// 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<= 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))<>(this.DB-sh)); } else this[this.t-1] |= x<= 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)< 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< 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+=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 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<= 0; --i) { r[i+ds+1] = (this[i]>>cbs)|c; c = (this[i]&bm)<= 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; for(var i = ds+1; i < this.t; ++i) { r[i-ds-1] |= (this[i]&bm)<>bs; } if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<>= 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<1)?y[ys-2]>>this.F2:0); var d1 = this.FV/yt, d2 = (1<= 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< 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; } 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 = { result: [0, 0], // return result stored here add: function(xl, xh, yl, yh) { var x = new goog.math.Long(xl, xh); var y = new goog.math.Long(yl, yh); var ret = x.add(y); Wrapper.result[0] = ret.low_; Wrapper.result[1] = ret.high_; }, subtract: function(xl, xh, yl, yh) { var x = new goog.math.Long(xl, xh); var y = new goog.math.Long(yl, yh); var ret = x.subtract(y); Wrapper.result[0] = ret.low_; Wrapper.result[1] = ret.high_; }, multiply: function(xl, xh, yl, yh) { var x = new goog.math.Long(xl, xh); var y = new goog.math.Long(yl, yh); var ret = x.multiply(y); Wrapper.result[0] = ret.low_; Wrapper.result[1] = ret.high_; }, makeTwo32: function() { Wrapper.two32 = new BigInteger(); Wrapper.two32.fromString('4294967296', 10); }, 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; }, divide: function(xl, xh, yl, yh, unsigned) { if (!Wrapper.two32) Wrapper.makeTwo32(); if (!unsigned) { var x = new goog.math.Long(xl, xh); var y = new goog.math.Long(yl, yh); var ret = x.div(y); Wrapper.result[0] = ret.low_; Wrapper.result[1] = ret.high_; } else { // slow precise bignum division var x = Wrapper.lh2bignum(xl >>> 0, xh >>> 0); var y = Wrapper.lh2bignum(yl >>> 0, yh >>> 0); var z = new BigInteger(); x.divRemTo(y, z, null); var l = new BigInteger(); var h = new BigInteger(); z.divRemTo(Wrapper.two32, h, l); Wrapper.result[0] = parseInt(l.toString()) | 0; Wrapper.result[1] = parseInt(h.toString()) | 0; } }, modulo: function(xl, xh, yl, yh, unsigned) { if (!Wrapper.two32) Wrapper.makeTwo32(); if (!unsigned) { var x = new goog.math.Long(xl, xh); var y = new goog.math.Long(yl, yh); var ret = x.modulo(y); Wrapper.result[0] = ret.low_; Wrapper.result[1] = ret.high_; } else { // slow precise bignum division var x = Wrapper.lh2bignum(xl >>> 0, xh >>> 0); var y = Wrapper.lh2bignum(yl >>> 0, yh >>> 0); var z = new BigInteger(); x.divRemTo(y, null, z); var l = new BigInteger(); var h = new BigInteger(); z.divRemTo(Wrapper.two32, h, l); Wrapper.result[0] = parseInt(l.toString()) | 0; Wrapper.result[1] = parseInt(h.toString()) | 0; } }, stringify: function(l, h, unsigned) { var ret = new goog.math.Long(l, h).toString(); if (unsigned && ret[0] == '-') { // unsign slowly using jsbn bignums if (!Wrapper.two64) { Wrapper.two64 = new BigInteger(); Wrapper.two64.fromString('18446744073709551616', 10); } var bignum = new BigInteger(); bignum.fromString(ret, 10); ret = new BigInteger(); Wrapper.two64.addTo(bignum, ret); ret = ret.toString(10); } return ret; } }; return Wrapper; })(); //======= end closure i64 code =======