* dice 6 [1-6]
* decimal [0-9]
* hexadecimal [0-9A-F]
+ * card [A2-9TJQK][CDHS]
*
* Automatically uses lowest entropy to avoid issues such as interpretting 0101
* as hexadecimal which would be 16 bits when really it's only 4 bits of binary
window.Entropy = new (function() {
+ var TWO = new libs.BigInteger.BigInteger(2);
+
// matchers returns an array of the matched events for each type of entropy.
// eg
// matchers.binary("010") returns ["0", "1", "0"]
return ints;
}
- this.fromString = function(rawEntropyStr) {
+ this.fromString = function(rawEntropyStr, baseStr) {
// Find type of entropy being used (binary, hex, dice etc)
- var base = getBase(rawEntropyStr);
+ var base = getBase(rawEntropyStr, baseStr);
// Convert dice to base6 entropy (ie 1-6 to 0-5)
// This is done by changing all 6s to 0s
if (base.str == "dice") {
return {
binaryStr: "",
cleanStr: "",
+ cleanHtml: "",
base: base,
};
}
- // Pull leading zeros off
- var leadingZeros = [];
- while (base.ints[0] == "0") {
- leadingZeros.push("0");
- base.ints.shift();
- }
- // Convert leading zeros to binary equivalent
- var numBinLeadingZeros = Math.floor(Math.log2(base.asInt) * leadingZeros.length);
- var binLeadingZeros = "";
- for (var i=0; i<numBinLeadingZeros; i++) {
- binLeadingZeros += "0";
- }
- // Handle entropy of zero
- if (base.ints.length == 0) {
- return {
- binaryStr: binLeadingZeros,
- cleanStr: leadingZeros.join(""),
- base: base,
- }
- }
- // If the first integer is small, it must be padded with zeros.
- // Otherwise the chance of the first bit being 1 is 100%, which is
- // obviously incorrect.
- // This is not perfect for unusual bases, so is only done for bases
- // of 2^n, eg octal or hexadecimal
- if (base.asInt == 16) {
- var firstInt = base.ints[0];
- var firstIntBits = firstInt.toString(2).length;
- var maxFirstIntBits = (base.asInt-1).toString(2).length;
- var missingFirstIntBits = maxFirstIntBits - firstIntBits;
- for (var i=0; i<missingFirstIntBits; i++) {
- binLeadingZeros += "0";
- }
- }
// Convert base.ints to BigInteger.
// Due to using unusual bases, eg cards of base52, this is not as simple as
// using BigInteger.parse()
- var entropyInt = BigInteger.ZERO;
+ var entropyInt = libs.BigInteger.BigInteger.ZERO;
for (var i=base.ints.length-1; i>=0; i--) {
- var thisInt = BigInteger.parse(base.ints[i]);
+ var thisInt = libs.BigInteger.BigInteger.parse(base.ints[i]);
var power = (base.ints.length - 1) - i;
- var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
+ var additionalEntropy = libs.BigInteger.BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
entropyInt = entropyInt.add(additionalEntropy);
}
- // Convert entropy to different formats
- var entropyBin = binLeadingZeros + entropyInt.toString(2);
+ // Convert entropy to binary
+ var entropyBin = entropyInt.toString(2);
+ // If the first integer is small, it must be padded with zeros.
+ // Otherwise the chance of the first bit being 1 is 100%, which is
+ // obviously incorrect.
+ // This is not perfect for non-2^n bases.
+ var expectedBits = Math.floor(base.parts.length * Math.log2(base.asInt));
+ while (entropyBin.length < expectedBits) {
+ entropyBin = "0" + entropyBin;
+ }
+ // Calculate the number of bits per event
+ var bitsPerEvent = Math.log2(base.asInt);
+ // Cards binary must be handled differently, since they're not replaced
+ if (base.asInt == 52) {
+ var cardEntropy = processCardEntropy(base.parts);
+ entropyBin = cardEntropy.binaryStr;
+ bitsPerEvent = cardEntropy.bitsPerEvent;
+ }
+ // Supply a 'filtered' entropy string for display purposes
var entropyClean = base.parts.join("");
+ var entropyHtml = base.parts.join("");
if (base.asInt == 52) {
entropyClean = base.parts.join(" ").toUpperCase();
entropyClean = entropyClean.replace(/C/g, "\u2663");
entropyClean = entropyClean.replace(/D/g, "\u2666");
entropyClean = entropyClean.replace(/H/g, "\u2665");
entropyClean = entropyClean.replace(/S/g, "\u2660");
+ entropyHtml = base.parts.join(" ").toUpperCase();
+ entropyHtml = entropyHtml.replace(/C/g, "<span class='card-suit club'>\u2663</span>");
+ entropyHtml = entropyHtml.replace(/D/g, "<span class='card-suit diamond'>\u2666</span>");
+ entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
+ entropyHtml = entropyHtml.replace(/S/g, "<span class='card-suit spade'>\u2660</span>");
}
+ // Return the result
var e = {
binaryStr: entropyBin,
cleanStr: entropyClean,
+ cleanHtml: entropyHtml,
+ bitsPerEvent: bitsPerEvent,
base: base,
}
return e;
}
- function getBase(str) {
+ function getSortedDeck() {
+ var s = [];
+ var suits = "CDHS";
+ var values = "A23456789TJQK";
+ for (var i=0; i<suits.length; i++) {
+ for (var j=0; j<values.length; j++) {
+ s.push(values[j]+suits[i]);
+ }
+ }
+ return s;
+ }
+
+ function getBase(str, baseStr) {
// Need to get the lowest base for the supplied entropy.
// This prevents interpreting, say, dice rolls as hexadecimal.
var binaryMatches = matchers.binary(str);
var hexMatches = matchers.hex(str);
+ var autodetect = baseStr === undefined;
// Find the lowest base that can be used, whilst ignoring any irrelevant chars
- if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((binaryMatches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "binary") {
var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
return {
ints: ints,
}
}
var cardMatches = matchers.card(str);
- if (cardMatches.length >= hexMatches.length / 2) {
+ if ((cardMatches.length >= hexMatches.length / 2 && autodetect) || baseStr === "card") {
var ints = convertCardsToInts(cardMatches);
return {
ints: ints,
}
}
var diceMatches = matchers.dice(str);
- if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((diceMatches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "dice") {
var ints = diceMatches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
var base6Matches = matchers.base6(str);
- if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((base6Matches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "base 6") {
var ints = base6Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
var base10Matches = matchers.base10(str);
- if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((base10Matches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "base 10") {
var ints = base10Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
+ // Assume cards are NOT replaced.
+ // Additional entropy decreases as more cards are used. This means
+ // total possible entropy is measured using n!, not base^n.
+ // eg the second last card can be only one of two, not one of fifty two
+ // so the added entropy for that card is only one bit at most
+ function processCardEntropy(cards) {
+ // Track how many instances of each card have been used, and thus
+ // how many decks are in use.
+ var cardCounts = {};
+ var numberOfDecks = 0;
+ // Work out number of decks by max(duplicates)
+ for (var i=0; i<cards.length; i++) {
+ // Get the card that was drawn
+ var cardLower = cards[i];
+ var card = cardLower.toUpperCase();
+ // Initialize the count for this card if needed
+ if (!(card in cardCounts)) {
+ cardCounts[card] = 0;
+ }
+ cardCounts[card] += 1;
+ // See if this is max(duplicates)
+ if (cardCounts[card] > numberOfDecks) {
+ numberOfDecks = cardCounts[card];
+ }
+ }
+ // Work out the total number of bits for this many decks
+ // See http://crypto.stackexchange.com/q/41886
+ var gainedBits = 0;
+ // Equivalent of Math.log2(factorial(52*numberOfDecks))
+ // which becomes infinity for numberOfDecks > 4
+ for (var i=1; i<=52*numberOfDecks; i++) {
+ gainedBits = gainedBits + Math.log2(i);
+ }
+ var lostBits = 52 * Math.log2(factorial(numberOfDecks));
+ var maxBits = gainedBits - lostBits;
+ // Convert the drawn cards to a binary representation.
+ // The exact technique for doing this is unclear.
+ // See
+ // http://crypto.stackexchange.com/a/41896
+ // "I even doubt that this is well defined (only the average entropy
+ // is, I believe)."
+ // See
+ // https://github.com/iancoleman/bip39/issues/33#issuecomment-263021856
+ // "The binary representation can be the first log(permutations,2) bits
+ // of the sha-2 hash of the normalized deck string."
+ //
+ // In this specific implementation, the first N bits of the hash of the
+ // normalized cards string is being used. Uppercase, no spaces; eg
+ // sha256("AH8DQSTC2H")
+ var totalCards = numberOfDecks * 52;
+ var percentUsed = cards.length / totalCards;
+ // Calculate the average number of bits of entropy for the number of
+ // cards drawn.
+ var numberOfBits = Math.floor(maxBits * percentUsed);
+ // Create a normalized string of the selected cards
+ var normalizedCards = cards.join("").toUpperCase();
+ // Convert to binary using the SHA256 hash of the normalized cards.
+ // If the number of bits is more than 256, multiple hashes
+ // are used until the required number of bits is reached.
+ var entropyBin = "";
+ var iterations = 0;
+ while (entropyBin.length < numberOfBits) {
+ var hashedCards = sjcl.hash.sha256.hash(normalizedCards + ":" + iterations);
+ var hashHex = sjcl.codec.hex.fromBits(hashedCards);
+ for (var i=0; i<hashHex.length; i++) {
+ var decimal = parseInt(hashHex[i], 16);
+ var binary = decimal.toString(2);
+ while (binary.length < 4) {
+ binary = "0" + binary;
+ }
+ entropyBin = entropyBin + binary;
+ }
+ iterations = iterations + 1;
+ }
+ // Truncate to the appropriate number of bits.
+ entropyBin = entropyBin.substring(0, numberOfBits);
+ // Get the number of bits per event
+ bitsPerEvent = maxBits / totalCards;
+ return {
+ binaryStr: entropyBin,
+ bitsPerEvent: bitsPerEvent,
+ }
+ }
+
// Polyfill for Math.log2
// See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
Math.log2 = Math.log2 || function(x) {
// Math.LOG2E
// log2(8) gave 2.9999999999999996 which when floored causes issues.
// So instead use the BigInteger library to get it right.
- return BigInteger.log(x) / BigInteger.log(2);
+ return libs.BigInteger.BigInteger.log(x) / libs.BigInteger.BigInteger.log(2);
};
-})();
-
-
-// BigInteger library included here because
-// only the entropy library depends on it
-// so if entropy detection is removed so is the dependency
-
-
-/*
- JavaScript BigInteger library version 0.9.1
- http://silentmatt.com/biginteger/
-
- Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
- Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
- Licensed under the MIT license.
-
- Support for arbitrary internal representation base was added by
- Vitaly Magerya.
-*/
-
-/*
- File: biginteger.js
-
- Exports:
-
- <BigInteger>
-*/
-(function(exports) {
-"use strict";
-/*
- Class: BigInteger
- An arbitrarily-large integer.
-
- <BigInteger> objects should be considered immutable. None of the "built-in"
- methods modify *this* or their arguments. All properties should be
- considered private.
-
- All the methods of <BigInteger> instances can be called "statically". The
- static versions are convenient if you don't already have a <BigInteger>
- object.
-
- As an example, these calls are equivalent.
-
- > BigInteger(4).multiply(5); // returns BigInteger(20);
- > BigInteger.multiply(4, 5); // returns BigInteger(20);
-
- > var a = 42;
- > var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
-*/
-
-var CONSTRUCT = {}; // Unique token to call "private" version of constructor
-
-/*
- Constructor: BigInteger()
- Convert a value to a <BigInteger>.
-
- Although <BigInteger()> is the constructor for <BigInteger> objects, it is
- best not to call it as a constructor. If *n* is a <BigInteger> object, it is
- simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
- without a radix argument.
-
- > var n0 = BigInteger(); // Same as <BigInteger.ZERO>
- > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
- > var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
- > var n3 = BigInteger(n2); // Return n2, unchanged
-
- The constructor form only takes an array and a sign. *n* must be an
- array of numbers in little-endian order, where each digit is between 0
- and BigInteger.base. The second parameter sets the sign: -1 for
- negative, +1 for positive, or 0 for zero. The array is *not copied and
- may be modified*. If the array contains only zeros, the sign parameter
- is ignored and is forced to zero.
-
- > new BigInteger([5], -1): create a new BigInteger with value -5
-
- Parameters:
-
- n - Value to convert to a <BigInteger>.
-
- Returns:
-
- A <BigInteger> value.
-
- See Also:
-
- <parse>, <BigInteger>
-*/
-function BigInteger(n, s, token) {
- if (token !== CONSTRUCT) {
- if (n instanceof BigInteger) {
- return n;
- }
- else if (typeof n === "undefined") {
- return ZERO;
- }
- return BigInteger.parse(n);
- }
-
- n = n || []; // Provide the nullary constructor for subclasses.
- while (n.length && !n[n.length - 1]) {
- --n.length;
- }
- this._d = n;
- this._s = n.length ? (s || 1) : 0;
-}
-
-BigInteger._construct = function(n, s) {
- return new BigInteger(n, s, CONSTRUCT);
-};
-
-// Base-10 speedup hacks in parse, toString, exp10 and log functions
-// require base to be a power of 10. 10^7 is the largest such power
-// that won't cause a precision loss when digits are multiplied.
-var BigInteger_base = 10000000;
-var BigInteger_base_log10 = 7;
-
-BigInteger.base = BigInteger_base;
-BigInteger.base_log10 = BigInteger_base_log10;
-
-var ZERO = new BigInteger([], 0, CONSTRUCT);
-// Constant: ZERO
-// <BigInteger> 0.
-BigInteger.ZERO = ZERO;
-
-var ONE = new BigInteger([1], 1, CONSTRUCT);
-// Constant: ONE
-// <BigInteger> 1.
-BigInteger.ONE = ONE;
-
-var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT);
-// Constant: M_ONE
-// <BigInteger> -1.
-BigInteger.M_ONE = M_ONE;
-
-// Constant: _0
-// Shortcut for <ZERO>.
-BigInteger._0 = ZERO;
-
-// Constant: _1
-// Shortcut for <ONE>.
-BigInteger._1 = ONE;
-
-/*
- Constant: small
- Array of <BigIntegers> from 0 to 36.
-
- These are used internally for parsing, but useful when you need a "small"
- <BigInteger>.
-
- See Also:
-
- <ZERO>, <ONE>, <_0>, <_1>
-*/
-BigInteger.small = [
- ZERO,
- ONE,
- /* Assuming BigInteger_base > 36 */
- new BigInteger( [2], 1, CONSTRUCT),
- new BigInteger( [3], 1, CONSTRUCT),
- new BigInteger( [4], 1, CONSTRUCT),
- new BigInteger( [5], 1, CONSTRUCT),
- new BigInteger( [6], 1, CONSTRUCT),
- new BigInteger( [7], 1, CONSTRUCT),
- new BigInteger( [8], 1, CONSTRUCT),
- new BigInteger( [9], 1, CONSTRUCT),
- new BigInteger([10], 1, CONSTRUCT),
- new BigInteger([11], 1, CONSTRUCT),
- new BigInteger([12], 1, CONSTRUCT),
- new BigInteger([13], 1, CONSTRUCT),
- new BigInteger([14], 1, CONSTRUCT),
- new BigInteger([15], 1, CONSTRUCT),
- new BigInteger([16], 1, CONSTRUCT),
- new BigInteger([17], 1, CONSTRUCT),
- new BigInteger([18], 1, CONSTRUCT),
- new BigInteger([19], 1, CONSTRUCT),
- new BigInteger([20], 1, CONSTRUCT),
- new BigInteger([21], 1, CONSTRUCT),
- new BigInteger([22], 1, CONSTRUCT),
- new BigInteger([23], 1, CONSTRUCT),
- new BigInteger([24], 1, CONSTRUCT),
- new BigInteger([25], 1, CONSTRUCT),
- new BigInteger([26], 1, CONSTRUCT),
- new BigInteger([27], 1, CONSTRUCT),
- new BigInteger([28], 1, CONSTRUCT),
- new BigInteger([29], 1, CONSTRUCT),
- new BigInteger([30], 1, CONSTRUCT),
- new BigInteger([31], 1, CONSTRUCT),
- new BigInteger([32], 1, CONSTRUCT),
- new BigInteger([33], 1, CONSTRUCT),
- new BigInteger([34], 1, CONSTRUCT),
- new BigInteger([35], 1, CONSTRUCT),
- new BigInteger([36], 1, CONSTRUCT)
-];
-
-// Used for parsing/radix conversion
-BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
-
-/*
- Method: toString
- Convert a <BigInteger> to a string.
-
- When *base* is greater than 10, letters are upper case.
-
- Parameters:
-
- base - Optional base to represent the number in (default is base 10).
- Must be between 2 and 36 inclusive, or an Error will be thrown.
-
- Returns:
-
- The string representation of the <BigInteger>.
-*/
-BigInteger.prototype.toString = function(base) {
- base = +base || 10;
- if (base < 2 || base > 36) {
- throw new Error("illegal radix " + base + ".");
- }
- if (this._s === 0) {
- return "0";
- }
- if (base === 10) {
- var str = this._s < 0 ? "-" : "";
- str += this._d[this._d.length - 1].toString();
- for (var i = this._d.length - 2; i >= 0; i--) {
- var group = this._d[i].toString();
- while (group.length < BigInteger_base_log10) group = '0' + group;
- str += group;
- }
- return str;
- }
- else {
- var numerals = BigInteger.digits;
- base = BigInteger.small[base];
- var sign = this._s;
-
- var n = this.abs();
- var digits = [];
- var digit;
-
- while (n._s !== 0) {
- var divmod = n.divRem(base);
- n = divmod[0];
- digit = divmod[1];
- // TODO: This could be changed to unshift instead of reversing at the end.
- // Benchmark both to compare speeds.
- digits.push(numerals[digit.valueOf()]);
- }
- return (sign < 0 ? "-" : "") + digits.reverse().join("");
- }
-};
-
-// Verify strings for parsing
-BigInteger.radixRegex = [
- /^$/,
- /^$/,
- /^[01]*$/,
- /^[012]*$/,
- /^[0-3]*$/,
- /^[0-4]*$/,
- /^[0-5]*$/,
- /^[0-6]*$/,
- /^[0-7]*$/,
- /^[0-8]*$/,
- /^[0-9]*$/,
- /^[0-9aA]*$/,
- /^[0-9abAB]*$/,
- /^[0-9abcABC]*$/,
- /^[0-9a-dA-D]*$/,
- /^[0-9a-eA-E]*$/,
- /^[0-9a-fA-F]*$/,
- /^[0-9a-gA-G]*$/,
- /^[0-9a-hA-H]*$/,
- /^[0-9a-iA-I]*$/,
- /^[0-9a-jA-J]*$/,
- /^[0-9a-kA-K]*$/,
- /^[0-9a-lA-L]*$/,
- /^[0-9a-mA-M]*$/,
- /^[0-9a-nA-N]*$/,
- /^[0-9a-oA-O]*$/,
- /^[0-9a-pA-P]*$/,
- /^[0-9a-qA-Q]*$/,
- /^[0-9a-rA-R]*$/,
- /^[0-9a-sA-S]*$/,
- /^[0-9a-tA-T]*$/,
- /^[0-9a-uA-U]*$/,
- /^[0-9a-vA-V]*$/,
- /^[0-9a-wA-W]*$/,
- /^[0-9a-xA-X]*$/,
- /^[0-9a-yA-Y]*$/,
- /^[0-9a-zA-Z]*$/
-];
-
-/*
- Function: parse
- Parse a string into a <BigInteger>.
-
- *base* is optional but, if provided, must be from 2 to 36 inclusive. If
- *base* is not provided, it will be guessed based on the leading characters
- of *s* as follows:
-
- - "0x" or "0X": *base* = 16
- - "0c" or "0C": *base* = 8
- - "0b" or "0B": *base* = 2
- - else: *base* = 10
-
- If no base is provided, or *base* is 10, the number can be in exponential
- form. For example, these are all valid:
-
- > BigInteger.parse("1e9"); // Same as "1000000000"
- > BigInteger.parse("1.234*10^3"); // Same as 1234
- > BigInteger.parse("56789 * 10 ** -2"); // Same as 567
-
- If any characters fall outside the range defined by the radix, an exception
- will be thrown.
-
- Parameters:
-
- s - The string to parse.
- base - Optional radix (default is to guess based on *s*).
-
- Returns:
-
- a <BigInteger> instance.
-*/
-BigInteger.parse = function(s, base) {
- // Expands a number in exponential form to decimal form.
- // expandExponential("-13.441*10^5") === "1344100";
- // expandExponential("1.12300e-1") === "0.112300";
- // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
- function expandExponential(str) {
- str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
-
- return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) {
- c = +c;
- var l = c < 0;
- var i = n.length + c;
- x = (l ? n : f).length;
- c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
- var z = (new Array(c + 1)).join("0");
- var r = n + f;
- return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
- });
- }
-
- s = s.toString();
- if (typeof base === "undefined" || +base === 10) {
- s = expandExponential(s);
- }
-
- var prefixRE;
- if (typeof base === "undefined") {
- prefixRE = '0[xcb]';
- }
- else if (base == 16) {
- prefixRE = '0x';
- }
- else if (base == 8) {
- prefixRE = '0c';
- }
- else if (base == 2) {
- prefixRE = '0b';
- }
- else {
- prefixRE = '';
- }
- var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s);
- if (parts) {
- var sign = parts[1] || "+";
- var baseSection = parts[2] || "";
- var digits = parts[3] || "";
-
- if (typeof base === "undefined") {
- // Guess base
- if (baseSection === "0x" || baseSection === "0X") { // Hex
- base = 16;
- }
- else if (baseSection === "0c" || baseSection === "0C") { // Octal
- base = 8;
- }
- else if (baseSection === "0b" || baseSection === "0B") { // Binary
- base = 2;
- }
- else {
- base = 10;
- }
- }
- else if (base < 2 || base > 36) {
- throw new Error("Illegal radix " + base + ".");
- }
-
- base = +base;
-
- // Check for digits outside the range
- if (!(BigInteger.radixRegex[base].test(digits))) {
- throw new Error("Bad digit for radix " + base);
- }
-
- // Strip leading zeros, and convert to array
- digits = digits.replace(/^0+/, "").split("");
- if (digits.length === 0) {
- return ZERO;
- }
-
- // Get the sign (we know it's not zero)
- sign = (sign === "-") ? -1 : 1;
-
- // Optimize 10
- if (base == 10) {
- var d = [];
- while (digits.length >= BigInteger_base_log10) {
- d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10));
- }
- d.push(parseInt(digits.join(''), 10));
- return new BigInteger(d, sign, CONSTRUCT);
- }
-
- // Do the conversion
- var d = ZERO;
- base = BigInteger.small[base];
- var small = BigInteger.small;
- for (var i = 0; i < digits.length; i++) {
- d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
- }
- return new BigInteger(d._d, sign, CONSTRUCT);
- }
- else {
- throw new Error("Invalid BigInteger format: " + s);
- }
-};
-
-/*
- Function: add
- Add two <BigIntegers>.
-
- Parameters:
-
- n - The number to add to *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- The numbers added together.
-
- See Also:
-
- <subtract>, <multiply>, <quotient>, <next>
-*/
-BigInteger.prototype.add = function(n) {
- if (this._s === 0) {
- return BigInteger(n);
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return this;
- }
- if (this._s !== n._s) {
- n = n.negate();
- return this.subtract(n);
- }
-
- var a = this._d;
- var b = n._d;
- var al = a.length;
- var bl = b.length;
- var sum = new Array(Math.max(al, bl) + 1);
- var size = Math.min(al, bl);
- var carry = 0;
- var digit;
-
- for (var i = 0; i < size; i++) {
- digit = a[i] + b[i] + carry;
- sum[i] = digit % BigInteger_base;
- carry = (digit / BigInteger_base) | 0;
- }
- if (bl > al) {
- a = b;
- al = bl;
- }
- for (i = size; carry && i < al; i++) {
- digit = a[i] + carry;
- sum[i] = digit % BigInteger_base;
- carry = (digit / BigInteger_base) | 0;
- }
- if (carry) {
- sum[i] = carry;
- }
-
- for ( ; i < al; i++) {
- sum[i] = a[i];
- }
-
- return new BigInteger(sum, this._s, CONSTRUCT);
-};
-
-/*
- Function: negate
- Get the additive inverse of a <BigInteger>.
-
- Returns:
-
- A <BigInteger> with the same magnatude, but with the opposite sign.
-
- See Also:
-
- <abs>
-*/
-BigInteger.prototype.negate = function() {
- return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT);
-};
-
-/*
- Function: abs
- Get the absolute value of a <BigInteger>.
-
- Returns:
-
- A <BigInteger> with the same magnatude, but always positive (or zero).
-
- See Also:
-
- <negate>
-*/
-BigInteger.prototype.abs = function() {
- return (this._s < 0) ? this.negate() : this;
-};
-
-/*
- Function: subtract
- Subtract two <BigIntegers>.
-
- Parameters:
-
- n - The number to subtract from *this*. Will be converted to a <BigInteger>.
-
- Returns:
-
- The *n* subtracted from *this*.
-
- See Also:
-
- <add>, <multiply>, <quotient>, <prev>
-*/
-BigInteger.prototype.subtract = function(n) {
- if (this._s === 0) {
- return BigInteger(n).negate();
- }
-
- n = BigInteger(n);
- if (n._s === 0) {
- return this;
- }
- if (this._s !== n._s) {
- n = n.negate();
- return this.add(n);
- }
-
- var m = this;
- // 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]);
- }
+ // Depends on BigInteger
+ function factorial(n) {
+ if (n == 0) {
+ return 1;
+ }
+ f = libs.BigInteger.BigInteger.ONE;
+ for (var i=1; i<=n; i++) {
+ f = f.multiply(new libs.BigInteger.BigInteger(i));
+ }
+ return f;
+ }
- BigInteger.exp10 = function(x, n) {
- return BigInteger(x).exp10(n);
- };
- })();
})();
-
-exports.BigInteger = BigInteger;
-})(typeof exports !== 'undefined' ? exports : this);
projects / perso / Immae / Projets / Cryptomonnaies / BIP39.git / blobdiff