Dice conversion to Base 6 uses arrays not strings

[perso/Immae/Projets/Cryptomonnaies/BIP39.git] / src / js / entropy.js

/*
 * Detects entropy from a string.
 *
 * Formats include:
 * binary [0-1]
 * base 6 [0-5]
 * dice 6 [1-6]
 * decimal [0-9]
 * hexadecimal [0-9A-F]
 *
 * 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
 * entropy.
 */

window.Entropy = new (function() {

    // matchers returns an array of the matched events for each type of entropy.
    // eg
    // matchers.binary("010") returns ["0", "1", "0"]
    // matchers.binary("a10") returns ["1", "0"]
    // matchers.hex("a10") returns ["a", "1", "0"]
    var matchers = {
        binary: function(str) {
            return str.match(/[0-1]/gi) || [];
        },
        base6: function(str) {
            return str.match(/[0-5]/gi) || [];
        },
        dice: function(str) {
            return str.match(/[1-6]/gi) || []; // ie dice numbers
        },
        base10: function(str) {
            return str.match(/[0-9]/gi) || [];
        },
        hex: function(str) {
            return str.match(/[0-9A-F]/gi) || [];
        },
        card: function(str) {
            // Format is NumberSuit, eg
            // AH ace of hearts
            // 8C eight of clubs
            // TD ten of diamonds
            // JS jack of spades
            // QH queen of hearts
            // KC king of clubs
            return str.match(/([A2-9TJQK][CDHS])/gi) || [];
        }
    }

    // Convert array of cards from ["ac", "4d", "ks"]
    // to numbers between 0 and 51 [0, 16, 51]
    function convertCardsToInts(cards) {
        var ints = [];
        var values = "a23456789tjqk";
        var suits = "cdhs";
        for (var i=0; i<cards.length; i++) {
            var card = cards[i].toLowerCase();
            var value = card[0];
            var suit = card[1];
            var asInt = 13 * suits.indexOf(suit) + values.indexOf(value);
            ints.push(asInt);
        }
        return ints;
    }

    this.fromString = function(rawEntropyStr) {
        // Find type of entropy being used (binary, hex, dice etc)
        var base = getBase(rawEntropyStr);
        // Convert dice to base6 entropy (ie 1-6 to 0-5)
        // This is done by changing all 6s to 0s
        if (base.str == "dice") {
            var newParts = [];
            var newInts = [];
            for (var i=0; i<base.parts.length; i++) {
                var c = base.parts[i];
                if ("12345".indexOf(c) > -1) {
                    newParts[i] = base.parts[i];
                    newInts[i] = base.ints[i];
                }
                else {
                    newParts[i] = "0";
                    newInts[i] = 0;
                }
            }
            base.str = "base 6 (dice)";
            base.ints = newInts;
            base.parts = newParts;
            base.matcher = matchers.base6;
        }
        // Detect empty entropy
        if (base.parts.length == 0) {
            return {
                binaryStr: "",
                cleanStr: "",
                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;
        for (var i=base.ints.length-1; i>=0; i--) {
            var thisInt = BigInteger.parse(base.ints[i]);
            var power = (base.ints.length - 1) - i;
            var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
            entropyInt = entropyInt.add(additionalEntropy);
        }
        // Convert entropy to different formats
        var entropyBin = binLeadingZeros + entropyInt.toString(2);
        var entropyClean = base.parts.join("");
        var e = {
            binaryStr: entropyBin,
            cleanStr: entropyClean,
            base: base,
        }
        return e;
    }

    function getBase(str) {
        // 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);
        // Find the lowest base that can be used, whilst ignoring any irrelevant chars
        if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
            var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
            return {
                ints: ints,
                parts: binaryMatches,
                matcher: matchers.binary,
                asInt: 2,
                str: "binary",
            }
        }
        var cardMatches = matchers.card(str);
        if (cardMatches.length >= hexMatches.length / 2) {
            var ints = convertCardsToInts(cardMatches);
            return {
                ints: ints,
                parts: cardMatches,
                matcher: matchers.card,
                asInt: 52,
                str: "card",
            }
        }
        var diceMatches = matchers.dice(str);
        if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
            var ints = diceMatches.map(function(i) { return parseInt(i) });
            return {
                ints: ints,
                parts: diceMatches,
                matcher: matchers.dice,
                asInt: 6,
                str: "dice",
            }
        }
        var base6Matches = matchers.base6(str);
        if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
            var ints = base6Matches.map(function(i) { return parseInt(i) });
            return {
                ints: ints,
                parts: base6Matches,
                matcher: matchers.base6,
                asInt: 6,
                str: "base 6",
            }
        }
        var base10Matches = matchers.base10(str);
        if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
            var ints = base10Matches.map(function(i) { return parseInt(i) });
            return {
                ints: ints,
                parts: base10Matches,
                matcher: matchers.base10,
                asInt: 10,
                str: "base 10",
            }
        }
        var ints = hexMatches.map(function(i) { return parseInt(i, 16) });
        return {
            ints: ints,
            parts: hexMatches,
            matcher: matchers.hex,
            asInt: 16,
            str: "hexadecimal",
        }
    }

    // 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) {
        // The polyfill isn't good enough because of the poor accuracy of
        // 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);
    };

})();


// 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]);
                }

                BigInteger.exp10 = function(x, n) {
                        return BigInteger(x).exp10(n);
                };
        })();
})();

exports.BigInteger = BigInteger;
})(typeof exports !== 'undefined' ? exports : this);