BigInt.js

  /*
        JavaScript silentBigInteger 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:

                <silentBigInteger>
*/
  (function(exports) {
    "use strict";
/*
        Class: silentBigInteger
        An arbitrarily-large integer.

        <silentBigInteger> 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 <silentBigInteger> instances can be called "statically". The
        static versions are convenient if you don't already have a <silentBigInteger>
        object.

        As an example, these calls are equivalent.

        > silentBigInteger(4).multiply(5); // returns silentBigInteger(20);
        > silentBigInteger.multiply(4, 5); // returns silentBigInteger(20);

        > var a = 42;
        > var a = silentBigInteger.toJSValue("0b101010"); // Not completely useless...
*/

    // IE doesn't support Array.prototype.map
    if (!Array.prototype.map) {
      Array.prototype.map = function(fun /*, thisp*/ ) {
        var len = this.length >>> 0;
        if (typeof fun !== "function") {
          throw new TypeError();
        }

        var res = new Array(len);
        var thisp = arguments[1];
        for (var i = 0; i < len; i++) {
          if (i in this) {
            res[i] = fun.call(thisp, this[i], i, this);
          }
        }

        return res;
      };
    }

    var CONSTRUCT = {}; // Unique token to call "private" version of constructor
/*
        Constructor: silentBigInteger()
        Convert a value to a <silentBigInteger>.

        Although <silentBigInteger()> is the constructor for <silentBigInteger> objects, it is
        best not to call it as a constructor. If *n* is a <silentBigInteger> object, it is
        simply returned as-is. Otherwise, <silentBigInteger()> is equivalent to <parse>
        without a radix argument.

        > var n0 = silentBigInteger();      // Same as <silentBigInteger.ZERO>
        > var n1 = silentBigInteger("123"); // Create a new <silentBigInteger> with value 123
        > var n2 = silentBigInteger(123);   // Create a new <silentBigInteger> with value 123
        > var n3 = silentBigInteger(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 silentBigInteger.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 silentBigInteger([5], -1): create a new silentBigInteger with value -5

        Parameters:

                n - Value to convert to a <silentBigInteger>.

        Returns:

                A <silentBigInteger> value.

        See Also:

                <parse>, <silentBigInteger>
*/

    function silentBigInteger(n, s, token) {
      if (token !== CONSTRUCT) {
        if (n instanceof silentBigInteger) {
          return n;
        } else if (typeof n === "undefined") {
          return ZERO;
        }
        return silentBigInteger.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;
    }

    silentBigInteger._construct = function(n, s) {
      return new silentBigInteger(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;

    silentBigInteger.base = BigInteger_base;
    silentBigInteger.base_log10 = BigInteger_base_log10;

    var ZERO = new silentBigInteger([], 0, CONSTRUCT);
    // Constant: ZERO
    // <silentBigInteger> 0.
    silentBigInteger.ZERO = ZERO;

    var ONE = new silentBigInteger([1], 1, CONSTRUCT);
    // Constant: ONE
    // <silentBigInteger> 1.
    silentBigInteger.ONE = ONE;

    var M_ONE = new silentBigInteger(ONE._d, -1, CONSTRUCT);
    // Constant: M_ONE
    // <silentBigInteger> -1.
    silentBigInteger.M_ONE = M_ONE;

    // Constant: _0
    // Shortcut for <ZERO>.
    silentBigInteger._0 = ZERO;

    // Constant: _1
    // Shortcut for <ONE>.
    silentBigInteger._1 = ONE;

/*
        Constant: small
        Array of <BigIntegers> from 0 to 36.

        These are used internally for parsing, but useful when you need a "small"
        <silentBigInteger>.

        See Also:

                <ZERO>, <ONE>, <_0>, <_1>
*/
    silentBigInteger.small = [
    ZERO, ONE, /* Assuming BigInteger_base > 36 */
    new silentBigInteger([2], 1, CONSTRUCT), new silentBigInteger([3], 1, CONSTRUCT), new silentBigInteger([4], 1, CONSTRUCT), new silentBigInteger([5], 1, CONSTRUCT), new silentBigInteger([6], 1, CONSTRUCT), new silentBigInteger([7], 1, CONSTRUCT), new silentBigInteger([8], 1, CONSTRUCT), new silentBigInteger([9], 1, CONSTRUCT), new silentBigInteger([10], 1, CONSTRUCT), new silentBigInteger([11], 1, CONSTRUCT), new silentBigInteger([12], 1, CONSTRUCT), new silentBigInteger([13], 1, CONSTRUCT), new silentBigInteger([14], 1, CONSTRUCT), new silentBigInteger([15], 1, CONSTRUCT), new silentBigInteger([16], 1, CONSTRUCT), new silentBigInteger([17], 1, CONSTRUCT), new silentBigInteger([18], 1, CONSTRUCT), new silentBigInteger([19], 1, CONSTRUCT), new silentBigInteger([20], 1, CONSTRUCT), new silentBigInteger([21], 1, CONSTRUCT), new silentBigInteger([22], 1, CONSTRUCT), new silentBigInteger([23], 1, CONSTRUCT), new silentBigInteger([24], 1, CONSTRUCT), new silentBigInteger([25], 1, CONSTRUCT), new silentBigInteger([26], 1, CONSTRUCT), new silentBigInteger([27], 1, CONSTRUCT), new silentBigInteger([28], 1, CONSTRUCT), new silentBigInteger([29], 1, CONSTRUCT), new silentBigInteger([30], 1, CONSTRUCT), new silentBigInteger([31], 1, CONSTRUCT), new silentBigInteger([32], 1, CONSTRUCT), new silentBigInteger([33], 1, CONSTRUCT), new silentBigInteger([34], 1, CONSTRUCT), new silentBigInteger([35], 1, CONSTRUCT), new silentBigInteger([36], 1, CONSTRUCT)];

    // Used for parsing/radix conversion
    silentBigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");

/*
        Method: toString
        Convert a <silentBigInteger> 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 <silentBigInteger>.
*/
    silentBigInteger.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 = silentBigInteger.digits;
        base = silentBigInteger.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
    silentBigInteger.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 <silentBigInteger>.

        *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:

        > silentBigInteger.parse("1e9");              // Same as "1000000000"
        > silentBigInteger.parse("1.234*10^3");       // Same as 1234
        > silentBigInteger.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 <silentBigInteger> instance.
*/
    silentBigInteger.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 (!(silentBigInteger.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 - silentBigInteger.base_log10, silentBigInteger.base_log10).join(''), 10));
          }
          d.push(parseInt(digits.join(''), 10));
          return new silentBigInteger(d, sign, CONSTRUCT);
        }

        // Optimize base
        if (base === BigInteger_base) {
          return new silentBigInteger(digits.map(Number).reverse(), sign, CONSTRUCT);
        }

        // Do the conversion
        var d = ZERO;
        base = silentBigInteger.small[base];
        var small = silentBigInteger.small;
        for (var i = 0; i < digits.length; i++) {
          d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
        }
        return new silentBigInteger(d._d, sign, CONSTRUCT);
      } else {
        throw new Error("Invalid silentBigInteger format: " + s);
      }
    };

/*
        Function: add
        Add two <BigIntegers>.

        Parameters:

                n - The number to add to *this*. Will be converted to a <silentBigInteger>.

        Returns:

                The numbers added together.

        See Also:

                <subtract>, <multiply>, <quotient>, <next>
*/
    silentBigInteger.prototype.add = function(n) {
      if (this._s === 0) {
        return silentBigInteger(n);
      }

      n = silentBigInteger(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 silentBigInteger(sum, this._s, CONSTRUCT);
    };

/*
        Function: negate
        Get the additive inverse of a <silentBigInteger>.

        Returns:

                A <silentBigInteger> with the same magnatude, but with the opposite sign.

        See Also:

                <abs>
*/
    silentBigInteger.prototype.negate = function() {
      return new silentBigInteger(this._d, (-this._s) | 0, CONSTRUCT);
    };

/*
        Function: abs
        Get the absolute value of a <silentBigInteger>.

        Returns:

                A <silentBigInteger> with the same magnatude, but always positive (or zero).

        See Also:

                <negate>
*/
    silentBigInteger.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 <silentBigInteger>.

        Returns:

                The *n* subtracted from *this*.

        See Also:

                <add>, <multiply>, <quotient>, <prev>
*/
    silentBigInteger.prototype.subtract = function(n) {
      if (this._s === 0) {
        return silentBigInteger(n).negate();
      }

      n = silentBigInteger(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 silentBigInteger(n._d, 1, CONSTRUCT);
        n = new silentBigInteger(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 silentBigInteger(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 silentBigInteger(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 silentBigInteger(sum, sign, CONSTRUCT);
      }

/*
                Function: next
                Get the next <silentBigInteger> (add one).

                Returns:

                        *this* + 1.

                See Also:

                        <add>, <prev>
        */
      silentBigInteger.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 <silentBigInteger> (subtract one).

                Returns:

                        *this* - 1.

                See Also:

                        <next>, <subtract>
        */
      silentBigInteger.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 <silentBigInteger>.

        Returns:

                -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.

        See Also:

                <compare>, <abs>
*/
    silentBigInteger.prototype.compareAbs = function(n) {
      if (this === n) {
        return 0;
      }

      if (!(n instanceof silentBigInteger)) {
        if (!isFinite(n)) {
          return (isNaN(n) ? n : -1);
        }
        n = silentBigInteger(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 <silentBigInteger>.

        Returns:

                -1, 0, or +1 if *this* is less than, equal to, or greater than *n*.

        See Also:

                <compareAbs>, <isPositive>, <isNegative>, <isUnit>
*/
    silentBigInteger.prototype.compare = function(n) {
      if (this === n) {
        return 0;
      }

      n = silentBigInteger(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 <silentBigInteger.ONE> or <silentBigInteger.M_ONE>.

        See Also:

                <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
                <silentBigInteger.ONE>, <silentBigInteger.M_ONE>
*/
    silentBigInteger.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
                <silentBigInteger>.

        Returns:

                The numbers multiplied together.

        See Also:

                <add>, <subtract>, <quotient>, <square>
*/
    silentBigInteger.prototype.multiply = function(n) {
      // TODO: Consider adding Karatsuba multiplication for large numbers
      if (this._s === 0) {
        return ZERO;
      }

      n = silentBigInteger(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 silentBigInteger(partial, this._s * n._s, CONSTRUCT);
    };

    // Multiply a silentBigInteger 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
    silentBigInteger.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 silentBigInteger([(digit % BigInteger_base) | 0, (digit / BigInteger_base) | 0], 1, CONSTRUCT);
        }
        return new silentBigInteger([digit], 1, CONSTRUCT);
      }

      if (n === 2) {
        return this.add(this);
      }
      if (this.isUnit()) {
        return new silentBigInteger([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 silentBigInteger(partial, 1, CONSTRUCT);
    };

/*
        Function: square
        Multiply a <silentBigInteger> by itself.

        This is slightly faster than regular multiplication, since it removes the
        duplicated multiplcations.

        Returns:

                > this.multiply(this)

        See Also:
                <multiply>
*/
    silentBigInteger.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 silentBigInteger(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 <silentBigInteger>.

        Returns:

                The *this* / *n*, truncated to an integer.

        See Also:

                <add>, <subtract>, <multiply>, <divRem>, <remainder>
*/
    silentBigInteger.prototype.quotient = function(n) {
      return this.divRem(n)[0];
    };

/*
        Function: divide
        Deprecated synonym for <quotient>.
*/
    silentBigInteger.prototype.divide = silentBigInteger.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 <silentBigInteger>.

        Returns:

                *this* % *n*.

        See Also:

                <divRem>, <quotient>
*/
    silentBigInteger.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 <silentBigInteger>.

        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>
*/
    silentBigInteger.prototype.divRem = function(n) {
      n = silentBigInteger(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 silentBigInteger([], 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 silentBigInteger(quot.reverse(), sign, CONSTRUCT), new silentBigInteger(part._d, this._s, CONSTRUCT)];
    };

    // Throws an exception if n is outside of (-silentBigInteger.base, -1] or
    // [1, silentBigInteger.base).  It's not necessary to call this, since the
    // other division functions will call it if they are able to.
    silentBigInteger.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 silentBigInteger(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 silentBigInteger([(this._d[0] / n) | 0], 1, CONSTRUCT);
        r = new silentBigInteger([(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 silentBigInteger([diff], 1, CONSTRUCT);
      if (this._s < 0) {
        r = r.negate();
      }
      return [new silentBigInteger(quot.reverse(), sign, CONSTRUCT), r];
    };

/*
        Function: isEven
        Return true iff *this* is divisible by two.

        Note that <silentBigInteger.ZERO> is even.

        Returns:

                true if *this* is even, false otherwise.

        See Also:

                <isOdd>
*/
    silentBigInteger.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>
*/
    silentBigInteger.prototype.isOdd = function() {
      return !this.isEven();
    };

/*
        Function: sign
        Get the sign of a <silentBigInteger>.

        Returns:

                * -1 if *this* < 0
                * 0 if *this* == 0
                * +1 if *this* > 0

        See Also:

                <isZero>, <isPositive>, <isNegative>, <compare>, <silentBigInteger.ZERO>
*/
    silentBigInteger.prototype.sign = function() {
      return this._s;
    };

/*
        Function: isPositive
        Return true iff *this* > 0.

        Returns:

                true if *this*.compare(<silentBigInteger.ZERO>) == 1.

        See Also:

                <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <silentBigInteger.ZERO>
*/
    silentBigInteger.prototype.isPositive = function() {
      return this._s > 0;
    };

/*
        Function: isNegative
        Return true iff *this* < 0.

        Returns:

                true if *this*.compare(<silentBigInteger.ZERO>) == -1.

        See Also:

                <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <silentBigInteger.ZERO>
*/
    silentBigInteger.prototype.isNegative = function() {
      return this._s < 0;
    };

/*
        Function: isZero
        Return true iff *this* == 0.

        Returns:

                true if *this*.compare(<silentBigInteger.ZERO>) == 0.

        See Also:

                <sign>, <isPositive>, <isNegative>, <isUnit>, <silentBigInteger.ZERO>
*/
    silentBigInteger.prototype.isZero = function() {
      return this._s === 0;
    };

/*
        Function: exp10
        Multiply a <silentBigInteger> by a power of 10.

        This is equivalent to, but faster than

        > if (n >= 0) {
        >     return this.multiply(silentBigInteger("1e" + n));
        > }
        > else { // n <= 0
        >     return this.quotient(silentBigInteger("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 <silentBigInteger.MAX_EXP>
                (0x7FFFFFFF), or an exception will be thrown.

        Returns:

                *this* * (10 ** *n*), truncated to an integer if necessary.

        See Also:

                <pow>, <multiply>
*/
    silentBigInteger.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 silentBigInteger.exp10");
      }
      if (n > 0) {
        var k = new silentBigInteger(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 silentBigInteger(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 <silentBigInteger> to a power.

        In this implementation, 0**0 is 1.

        Parameters:

                n - The exponent to raise *this* by. *n* must be no greater than
                <silentBigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.

        Returns:

                *this* raised to the *nth* power.

        See Also:

                <modPow>
*/
    silentBigInteger.prototype.pow = function(n) {
      if (this.isUnit()) {
        if (this._s > 0) {
          return this;
        } else {
          return silentBigInteger(n).isOdd() ? this : this.negate();
        }
      }

      n = silentBigInteger(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 silentBigInteger.pow");
      }
      var x = this;
      var aux = ONE;
      var two = silentBigInteger.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 <silentBigInteger> to a power (mod m).

        Because it is reduced by a modulus, <modPow> is not limited by
        <silentBigInteger.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>
*/
    silentBigInteger.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(silentBigInteger.small[2]);
        if (exponent.isPositive()) {
          base = base.square().remainder(modulus);
        }
      }

      return result;
    };

/*
        Function: log
        Get the natural logarithm of a <silentBigInteger> 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>
*/
    silentBigInteger.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 silentBigInteger(firstNdigits, 1, CONSTRUCT)).valueOf()) + (l - N) * Math.log(BigInteger_base);
    };

/*
        Function: valueOf
        Convert a <silentBigInteger> to a native JavaScript integer.

        This is called automatically by JavaScipt to convert a <silentBigInteger> to a
        native value.

        Returns:

                > parseInt(this.toString(), 10)

        See Also:

                <toString>, <toJSValue>
*/
    silentBigInteger.prototype.valueOf = function() {
      return parseInt(this.toString(), 10);
    };

/*
        Function: toJSValue
        Convert a <silentBigInteger> to a native JavaScript integer.

        This is the same as valueOf, but more explicitly named.

        Returns:

                > parseInt(this.toString(), 10)

        See Also:

                <toString>, <valueOf>
*/
    silentBigInteger.prototype.toJSValue = function() {
      return parseInt(this.toString(), 10);
    };

    var MAX_EXP = silentBigInteger(0x7FFFFFFF);
    // Constant: MAX_EXP
    // The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
    silentBigInteger.MAX_EXP = MAX_EXP;

    (function() {
      function makeUnary(fn) {
        return function(a) {
          return fn.call(silentBigInteger(a));
        };
      }

      function makeBinary(fn) {
        return function(a, b) {
          return fn.call(silentBigInteger(a), silentBigInteger(b));
        };
      }

      function makeTrinary(fn) {
        return function(a, b, c) {
          return fn.call(silentBigInteger(a), silentBigInteger(b), silentBigInteger(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];
          silentBigInteger[fn] = makeUnary(silentBigInteger.prototype[fn]);
        }

        for (i = 0; i < binary.length; i++) {
          fn = binary[i];
          silentBigInteger[fn] = makeBinary(silentBigInteger.prototype[fn]);
        }

        for (i = 0; i < trinary.length; i++) {
          fn = trinary[i];
          silentBigInteger[fn] = makeTrinary(silentBigInteger.prototype[fn]);
        }

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

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