - 2; i >= 0; i--) {
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var group = this._d[i].toString();
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while (group.length < BigInteger_base_log10) group = '0' + group;
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str += group;
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}
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return str;
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}
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else {
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var numerals = BigInteger.digits;
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base = BigInteger.small[base];
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var sign = this._s;
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var n = this.abs();
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var digits = [];
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var digit;
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while (n._s !== 0) {
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var divmod = n.divRem(base);
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n = divmod[0];
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digit = divmod[1];
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// TODO: This could be changed to unshift instead of reversing at the end.
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// Benchmark both to compare speeds.
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digits.push(numerals[digit.valueOf()]);
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}
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return (sign < 0 ? "-" : "") + digits.reverse().join("");
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}
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};
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// Verify strings for parsing
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BigInteger.radixRegex = [
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/^$/,
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/^$/,
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/^[01]*$/,
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/^[012]*$/,
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/^[0-3]*$/,
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/^[0-4]*$/,
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/^[0-5]*$/,
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/^[0-6]*$/,
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/^[0-7]*$/,
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/^[0-8]*$/,
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/^[0-9]*$/,
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/^[0-9aA]*$/,
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/^[0-9abAB]*$/,
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/^[0-9abcABC]*$/,
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/^[0-9a-dA-D]*$/,
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/^[0-9a-eA-E]*$/,
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/^[0-9a-fA-F]*$/,
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/^[0-9a-gA-G]*$/,
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/^[0-9a-hA-H]*$/,
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/^[0-9a-iA-I]*$/,
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/^[0-9a-jA-J]*$/,
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/^[0-9a-kA-K]*$/,
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/^[0-9a-lA-L]*$/,
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/^[0-9a-mA-M]*$/,
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/^[0-9a-nA-N]*$/,
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/^[0-9a-oA-O]*$/,
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/^[0-9a-pA-P]*$/,
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/^[0-9a-qA-Q]*$/,
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/^[0-9a-rA-R]*$/,
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/^[0-9a-sA-S]*$/,
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/^[0-9a-tA-T]*$/,
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/^[0-9a-uA-U]*$/,
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/^[0-9a-vA-V]*$/,
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/^[0-9a-wA-W]*$/,
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/^[0-9a-xA-X]*$/,
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/^[0-9a-yA-Y]*$/,
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/^[0-9a-zA-Z]*$/
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];
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/*
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Function: parse
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Parse a string into a <BigInteger>.
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*base* is optional but, if provided, must be from 2 to 36 inclusive. If
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*base* is not provided, it will be guessed based on the leading characters
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of *s* as follows:
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- "0x" or "0X": *base* = 16
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- "0c" or "0C": *base* = 8
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- "0b" or "0B": *base* = 2
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- else: *base* = 10
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If no base is provided, or *base* is 10, the number can be in exponential
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form. For example, these are all valid:
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> BigInteger.parse("1e9"); // Same as "1000000000"
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> BigInteger.parse("1.234*10^3"); // Same as 1234
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> BigInteger.parse("56789 * 10 ** -2"); // Same as 567
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If any characters fall outside the range defined by the radix, an exception
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will be thrown.
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Parameters:
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s - The string to parse.
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base - Optional radix (default is to guess based on *s*).
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Returns:
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a <BigInteger> instance.
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*/
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BigInteger.parse = function(s, base) {
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// Expands a number in exponential form to decimal form.
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// expandExponential("-13.441*10^5") === "1344100";
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// expandExponential("1.12300e-1") === "0.112300";
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// expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
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function expandExponential(str) {
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str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
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return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) {
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c = +c;
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var l = c < 0;
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var i = n.length + c;
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x = (l ? n : f).length;
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c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
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var z = (new Array(c + 1)).join("0");
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var r = n + f;
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return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
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});
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}
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s = s.toString();
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if (typeof base === "undefined" || +base === 10) {
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s = expandExponential(s);
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}
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var prefixRE;
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if (typeof base === "undefined") {
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prefixRE = '0[xcb]';
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}
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else if (base == 16) {
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prefixRE = '0x';
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}
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else if (base == 8) {
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prefixRE = '0c';
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}
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else if (base == 2) {
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prefixRE = '0b';
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}
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else {
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prefixRE = '';
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}
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var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s);
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if (parts) {
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var sign = parts[1] || "+";
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var baseSection = parts[2] || "";
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var digits = parts[3] || "";
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if (typeof base === "undefined") {
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// Guess base
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if (baseSection === "0x" || baseSection === "0X") { // Hex
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base = 16;
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}
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else if (baseSection === "0c" || baseSection === "0C") { // Octal
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base = 8;
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}
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else if (baseSection === "0b" || baseSection === "0B") { // Binary
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base = 2;
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}
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else {
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base = 10;
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}
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}
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else if (base < 2 || base > 36) {
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throw new Error("Illegal radix " + base + ".");
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}
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base = +base;
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// Check for digits outside the range
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if (!(BigInteger.radixRegex[base].test(digits))) {
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throw new Error("Bad digit for radix " + base);
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}
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// Strip leading zeros, and convert to array
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digits = digits.replace(/^0+/, "").split("");
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if (digits.length === 0) {
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return ZERO;
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}
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// Get the sign (we know it's not zero)
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sign = (sign === "-") ? -1 : 1;
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// Optimize 10
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if (base == 10) {
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var d = [];
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while (digits.length >= BigInteger_base_log10) {
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d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10));
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}
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d.push(parseInt(digits.join(''), 10));
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return new BigInteger(d, sign, CONSTRUCT);
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}
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// Do the conversion
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var d = ZERO;
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base = BigInteger.small[base];
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var small = BigInteger.small;
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for (var i = 0; i < digits.length; i++) {
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d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
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}
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return new BigInteger(d._d, sign, CONSTRUCT);
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}
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else {
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throw new Error("Invalid BigInteger format: " + s);
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}
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};
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/*
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Function: add
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Add two <BigIntegers>.
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Parameters:
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n - The number to add to *this*. Will be converted to a <BigInteger>.
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Returns:
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The numbers added together.
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See Also:
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<subtract>, <multiply>, <quotient>, <next>
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*/
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BigInteger.prototype.add = function(n) {
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if (this._s === 0) {
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return BigInteger(n);
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}
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n = BigInteger(n);
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if (n._s === 0) {
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return this;
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}
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if (this._s !== n._s) {
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n = n.negate();
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return this.subtract(n);
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}
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var a = this._d;
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var b = n._d;
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var al = a.length;
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var bl = b.length;
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var sum = new Array(Math.max(al, bl) + 1);
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var size = Math.min(al, bl);
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var carry = 0;
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var digit;
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for (var i = 0; i < size; i++) {
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digit = a[i] + b[i] + carry;
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sum[i] = digit % BigInteger_base;
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carry = (digit / BigInteger_base) | 0;
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}
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if (bl > al) {
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a = b;
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al = bl;
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}
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for (i = size; carry && i < al; i++) {
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digit = a[i] + carry;
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sum[i] = digit % BigInteger_base;
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carry = (digit / BigInteger_base) | 0;
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}
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if (carry) {
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sum[i] = carry;
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}
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for ( ; i < al; i++) {
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sum[i] = a[i];
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}
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return new BigInteger(sum, this._s, CONSTRUCT);
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};
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/*
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Function: negate
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Get the additive inverse of a <BigInteger>.
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Returns:
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A <BigInteger> with the same magnatude, but with the opposite sign.
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See Also:
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<abs>
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*/
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BigInteger.prototype.negate = function() {
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return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT);
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};
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/*
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Function: abs
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Get the absolute value of a <BigInteger>.
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Returns:
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A <BigInteger> with the same magnatude, but always positive (or zero).
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See Also:
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<negate>
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*/
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BigInteger.prototype.abs = function() {
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return (this._s < 0) ? this.negate() : this;
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};
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/*
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Function: subtract
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Subtract two <BigIntegers>.
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Parameters:
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n - The number to subtract from *this*. Will be converted to a <BigInteger>.
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Returns:
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The *n* subtracted from *this*.
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See Also:
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<add>, <multiply>, <quotient>, <prev>
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*/
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|
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;
|
|
// negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
|
|
if (this._s < 0) {
|
|
m = new BigInteger(n._d, 1, CONSTRUCT);
|
|
n = new BigInteger(this._d, 1, CONSTRUCT);
|
|
}
|
|
|
|
// Both are positive => a - b
|
|
var sign = m.compareAbs(n);
|
|
if (sign === 0) {
|
|
return ZERO;
|
|
}
|
|
else if (sign < 0) {
|
|
// swap m and n
|
|
var 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, CONSTRUCT);
|
|
};
|
|
|
|
(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, CONSTRUCT);
|
|
}
|
|
|
|
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, CONSTRUCT);
|
|
}
|
|
|
|
/*
|
|
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 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 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 === ONE ||
|
|
this === 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 ZERO;
|
|
}
|
|
|
|
n = BigInteger(n);
|
|
if (n._s === 0) {
|
|
return 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, CONSTRUCT);
|
|
};
|
|
|
|
// 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 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, CONSTRUCT);
|
|
}
|
|
return new BigInteger([digit], 1, CONSTRUCT);
|
|
}
|
|
|
|
if (n === 2) {
|
|
return this.add(this);
|
|
}
|
|
if (this.isUnit()) {
|
|
return new BigInteger([n], 1, CONSTRUCT);
|
|
}
|
|
|
|
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) {
|
|
partial[j] = carry;
|
|
}
|
|
|
|
return new BigInteger(partial, 1, CONSTRUCT);
|
|
};
|
|
|
|
/*
|
|
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 ZERO;
|
|
}
|
|
if (this.isUnit()) {
|
|
return 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, CONSTRUCT);
|
|
};
|
|
|
|
/*
|
|
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 [ZERO, 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 ? ONE : M_ONE, ZERO];
|
|
case -1: // |n1| < |n2|
|
|
return [ZERO, this];
|
|
}
|
|
|
|
var sign = this._s * n._s;
|
|
var a = n.abs();
|
|
var b_digits = this._d;
|
|
var b_index = b_digits.length;
|
|
var digits = n._d.length;
|
|
var quot = [];
|
|
var guess;
|
|
|
|
var part = new BigInteger([], 0, CONSTRUCT);
|
|
|
|
while (b_index) {
|
|
part._d.unshift(b_digits[--b_index]);
|
|
part = new BigInteger(part._d, 1, CONSTRUCT);
|
|
|
|
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, CONSTRUCT),
|
|
new BigInteger(part._d, this._s, CONSTRUCT)];
|
|
};
|
|
|
|
// 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 [ZERO, ZERO];
|
|
}
|
|
|
|
if (n === 1 || n === -1) {
|
|
return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign, CONSTRUCT), 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, CONSTRUCT);
|
|
r = new BigInteger([(this._d[0] % n) | 0], 1, CONSTRUCT);
|
|
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, CONSTRUCT);
|
|
if (this._s < 0) {
|
|
r = r.negate();
|
|
}
|
|
return [new BigInteger(quot.reverse(), sign, CONSTRUCT), 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(MAX_EXP)) {
|
|
throw new Error("exponent too large in BigInteger.exp10");
|
|
}
|
|
// Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case
|
|
if (this._s === 0) {
|
|
return ZERO;
|
|
}
|
|
if (n > 0) {
|
|
var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
|
|
|
|
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 ZERO;
|
|
} else {
|
|
var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
|
|
|
|
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 ONE;
|
|
}
|
|
else if (n._s < 0) {
|
|
if (this._s === 0) {
|
|
throw new Error("Divide by zero");
|
|
}
|
|
else {
|
|
return ZERO;
|
|
}
|
|
}
|
|
if (this._s === 0) {
|
|
return ZERO;
|
|
}
|
|
if (n.isUnit()) {
|
|
return this;
|
|
}
|
|
|
|
if (n.compareAbs(MAX_EXP) > 0) {
|
|
throw new Error("exponent too large in BigInteger.pow");
|
|
}
|
|
var x = this;
|
|
var aux = 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 = 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, CONSTRUCT)).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);
|
|
};
|
|
|
|
var MAX_EXP = BigInteger(0x7FFFFFFF);
|
|
// Constant: MAX_EXP
|
|
// The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
|
|
BigInteger.MAX_EXP = MAX_EXP;
|
|
|
|
(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);
|
|
};
|
|
})();
|
|
})();
|
|
|
|
exports.BigInteger = BigInteger;
|
|
})(typeof exports !== 'undefined' ? exports : this);
|