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// Copyright 2009 The Closure Library Authors. All Rights Reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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//      http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS-IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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/**
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 * @fileoverview Defines a Long class for representing a 64-bit two's-complement
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 * integer value, which faithfully simulates the behavior of a Java "long". This
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 * implementation is derived from LongLib in GWT.
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 *
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 */
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goog.provide('goog.math.Long');
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goog.require('goog.asserts');
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goog.require('goog.reflect');
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27

28

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/**
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 * Constructs a 64-bit two's-complement integer, given its low and high 32-bit
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 * values as *signed* integers.  See the from* functions below for more
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 * convenient ways of constructing Longs.
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 *
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 * The internal representation of a long is the two given signed, 32-bit values.
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 * We use 32-bit pieces because these are the size of integers on which
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 * Javascript performs bit-operations.  For operations like addition and
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 * multiplication, we split each number into 16-bit pieces, which can easily be
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 * multiplied within Javascript's floating-point representation without overflow
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 * or change in sign.
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 *
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 * In the algorithms below, we frequently reduce the negative case to the
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 * positive case by negating the input(s) and then post-processing the result.
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 * Note that we must ALWAYS check specially whether those values are MIN_VALUE
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 * (-2^63) because -MIN_VALUE == MIN_VALUE (since 2^63 cannot be represented as
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 * a positive number, it overflows back into a negative).  Not handling this
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 * case would often result in infinite recursion.
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 *
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 * @param {number} low  The low (signed) 32 bits of the long.
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 * @param {number} high  The high (signed) 32 bits of the long.
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 * @struct
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 * @constructor
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 * @final
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 */
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goog.math.Long = function(low, high) {
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  /**
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   * @type {number}
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   * @private
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   */
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  this.low_ = low | 0;  // force into 32 signed bits.
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  /**
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   * @type {number}
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   * @private
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   */
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  this.high_ = high | 0;  // force into 32 signed bits.
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};
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68

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// NOTE: Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the
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// from* methods on which they depend.
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/**
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 * A cache of the Long representations of small integer values.
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 * @type {!Object<number, !goog.math.Long>}
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 * @private
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 */
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goog.math.Long.IntCache_ = {};
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80

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/**
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 * A cache of the Long representations of common values.
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 * @type {!Object<goog.math.Long.ValueCacheId_, !goog.math.Long>}
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 * @private
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 */
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goog.math.Long.valueCache_ = {};
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/**
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 * Returns a cached long number representing the given (32-bit) integer value.
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 * @param {number} value The 32-bit integer in question.
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 * @return {!goog.math.Long} The corresponding Long value.
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 * @private
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 */
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goog.math.Long.getCachedIntValue_ = function(value) {
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  return goog.reflect.cache(goog.math.Long.IntCache_, value, function(val) {
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    return new goog.math.Long(val, val < 0 ? -1 : 0);
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  });
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};
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/**
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 * The array of maximum values of a Long in string representation for a given
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 * radix between 2 and 36, inclusive.
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 * @private @const {!Array<string>}
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 */
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goog.math.Long.MAX_VALUE_FOR_RADIX_ = [
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  '', '',  // unused
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  '111111111111111111111111111111111111111111111111111111111111111',
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  // base 2
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  '2021110011022210012102010021220101220221',  // base 3
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  '13333333333333333333333333333333',          // base 4
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  '1104332401304422434310311212',              // base 5
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  '1540241003031030222122211',                 // base 6
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  '22341010611245052052300',                   // base 7
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  '777777777777777777777',                     // base 8
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  '67404283172107811827',                      // base 9
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  '9223372036854775807',                       // base 10
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  '1728002635214590697',                       // base 11
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  '41a792678515120367',                        // base 12
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  '10b269549075433c37',                        // base 13
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  '4340724c6c71dc7a7',                         // base 14
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  '160e2ad3246366807',                         // base 15
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  '7fffffffffffffff',                          // base 16
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  '33d3d8307b214008',                          // base 17
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  '16agh595df825fa7',                          // base 18
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  'ba643dci0ffeehh',                           // base 19
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  '5cbfjia3fh26ja7',                           // base 20
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  '2heiciiie82dh97',                           // base 21
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  '1adaibb21dckfa7',                           // base 22
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  'i6k448cf4192c2',                            // base 23
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  'acd772jnc9l0l7',                            // base 24
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  '64ie1focnn5g77',                            // base 25
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  '3igoecjbmca687',                            // base 26
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  '27c48l5b37oaop',                            // base 27
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  '1bk39f3ah3dmq7',                            // base 28
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  'q1se8f0m04isb',                             // base 29
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  'hajppbc1fc207',                             // base 30
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  'bm03i95hia437',                             // base 31
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  '7vvvvvvvvvvvv',                             // base 32
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  '5hg4ck9jd4u37',                             // base 33
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  '3tdtk1v8j6tpp',                             // base 34
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  '2pijmikexrxp7',                             // base 35
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  '1y2p0ij32e8e7'                              // base 36
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];
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/**
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 * The array of minimum values of a Long in string representation for a given
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 * radix between 2 and 36, inclusive.
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 * @private @const {!Array<string>}
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 */
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goog.math.Long.MIN_VALUE_FOR_RADIX_ = [
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  '', '',  // unused
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  '-1000000000000000000000000000000000000000000000000000000000000000',
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  // base 2
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  '-2021110011022210012102010021220101220222',  // base 3
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  '-20000000000000000000000000000000',          // base 4
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  '-1104332401304422434310311213',              // base 5
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  '-1540241003031030222122212',                 // base 6
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  '-22341010611245052052301',                   // base 7
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  '-1000000000000000000000',                    // base 8
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  '-67404283172107811828',                      // base 9
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  '-9223372036854775808',                       // base 10
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  '-1728002635214590698',                       // base 11
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  '-41a792678515120368',                        // base 12
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  '-10b269549075433c38',                        // base 13
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  '-4340724c6c71dc7a8',                         // base 14
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  '-160e2ad3246366808',                         // base 15
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  '-8000000000000000',                          // base 16
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  '-33d3d8307b214009',                          // base 17
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  '-16agh595df825fa8',                          // base 18
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  '-ba643dci0ffeehi',                           // base 19
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  '-5cbfjia3fh26ja8',                           // base 20
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  '-2heiciiie82dh98',                           // base 21
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  '-1adaibb21dckfa8',                           // base 22
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  '-i6k448cf4192c3',                            // base 23
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  '-acd772jnc9l0l8',                            // base 24
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  '-64ie1focnn5g78',                            // base 25
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  '-3igoecjbmca688',                            // base 26
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  '-27c48l5b37oaoq',                            // base 27
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  '-1bk39f3ah3dmq8',                            // base 28
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  '-q1se8f0m04isc',                             // base 29
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  '-hajppbc1fc208',                             // base 30
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  '-bm03i95hia438',                             // base 31
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  '-8000000000000',                             // base 32
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  '-5hg4ck9jd4u38',                             // base 33
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  '-3tdtk1v8j6tpq',                             // base 34
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  '-2pijmikexrxp8',                             // base 35
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  '-1y2p0ij32e8e8'                              // base 36
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];
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/**
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 * Returns a Long representing the given (32-bit) integer value.
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 * @param {number} value The 32-bit integer in question.
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 * @return {!goog.math.Long} The corresponding Long value.
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 */
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goog.math.Long.fromInt = function(value) {
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  var intValue = value | 0;
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  goog.asserts.assert(value === intValue, 'value should be a 32-bit integer');
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  if (-128 <= intValue && intValue < 128) {
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    return goog.math.Long.getCachedIntValue_(intValue);
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  } else {
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    return new goog.math.Long(intValue, intValue < 0 ? -1 : 0);
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  }
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};
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/**
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 * Returns a Long representing the given value.
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 * NaN will be returned as zero. Infinity is converted to max value and
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 * -Infinity to min value.
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 * @param {number} value The number in question.
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 * @return {!goog.math.Long} The corresponding Long value.
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 */
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goog.math.Long.fromNumber = function(value) {
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  if (isNaN(value)) {
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    return goog.math.Long.getZero();
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  } else if (value <= -goog.math.Long.TWO_PWR_63_DBL_) {
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    return goog.math.Long.getMinValue();
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  } else if (value + 1 >= goog.math.Long.TWO_PWR_63_DBL_) {
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    return goog.math.Long.getMaxValue();
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  } else if (value < 0) {
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    return goog.math.Long.fromNumber(-value).negate();
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  } else {
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    return new goog.math.Long(
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        (value % goog.math.Long.TWO_PWR_32_DBL_) | 0,
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        (value / goog.math.Long.TWO_PWR_32_DBL_) | 0);
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  }
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};
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/**
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 * Returns a Long representing the 64-bit integer that comes by concatenating
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 * the given high and low bits.  Each is assumed to use 32 bits.
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 * @param {number} lowBits The low 32-bits.
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 * @param {number} highBits The high 32-bits.
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 * @return {!goog.math.Long} The corresponding Long value.
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 */
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goog.math.Long.fromBits = function(lowBits, highBits) {
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  return new goog.math.Long(lowBits, highBits);
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};
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/**
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 * Returns a Long representation of the given string, written using the given
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 * radix.
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 * @param {string} str The textual representation of the Long.
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 * @param {number=} opt_radix The radix in which the text is written.
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 * @return {!goog.math.Long} The corresponding Long value.
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 */
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goog.math.Long.fromString = function(str, opt_radix) {
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  if (str.length == 0) {
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    throw Error('number format error: empty string');
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  }
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  var radix = opt_radix || 10;
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  if (radix < 2 || 36 < radix) {
259
    throw Error('radix out of range: ' + radix);
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  }
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262
  if (str.charAt(0) == '-') {
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    return goog.math.Long.fromString(str.substring(1), radix).negate();
264
  } else if (str.indexOf('-') >= 0) {
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    throw Error('number format error: interior "-" character: ' + str);
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  }
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  // Do several (8) digits each time through the loop, so as to
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  // minimize the calls to the very expensive emulated div.
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  var radixToPower = goog.math.Long.fromNumber(Math.pow(radix, 8));
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  var result = goog.math.Long.getZero();
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  for (var i = 0; i < str.length; i += 8) {
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    var size = Math.min(8, str.length - i);
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    var value = parseInt(str.substring(i, i + size), radix);
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    if (size < 8) {
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      var power = goog.math.Long.fromNumber(Math.pow(radix, size));
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      result = result.multiply(power).add(goog.math.Long.fromNumber(value));
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    } else {
280
      result = result.multiply(radixToPower);
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      result = result.add(goog.math.Long.fromNumber(value));
282
    }
283
  }
284
  return result;
285
};
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/**
288
 * Returns the boolean value of whether the input string is within a Long's
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 * range. Assumes an input string containing only numeric characters with an
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 * optional preceding '-'.
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 * @param {string} str The textual representation of the Long.
292
 * @param {number=} opt_radix The radix in which the text is written.
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 * @return {boolean} Whether the string is within the range of a Long.
294
 */
295
goog.math.Long.isStringInRange = function(str, opt_radix) {
296
  var radix = opt_radix || 10;
297
  if (radix < 2 || 36 < radix) {
298
    throw Error('radix out of range: ' + radix);
299
  }
300

301
  var extremeValue = (str.charAt(0) == '-') ?
302
      goog.math.Long.MIN_VALUE_FOR_RADIX_[radix] :
303
      goog.math.Long.MAX_VALUE_FOR_RADIX_[radix];
304

305
  if (str.length < extremeValue.length) {
306
    return true;
307
  } else if (str.length == extremeValue.length && str <= extremeValue) {
308
    return true;
309
  } else {
310
    return false;
311
  }
312
};
313

314
// NOTE: the compiler should inline these constant values below and then remove
315
// these variables, so there should be no runtime penalty for these.
316

317

318
/**
319
 * Number used repeated below in calculations.  This must appear before the
320
 * first call to any from* function below.
321
 * @type {number}
322
 * @private
323
 */
324
goog.math.Long.TWO_PWR_16_DBL_ = 1 << 16;
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326

327
/**
328
 * @type {number}
329
 * @private
330
 */
331
goog.math.Long.TWO_PWR_32_DBL_ =
332
    goog.math.Long.TWO_PWR_16_DBL_ * goog.math.Long.TWO_PWR_16_DBL_;
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334

335
/**
336
 * @type {number}
337
 * @private
338
 */
339
goog.math.Long.TWO_PWR_64_DBL_ =
340
    goog.math.Long.TWO_PWR_32_DBL_ * goog.math.Long.TWO_PWR_32_DBL_;
341

342

343
/**
344
 * @type {number}
345
 * @private
346
 */
347
goog.math.Long.TWO_PWR_63_DBL_ = goog.math.Long.TWO_PWR_64_DBL_ / 2;
348

349

350
/**
351
 * @return {!goog.math.Long}
352
 * @public
353
 */
354
goog.math.Long.getZero = function() {
355
  return goog.math.Long.getCachedIntValue_(0);
356
};
357

358

359
/**
360
 * @return {!goog.math.Long}
361
 * @public
362
 */
363
goog.math.Long.getOne = function() {
364
  return goog.math.Long.getCachedIntValue_(1);
365
};
366

367

368
/**
369
 * @return {!goog.math.Long}
370
 * @public
371
 */
372
goog.math.Long.getNegOne = function() {
373
  return goog.math.Long.getCachedIntValue_(-1);
374
};
375

376

377
/**
378
 * @return {!goog.math.Long}
379
 * @public
380
 */
381
goog.math.Long.getMaxValue = function() {
382
  return goog.reflect.cache(
383
      goog.math.Long.valueCache_, goog.math.Long.ValueCacheId_.MAX_VALUE,
384
      function() {
385
        return goog.math.Long.fromBits(0xFFFFFFFF | 0, 0x7FFFFFFF | 0);
386
      });
387
};
388

389

390
/**
391
 * @return {!goog.math.Long}
392
 * @public
393
 */
394
goog.math.Long.getMinValue = function() {
395
  return goog.reflect.cache(
396
      goog.math.Long.valueCache_, goog.math.Long.ValueCacheId_.MIN_VALUE,
397
      function() { return goog.math.Long.fromBits(0, 0x80000000 | 0); });
398
};
399

400

401
/**
402
 * @return {!goog.math.Long}
403
 * @public
404
 */
405
goog.math.Long.getTwoPwr24 = function() {
406
  return goog.reflect.cache(
407
      goog.math.Long.valueCache_, goog.math.Long.ValueCacheId_.TWO_PWR_24,
408
      function() { return goog.math.Long.fromInt(1 << 24); });
409
};
410

411

412
/** @return {number} The value, assuming it is a 32-bit integer. */
413
goog.math.Long.prototype.toInt = function() {
414
  return this.low_;
415
};
416

417

418
/** @return {number} The closest floating-point representation to this value. */
419
goog.math.Long.prototype.toNumber = function() {
420
  return this.high_ * goog.math.Long.TWO_PWR_32_DBL_ +
421
      this.getLowBitsUnsigned();
422
};
423

424

425
/**
426
 * @param {number=} opt_radix The radix in which the text should be written.
427
 * @return {string} The textual representation of this value.
428
 * @override
429
 */
430
goog.math.Long.prototype.toString = function(opt_radix) {
431
  var radix = opt_radix || 10;
432
  if (radix < 2 || 36 < radix) {
433
    throw Error('radix out of range: ' + radix);
434
  }
435

436
  if (this.isZero()) {
437
    return '0';
438
  }
439

440
  if (this.isNegative()) {
441
    if (this.equals(goog.math.Long.getMinValue())) {
442
      // We need to change the Long value before it can be negated, so we remove
443
      // the bottom-most digit in this base and then recurse to do the rest.
444
      var radixLong = goog.math.Long.fromNumber(radix);
445
      var div = this.div(radixLong);
446
      var rem = div.multiply(radixLong).subtract(this);
447
      return div.toString(radix) + rem.toInt().toString(radix);
448
    } else {
449
      return '-' + this.negate().toString(radix);
450
    }
451
  }
452

453
  // Do several (6) digits each time through the loop, so as to
454
  // minimize the calls to the very expensive emulated div.
455
  var radixToPower = goog.math.Long.fromNumber(Math.pow(radix, 6));
456

457
  var rem = this;
458
  var result = '';
459
  while (true) {
460
    var remDiv = rem.div(radixToPower);
461
    // The right shifting fixes negative values in the case when
462
    // intval >= 2^31; for more details see
463
    // https://github.com/google/closure-library/pull/498
464
    var intval = rem.subtract(remDiv.multiply(radixToPower)).toInt() >>> 0;
465
    var digits = intval.toString(radix);
466

467
    rem = remDiv;
468
    if (rem.isZero()) {
469
      return digits + result;
470
    } else {
471
      while (digits.length < 6) {
472
        digits = '0' + digits;
473
      }
474
      result = '' + digits + result;
475
    }
476
  }
477
};
478

479

480
/** @return {number} The high 32-bits as a signed value. */
481
goog.math.Long.prototype.getHighBits = function() {
482
  return this.high_;
483
};
484

485

486
/** @return {number} The low 32-bits as a signed value. */
487
goog.math.Long.prototype.getLowBits = function() {
488
  return this.low_;
489
};
490

491

492
/** @return {number} The low 32-bits as an unsigned value. */
493
goog.math.Long.prototype.getLowBitsUnsigned = function() {
494
  return (this.low_ >= 0) ? this.low_ :
495
                            goog.math.Long.TWO_PWR_32_DBL_ + this.low_;
496
};
497

498

499
/**
500
 * @return {number} Returns the number of bits needed to represent the absolute
501
 *     value of this Long.
502
 */
503
goog.math.Long.prototype.getNumBitsAbs = function() {
504
  if (this.isNegative()) {
505
    if (this.equals(goog.math.Long.getMinValue())) {
506
      return 64;
507
    } else {
508
      return this.negate().getNumBitsAbs();
509
    }
510
  } else {
511
    var val = this.high_ != 0 ? this.high_ : this.low_;
512
    for (var bit = 31; bit > 0; bit--) {
513
      if ((val & (1 << bit)) != 0) {
514
        break;
515
      }
516
    }
517
    return this.high_ != 0 ? bit + 33 : bit + 1;
518
  }
519
};
520

521

522
/** @return {boolean} Whether this value is zero. */
523
goog.math.Long.prototype.isZero = function() {
524
  return this.high_ == 0 && this.low_ == 0;
525
};
526

527

528
/** @return {boolean} Whether this value is negative. */
529
goog.math.Long.prototype.isNegative = function() {
530
  return this.high_ < 0;
531
};
532

533

534
/** @return {boolean} Whether this value is odd. */
535
goog.math.Long.prototype.isOdd = function() {
536
  return (this.low_ & 1) == 1;
537
};
538

539

540
/**
541
 * @param {goog.math.Long} other Long to compare against.
542
 * @return {boolean} Whether this Long equals the other.
543
 */
544
goog.math.Long.prototype.equals = function(other) {
545
  return (this.high_ == other.high_) && (this.low_ == other.low_);
546
};
547

548

549
/**
550
 * @param {goog.math.Long} other Long to compare against.
551
 * @return {boolean} Whether this Long does not equal the other.
552
 */
553
goog.math.Long.prototype.notEquals = function(other) {
554
  return (this.high_ != other.high_) || (this.low_ != other.low_);
555
};
556

557

558
/**
559
 * @param {goog.math.Long} other Long to compare against.
560
 * @return {boolean} Whether this Long is less than the other.
561
 */
562
goog.math.Long.prototype.lessThan = function(other) {
563
  return this.compare(other) < 0;
564
};
565

566

567
/**
568
 * @param {goog.math.Long} other Long to compare against.
569
 * @return {boolean} Whether this Long is less than or equal to the other.
570
 */
571
goog.math.Long.prototype.lessThanOrEqual = function(other) {
572
  return this.compare(other) <= 0;
573
};
574

575

576
/**
577
 * @param {goog.math.Long} other Long to compare against.
578
 * @return {boolean} Whether this Long is greater than the other.
579
 */
580
goog.math.Long.prototype.greaterThan = function(other) {
581
  return this.compare(other) > 0;
582
};
583

584

585
/**
586
 * @param {goog.math.Long} other Long to compare against.
587
 * @return {boolean} Whether this Long is greater than or equal to the other.
588
 */
589
goog.math.Long.prototype.greaterThanOrEqual = function(other) {
590
  return this.compare(other) >= 0;
591
};
592

593

594
/**
595
 * Compares this Long with the given one.
596
 * @param {goog.math.Long} other Long to compare against.
597
 * @return {number} 0 if they are the same, 1 if the this is greater, and -1
598
 *     if the given one is greater.
599
 */
600
goog.math.Long.prototype.compare = function(other) {
601
  if (this.equals(other)) {
602
    return 0;
603
  }
604

605
  var thisNeg = this.isNegative();
606
  var otherNeg = other.isNegative();
607
  if (thisNeg && !otherNeg) {
608
    return -1;
609
  }
610
  if (!thisNeg && otherNeg) {
611
    return 1;
612
  }
613

614
  // at this point, the signs are the same, so subtraction will not overflow
615
  if (this.subtract(other).isNegative()) {
616
    return -1;
617
  } else {
618
    return 1;
619
  }
620
};
621

622

623
/** @return {!goog.math.Long} The negation of this value. */
624
goog.math.Long.prototype.negate = function() {
625
  if (this.equals(goog.math.Long.getMinValue())) {
626
    return goog.math.Long.getMinValue();
627
  } else {
628
    return this.not().add(goog.math.Long.getOne());
629
  }
630
};
631

632

633
/**
634
 * Returns the sum of this and the given Long.
635
 * @param {goog.math.Long} other Long to add to this one.
636
 * @return {!goog.math.Long} The sum of this and the given Long.
637
 */
638
goog.math.Long.prototype.add = function(other) {
639
  // Divide each number into 4 chunks of 16 bits, and then sum the chunks.
640

641
  var a48 = this.high_ >>> 16;
642
  var a32 = this.high_ & 0xFFFF;
643
  var a16 = this.low_ >>> 16;
644
  var a00 = this.low_ & 0xFFFF;
645

646
  var b48 = other.high_ >>> 16;
647
  var b32 = other.high_ & 0xFFFF;
648
  var b16 = other.low_ >>> 16;
649
  var b00 = other.low_ & 0xFFFF;
650

651
  var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
652
  c00 += a00 + b00;
653
  c16 += c00 >>> 16;
654
  c00 &= 0xFFFF;
655
  c16 += a16 + b16;
656
  c32 += c16 >>> 16;
657
  c16 &= 0xFFFF;
658
  c32 += a32 + b32;
659
  c48 += c32 >>> 16;
660
  c32 &= 0xFFFF;
661
  c48 += a48 + b48;
662
  c48 &= 0xFFFF;
663
  return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
664
};
665

666

667
/**
668
 * Returns the difference of this and the given Long.
669
 * @param {goog.math.Long} other Long to subtract from this.
670
 * @return {!goog.math.Long} The difference of this and the given Long.
671
 */
672
goog.math.Long.prototype.subtract = function(other) {
673
  return this.add(other.negate());
674
};
675

676

677
/**
678
 * Returns the product of this and the given long.
679
 * @param {goog.math.Long} other Long to multiply with this.
680
 * @return {!goog.math.Long} The product of this and the other.
681
 */
682
goog.math.Long.prototype.multiply = function(other) {
683
  if (this.isZero()) {
684
    return goog.math.Long.getZero();
685
  } else if (other.isZero()) {
686
    return goog.math.Long.getZero();
687
  }
688

689
  if (this.equals(goog.math.Long.getMinValue())) {
690
    return other.isOdd() ? goog.math.Long.getMinValue() :
691
                           goog.math.Long.getZero();
692
  } else if (other.equals(goog.math.Long.getMinValue())) {
693
    return this.isOdd() ? goog.math.Long.getMinValue() :
694
                          goog.math.Long.getZero();
695
  }
696

697
  if (this.isNegative()) {
698
    if (other.isNegative()) {
699
      return this.negate().multiply(other.negate());
700
    } else {
701
      return this.negate().multiply(other).negate();
702
    }
703
  } else if (other.isNegative()) {
704
    return this.multiply(other.negate()).negate();
705
  }
706

707
  // If both longs are small, use float multiplication
708
  if (this.lessThan(goog.math.Long.getTwoPwr24()) &&
709
      other.lessThan(goog.math.Long.getTwoPwr24())) {
710
    return goog.math.Long.fromNumber(this.toNumber() * other.toNumber());
711
  }
712

713
  // Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
714
  // We can skip products that would overflow.
715

716
  var a48 = this.high_ >>> 16;
717
  var a32 = this.high_ & 0xFFFF;
718
  var a16 = this.low_ >>> 16;
719
  var a00 = this.low_ & 0xFFFF;
720

721
  var b48 = other.high_ >>> 16;
722
  var b32 = other.high_ & 0xFFFF;
723
  var b16 = other.low_ >>> 16;
724
  var b00 = other.low_ & 0xFFFF;
725

726
  var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
727
  c00 += a00 * b00;
728
  c16 += c00 >>> 16;
729
  c00 &= 0xFFFF;
730
  c16 += a16 * b00;
731
  c32 += c16 >>> 16;
732
  c16 &= 0xFFFF;
733
  c16 += a00 * b16;
734
  c32 += c16 >>> 16;
735
  c16 &= 0xFFFF;
736
  c32 += a32 * b00;
737
  c48 += c32 >>> 16;
738
  c32 &= 0xFFFF;
739
  c32 += a16 * b16;
740
  c48 += c32 >>> 16;
741
  c32 &= 0xFFFF;
742
  c32 += a00 * b32;
743
  c48 += c32 >>> 16;
744
  c32 &= 0xFFFF;
745
  c48 += a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48;
746
  c48 &= 0xFFFF;
747
  return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
748
};
749

750

751
/**
752
 * Returns this Long divided by the given one.
753
 * @param {goog.math.Long} other Long by which to divide.
754
 * @return {!goog.math.Long} This Long divided by the given one.
755
 */
756
goog.math.Long.prototype.div = function(other) {
757
  if (other.isZero()) {
758
    throw Error('division by zero');
759
  } else if (this.isZero()) {
760
    return goog.math.Long.getZero();
761
  }
762

763
  if (this.equals(goog.math.Long.getMinValue())) {
764
    if (other.equals(goog.math.Long.getOne()) ||
765
        other.equals(goog.math.Long.getNegOne())) {
766
      return goog.math.Long.getMinValue();  // recall -MIN_VALUE == MIN_VALUE
767
    } else if (other.equals(goog.math.Long.getMinValue())) {
768
      return goog.math.Long.getOne();
769
    } else {
770
      // At this point, we have |other| >= 2, so |this/other| < |MIN_VALUE|.
771
      var halfThis = this.shiftRight(1);
772
      var approx = halfThis.div(other).shiftLeft(1);
773
      if (approx.equals(goog.math.Long.getZero())) {
774
        return other.isNegative() ? goog.math.Long.getOne() :
775
                                    goog.math.Long.getNegOne();
776
      } else {
777
        var rem = this.subtract(other.multiply(approx));
778
        var result = approx.add(rem.div(other));
779
        return result;
780
      }
781
    }
782
  } else if (other.equals(goog.math.Long.getMinValue())) {
783
    return goog.math.Long.getZero();
784
  }
785

786
  if (this.isNegative()) {
787
    if (other.isNegative()) {
788
      return this.negate().div(other.negate());
789
    } else {
790
      return this.negate().div(other).negate();
791
    }
792
  } else if (other.isNegative()) {
793
    return this.div(other.negate()).negate();
794
  }
795

796
  // Repeat the following until the remainder is less than other:  find a
797
  // floating-point that approximates remainder / other *from below*, add this
798
  // into the result, and subtract it from the remainder.  It is critical that
799
  // the approximate value is less than or equal to the real value so that the
800
  // remainder never becomes negative.
801
  var res = goog.math.Long.getZero();
802
  var rem = this;
803
  while (rem.greaterThanOrEqual(other)) {
804
    // Approximate the result of division. This may be a little greater or
805
    // smaller than the actual value.
806
    var approx = Math.max(1, Math.floor(rem.toNumber() / other.toNumber()));
807

808
    // We will tweak the approximate result by changing it in the 48-th digit or
809
    // the smallest non-fractional digit, whichever is larger.
810
    var log2 = Math.ceil(Math.log(approx) / Math.LN2);
811
    var delta = (log2 <= 48) ? 1 : Math.pow(2, log2 - 48);
812

813
    // Decrease the approximation until it is smaller than the remainder.  Note
814
    // that if it is too large, the product overflows and is negative.
815
    var approxRes = goog.math.Long.fromNumber(approx);
816
    var approxRem = approxRes.multiply(other);
817
    while (approxRem.isNegative() || approxRem.greaterThan(rem)) {
818
      approx -= delta;
819
      approxRes = goog.math.Long.fromNumber(approx);
820
      approxRem = approxRes.multiply(other);
821
    }
822

823
    // We know the answer can't be zero... and actually, zero would cause
824
    // infinite recursion since we would make no progress.
825
    if (approxRes.isZero()) {
826
      approxRes = goog.math.Long.getOne();
827
    }
828

829
    res = res.add(approxRes);
830
    rem = rem.subtract(approxRem);
831
  }
832
  return res;
833
};
834

835

836
/**
837
 * Returns this Long modulo the given one.
838
 * @param {goog.math.Long} other Long by which to mod.
839
 * @return {!goog.math.Long} This Long modulo the given one.
840
 */
841
goog.math.Long.prototype.modulo = function(other) {
842
  return this.subtract(this.div(other).multiply(other));
843
};
844

845

846
/** @return {!goog.math.Long} The bitwise-NOT of this value. */
847
goog.math.Long.prototype.not = function() {
848
  return goog.math.Long.fromBits(~this.low_, ~this.high_);
849
};
850

851

852
/**
853
 * Returns the bitwise-AND of this Long and the given one.
854
 * @param {goog.math.Long} other The Long with which to AND.
855
 * @return {!goog.math.Long} The bitwise-AND of this and the other.
856
 */
857
goog.math.Long.prototype.and = function(other) {
858
  return goog.math.Long.fromBits(
859
      this.low_ & other.low_, this.high_ & other.high_);
860
};
861

862

863
/**
864
 * Returns the bitwise-OR of this Long and the given one.
865
 * @param {goog.math.Long} other The Long with which to OR.
866
 * @return {!goog.math.Long} The bitwise-OR of this and the other.
867
 */
868
goog.math.Long.prototype.or = function(other) {
869
  return goog.math.Long.fromBits(
870
      this.low_ | other.low_, this.high_ | other.high_);
871
};
872

873

874
/**
875
 * Returns the bitwise-XOR of this Long and the given one.
876
 * @param {goog.math.Long} other The Long with which to XOR.
877
 * @return {!goog.math.Long} The bitwise-XOR of this and the other.
878
 */
879
goog.math.Long.prototype.xor = function(other) {
880
  return goog.math.Long.fromBits(
881
      this.low_ ^ other.low_, this.high_ ^ other.high_);
882
};
883

884

885
/**
886
 * Returns this Long with bits shifted to the left by the given amount.
887
 * @param {number} numBits The number of bits by which to shift.
888
 * @return {!goog.math.Long} This shifted to the left by the given amount.
889
 */
890
goog.math.Long.prototype.shiftLeft = function(numBits) {
891
  numBits &= 63;
892
  if (numBits == 0) {
893
    return this;
894
  } else {
895
    var low = this.low_;
896
    if (numBits < 32) {
897
      var high = this.high_;
898
      return goog.math.Long.fromBits(
899
          low << numBits, (high << numBits) | (low >>> (32 - numBits)));
900
    } else {
901
      return goog.math.Long.fromBits(0, low << (numBits - 32));
902
    }
903
  }
904
};
905

906

907
/**
908
 * Returns this Long with bits shifted to the right by the given amount.
909
 * The new leading bits match the current sign bit.
910
 * @param {number} numBits The number of bits by which to shift.
911
 * @return {!goog.math.Long} This shifted to the right by the given amount.
912
 */
913
goog.math.Long.prototype.shiftRight = function(numBits) {
914
  numBits &= 63;
915
  if (numBits == 0) {
916
    return this;
917
  } else {
918
    var high = this.high_;
919
    if (numBits < 32) {
920
      var low = this.low_;
921
      return goog.math.Long.fromBits(
922
          (low >>> numBits) | (high << (32 - numBits)), high >> numBits);
923
    } else {
924
      return goog.math.Long.fromBits(
925
          high >> (numBits - 32), high >= 0 ? 0 : -1);
926
    }
927
  }
928
};
929

930

931
/**
932
 * Returns this Long with bits shifted to the right by the given amount, with
933
 * zeros placed into the new leading bits.
934
 * @param {number} numBits The number of bits by which to shift.
935
 * @return {!goog.math.Long} This shifted to the right by the given amount, with
936
 *     zeros placed into the new leading bits.
937
 */
938
goog.math.Long.prototype.shiftRightUnsigned = function(numBits) {
939
  numBits &= 63;
940
  if (numBits == 0) {
941
    return this;
942
  } else {
943
    var high = this.high_;
944
    if (numBits < 32) {
945
      var low = this.low_;
946
      return goog.math.Long.fromBits(
947
          (low >>> numBits) | (high << (32 - numBits)), high >>> numBits);
948
    } else if (numBits == 32) {
949
      return goog.math.Long.fromBits(high, 0);
950
    } else {
951
      return goog.math.Long.fromBits(high >>> (numBits - 32), 0);
952
    }
953
  }
954
};
955

956

957
/**
958
 * @enum {number} Ids of commonly requested Long instances.
959
 * @private
960
 */
961
goog.math.Long.ValueCacheId_ = {
962
  MAX_VALUE: 1,
963
  MIN_VALUE: 2,
964
  TWO_PWR_24: 6
965
};
966

967