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1 /* |
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2 * Copyright (c) 2013, 2019, Oracle and/or its affiliates. All rights reserved. |
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3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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4 * |
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5 * This code is free software; you can redistribute it and/or modify it |
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6 * under the terms of the GNU General Public License version 2 only, as |
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7 * published by the Free Software Foundation. Oracle designates this |
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8 * particular file as subject to the "Classpath" exception as provided |
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9 * by Oracle in the LICENSE file that accompanied this code. |
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10 * |
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11 * This code is distributed in the hope that it will be useful, but WITHOUT |
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12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 * version 2 for more details (a copy is included in the LICENSE file that |
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15 * accompanied this code). |
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16 * |
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17 * You should have received a copy of the GNU General Public License version |
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18 * 2 along with this work; if not, write to the Free Software Foundation, |
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19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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20 * |
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21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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22 * or visit www.oracle.com if you need additional information or have any |
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23 * questions. |
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24 */ |
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25 |
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26 package java.util.random; |
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27 |
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28 import java.math.BigInteger; |
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29 import java.util.concurrent.atomic.AtomicLong; |
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30 import java.util.random.RandomGenerator.SplittableGenerator; |
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31 import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator; |
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32 |
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33 /** |
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34 * A generator of uniform pseudorandom values applicable for use in |
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35 * (among other contexts) isolated parallel computations that may |
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36 * generate subtasks. Class {@link L128X1024MixRandom} implements |
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37 * interfaces {@link RandomGenerator} and {@link SplittableGenerator}, |
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38 * and therefore supports methods for producing pseudorandomly chosen |
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39 * numbers of type {@code int}, {@code long}, {@code float}, and {@code double} |
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40 * as well as creating new split-off {@link L128X1024MixRandom} objects, |
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41 * with similar usages as for class {@link java.util.SplittableRandom}. |
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42 * <p> |
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43 * Series of generated values pass the TestU01 BigCrush and PractRand test suites |
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44 * that measure independence and uniformity properties of random number generators. |
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45 * (Most recently validated with |
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46 * <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a> |
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47 * and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>. |
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48 * Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()} |
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49 * method but also the result of bit-reversing each value produced by {@code nextLong()}.) |
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50 * These tests validate only the methods for certain |
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51 * types and ranges, but similar properties are expected to hold, at |
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52 * least approximately, for others as well. |
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53 * <p> |
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54 * {@link L128X1024MixRandom} is a specific member of the LXM family of algorithms |
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55 * for pseudorandom number generators. Every LXM generator consists of two |
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56 * subgenerators; one is an LCG (Linear Congruential Generator) and the other is |
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57 * an Xorshift generator. Each output of an LXM generator is the result of |
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58 * combining state from the LCG with state from the Xorshift generator by |
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59 * using a Mixing function (and then the state of the LCG and the state of the |
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60 * Xorshift generator are advanced). |
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61 * <p> |
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62 * The LCG subgenerator for {@link L128X256MixRandom} has an update step of the |
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63 * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all |
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64 * 128-bit integers; {@code s} is the mutable state, the multiplier {@code m} |
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65 * is fixed (the same for all instances of {@link L128X256MixRandom}) and the addend |
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66 * {@code a} is a parameter (a final field of the instance). The parameter |
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67 * {@code a} is required to be odd (this allows the LCG to have the maximal |
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68 * period, namely 2<sup>128</sup>); therefore there are 2<sup>127</sup> distinct choices |
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69 * of parameter. |
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70 * <p> |
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71 * The Xorshift subgenerator for {@link L128X1024MixRandom} is the {@code xoroshiro1024} |
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72 * algorithm (parameters 25, 27, and 36), without any final scrambler such as "+" or "**". |
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73 * Its state consists of an array {@code x} of sixteen {@code long} values, |
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74 * which can take on any values provided that they are not all zero. |
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75 * The period of this subgenerator is 2<sup>1024</sup>-1. |
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76 * <p> |
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77 * The mixing function for {@link L128X1024MixRandom} is {@link RandomSupport.mixLea64} |
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78 * applied to the argument {@code (sh + s0)}, where {@code sh} is the high half of {@code s} |
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79 * and {@code s0} is the most recently computed element of {@code x}. |
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80 * <p> |
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81 * Because the periods 2<sup>128</sup> and 2<sup>1024</sup>-1 of the two subgenerators |
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82 * are relatively prime, the <em>period</em> of any single {@link L128X1024MixRandom} object |
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83 * (the length of the series of generated 64-bit values before it repeats) is the product |
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84 * of the periods of the subgenerators, that is, 2<sup>128</sup>(2<sup>1024</sup>-1), |
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85 * which is just slightly smaller than 2<sup>1152</sup>. Moreover, if two distinct |
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86 * {@link L128X1024MixRandom} objects have different {@code a} parameters, then their |
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87 * cycles of produced values will be different. |
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88 * <p> |
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89 * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. |
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90 * For any specific instance of {@link L128X1024MixRandom}, over the course of its cycle each |
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91 * of the 2<sup>64</sup> possible {@code long} values will be produced |
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92 * 2<sup>64</sup>(2<sup>1024</sup>-1 times. The values produced by the {@code nextInt()}, |
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93 * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. |
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94 * <p> |
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95 * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be |
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96 * "very nearly" 16-equidistributed: all possible 16-tuples of 64-bit values are generated, |
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97 * and some pairs occur more often than others, but only very slightly more often. |
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98 * However, this conjecture has not yet been proven mathematically. |
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99 * If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()}, |
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100 * and {@code nextDouble()} methods are likewise approximately 16-equidistributed. |
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101 * <p> |
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102 * Method {@link #split} constructs and returns a new {@link L128X1024MixRandom} |
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103 * instance that shares no mutable state with the current instance. However, with |
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104 * very high probability, the values collectively generated by the two objects |
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105 * have the same statistical properties as if the same quantity of values were |
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106 * generated by a single thread using a single {@link L128X1024MixRandom} object. |
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107 * This is because, with high probability, distinct {@link L128X1024MixRandom} objects |
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108 * have distinct {@code a} parameters and therefore use distinct members of the |
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109 * algorithmic family; and even if their {@code a} parameters are the same, with |
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110 * very high probability they will traverse different parts of their common state |
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111 * cycle. |
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112 * <p> |
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113 * As with {@link java.util.SplittableRandom}, instances of |
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114 * {@link L128X1024MixRandom} are <em>not</em> thread-safe. |
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115 * They are designed to be split, not shared, across threads. For |
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116 * example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style |
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117 * computation using random numbers might include a construction |
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118 * of the form {@code new Subtask(someL128X1024MixRandom.split()).fork()}. |
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119 * <p> |
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120 * This class provides additional methods for generating random |
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121 * streams, that employ the above techniques when used in |
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122 * {@code stream.parallel()} mode. |
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123 * <p> |
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124 * Instances of {@link L128X1024MixRandom} are not cryptographically |
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125 * secure. Consider instead using {@link java.security.SecureRandom} |
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126 * in security-sensitive applications. Additionally, |
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127 * default-constructed instances do not use a cryptographically random |
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128 * seed unless the {@linkplain System#getProperty system property} |
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129 * {@code java.util.secureRandomSeed} is set to {@code true}. |
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130 * |
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131 * @since 14 |
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132 */ |
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133 public final class L128X1024MixRandom extends AbstractSplittableWithBrineGenerator { |
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134 |
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135 /* |
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136 * Implementation Overview. |
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137 * |
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138 * The 128-bit parameter `a` is represented as two long fields `ah` and `al`. |
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139 * The 128-bit state variable `s` is represented as two long fields `sh` and `sl`. |
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140 * |
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141 * The split operation uses the current generator to choose 20 |
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142 * new 64-bit long values that are then used to initialize the |
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143 * parameters `ah` and `al`, the state variables `sh`, `sl`, |
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144 * and the array `x` for a newly constructed generator. |
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145 * |
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146 * With extremely high probability, no two generators so chosen |
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147 * will have the same `a` parameter, and testing has indicated |
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148 * that the values generated by two instances of {@link L128X1024MixRandom} |
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149 * will be (approximately) independent if have different values for `a`. |
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150 * |
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151 * The default (no-argument) constructor, in essence, uses |
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152 * "defaultGen" to generate 20 new 64-bit values for the same |
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153 * purpose. Multiple generators created in this way will certainly |
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154 * differ in their `a` parameters. The defaultGen state must be accessed |
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155 * in a thread-safe manner, so we use an AtomicLong to represent |
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156 * this state. To bootstrap the defaultGen, we start off using a |
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157 * seed based on current time unless the |
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158 * java.util.secureRandomSeed property is set. This serves as a |
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159 * slimmed-down (and insecure) variant of SecureRandom that also |
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160 * avoids stalls that may occur when using /dev/random. |
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161 * |
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162 * File organization: First static fields, then instance |
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163 * fields, then constructors, then instance methods. |
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164 */ |
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165 |
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166 /* ---------------- static fields ---------------- */ |
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167 |
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168 /* |
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169 * The length of the array x. |
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170 */ |
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171 |
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172 private static final int N = 16; |
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173 |
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174 /** |
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175 * The seed generator for default constructors. |
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176 */ |
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177 private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); |
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178 |
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179 /* |
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180 * The period of this generator, which is (2**1024 - 1) * 2**128. |
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181 */ |
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182 private static final BigInteger PERIOD = |
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183 BigInteger.ONE.shiftLeft(N*64).subtract(BigInteger.ONE).shiftLeft(128); |
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184 |
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185 /* |
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186 * Low half of multiplier used in the LCG portion of the algorithm; |
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187 * the overall multiplier is (2**64 + ML). |
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188 * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). |
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189 * The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL |
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190 * are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493]. |
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191 */ |
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192 |
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193 private static final long ML = 0xd605bbb58c8abbfdL; |
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194 |
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195 /* ---------------- instance fields ---------------- */ |
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196 |
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197 /** |
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198 * The parameter that is used as an additive constant for the LCG. |
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199 * Must be odd (therefore al must be odd). |
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200 */ |
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201 private final long ah, al; |
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202 |
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203 /** |
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204 * The per-instance state: sh and sl for the LCG; the array x for the xorshift; |
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205 * p is the rotating pointer into the array x. |
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206 * At least one of the 16 elements of the array x must be nonzero. |
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207 */ |
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208 private long sh, sl; |
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209 private final long[] x; |
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210 private int p = N - 1; |
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211 |
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212 /* ---------------- constructors ---------------- */ |
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213 |
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214 /** |
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215 * Basic constructor that initializes all fields from parameters. |
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216 * It then adjusts the field values if necessary to ensure that |
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217 * all constraints on the values of fields are met. |
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218 * |
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219 * @param ah high half of the additive parameter for the LCG |
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220 * @param al low half of the additive parameter for the LCG |
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221 * @param sh high half of the initial state for the LCG |
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222 * @param sl low half of the initial state for the LCG |
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223 * @param x0 first word of the initial state for the xorshift generator |
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224 * @param x1 second word of the initial state for the xorshift generator |
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225 * @param x2 third word of the initial state for the xorshift generator |
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226 * @param x3 fourth word of the initial state for the xorshift generator |
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227 * @param x4 fifth word of the initial state for the xorshift generator |
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228 * @param x5 sixth word of the initial state for the xorshift generator |
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229 * @param x6 seventh word of the initial state for the xorshift generator |
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230 * @param x7 eight word of the initial state for the xorshift generator |
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231 * @param x8 ninth word of the initial state for the xorshift generator |
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232 * @param x9 tenth word of the initial state for the xorshift generator |
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233 * @param x10 eleventh word of the initial state for the xorshift generator |
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234 * @param x11 twelfth word of the initial state for the xorshift generator |
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235 * @param x12 thirteenth word of the initial state for the xorshift generator |
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236 * @param x13 fourteenth word of the initial state for the xorshift generator |
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237 * @param x14 fifteenth word of the initial state for the xorshift generator |
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238 * @param x15 sixteenth word of the initial state for the xorshift generator |
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239 */ |
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240 public L128X1024MixRandom(long ah, long al, long sh, long sl, |
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241 long x0, long x1, long x2, long x3, |
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242 long x4, long x5, long x6, long x7, |
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243 long x8, long x9, long x10, long x11, |
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244 long x12, long x13, long x14, long x15) { |
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245 // Force a to be odd. |
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246 this.ah = ah; |
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247 this.al = al | 1; |
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248 this.sh = sh; |
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249 this.sl = sl; |
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250 this.x = new long[N]; |
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251 this.x[0] = x0; |
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252 this.x[1] = x1; |
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253 this.x[2] = x2; |
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254 this.x[3] = x3; |
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255 this.x[4] = x4; |
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256 this.x[5] = x5; |
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257 this.x[6] = x6; |
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258 this.x[7] = x7; |
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259 this.x[8] = x8; |
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260 this.x[9] = x9; |
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261 this.x[10] = x10; |
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262 this.x[11] = x11; |
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263 this.x[12] = x12; |
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264 this.x[13] = x13; |
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265 this.x[14] = x14; |
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266 this.x[15] = x15; |
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267 // If x0, x1, ..., x15 are all zero (very unlikely), we must choose nonzero values. |
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268 if ((x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15) == 0) { |
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269 long v = sh; |
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270 // At least fifteen of the sixteen values generated here will be nonzero. |
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271 for (int j = 0; j < N; j++) { |
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272 this.x[j] = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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273 } |
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274 } |
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275 } |
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276 |
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277 /** |
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278 * Creates a new instance of {@link L128X1024MixRandom} using the |
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279 * specified {@code long} value as the initial seed. Instances of |
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280 * {@link L128X1024MixRandom} created with the same seed in the same |
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281 * program execution generate identical sequences of values. |
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282 * |
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283 * @param seed the initial seed |
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284 */ |
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285 public L128X1024MixRandom(long seed) { |
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286 // Using a value with irregularly spaced 1-bits to xor the seed |
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287 // argument tends to improve "pedestrian" seeds such as 0 or |
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288 // other small integers. We may as well use SILVER_RATIO_64. |
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289 // |
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290 // The seed is hashed by mixMurmur64 to produce the `a` parameter. |
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291 // The seed is hashed by mixStafford13 to produce the initial `x[0]`, |
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292 // which will then be used to produce the first generated value. |
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293 // The other x values are filled in as if by a SplitMix PRNG with |
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294 // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer. |
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295 this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
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296 RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64), |
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297 0, |
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298 1, |
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299 RandomSupport.mixStafford13(seed), |
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300 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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301 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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302 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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303 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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304 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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305 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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306 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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307 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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308 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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309 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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310 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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311 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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312 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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313 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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314 RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64)); |
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315 } |
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316 |
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317 /** |
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318 * Creates a new instance of {@link L128X1024MixRandom} that is likely to |
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319 * generate sequences of values that are statistically independent |
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320 * of those of any other instances in the current program execution, |
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321 * but may, and typically does, vary across program invocations. |
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322 */ |
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323 public L128X1024MixRandom() { |
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324 // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
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325 this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); |
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326 } |
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327 |
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328 /** |
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329 * Creates a new instance of {@link L128X1024MixRandom} using the specified array of |
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330 * initial seed bytes. Instances of {@link L128X1024MixRandom} created with the same |
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331 * seed array in the same program execution generate identical sequences of values. |
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332 * |
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333 * @param seed the initial seed |
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334 */ |
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335 public L128X1024MixRandom(byte[] seed) { |
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336 // Convert the seed to 20 long values, of which the last 16 are not all zero. |
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337 long[] data = RandomSupport.convertSeedBytesToLongs(seed, 20, 16); |
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338 long ah = data[0], al = data[1], sh = data[2], sl = data[3]; |
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339 // Force a to be odd. |
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340 this.ah = ah; |
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341 this.al = al | 1; |
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342 this.sh = sh; |
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343 this.sl = sl; |
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344 this.x = new long[N]; |
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345 for (int j = 0; j < N; j++) { |
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346 this.x[j] = data[4+j]; |
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347 } |
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348 } |
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349 |
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350 /* ---------------- public methods ---------------- */ |
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351 |
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352 /** |
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353 * Given 63 bits of "brine", constructs and returns a new instance of |
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354 * {@code L128X1024MixRandom} that shares no mutable state with this instance. |
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355 * However, with very high probability, the set of values collectively |
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356 * generated by the two objects has the same statistical properties as if |
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357 * same the quantity of values were generated by a single thread using |
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358 * a single {@code L128X1024MixRandom} object. Either or both of the two |
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359 * objects may be further split using the {@code split} method, |
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360 * and the same expected statistical properties apply to the |
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361 * entire set of generators constructed by such recursive splitting. |
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362 * |
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363 * @param source a {@code SplittableGenerator} instance to be used instead |
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364 * of this one as a source of pseudorandom bits used to |
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365 * initialize the state of the new ones. |
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366 * @param brine a long value, of which the low 63 bits are used to choose |
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367 * the {@code a} parameter for the new instance. |
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368 * @return a new instance of {@code L128X1024MixRandom} |
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369 */ |
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370 public SplittableGenerator split(SplittableGenerator source, long brine) { |
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371 // Pick a new instance "at random", but use the brine for (the low half of) `a`. |
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372 return new L128X1024MixRandom(source.nextLong(), brine << 1, |
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373 source.nextLong(), source.nextLong(), |
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374 source.nextLong(), source.nextLong(), |
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375 source.nextLong(), source.nextLong(), |
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376 source.nextLong(), source.nextLong(), |
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377 source.nextLong(), source.nextLong(), |
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378 source.nextLong(), source.nextLong(), |
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379 source.nextLong(), source.nextLong(), |
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380 source.nextLong(), source.nextLong(), |
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381 source.nextLong(), source.nextLong()); |
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382 } |
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383 |
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384 /** |
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385 * Returns a pseudorandom {@code long} value. |
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386 * |
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387 * @return a pseudorandom {@code long} value |
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388 */ |
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389 public long nextLong() { |
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390 // First part of xoroshiro1024: fetch array data |
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391 final int q = p; |
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392 final long s0 = x[p = (p + 1) & (N - 1)]; |
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393 long s15 = x[q]; |
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394 |
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395 // Compute the result based on current state information |
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396 // (this allows the computation to be overlapped with state update). |
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397 final long result = RandomSupport.mixLea64(sh + s0); |
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398 |
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399 // Update the LCG subgenerator |
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400 // The LCG is, in effect, s = ((1LL << 64) + ML) * s + a, if only we had 128-bit arithmetic. |
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401 final long u = ML * sl; |
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402 // Note that Math.multiplyHigh computes the high half of the product of signed values, |
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403 // but what we need is the high half of the product of unsigned values; for this we use the |
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404 // formula "unsignedMultiplyHigh(a, b) = multiplyHigh(a, b) + ((a >> 63) & b) + ((b >> 63) & a)"; |
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405 // in effect, each operand is added to the result iff the sign bit of the other operand is 1. |
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406 // (See Henry S. Warren, Jr., _Hacker's Delight_ (Second Edition), Addison-Wesley (2013), |
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407 // Section 8-3, p. 175; or see the First Edition, Addison-Wesley (2003), Section 8-3, p. 133.) |
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408 // If Math.unsignedMultiplyHigh(long, long) is ever implemented, the following line can become: |
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409 // sh = (ML * sh) + Math.unsignedMultiplyHigh(ML, sl) + sl + ah; |
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410 // and this entire comment can be deleted. |
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411 sh = (ML * sh) + (Math.multiplyHigh(ML, sl) + ((ML >> 63) & sl) + ((sl >> 63) & ML)) + sl + ah; |
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412 sl = u + al; |
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413 if (Long.compareUnsigned(sl, u) < 0) ++sh; // Handle the carry propagation from low half to high half. |
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414 |
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415 // Second part of xoroshiro1024: update array data |
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416 s15 ^= s0; |
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417 x[q] = Long.rotateLeft(s0, 25) ^ s15 ^ (s15 << 27); |
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418 x[p] = Long.rotateLeft(s15, 36); |
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419 |
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420 return result; |
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421 } |
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422 |
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423 /** |
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424 * Returns the period of this random generator. |
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425 * |
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426 * @return a {@link BigInteger} whose value is the number of distinct possible states of this |
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427 * {@link RandomGenerator} object (2<sup>128</sup>(2<sup>1024</sup>-1)). |
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428 */ |
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429 public BigInteger period() { |
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430 return PERIOD; |
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431 } |
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432 } |