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644 lines
15 KiB
644 lines
15 KiB
// BigInt, a suite of routines for performing multiple-precision arithmetic in
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// JavaScript.
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//
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// Copyright 1998-2005 David Shapiro.
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//
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// You may use, re-use, abuse,
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// copy, and modify this code to your liking, but please keep this header.
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// Thanks!
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//
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// Dave Shapiro
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// dave@ohdave.com
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// IMPORTANT THING: Be sure to set maxDigits according to your precision
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// needs. Use the setMaxDigits() function to do this. See comments below.
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//
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// Tweaked by Ian Bunning
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// Alterations:
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// Fix bug in function biFromHex(s) to allow
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// parsing of strings of length != 0 (mod 4)
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// Changes made by Dave Shapiro as of 12/30/2004:
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//
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// The BigInt() constructor doesn't take a string anymore. If you want to
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// create a BigInt from a string, use biFromDecimal() for base-10
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// representations, biFromHex() for base-16 representations, or
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// biFromString() for base-2-to-36 representations.
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//
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// biFromArray() has been removed. Use biCopy() instead, passing a BigInt
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// instead of an array.
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//
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// The BigInt() constructor now only constructs a zeroed-out array.
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// Alternatively, if you pass <true>, it won't construct any array. See the
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// biCopy() method for an example of this.
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//
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// Be sure to set maxDigits depending on your precision needs. The default
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// zeroed-out array ZERO_ARRAY is constructed inside the setMaxDigits()
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// function. So use this function to set the variable. DON'T JUST SET THE
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// VALUE. USE THE FUNCTION.
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//
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// ZERO_ARRAY exists to hopefully speed up construction of BigInts(). By
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// precalculating the zero array, we can just use slice(0) to make copies of
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// it. Presumably this calls faster native code, as opposed to setting the
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// elements one at a time. I have not done any timing tests to verify this
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// claim.
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// Max number = 10^16 - 2 = 9999999999999998;
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// 2^53 = 9007199254740992;
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var biRadixBase = 2;
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var biRadixBits = 16;
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var bitsPerDigit = biRadixBits;
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var biRadix = 1 << 16; // = 2^16 = 65536
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var biHalfRadix = biRadix >>> 1;
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var biRadixSquared = biRadix * biRadix;
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var maxDigitVal = biRadix - 1;
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var maxInteger = 9999999999999998;
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// maxDigits:
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// Change this to accommodate your largest number size. Use setMaxDigits()
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// to change it!
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//
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// In general, if you're working with numbers of size N bits, you'll need 2*N
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// bits of storage. Each digit holds 16 bits. So, a 1024-bit key will need
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//
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// 1024 * 2 / 16 = 128 digits of storage.
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//
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var maxDigits;
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var ZERO_ARRAY;
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var bigZero, bigOne;
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function setMaxDigits(value)
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{
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maxDigits = value;
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ZERO_ARRAY = new Array(maxDigits);
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for (var iza = 0; iza < ZERO_ARRAY.length; iza++) ZERO_ARRAY[iza] = 0;
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bigZero = new BigInt();
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bigOne = new BigInt();
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bigOne.digits[0] = 1;
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}
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setMaxDigits(20);
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// The maximum number of digits in base 10 you can convert to an
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// integer without JavaScript throwing up on you.
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var dpl10 = 15;
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// lr10 = 10 ^ dpl10
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var lr10 = biFromNumber(1000000000000000);
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function BigInt(flag)
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{
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if (typeof flag == "boolean" && flag == true) {
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this.digits = null;
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}
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else {
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this.digits = ZERO_ARRAY.slice(0);
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}
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this.isNeg = false;
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}
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function biFromDecimal(s)
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{
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var isNeg = s.charAt(0) == '-';
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var i = isNeg ? 1 : 0;
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var result;
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// Skip leading zeros.
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while (i < s.length && s.charAt(i) == '0') ++i;
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if (i == s.length) {
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result = new BigInt();
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}
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else {
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var digitCount = s.length - i;
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var fgl = digitCount % dpl10;
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if (fgl == 0) fgl = dpl10;
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result = biFromNumber(Number(s.substr(i, fgl)));
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i += fgl;
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while (i < s.length) {
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result = biAdd(biMultiply(result, lr10),
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biFromNumber(Number(s.substr(i, dpl10))));
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i += dpl10;
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}
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result.isNeg = isNeg;
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}
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return result;
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}
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function biCopy(bi)
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{
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var result = new BigInt(true);
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result.digits = bi.digits.slice(0);
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result.isNeg = bi.isNeg;
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return result;
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}
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function biFromNumber(i)
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{
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var result = new BigInt();
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result.isNeg = i < 0;
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i = Math.abs(i);
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var j = 0;
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while (i > 0) {
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result.digits[j++] = i & maxDigitVal;
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i >>= biRadixBits;
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}
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return result;
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}
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function reverseStr(s)
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{
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var result = "";
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for (var i = s.length - 1; i > -1; --i) {
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result += s.charAt(i);
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}
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return result;
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}
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var hexatrigesimalToChar = new Array(
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'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
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'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j',
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'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't',
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'u', 'v', 'w', 'x', 'y', 'z'
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);
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function biToString(x, radix)
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// 2 <= radix <= 36
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{
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var b = new BigInt();
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b.digits[0] = radix;
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var qr = biDivideModulo(x, b);
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var result = hexatrigesimalToChar[qr[1].digits[0]];
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while (biCompare(qr[0], bigZero) == 1) {
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qr = biDivideModulo(qr[0], b);
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digit = qr[1].digits[0];
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result += hexatrigesimalToChar[qr[1].digits[0]];
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}
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return (x.isNeg ? "-" : "") + reverseStr(result);
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}
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function biToDecimal(x)
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{
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var b = new BigInt();
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b.digits[0] = 10;
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var qr = biDivideModulo(x, b);
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var result = String(qr[1].digits[0]);
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while (biCompare(qr[0], bigZero) == 1) {
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qr = biDivideModulo(qr[0], b);
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result += String(qr[1].digits[0]);
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}
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return (x.isNeg ? "-" : "") + reverseStr(result);
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}
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var hexToChar = new Array('0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
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'a', 'b', 'c', 'd', 'e', 'f');
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function digitToHex(n)
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{
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var mask = 0xf;
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var result = "";
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for (i = 0; i < 4; ++i) {
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result += hexToChar[n & mask];
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n >>>= 4;
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}
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return reverseStr(result);
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}
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function biToHex(x)
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{
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var result = "";
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var n = biHighIndex(x);
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for (var i = biHighIndex(x); i > -1; --i) {
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result += digitToHex(x.digits[i]);
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}
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return result;
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}
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function charToHex(c)
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{
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var ZERO = 48;
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var NINE = ZERO + 9;
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var littleA = 97;
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var littleZ = littleA + 25;
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var bigA = 65;
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var bigZ = 65 + 25;
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var result;
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if (c >= ZERO && c <= NINE) {
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result = c - ZERO;
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} else if (c >= bigA && c <= bigZ) {
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result = 10 + c - bigA;
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} else if (c >= littleA && c <= littleZ) {
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result = 10 + c - littleA;
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} else {
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result = 0;
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}
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return result;
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}
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function hexToDigit(s)
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{
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var result = 0;
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var sl = Math.min(s.length, 4);
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for (var i = 0; i < sl; ++i) {
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result <<= 4;
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result |= charToHex(s.charCodeAt(i))
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}
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return result;
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}
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function biFromHex(s)
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{
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var result = new BigInt();
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var sl = s.length;
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for (var i = sl, j = 0; i > 0; i -= 4, ++j) {
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result.digits[j] = hexToDigit(s.substr(Math.max(i - 4, 0), Math.min(i, 4)));
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}
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return result;
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}
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function biFromString(s, radix)
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{
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var isNeg = s.charAt(0) == '-';
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var istop = isNeg ? 1 : 0;
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var result = new BigInt();
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var place = new BigInt();
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place.digits[0] = 1; // radix^0
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for (var i = s.length - 1; i >= istop; i--) {
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var c = s.charCodeAt(i);
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var digit = charToHex(c);
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var biDigit = biMultiplyDigit(place, digit);
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result = biAdd(result, biDigit);
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place = biMultiplyDigit(place, radix);
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}
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result.isNeg = isNeg;
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return result;
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}
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function biToBytes(x)
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// Returns a string containing raw bytes.
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{
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var result = "";
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for (var i = biHighIndex(x); i > -1; --i) {
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result += digitToBytes(x.digits[i]);
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}
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return result;
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}
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function digitToBytes(n)
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// Convert two-byte digit to string containing both bytes.
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{
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var c1 = String.fromCharCode(n & 0xff);
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n >>>= 8;
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var c2 = String.fromCharCode(n & 0xff);
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return c2 + c1;
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}
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function biDump(b)
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{
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return (b.isNeg ? "-" : "") + b.digits.join(" ");
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}
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function biAdd(x, y)
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{
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var result;
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if (x.isNeg != y.isNeg) {
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y.isNeg = !y.isNeg;
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result = biSubtract(x, y);
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y.isNeg = !y.isNeg;
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}
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else {
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result = new BigInt();
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var c = 0;
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var n;
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for (var i = 0; i < x.digits.length; ++i) {
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n = x.digits[i] + y.digits[i] + c;
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result.digits[i] = n & 0xffff;
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c = Number(n >= biRadix);
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}
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result.isNeg = x.isNeg;
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}
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return result;
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}
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function biSubtract(x, y)
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{
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var result;
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if (x.isNeg != y.isNeg) {
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y.isNeg = !y.isNeg;
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result = biAdd(x, y);
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y.isNeg = !y.isNeg;
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} else {
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result = new BigInt();
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var n, c;
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c = 0;
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for (var i = 0; i < x.digits.length; ++i) {
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n = x.digits[i] - y.digits[i] + c;
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result.digits[i] = n & 0xffff;
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// Stupid non-conforming modulus operation.
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if (result.digits[i] < 0) result.digits[i] += biRadix;
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c = 0 - Number(n < 0);
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}
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// Fix up the negative sign, if any.
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if (c == -1) {
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c = 0;
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for (var i = 0; i < x.digits.length; ++i) {
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n = 0 - result.digits[i] + c;
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result.digits[i] = n & 0xffff;
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// Stupid non-conforming modulus operation.
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if (result.digits[i] < 0) result.digits[i] += biRadix;
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c = 0 - Number(n < 0);
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}
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// Result is opposite sign of arguments.
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result.isNeg = !x.isNeg;
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} else {
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// Result is same sign.
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result.isNeg = x.isNeg;
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}
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}
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return result;
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}
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function biHighIndex(x)
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{
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var result = x.digits.length - 1;
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while (result > 0 && x.digits[result] == 0) --result;
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return result;
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}
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function biNumBits(x)
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{
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var n = biHighIndex(x);
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var d = x.digits[n];
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var m = (n + 1) * bitsPerDigit;
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var result;
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for (result = m; result > m - bitsPerDigit; --result) {
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if ((d & 0x8000) != 0) break;
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d <<= 1;
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}
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return result;
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}
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function biMultiply(x, y)
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{
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var result = new BigInt();
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var c;
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var n = biHighIndex(x);
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var t = biHighIndex(y);
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var u, uv, k;
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for (var i = 0; i <= t; ++i) {
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c = 0;
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k = i;
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for (j = 0; j <= n; ++j, ++k) {
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uv = result.digits[k] + x.digits[j] * y.digits[i] + c;
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result.digits[k] = uv & maxDigitVal;
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c = uv >>> biRadixBits;
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}
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result.digits[i + n + 1] = c;
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}
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// Someone give me a logical xor, please.
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result.isNeg = x.isNeg != y.isNeg;
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return result;
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}
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function biMultiplyDigit(x, y)
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{
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var n, c, uv;
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result = new BigInt();
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n = biHighIndex(x);
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c = 0;
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for (var j = 0; j <= n; ++j) {
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uv = result.digits[j] + x.digits[j] * y + c;
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result.digits[j] = uv & maxDigitVal;
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c = uv >>> biRadixBits;
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}
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result.digits[1 + n] = c;
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return result;
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}
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function arrayCopy(src, srcStart, dest, destStart, n)
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{
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var m = Math.min(srcStart + n, src.length);
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for (var i = srcStart, j = destStart; i < m; ++i, ++j) {
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dest[j] = src[i];
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}
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}
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var highBitMasks = new Array(0x0000, 0x8000, 0xC000, 0xE000, 0xF000, 0xF800,
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0xFC00, 0xFE00, 0xFF00, 0xFF80, 0xFFC0, 0xFFE0,
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0xFFF0, 0xFFF8, 0xFFFC, 0xFFFE, 0xFFFF);
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function biShiftLeft(x, n)
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{
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var digitCount = Math.floor(n / bitsPerDigit);
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var result = new BigInt();
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arrayCopy(x.digits, 0, result.digits, digitCount,
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result.digits.length - digitCount);
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var bits = n % bitsPerDigit;
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var rightBits = bitsPerDigit - bits;
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for (var i = result.digits.length - 1, i1 = i - 1; i > 0; --i, --i1) {
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result.digits[i] = ((result.digits[i] << bits) & maxDigitVal) |
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((result.digits[i1] & highBitMasks[bits]) >>>
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(rightBits));
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}
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result.digits[0] = ((result.digits[i] << bits) & maxDigitVal);
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result.isNeg = x.isNeg;
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return result;
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}
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var lowBitMasks = new Array(0x0000, 0x0001, 0x0003, 0x0007, 0x000F, 0x001F,
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0x003F, 0x007F, 0x00FF, 0x01FF, 0x03FF, 0x07FF,
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0x0FFF, 0x1FFF, 0x3FFF, 0x7FFF, 0xFFFF);
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function biShiftRight(x, n)
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{
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var digitCount = Math.floor(n / bitsPerDigit);
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var result = new BigInt();
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arrayCopy(x.digits, digitCount, result.digits, 0,
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x.digits.length - digitCount);
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var bits = n % bitsPerDigit;
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var leftBits = bitsPerDigit - bits;
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for (var i = 0, i1 = i + 1; i < result.digits.length - 1; ++i, ++i1) {
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result.digits[i] = (result.digits[i] >>> bits) |
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((result.digits[i1] & lowBitMasks[bits]) << leftBits);
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}
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result.digits[result.digits.length - 1] >>>= bits;
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result.isNeg = x.isNeg;
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return result;
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}
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function biMultiplyByRadixPower(x, n)
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{
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var result = new BigInt();
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arrayCopy(x.digits, 0, result.digits, n, result.digits.length - n);
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return result;
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}
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function biDivideByRadixPower(x, n)
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{
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var result = new BigInt();
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arrayCopy(x.digits, n, result.digits, 0, result.digits.length - n);
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return result;
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}
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function biModuloByRadixPower(x, n)
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{
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var result = new BigInt();
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arrayCopy(x.digits, 0, result.digits, 0, n);
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return result;
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}
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function biCompare(x, y)
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{
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if (x.isNeg != y.isNeg) {
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return 1 - 2 * Number(x.isNeg);
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}
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for (var i = x.digits.length - 1; i >= 0; --i) {
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if (x.digits[i] != y.digits[i]) {
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if (x.isNeg) {
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return 1 - 2 * Number(x.digits[i] > y.digits[i]);
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} else {
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return 1 - 2 * Number(x.digits[i] < y.digits[i]);
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}
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}
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}
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return 0;
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}
|
|
|
|
function biDivideModulo(x, y)
|
|
{
|
|
var nb = biNumBits(x);
|
|
var tb = biNumBits(y);
|
|
var origYIsNeg = y.isNeg;
|
|
var q, r;
|
|
if (nb < tb) {
|
|
// |x| < |y|
|
|
if (x.isNeg) {
|
|
q = biCopy(bigOne);
|
|
q.isNeg = !y.isNeg;
|
|
x.isNeg = false;
|
|
y.isNeg = false;
|
|
r = biSubtract(y, x);
|
|
// Restore signs, 'cause they're references.
|
|
x.isNeg = true;
|
|
y.isNeg = origYIsNeg;
|
|
} else {
|
|
q = new BigInt();
|
|
r = biCopy(x);
|
|
}
|
|
return new Array(q, r);
|
|
}
|
|
|
|
q = new BigInt();
|
|
r = x;
|
|
|
|
// Normalize Y.
|
|
var t = Math.ceil(tb / bitsPerDigit) - 1;
|
|
var lambda = 0;
|
|
while (y.digits[t] < biHalfRadix) {
|
|
y = biShiftLeft(y, 1);
|
|
++lambda;
|
|
++tb;
|
|
t = Math.ceil(tb / bitsPerDigit) - 1;
|
|
}
|
|
// Shift r over to keep the quotient constant. We'll shift the
|
|
// remainder back at the end.
|
|
r = biShiftLeft(r, lambda);
|
|
nb += lambda; // Update the bit count for x.
|
|
var n = Math.ceil(nb / bitsPerDigit) - 1;
|
|
|
|
var b = biMultiplyByRadixPower(y, n - t);
|
|
while (biCompare(r, b) != -1) {
|
|
++q.digits[n - t];
|
|
r = biSubtract(r, b);
|
|
}
|
|
for (var i = n; i > t; --i) {
|
|
var ri = (i >= r.digits.length) ? 0 : r.digits[i];
|
|
var ri1 = (i - 1 >= r.digits.length) ? 0 : r.digits[i - 1];
|
|
var ri2 = (i - 2 >= r.digits.length) ? 0 : r.digits[i - 2];
|
|
var yt = (t >= y.digits.length) ? 0 : y.digits[t];
|
|
var yt1 = (t - 1 >= y.digits.length) ? 0 : y.digits[t - 1];
|
|
if (ri == yt) {
|
|
q.digits[i - t - 1] = maxDigitVal;
|
|
} else {
|
|
q.digits[i - t - 1] = Math.floor((ri * biRadix + ri1) / yt);
|
|
}
|
|
|
|
var c1 = q.digits[i - t - 1] * ((yt * biRadix) + yt1);
|
|
var c2 = (ri * biRadixSquared) + ((ri1 * biRadix) + ri2);
|
|
while (c1 > c2) {
|
|
--q.digits[i - t - 1];
|
|
c1 = q.digits[i - t - 1] * ((yt * biRadix) | yt1);
|
|
c2 = (ri * biRadix * biRadix) + ((ri1 * biRadix) + ri2);
|
|
}
|
|
|
|
b = biMultiplyByRadixPower(y, i - t - 1);
|
|
r = biSubtract(r, biMultiplyDigit(b, q.digits[i - t - 1]));
|
|
if (r.isNeg) {
|
|
r = biAdd(r, b);
|
|
--q.digits[i - t - 1];
|
|
}
|
|
}
|
|
r = biShiftRight(r, lambda);
|
|
// Fiddle with the signs and stuff to make sure that 0 <= r < y.
|
|
q.isNeg = x.isNeg != origYIsNeg;
|
|
if (x.isNeg) {
|
|
if (origYIsNeg) {
|
|
q = biAdd(q, bigOne);
|
|
} else {
|
|
q = biSubtract(q, bigOne);
|
|
}
|
|
y = biShiftRight(y, lambda);
|
|
r = biSubtract(y, r);
|
|
}
|
|
// Check for the unbelievably stupid degenerate case of r == -0.
|
|
if (r.digits[0] == 0 && biHighIndex(r) == 0) r.isNeg = false;
|
|
|
|
return new Array(q, r);
|
|
}
|
|
|
|
function biDivide(x, y)
|
|
{
|
|
return biDivideModulo(x, y)[0];
|
|
}
|
|
|
|
function biModulo(x, y)
|
|
{
|
|
return biDivideModulo(x, y)[1];
|
|
}
|
|
|
|
function biMultiplyMod(x, y, m)
|
|
{
|
|
return biModulo(biMultiply(x, y), m);
|
|
}
|
|
|
|
function biPow(x, y)
|
|
{
|
|
var result = bigOne;
|
|
var a = x;
|
|
while (true) {
|
|
if ((y & 1) != 0) result = biMultiply(result, a);
|
|
y >>= 1;
|
|
if (y == 0) break;
|
|
a = biMultiply(a, a);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
function biPowMod(x, y, m)
|
|
{
|
|
var result = bigOne;
|
|
var a = x;
|
|
var k = y;
|
|
while (true) {
|
|
if ((k.digits[0] & 1) != 0) result = biMultiplyMod(result, a, m);
|
|
k = biShiftRight(k, 1);
|
|
if (k.digits[0] == 0 && biHighIndex(k) == 0) break;
|
|
a = biMultiplyMod(a, a, m);
|
|
}
|
|
return result;
|
|
}
|
|
|