javascript 大数值数据运算

javascript数字运算结果不准确：

1、浮点型数字进行运算时，基本四则运算结果都可能不准确，一般是把浮点型数据转换为整型运算，然后在还原处理。

这种情况下可以用一些常用转换方法计算，如下：

/**
 * 加法运算
 */
function numAdd(num1, num2) {
    var baseNum, baseNum1, baseNum2;
    try {
        baseNum1 = num1.toString().split(".")[1].length;
    } catch (e) {
        baseNum1 = 0;
    }
    try {
        baseNum2 = num2.toString().split(".")[1].length;
    } catch (e) {
        baseNum2 = 0;
    }
    baseNum = Math.pow(10, Math.max(baseNum1, baseNum2));
    return (num1 * baseNum + num2 * baseNum) / baseNum;
};

/**
 * 减法运算
 */
function numSub(num1, num2) {
    var baseNum, baseNum1, baseNum2;
    var precision;
    //精度    
    try {
        baseNum1 = num1.toString().split(".")[1].length;
    } catch (e) {
        baseNum1 = 0;
    }
    try {
        baseNum2 = num2.toString().split(".")[1].length;
    } catch (e) {
        baseNum2 = 0;
    }
    baseNum = Math.pow(10, Math.max(baseNum1, baseNum2));
    precision = (baseNum1 >= baseNum2) ? baseNum1 : baseNum2;
    return ((num1 * baseNum - num2 * baseNum) / baseNum).toFixed(precision);
}

/**
 * 乘法运算
 */
function numMulti(num1, num2) {
    var baseNum = 0;
    try {
        baseNum += num1.toString().split(".")[1].length;
    } catch (e) {
    }
    try {
        baseNum += num2.toString().split(".")[1].length;
    } catch (e) {
    }
    return Number(num1.toString().replace(".", ""))
            * Number(num2.toString().replace(".", "")) / Math.pow(10, baseNum);
};


/**
 * 除法運算
 */
function numDiv(num1, num2) {
    var baseNum1 = 0, baseNum2 = 0;
    var baseNum3, baseNum4;
    try {
        baseNum1 = num1.toString().split(".")[1].length;
    } catch (e) {
        baseNum1 = 0;
    }
    try {
        baseNum2 = num2.toString().split(".")[1].length;
    } catch (e) {
        baseNum2 = 0;
    }
    with (Math) {
        baseNum3 = Number(num1.toString().replace(".", ""));
        baseNum4 = Number(num2.toString().replace(".", ""));
        return (baseNum3 / baseNum4) * pow(10, baseNum2 - baseNum1);
    }
}

2、整数运算在数字特别大的时候，计算结果的尾数也会不准确。如超过9个9乘以本身的乘法运算时，计算出的结果最大是999999998000000000，正常结果个位数应该为1，但是js运算结果将个位数去掉了,类似数据比较大时，经验证，7位数乘以7位数还是正常的，超过后就不准确了。网上搜到国外有个针对js计算大数值的情况，乘法运算可支持15位以内的运算。如下是js算法全文

  

/*
    JavaScript BigInteger library version 0.9
    http://silentmatt.com/biginteger/

    Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
    Copyright (c) 2010,2011 by John Tobey <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*10s*(^|**)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);
    part._s = 1;

    while (b_index) {
        part._d.unshift(b_digits[--b_index]);

        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();
        if (part._d.length === 0) {
            part._s = 0;
        }
    }

    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");
    }
    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);