path: root/src/long.js

// TODO: strip out parts of this we do not need

//======= begin closure i64 code =======

// Copyright 2009 The Closure Library Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS-IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

/**
 * @fileoverview Defines a Long class for representing a 64-bit two's-complement
 * integer value, which faithfully simulates the behavior of a Java "long". This
 * implementation is derived from LongLib in GWT.
 *
 */

var i64Math = (function() { // Emscripten wrapper
  var goog = { math: {} };


  /**
   * Constructs a 64-bit two's-complement integer, given its low and high 32-bit
   * values as *signed* integers.  See the from* functions below for more
   * convenient ways of constructing Longs.
   *
   * The internal representation of a long is the two given signed, 32-bit values.
   * We use 32-bit pieces because these are the size of integers on which
   * Javascript performs bit-operations.  For operations like addition and
   * multiplication, we split each number into 16-bit pieces, which can easily be
   * multiplied within Javascript's floating-point representation without overflow
   * or change in sign.
   *
   * In the algorithms below, we frequently reduce the negative case to the
   * positive case by negating the input(s) and then post-processing the result.
   * Note that we must ALWAYS check specially whether those values are MIN_VALUE
   * (-2^63) because -MIN_VALUE == MIN_VALUE (since 2^63 cannot be represented as
   * a positive number, it overflows back into a negative).  Not handling this
   * case would often result in infinite recursion.
   *
   * @param {number} low  The low (signed) 32 bits of the long.
   * @param {number} high  The high (signed) 32 bits of the long.
   * @constructor
   */
  goog.math.Long = function(low, high) {
    /**
     * @type {number}
     * @private
     */
    this.low_ = low | 0;  // force into 32 signed bits.

    /**
     * @type {number}
     * @private
     */
    this.high_ = high | 0;  // force into 32 signed bits.
  };


  // NOTE: Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the
  // from* methods on which they depend.


  /**
   * A cache of the Long representations of small integer values.
   * @type {!Object}
   * @private
   */
  goog.math.Long.IntCache_ = {};


  /**
   * Returns a Long representing the given (32-bit) integer value.
   * @param {number} value The 32-bit integer in question.
   * @return {!goog.math.Long} The corresponding Long value.
   */
  goog.math.Long.fromInt = function(value) {
    if (-128 <= value && value < 128) {
      var cachedObj = goog.math.Long.IntCache_[value];
      if (cachedObj) {
        return cachedObj;
      }
    }

    var obj = new goog.math.Long(value | 0, value < 0 ? -1 : 0);
    if (-128 <= value && value < 128) {
      goog.math.Long.IntCache_[value] = obj;
    }
    return obj;
  };


  /**
   * Returns a Long representing the given value, provided that it is a finite
   * number.  Otherwise, zero is returned.
   * @param {number} value The number in question.
   * @return {!goog.math.Long} The corresponding Long value.
   */
  goog.math.Long.fromNumber = function(value) {
    if (isNaN(value) || !isFinite(value)) {
      return goog.math.Long.ZERO;
    } else if (value <= -goog.math.Long.TWO_PWR_63_DBL_) {
      return goog.math.Long.MIN_VALUE;
    } else if (value + 1 >= goog.math.Long.TWO_PWR_63_DBL_) {
      return goog.math.Long.MAX_VALUE;
    } else if (value < 0) {
      return goog.math.Long.fromNumber(-value).negate();
    } else {
      return new goog.math.Long(
          (value % goog.math.Long.TWO_PWR_32_DBL_) | 0,
          (value / goog.math.Long.TWO_PWR_32_DBL_) | 0);
    }
  };


  /**
   * Returns a Long representing the 64-bit integer that comes by concatenating
   * the given high and low bits.  Each is assumed to use 32 bits.
   * @param {number} lowBits The low 32-bits.
   * @param {number} highBits The high 32-bits.
   * @return {!goog.math.Long} The corresponding Long value.
   */
  goog.math.Long.fromBits = function(lowBits, highBits) {
    return new goog.math.Long(lowBits, highBits);
  };


  /**
   * Returns a Long representation of the given string, written using the given
   * radix.
   * @param {string} str The textual representation of the Long.
   * @param {number=} opt_radix The radix in which the text is written.
   * @return {!goog.math.Long} The corresponding Long value.
   */
  goog.math.Long.fromString = function(str, opt_radix) {
    if (str.length == 0) {
      throw Error('number format error: empty string');
    }

    var radix = opt_radix || 10;
    if (radix < 2 || 36 < radix) {
      throw Error('radix out of range: ' + radix);
    }

    if (str.charAt(0) == '-') {
      return goog.math.Long.fromString(str.substring(1), radix).negate();
    } else if (str.indexOf('-') >= 0) {
      throw Error('number format error: interior "-" character: ' + str);
    }

    // Do several (8) digits each time through the loop, so as to
    // minimize the calls to the very expensive emulated div.
    var radixToPower = goog.math.Long.fromNumber(Math.pow(radix, 8));

    var result = goog.math.Long.ZERO;
    for (var i = 0; i < str.length; i += 8) {
      var size = Math.min(8, str.length - i);
      var value = parseInt(str.substring(i, i + size), radix);
      if (size < 8) {
        var power = goog.math.Long.fromNumber(Math.pow(radix, size));
        result = result.multiply(power).add(goog.math.Long.fromNumber(value));
      } else {
        result = result.multiply(radixToPower);
        result = result.add(goog.math.Long.fromNumber(value));
      }
    }
    return result;
  };


  // NOTE: the compiler should inline these constant values below and then remove
  // these variables, so there should be no runtime penalty for these.


  /**
   * Number used repeated below in calculations.  This must appear before the
   * first call to any from* function below.
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_16_DBL_ = 1 << 16;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_24_DBL_ = 1 << 24;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_32_DBL_ =
      goog.math.Long.TWO_PWR_16_DBL_ * goog.math.Long.TWO_PWR_16_DBL_;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_31_DBL_ =
      goog.math.Long.TWO_PWR_32_DBL_ / 2;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_48_DBL_ =
      goog.math.Long.TWO_PWR_32_DBL_ * goog.math.Long.TWO_PWR_16_DBL_;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_64_DBL_ =
      goog.math.Long.TWO_PWR_32_DBL_ * goog.math.Long.TWO_PWR_32_DBL_;


  /**
   * @type {number}
   * @private
   */
  goog.math.Long.TWO_PWR_63_DBL_ =
      goog.math.Long.TWO_PWR_64_DBL_ / 2;


  /** @type {!goog.math.Long} */
  goog.math.Long.ZERO = goog.math.Long.fromInt(0);


  /** @type {!goog.math.Long} */
  goog.math.Long.ONE = goog.math.Long.fromInt(1);


  /** @type {!goog.math.Long} */
  goog.math.Long.NEG_ONE = goog.math.Long.fromInt(-1);


  /** @type {!goog.math.Long} */
  goog.math.Long.MAX_VALUE =
      goog.math.Long.fromBits(0xFFFFFFFF | 0, 0x7FFFFFFF | 0);


  /** @type {!goog.math.Long} */
  goog.math.Long.MIN_VALUE = goog.math.Long.fromBits(0, 0x80000000 | 0);


  /**
   * @type {!goog.math.Long}
   * @private
   */
  goog.math.Long.TWO_PWR_24_ = goog.math.Long.fromInt(1 << 24);


  /** @return {number} The value, assuming it is a 32-bit integer. */
  goog.math.Long.prototype.toInt = function() {
    return this.low_;
  };


  /** @return {number} The closest floating-point representation to this value. */
  goog.math.Long.prototype.toNumber = function() {
    return this.high_ * goog.math.Long.TWO_PWR_32_DBL_ +
           this.getLowBitsUnsigned();
  };


  /**
   * @param {number=} opt_radix The radix in which the text should be written.
   * @return {string} The textual representation of this value.
   */
  goog.math.Long.prototype.toString = function(opt_radix) {
    var radix = opt_radix || 10;
    if (radix < 2 || 36 < radix) {
      throw Error('radix out of range: ' + radix);
    }

    if (this.isZero()) {
      return '0';
    }

    if (this.isNegative()) {
      if (this.equals(goog.math.Long.MIN_VALUE)) {
        // We need to change the Long value before it can be negated, so we remove
        // the bottom-most digit in this base and then recurse to do the rest.
        var radixLong = goog.math.Long.fromNumber(radix);
        var div = this.div(radixLong);
        var rem = div.multiply(radixLong).subtract(this);
        return div.toString(radix) + rem.toInt().toString(radix);
      } else {
        return '-' + this.negate().toString(radix);
      }
    }

    // Do several (6) digits each time through the loop, so as to
    // minimize the calls to the very expensive emulated div.
    var radixToPower = goog.math.Long.fromNumber(Math.pow(radix, 6));

    var rem = this;
    var result = '';
    while (true) {
      var remDiv = rem.div(radixToPower);
      var intval = rem.subtract(remDiv.multiply(radixToPower)).toInt();
      var digits = intval.toString(radix);

      rem = remDiv;
      if (rem.isZero()) {
        return digits + result;
      } else {
        while (digits.length < 6) {
          digits = '0' + digits;
        }
        result = '' + digits + result;
      }
    }
  };


  /** @return {number} The high 32-bits as a signed value. */
  goog.math.Long.prototype.getHighBits = function() {
    return this.high_;
  };


  /** @return {number} The low 32-bits as a signed value. */
  goog.math.Long.prototype.getLowBits = function() {
    return this.low_;
  };


  /** @return {number} The low 32-bits as an unsigned value. */
  goog.math.Long.prototype.getLowBitsUnsigned = function() {
    return (this.low_ >= 0) ?
        this.low_ : goog.math.Long.TWO_PWR_32_DBL_ + this.low_;
  };


  /**
   * @return {number} Returns the number of bits needed to represent the absolute
   *     value of this Long.
   */
  goog.math.Long.prototype.getNumBitsAbs = function() {
    if (this.isNegative()) {
      if (this.equals(goog.math.Long.MIN_VALUE)) {
        return 64;
      } else {
        return this.negate().getNumBitsAbs();
      }
    } else {
      var val = this.high_ != 0 ? this.high_ : this.low_;
      for (var bit = 31; bit > 0; bit--) {
        if ((val & (1 << bit)) != 0) {
          break;
        }
      }
      return this.high_ != 0 ? bit + 33 : bit + 1;
    }
  };


  /** @return {boolean} Whether this value is zero. */
  goog.math.Long.prototype.isZero = function() {
    return this.high_ == 0 && this.low_ == 0;
  };


  /** @return {boolean} Whether this value is negative. */
  goog.math.Long.prototype.isNegative = function() {
    return this.high_ < 0;
  };


  /** @return {boolean} Whether this value is odd. */
  goog.math.Long.prototype.isOdd = function() {
    return (this.low_ & 1) == 1;
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long equals the other.
   */
  goog.math.Long.prototype.equals = function(other) {
    return (this.high_ == other.high_) && (this.low_ == other.low_);
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long does not equal the other.
   */
  goog.math.Long.prototype.notEquals = function(other) {
    return (this.high_ != other.high_) || (this.low_ != other.low_);
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long is less than the other.
   */
  goog.math.Long.prototype.lessThan = function(other) {
    return this.compare(other) < 0;
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long is less than or equal to the other.
   */
  goog.math.Long.prototype.lessThanOrEqual = function(other) {
    return this.compare(other) <= 0;
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long is greater than the other.
   */
  goog.math.Long.prototype.greaterThan = function(other) {
    return this.compare(other) > 0;
  };


  /**
   * @param {goog.math.Long} other Long to compare against.
   * @return {boolean} Whether this Long is greater than or equal to the other.
   */
  goog.math.Long.prototype.greaterThanOrEqual = function(other) {
    return this.compare(other) >= 0;
  };


  /**
   * Compares this Long with the given one.
   * @param {goog.math.Long} other Long to compare against.
   * @return {number} 0 if they are the same, 1 if the this is greater, and -1
   *     if the given one is greater.
   */
  goog.math.Long.prototype.compare = function(other) {
    if (this.equals(other)) {
      return 0;
    }

    var thisNeg = this.isNegative();
    var otherNeg = other.isNegative();
    if (thisNeg && !otherNeg) {
      return -1;
    }
    if (!thisNeg && otherNeg) {
      return 1;
    }

    // at this point, the signs are the same, so subtraction will not overflow
    if (this.subtract(other).isNegative()) {
      return -1;
    } else {
      return 1;
    }
  };


  /** @return {!goog.math.Long} The negation of this value. */
  goog.math.Long.prototype.negate = function() {
    if (this.equals(goog.math.Long.MIN_VALUE)) {
      return goog.math.Long.MIN_VALUE;
    } else {
      return this.not().add(goog.math.Long.ONE);
    }
  };


  /**
   * Returns the sum of this and the given Long.
   * @param {goog.math.Long} other Long to add to this one.
   * @return {!goog.math.Long} The sum of this and the given Long.
   */
  goog.math.Long.prototype.add = function(other) {
    // Divide each number into 4 chunks of 16 bits, and then sum the chunks.

    var a48 = this.high_ >>> 16;
    var a32 = this.high_ & 0xFFFF;
    var a16 = this.low_ >>> 16;
    var a00 = this.low_ & 0xFFFF;

    var b48 = other.high_ >>> 16;
    var b32 = other.high_ & 0xFFFF;
    var b16 = other.low_ >>> 16;
    var b00 = other.low_ & 0xFFFF;

    var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
    c00 += a00 + b00;
    c16 += c00 >>> 16;
    c00 &= 0xFFFF;
    c16 += a16 + b16;
    c32 += c16 >>> 16;
    c16 &= 0xFFFF;
    c32 += a32 + b32;
    c48 += c32 >>> 16;
    c32 &= 0xFFFF;
    c48 += a48 + b48;
    c48 &= 0xFFFF;
    return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
  };


  /**
   * Returns the difference of this and the given Long.
   * @param {goog.math.Long} other Long to subtract from this.
   * @return {!goog.math.Long} The difference of this and the given Long.
   */
  goog.math.Long.prototype.subtract = function(other) {
    return this.add(other.negate());
  };


  /**
   * Returns the product of this and the given long.
   * @param {goog.math.Long} other Long to multiply with this.
   * @return {!goog.math.Long} The product of this and the other.
   */
  goog.math.Long.prototype.multiply = function(other) {
    if (this.isZero()) {
      return goog.math.Long.ZERO;
    } else if (other.isZero()) {
      return goog.math.Long.ZERO;
    }

    if (this.equals(goog.math.Long.MIN_VALUE)) {
      return other.isOdd() ? goog.math.Long.MIN_VALUE : goog.math.Long.ZERO;
    } else if (other.equals(goog.math.Long.MIN_VALUE)) {
      return this.isOdd() ? goog.math.Long.MIN_VALUE : goog.math.Long.ZERO;
    }

    if (this.isNegative()) {
      if (other.isNegative()) {
        return this.negate().multiply(other.negate());
      } else {
        return this.negate().multiply(other).negate();
      }
    } else if (other.isNegative()) {
      return this.multiply(other.negate()).negate();
    }

    // If both longs are small, use float multiplication
    if (this.lessThan(goog.math.Long.TWO_PWR_24_) &&
        other.lessThan(goog.math.Long.TWO_PWR_24_)) {
      return goog.math.Long.fromNumber(this.toNumber() * other.toNumber());
    }

    // Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
    // We can skip products that would overflow.

    var a48 = this.high_ >>> 16;
    var a32 = this.high_ & 0xFFFF;
    var a16 = this.low_ >>> 16;
    var a00 = this.low_ & 0xFFFF;

    var b48 = other.high_ >>> 16;
    var b32 = other.high_ & 0xFFFF;
    var b16 = other.low_ >>> 16;
    var b00 = other.low_ & 0xFFFF;

    var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
    c00 += a00 * b00;
    c16 += c00 >>> 16;
    c00 &= 0xFFFF;
    c16 += a16 * b00;
    c32 += c16 >>> 16;
    c16 &= 0xFFFF;
    c16 += a00 * b16;
    c32 += c16 >>> 16;
    c16 &= 0xFFFF;
    c32 += a32 * b00;
    c48 += c32 >>> 16;
    c32 &= 0xFFFF;
    c32 += a16 * b16;
    c48 += c32 >>> 16;
    c32 &= 0xFFFF;
    c32 += a00 * b32;
    c48 += c32 >>> 16;
    c32 &= 0xFFFF;
    c48 += a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48;
    c48 &= 0xFFFF;
    return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
  };


  /**
   * Returns this Long divided by the given one.
   * @param {goog.math.Long} other Long by which to divide.
   * @return {!goog.math.Long} This Long divided by the given one.
   */
  goog.math.Long.prototype.div = function(other) {
    if (other.isZero()) {
      throw Error('division by zero');
    } else if (this.isZero()) {
      return goog.math.Long.ZERO;
    }

    if (this.equals(goog.math.Long.MIN_VALUE)) {
      if (other.equals(goog.math.Long.ONE) ||
          other.equals(goog.math.Long.NEG_ONE)) {
        return goog.math.Long.MIN_VALUE;  // recall that -MIN_VALUE == MIN_VALUE
      } else if (other.equals(goog.math.Long.MIN_VALUE)) {
        return goog.math.Long.ONE;
      } else {
        // At this point, we have |other| >= 2, so |this/other| < |MIN_VALUE|.
        var halfThis = this.shiftRight(1);
        var approx = halfThis.div(other).shiftLeft(1);
        if (approx.equals(goog.math.Long.ZERO)) {
          return other.isNegative() ? goog.math.Long.ONE : goog.math.Long.NEG_ONE;
        } else {
          var rem = this.subtract(other.multiply(approx));
          var result = approx.add(rem.div(other));
          return result;
        }
      }
    } else if (other.equals(goog.math.Long.MIN_VALUE)) {
      return goog.math.Long.ZERO;
    }

    if (this.isNegative()) {
      if (other.isNegative()) {
        return this.negate().div(other.negate());
      } else {
        return this.negate().div(other).negate();
      }
    } else if (other.isNegative()) {
      return this.div(other.negate()).negate();
    }

    // Repeat the following until the remainder is less than other:  find a
    // floating-point that approximates remainder / other *from below*, add this
    // into the result, and subtract it from the remainder.  It is critical that
    // the approximate value is less than or equal to the real value so that the
    // remainder never becomes negative.
    var res = goog.math.Long.ZERO;
    var rem = this;
    while (rem.greaterThanOrEqual(other)) {
      // Approximate the result of division. This may be a little greater or
      // smaller than the actual value.
      var approx = Math.max(1, Math.floor(rem.toNumber() / other.toNumber()));

      // We will tweak the approximate result by changing it in the 48-th digit or
      // the smallest non-fractional digit, whichever is larger.
      var log2 = Math.ceil(Math.log(approx) / Math.LN2);
      var delta = (log2 <= 48) ? 1 : Math.pow(2, log2 - 48);

      // Decrease the approximation until it is smaller than the remainder.  Note
      // that if it is too large, the product overflows and is negative.
      var approxRes = goog.math.Long.fromNumber(approx);
      var approxRem = approxRes.multiply(other);
      while (approxRem.isNegative() || approxRem.greaterThan(rem)) {
        approx -= delta;
        approxRes = goog.math.Long.fromNumber(approx);
        approxRem = approxRes.multiply(other);
      }

      // We know the answer can't be zero... and actually, zero would cause
      // infinite recursion since we would make no progress.
      if (approxRes.isZero()) {
        approxRes = goog.math.Long.ONE;
      }

      res = res.add(approxRes);
      rem = rem.subtract(approxRem);
    }
    return res;
  };


  /**
   * Returns this Long modulo the given one.
   * @param {goog.math.Long} other Long by which to mod.
   * @return {!goog.math.Long} This Long modulo the given one.
   */
  goog.math.Long.prototype.modulo = function(other) {
    return this.subtract(this.div(other).multiply(other));
  };


  /** @return {!goog.math.Long} The bitwise-NOT of this value. */
  goog.math.Long.prototype.not = function() {
    return goog.math.Long.fromBits(~this.low_, ~this.high_);
  };


  /**
   * Returns the bitwise-AND of this Long and the given one.
   * @param {goog.math.Long} other The Long with which to AND.
   * @return {!goog.math.Long} The bitwise-AND of this and the other.
   */
  goog.math.Long.prototype.and = function(other) {
    return goog.math.Long.fromBits(this.low_ & other.low_,
                                   this.high_ & other.high_);
  };


  /**
   * Returns the bitwise-OR of this Long and the given one.
   * @param {goog.math.Long} other The Long with which to OR.
   * @return {!goog.math.Long} The bitwise-OR of this and the other.
   */
  goog.math.Long.prototype.or = function(other) {
    return goog.math.Long.fromBits(this.low_ | other.low_,
                                   this.high_ | other.high_);
  };


  /**
   * Returns the bitwise-XOR of this Long and the given one.
   * @param {goog.math.Long} other The Long with which to XOR.
   * @return {!goog.math.Long} The bitwise-XOR of this and the other.
   */
  goog.math.Long.prototype.xor = function(other) {
    return goog.math.Long.fromBits(this.low_ ^ other.low_,
                                   this.high_ ^ other.high_);
  };


  /**
   * Returns this Long with bits shifted to the left by the given amount.
   * @param {number} numBits The number of bits by which to shift.
   * @return {!goog.math.Long} This shifted to the left by the given amount.
   */
  goog.math.Long.prototype.shiftLeft = function(numBits) {
    numBits &= 63;
    if (numBits == 0) {
      return this;
    } else {
      var low = this.low_;
      if (numBits < 32) {
        var high = this.high_;
        return goog.math.Long.fromBits(
            low << numBits,
            (high << numBits) | (low >>> (32 - numBits)));
      } else {
        return goog.math.Long.fromBits(0, low << (numBits - 32));
      }
    }
  };


  /**
   * Returns this Long with bits shifted to the right by the given amount.
   * @param {number} numBits The number of bits by which to shift.
   * @return {!goog.math.Long} This shifted to the right by the given amount.
   */
  goog.math.Long.prototype.shiftRight = function(numBits) {
    numBits &= 63;
    if (numBits == 0) {
      return this;
    } else {
      var high = this.high_;
      if (numBits < 32) {
        var low = this.low_;
        return goog.math.Long.fromBits(
            (low >>> numBits) | (high << (32 - numBits)),
            high >> numBits);
      } else {
        return goog.math.Long.fromBits(
            high >> (numBits - 32),
            high >= 0 ? 0 : -1);
      }
    }
  };


  /**
   * Returns this Long with bits shifted to the right by the given amount, with
   * the new top bits matching the current sign bit.
   * @param {number} numBits The number of bits by which to shift.
   * @return {!goog.math.Long} This shifted to the right by the given amount, with
   *     zeros placed into the new leading bits.
   */
  goog.math.Long.prototype.shiftRightUnsigned = function(numBits) {
    numBits &= 63;
    if (numBits == 0) {
      return this;
    } else {
      var high = this.high_;
      if (numBits < 32) {
        var low = this.low_;
        return goog.math.Long.fromBits(
            (low >>> numBits) | (high << (32 - numBits)),
            high >>> numBits);
      } else if (numBits == 32) {
        return goog.math.Long.fromBits(high, 0);
      } else {
        return goog.math.Long.fromBits(high >>> (numBits - 32), 0);
      }
    }
  };

  //======= begin jsbn =======

  var navigator = { appName: 'Modern Browser' }; // polyfill a little

  // Copyright (c) 2005  Tom Wu
  // All Rights Reserved.
  // http://www-cs-students.stanford.edu/~tjw/jsbn/

  /*
   * Copyright (c) 2003-2005  Tom Wu
   * All Rights Reserved.
   *
   * Permission is hereby granted, free of charge, to any person obtaining
   * a copy of this software and associated documentation files (the
   * "Software"), to deal in the Software without restriction, including
   * without limitation the rights to use, copy, modify, merge, publish,
   * distribute, sublicense, and/or sell copies of the Software, and to
   * permit persons to whom the Software is furnished to do so, subject to
   * the following conditions:
   *
   * The above copyright notice and this permission notice shall be
   * included in all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, 
   * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY 
   * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.  
   *
   * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
   * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
   * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
   * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
   * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
   *
   * In addition, the following condition applies:
   *
   * All redistributions must retain an intact copy of this copyright notice
   * and disclaimer.
   */

  // Basic JavaScript BN library - subset useful for RSA encryption.

  // Bits per digit
  var dbits;

  // JavaScript engine analysis
  var canary = 0xdeadbeefcafe;
  var j_lm = ((canary&0xffffff)==0xefcafe);

  // (public) Constructor
  function BigInteger(a,b,c) {
    if(a != null)
      if("number" == typeof a) this.fromNumber(a,b,c);
      else if(b == null && "string" != typeof a) this.fromString(a,256);
      else this.fromString(a,b);
  }

  // return new, unset BigInteger
  function nbi() { return new BigInteger(null); }

  // am: Compute w_j += (x*this_i), propagate carries,
  // c is initial carry, returns final carry.
  // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
  // We need to select the fastest one that works in this environment.

  // am1: use a single mult and divide to get the high bits,
  // max digit bits should be 26 because
  // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
  function am1(i,x,w,j,c,n) {
    while(--n >= 0) {
      var v = x*this[i++]+w[j]+c;
      c = Math.floor(v/0x4000000);
      w[j++] = v&0x3ffffff;
    }
    return c;
  }
  // am2 avoids a big mult-and-extract completely.
  // Max digit bits should be <= 30 because we do bitwise ops
  // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
  function am2(i,x,w,j,c,n) {
    var xl = x&0x7fff, xh = x>>15;
    while(--n >= 0) {
      var l = this[i]&0x7fff;
      var h = this[i++]>>15;
      var m = xh*l+h*xl;
      l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
      c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
      w[j++] = l&0x3fffffff;
    }
    return c;
  }
  // Alternately, set max digit bits to 28 since some
  // browsers slow down when dealing with 32-bit numbers.
  function am3(i,x,w,j,c,n) {
    var xl = x&0x3fff, xh = x>>14;
    while(--n >= 0) {
      var l = this[i]&0x3fff;
      var h = this[i++]>>14;
      var m = xh*l+h*xl;
      l = xl*l+((m&0x3fff)<<14)+w[j]+c;
      c = (l>>28)+(m>>14)+xh*h;
      w[j++] = l&0xfffffff;
    }
    return c;
  }
  if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
    BigInteger.prototype.am = am2;
    dbits = 30;
  }
  else if(j_lm && (navigator.appName != "Netscape")) {
    BigInteger.prototype.am = am1;
    dbits = 26;
  }
  else { // Mozilla/Netscape seems to prefer am3
    BigInteger.prototype.am = am3;
    dbits = 28;
  }

  BigInteger.prototype.DB = dbits;
  BigInteger.prototype.DM = ((1<<dbits)-1);
  BigInteger.prototype.DV = (1<<dbits);

  var BI_FP = 52;
  BigInteger.prototype.FV = Math.pow(2,BI_FP);
  BigInteger.prototype.F1 = BI_FP-dbits;
  BigInteger.prototype.F2 = 2*dbits-BI_FP;

  // Digit conversions
  var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
  var BI_RC = new Array();
  var rr,vv;
  rr = "0".charCodeAt(0);
  for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
  rr = "a".charCodeAt(0);
  for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
  rr = "A".charCodeAt(0);
  for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;

  function int2char(n) { return BI_RM.charAt(n); }
  function intAt(s,i) {
    var c = BI_RC[s.charCodeAt(i)];
    return (c==null)?-1:c;
  }

  // (protected) copy this to r
  function bnpCopyTo(r) {
    for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
    r.t = this.t;
    r.s = this.s;
  }

  // (protected) set from integer value x, -DV <= x < DV
  function bnpFromInt(x) {
    this.t = 1;
    this.s = (x<0)?-1:0;
    if(x > 0) this[0] = x;
    else if(x < -1) this[0] = x+DV;
    else this.t = 0;
  }

  // return bigint initialized to value
  function nbv(i) { var r = nbi(); r.fromInt(i); return r; }

  // (protected) set from string and radix
  function bnpFromString(s,b) {
    var k;
    if(b == 16) k = 4;
    else if(b == 8) k = 3;
    else if(b == 256) k = 8; // byte array
    else if(b == 2) k = 1;
    else if(b == 32) k = 5;
    else if(b == 4) k = 2;
    else { this.fromRadix(s,b); return; }
    this.t = 0;
    this.s = 0;
    var i = s.length, mi = false, sh = 0;
    while(--i >= 0) {
      var x = (k==8)?s[i]&0xff:intAt(s,i);
      if(x < 0) {
        if(s.charAt(i) == "-") mi = true;
        continue;
      }
      mi = false;
      if(sh == 0)
        this[this.t++] = x;
      else if(sh+k > this.DB) {
        this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
        this[this.t++] = (x>>(this.DB-sh));
      }
      else
        this[this.t-1] |= x<<sh;
      sh += k;
      if(sh >= this.DB) sh -= this.DB;
    }
    if(k == 8 && (s[0]&0x80) != 0) {
      this.s = -1;
      if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
    }
    this.clamp();
    if(mi) BigInteger.ZERO.subTo(this,this);
  }

  // (protected) clamp off excess high words
  function bnpClamp() {
    var c = this.s&this.DM;
    while(this.t > 0 && this[this.t-1] == c) --this.t;
  }

  // (public) return string representation in given radix
  function bnToString(b) {
    if(this.s < 0) return "-"+this.negate().toString(b);
    var k;
    if(b == 16) k = 4;
    else if(b == 8) k = 3;
    else if(b == 2) k = 1;
    else if(b == 32) k = 5;
    else if(b == 4) k = 2;
    else return this.toRadix(b);
    var km = (1<<k)-1, d, m = false, r = "", i = this.t;
    var p = this.DB-(i*this.DB)%k;
    if(i-- > 0) {
      if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
      while(i >= 0) {
        if(p < k) {
          d = (this[i]&((1<<p)-1))<<(k-p);
          d |= this[--i]>>(p+=this.DB-k);
        }
        else {
          d = (this[i]>>(p-=k))&km;
          if(p <= 0) { p += this.DB; --i; }
        }
        if(d > 0) m = true;
        if(m) r += int2char(d);
      }
    }
    return m?r:"0";
  }

  // (public) -this
  function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }

  // (public) |this|
  function bnAbs() { return (this.s<0)?this.negate():this; }

  // (public) return + if this > a, - if this < a, 0 if equal
  function bnCompareTo(a) {
    var r = this.s-a.s;
    if(r != 0) return r;
    var i = this.t;
    r = i-a.t;
    if(r != 0) return (this.s<0)?-r:r;
    while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
    return 0;
  }

  // returns bit length of the integer x
  function nbits(x) {
    var r = 1, t;
    if((t=x>>>16) != 0) { x = t; r += 16; }
    if((t=x>>8) != 0) { x = t; r += 8; }
    if((t=x>>4) != 0) { x = t; r += 4; }
    if((t=x>>2) != 0) { x = t; r += 2; }
    if((t=x>>1) != 0) { x = t; r += 1; }
    return r;
  }

  // (public) return the number of bits in "this"
  function bnBitLength() {
    if(this.t <= 0) return 0;
    return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
  }

  // (protected) r = this << n*DB
  function bnpDLShiftTo(n,r) {
    var i;
    for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
    for(i = n-1; i >= 0; --i) r[i] = 0;
    r.t = this.t+n;
    r.s = this.s;
  }

  // (protected) r = this >> n*DB
  function bnpDRShiftTo(n,r) {
    for(var i = n; i < this.t; ++i) r[i-n] = this[i];
    r.t = Math.max(this.t-n,0);
    r.s = this.s;
  }

  // (protected) r = this << n
  function bnpLShiftTo(n,r) {
    var bs = n%this.DB;
    var cbs = this.DB-bs;
    var bm = (1<<cbs)-1;
    var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
    for(i = this.t-1; i >= 0; --i) {
      r[i+ds+1] = (this[i]>>cbs)|c;
      c = (this[i]&bm)<<bs;
    }
    for(i = ds-1; i >= 0; --i) r[i] = 0;
    r[ds] = c;
    r.t = this.t+ds+1;
    r.s = this.s;
    r.clamp();
  }

  // (protected) r = this >> n
  function bnpRShiftTo(n,r) {
    r.s = this.s;
    var ds = Math.floor(n/this.DB);
    if(ds >= this.t) { r.t = 0; return; }
    var bs = n%this.DB;
    var cbs = this.DB-bs;
    var bm = (1<<bs)-1;
    r[0] = this[ds]>>bs;
    for(var i = ds+1; i < this.t; ++i) {
      r[i-ds-1] |= (this[i]&bm)<<cbs;
      r[i-ds] = this[i]>>bs;
    }
    if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
    r.t = this.t-ds;
    r.clamp();
  }

  // (protected) r = this - a
  function bnpSubTo(a,r) {
    var i = 0, c = 0, m = Math.min(a.t,this.t);
    while(i < m) {
      c += this[i]-a[i];
      r[i++] = c&this.DM;
      c >>= this.DB;
    }
    if(a.t < this.t) {
      c -= a.s;
      while(i < this.t) {
        c += this[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
      }
      c += this.s;
    }
    else {
      c += this.s;
      while(i < a.t) {
        c -= a[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
      }
      c -= a.s;
    }
    r.s = (c<0)?-1:0;
    if(c < -1) r[i++] = this.DV+c;
    else if(c > 0) r[i++] = c;
    r.t = i;
    r.clamp();
  }

  // (protected) r = this * a, r != this,a (HAC 14.12)
  // "this" should be the larger one if appropriate.
  function bnpMultiplyTo(a,r) {
    var x = this.abs(), y = a.abs();
    var i = x.t;
    r.t = i+y.t;
    while(--i >= 0) r[i] = 0;
    for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
    r.s = 0;
    r.clamp();
    if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
  }

  // (protected) r = this^2, r != this (HAC 14.16)
  function bnpSquareTo(r) {
    var x = this.abs();
    var i = r.t = 2*x.t;
    while(--i >= 0) r[i] = 0;
    for(i = 0; i < x.t-1; ++i) {
      var c = x.am(i,x[i],r,2*i,0,1);
      if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
        r[i+x.t] -= x.DV;
        r[i+x.t+1] = 1;
      }
    }
    if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
    r.s = 0;
    r.clamp();
  }

  // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
  // r != q, this != m.  q or r may be null.
  function bnpDivRemTo(m,q,r) {
    var pm = m.abs();
    if(pm.t <= 0) return;
    var pt = this.abs();
    if(pt.t < pm.t) {
      if(q != null) q.fromInt(0);
      if(r != null) this.copyTo(r);
      return;
    }
    if(r == null) r = nbi();
    var y = nbi(), ts = this.s, ms = m.s;
    var nsh = this.DB-nbits(pm[pm.t-1]);	// normalize modulus
    if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
    else { pm.copyTo(y); pt.copyTo(r); }
    var ys = y.t;
    var y0 = y[ys-1];
    if(y0 == 0) return;
    var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
    var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
    var i = r.t, j = i-ys, t = (q==null)?nbi():q;
    y.dlShiftTo(j,t);
    if(r.compareTo(t) >= 0) {
      r[r.t++] = 1;
      r.subTo(t,r);
    }
    BigInteger.ONE.dlShiftTo(ys,t);
    t.subTo(y,y);	// "negative" y so we can replace sub with am later
    while(y.t < ys) y[y.t++] = 0;
    while(--j >= 0) {
      // Estimate quotient digit
      var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
      if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
        y.dlShiftTo(j,t);
        r.subTo(t,r);
        while(r[i] < --qd) r.subTo(t,r);
      }
    }
    if(q != null) {
      r.drShiftTo(ys,q);
      if(ts != ms) BigInteger.ZERO.subTo(q,q);
    }
    r.t = ys;
    r.clamp();
    if(nsh > 0) r.rShiftTo(nsh,r);	// Denormalize remainder
    if(ts < 0) BigInteger.ZERO.subTo(r,r);
  }

  // (public) this mod a
  function bnMod(a) {
    var r = nbi();
    this.abs().divRemTo(a,null,r);
    if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
    return r;
  }

  // Modular reduction using "classic" algorithm
  function Classic(m) { this.m = m; }
  function cConvert(x) {
    if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
    else return x;
  }
  function cRevert(x) { return x; }
  function cReduce(x) { x.divRemTo(this.m,null,x); }
  function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
  function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }

  Classic.prototype.convert = cConvert;
  Classic.prototype.revert = cRevert;
  Classic.prototype.reduce = cReduce;
  Classic.prototype.mulTo = cMulTo;
  Classic.prototype.sqrTo = cSqrTo;

  // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
  // justification:
  //         xy == 1 (mod m)
  //         xy =  1+km
  //   xy(2-xy) = (1+km)(1-km)
  // x[y(2-xy)] = 1-k^2m^2
  // x[y(2-xy)] == 1 (mod m^2)
  // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
  // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
  // JS multiply "overflows" differently from C/C++, so care is needed here.
  function bnpInvDigit() {
    if(this.t < 1) return 0;
    var x = this[0];
    if((x&1) == 0) return 0;
    var y = x&3;		// y == 1/x mod 2^2
    y = (y*(2-(x&0xf)*y))&0xf;	// y == 1/x mod 2^4
    y = (y*(2-(x&0xff)*y))&0xff;	// y == 1/x mod 2^8
    y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;	// y == 1/x mod 2^16
    // last step - calculate inverse mod DV directly;
    // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
    y = (y*(2-x*y%this.DV))%this.DV;		// y == 1/x mod 2^dbits
    // we really want the negative inverse, and -DV < y < DV
    return (y>0)?this.DV-y:-y;
  }

  // Montgomery reduction
  function Montgomery(m) {
    this.m = m;
    this.mp = m.invDigit();
    this.mpl = this.mp&0x7fff;
    this.mph = this.mp>>15;
    this.um = (1<<(m.DB-15))-1;
    this.mt2 = 2*m.t;
  }

  // xR mod m
  function montConvert(x) {
    var r = nbi();
    x.abs().dlShiftTo(this.m.t,r);
    r.divRemTo(this.m,null,r);
    if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
    return r;
  }

  // x/R mod m
  function montRevert(x) {
    var r = nbi();
    x.copyTo(r);
    this.reduce(r);
    return r;
  }

  // x = x/R mod m (HAC 14.32)
  function montReduce(x) {
    while(x.t <= this.mt2)	// pad x so am has enough room later
      x[x.t++] = 0;
    for(var i = 0; i < this.m.t; ++i) {
      // faster way of calculating u0 = x[i]*mp mod DV
      var j = x[i]&0x7fff;
      var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
      // use am to combine the multiply-shift-add into one call
      j = i+this.m.t;
      x[j] += this.m.am(0,u0,x,i,0,this.m.t);
      // propagate carry
      while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
    }
    x.clamp();
    x.drShiftTo(this.m.t,x);
    if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
  }

  // r = "x^2/R mod m"; x != r
  function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }

  // r = "xy/R mod m"; x,y != r
  function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }

  Montgomery.prototype.convert = montConvert;
  Montgomery.prototype.revert = montRevert;
  Montgomery.prototype.reduce = montReduce;
  Montgomery.prototype.mulTo = montMulTo;
  Montgomery.prototype.sqrTo = montSqrTo;

  // (protected) true iff this is even
  function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }

  // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
  function bnpExp(e,z) {
    if(e > 0xffffffff || e < 1) return BigInteger.ONE;
    var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
    g.copyTo(r);
    while(--i >= 0) {
      z.sqrTo(r,r2);
      if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
      else { var t = r; r = r2; r2 = t; }
    }
    return z.revert(r);
  }

  // (public) this^e % m, 0 <= e < 2^32
  function bnModPowInt(e,m) {
    var z;
    if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
    return this.exp(e,z);
  }

  // protected
  BigInteger.prototype.copyTo = bnpCopyTo;
  BigInteger.prototype.fromInt = bnpFromInt;
  BigInteger.prototype.fromString = bnpFromString;
  BigInteger.prototype.clamp = bnpClamp;
  BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
  BigInteger.prototype.drShiftTo = bnpDRShiftTo;
  BigInteger.prototype.lShiftTo = bnpLShiftTo;
  BigInteger.prototype.rShiftTo = bnpRShiftTo;
  BigInteger.prototype.subTo = bnpSubTo;
  BigInteger.prototype.multiplyTo = bnpMultiplyTo;
  BigInteger.prototype.squareTo = bnpSquareTo;
  BigInteger.prototype.divRemTo = bnpDivRemTo;
  BigInteger.prototype.invDigit = bnpInvDigit;
  BigInteger.prototype.isEven = bnpIsEven;
  BigInteger.prototype.exp = bnpExp;

  // public
  BigInteger.prototype.toString = bnToString;
  BigInteger.prototype.negate = bnNegate;
  BigInteger.prototype.abs = bnAbs;
  BigInteger.prototype.compareTo = bnCompareTo;
  BigInteger.prototype.bitLength = bnBitLength;
  BigInteger.prototype.mod = bnMod;
  BigInteger.prototype.modPowInt = bnModPowInt;

  // "constants"
  BigInteger.ZERO = nbv(0);
  BigInteger.ONE = nbv(1);

  // jsbn2 stuff

  // (protected) convert from radix string
  function bnpFromRadix(s,b) {
    this.fromInt(0);
    if(b == null) b = 10;
    var cs = this.chunkSize(b);
    var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
    for(var i = 0; i < s.length; ++i) {
      var x = intAt(s,i);
      if(x < 0) {
        if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
        continue;
      }
      w = b*w+x;
      if(++j >= cs) {
        this.dMultiply(d);
        this.dAddOffset(w,0);
        j = 0;
        w = 0;
      }
    }
    if(j > 0) {
      this.dMultiply(Math.pow(b,j));
      this.dAddOffset(w,0);
    }
    if(mi) BigInteger.ZERO.subTo(this,this);
  }

  // (protected) return x s.t. r^x < DV
  function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }

  // (public) 0 if this == 0, 1 if this > 0
  function bnSigNum() {
    if(this.s < 0) return -1;
    else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
    else return 1;
  }

  // (protected) this *= n, this >= 0, 1 < n < DV
  function bnpDMultiply(n) {
    this[this.t] = this.am(0,n-1,this,0,0,this.t);
    ++this.t;
    this.clamp();
  }

  // (protected) this += n << w words, this >= 0
  function bnpDAddOffset(n,w) {
    if(n == 0) return;
    while(this.t <= w) this[this.t++] = 0;
    this[w] += n;
    while(this[w] >= this.DV) {
      this[w] -= this.DV;
      if(++w >= this.t) this[this.t++] = 0;
      ++this[w];
    }
  }

  // (protected) convert to radix string
  function bnpToRadix(b) {
    if(b == null) b = 10;
    if(this.signum() == 0 || b < 2 || b > 36) return "0";
    var cs = this.chunkSize(b);
    var a = Math.pow(b,cs);
    var d = nbv(a), y = nbi(), z = nbi(), r = "";
    this.divRemTo(d,y,z);
    while(y.signum() > 0) {
      r = (a+z.intValue()).toString(b).substr(1) + r;
      y.divRemTo(d,y,z);
    }
    return z.intValue().toString(b) + r;
  }

  // (public) return value as integer
  function bnIntValue() {
    if(this.s < 0) {
      if(this.t == 1) return this[0]-this.DV;
      else if(this.t == 0) return -1;
    }
    else if(this.t == 1) return this[0];
    else if(this.t == 0) return 0;
    // assumes 16 < DB < 32
    return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
  }

  // (protected) r = this + a
  function bnpAddTo(a,r) {
    var i = 0, c = 0, m = Math.min(a.t,this.t);
    while(i < m) {
      c += this[i]+a[i];
      r[i++] = c&this.DM;
      c >>= this.DB;
    }
    if(a.t < this.t) {
      c += a.s;
      while(i < this.t) {
        c += this[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
      }
      c += this.s;
    }
    else {
      c += this.s;
      while(i < a.t) {
        c += a[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
      }
      c += a.s;
    }
    r.s = (c<0)?-1:0;
    if(c > 0) r[i++] = c;
    else if(c < -1) r[i++] = this.DV+c;
    r.t = i;
    r.clamp();
  }

  BigInteger.prototype.fromRadix = bnpFromRadix;
  BigInteger.prototype.chunkSize = bnpChunkSize;
  BigInteger.prototype.signum = bnSigNum;
  BigInteger.prototype.dMultiply = bnpDMultiply;
  BigInteger.prototype.dAddOffset = bnpDAddOffset;
  BigInteger.prototype.toRadix = bnpToRadix;
  BigInteger.prototype.intValue = bnIntValue;
  BigInteger.prototype.addTo = bnpAddTo;

  //======= end jsbn =======

  // Emscripten wrapper
  var Wrapper = {
    abs: function(l, h) {
      var x = new goog.math.Long(l, h);
      var ret;
      if (x.isNegative()) {
        ret = x.negate();
      } else {
        ret = x;
      }
      HEAP32[tempDoublePtr>>2] = ret.low_;
      HEAP32[tempDoublePtr+4>>2] = ret.high_;
    },
    ensureTemps: function() {
      if (Wrapper.ensuredTemps) return;
      Wrapper.ensuredTemps = true;
      Wrapper.two32 = new BigInteger();
      Wrapper.two32.fromString('4294967296', 10);
      Wrapper.two64 = new BigInteger();
      Wrapper.two64.fromString('18446744073709551616', 10);
      Wrapper.temp1 = new BigInteger();
      Wrapper.temp2 = new BigInteger();
    },
    lh2bignum: function(l, h) {
      var a = new BigInteger();
      a.fromString(h.toString(), 10);
      var b = new BigInteger();
      a.multiplyTo(Wrapper.two32, b);
      var c = new BigInteger();
      c.fromString(l.toString(), 10);
      var d = new BigInteger();
      c.addTo(b, d);
      return d;
    },
    stringify: function(l, h, unsigned) {
      var ret = new goog.math.Long(l, h).toString();
      if (unsigned && ret[0] == '-') {
        // unsign slowly using jsbn bignums
        Wrapper.ensureTemps();
        var bignum = new BigInteger();
        bignum.fromString(ret, 10);
        ret = new BigInteger();
        Wrapper.two64.addTo(bignum, ret);
        ret = ret.toString(10);
      }
      return ret;
    },
    fromString: function(str, base, min, max, unsigned) {
      Wrapper.ensureTemps();
      var bignum = new BigInteger();
      bignum.fromString(str, base);
      var bigmin = new BigInteger();
      bigmin.fromString(min, 10);
      var bigmax = new BigInteger();
      bigmax.fromString(max, 10);
      if (unsigned && bignum.compareTo(BigInteger.ZERO) < 0) {
        var temp = new BigInteger();
        bignum.addTo(Wrapper.two64, temp);
        bignum = temp;
      }
      var error = false;
      if (bignum.compareTo(bigmin) < 0) {
        bignum = bigmin;
        error = true;
      } else if (bignum.compareTo(bigmax) > 0) {
        bignum = bigmax;
        error = true;
      }
      var ret = goog.math.Long.fromString(bignum.toString()); // min-max checks should have clamped this to a range goog.math.Long can handle well
      HEAP32[tempDoublePtr>>2] = ret.low_;
      HEAP32[tempDoublePtr+4>>2] = ret.high_;
      if (error) throw 'range error';
    }
  };
  return Wrapper;
})();

//======= end closure i64 code =======