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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 L128X128MixRandom} 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 L128X128MixRandom} 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 L128X128MixRandom} 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 L128X128MixRandom} is the {@code xoroshiro128} algorithm, |
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72 * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**". |
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73 * Its state consists of two {@code long} fields {@code x0} and {@code x1}, |
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74 * which can take on any values provided that they are not both zero. |
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75 * The period of this subgenerator is 2<sup>128</sup>-1. |
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76 * <p> |
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77 * The mixing function for {@link L128X128MixRandom} is {@link RandomSupport.mixLea64} |
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78 * applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}. |
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79 * <p> |
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80 * Because the periods 2<sup>128</sup> and 2<sup>128</sup>-1 of the two subgenerators |
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81 * are relatively prime, the <em>period</em> of any single {@link L128X128MixRandom} object |
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82 * (the length of the series of generated 64-bit values before it repeats) is the product |
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83 * of the periods of the subgenerators, that is, 2<sup>128</sup>(2<sup>128</sup>-1), |
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84 * which is just slightly smaller than 2<sup>256</sup>. Moreover, if two distinct |
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85 * {@link L128X128MixRandom} objects have different {@code a} parameters, then their |
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86 * cycles of produced values will be different. |
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87 * <p> |
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88 * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. |
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89 * For any specific instance of {@link L128X128MixRandom}, over the course of its cycle each |
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90 * of the 2<sup>64</sup> possible {@code long} values will be produced |
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91 * 2<sup>64</sup>(2<sup>128</sup>-1) times. The values produced by the {@code nextInt()}, |
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92 * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. |
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93 * <p> |
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94 * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be |
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95 * "very nearly" 2-equidistributed: all possible pairs of 64-bit values are generated, |
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96 * and some pairs occur more often than others, but only very slightly more often. |
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97 * However, this conjecture has not yet been proven mathematically. |
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98 * If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()}, |
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99 * and {@code nextDouble()} methods are likewise approximately 2-equidistributed. |
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100 * <p> |
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101 * Method {@link #split} constructs and returns a new {@link L128X128MixRandom} |
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102 * instance that shares no mutable state with the current instance. However, with |
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103 * very high probability, the values collectively generated by the two objects |
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104 * have the same statistical properties as if the same quantity of values were |
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105 * generated by a single thread using a single {@link L128X128MixRandom} object. |
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106 * This is because, with high probability, distinct {@link L128X128MixRandom} objects |
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107 * have distinct {@code a} parameters and therefore use distinct members of the |
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108 * algorithmic family; and even if their {@code a} parameters are the same, with |
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109 * very high probability they will traverse different parts of their common state |
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110 * cycle. |
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111 * <p> |
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112 * As with {@link java.util.SplittableRandom}, instances of |
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113 * {@link L128X128MixRandom} are <em>not</em> thread-safe. |
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114 * They are designed to be split, not shared, across threads. For |
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115 * example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style |
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116 * computation using random numbers might include a construction |
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117 * of the form {@code new Subtask(someL128X128MixRandom.split()).fork()}. |
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118 * <p> |
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119 * This class provides additional methods for generating random |
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120 * streams, that employ the above techniques when used in |
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121 * {@code stream.parallel()} mode. |
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122 * <p> |
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123 * Instances of {@link L128X128MixRandom} are not cryptographically |
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124 * secure. Consider instead using {@link java.security.SecureRandom} |
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125 * in security-sensitive applications. Additionally, |
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126 * default-constructed instances do not use a cryptographically random |
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127 * seed unless the {@linkplain System#getProperty system property} |
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128 * {@code java.util.secureRandomSeed} is set to {@code true}. |
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129 * |
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130 * @since 14 |
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131 */ |
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132 public final class L128X128MixRandom extends AbstractSplittableWithBrineGenerator { |
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133 |
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134 /* |
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135 * Implementation Overview. |
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136 * |
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137 * The split operation uses the current generator to choose four new 64-bit |
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138 * long values that are then used to initialize the parameter `a` and the |
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139 * state variables `s`, `x0`, and `x1` for a newly constructed generator. |
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140 * |
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141 * With extremely high probability, no two generators so chosen |
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142 * will have the same `a` parameter, and testing has indicated |
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143 * that the values generated by two instances of {@link L128X128MixRandom} |
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144 * will be (approximately) independent if have different values for `a`. |
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145 * |
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146 * The default (no-argument) constructor, in essence, uses |
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147 * "defaultGen" to generate four new 64-bit values for the same |
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148 * purpose. Multiple generators created in this way will certainly |
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149 * differ in their `a` parameters. The defaultGen state must be accessed |
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150 * in a thread-safe manner, so we use an AtomicLong to represent |
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151 * this state. To bootstrap the defaultGen, we start off using a |
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152 * seed based on current time unless the |
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153 * java.util.secureRandomSeed property is set. This serves as a |
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154 * slimmed-down (and insecure) variant of SecureRandom that also |
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155 * avoids stalls that may occur when using /dev/random. |
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156 * |
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157 * File organization: First static fields, then instance |
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158 * fields, then constructors, then instance methods. |
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159 */ |
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160 |
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161 /* ---------------- static fields ---------------- */ |
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162 |
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163 /** |
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164 * The seed generator for default constructors. |
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165 */ |
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166 private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); |
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167 |
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168 /* |
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169 * The period of this generator, which is (2**128 - 1) * 2**128. |
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170 */ |
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171 private static final BigInteger PERIOD = |
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172 BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE).shiftLeft(128); |
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173 |
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174 /* |
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175 * Low half of multiplier used in the LCG portion of the algorithm; |
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176 * the overall multiplier is (2**64 + ML). |
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177 * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). |
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178 * The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL |
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179 * are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493]. |
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180 */ |
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181 |
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182 private static final long ML = 0xd605bbb58c8abbfdL; |
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183 |
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184 /* ---------------- instance fields ---------------- */ |
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185 |
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186 /** |
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187 * The parameter that is used as an additive constant for the LCG. |
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188 * Must be odd (therefore al must be odd). |
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189 */ |
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190 private final long ah, al; |
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191 |
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192 /** |
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193 * The per-instance state: sh and sl for the LCG; x0 and x1 for the xorshift. |
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194 * At least one of x0 and x1 must be nonzero. |
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195 */ |
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196 private long sh, sl, x0, x1; |
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197 |
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198 /* ---------------- constructors ---------------- */ |
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199 |
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200 /** |
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201 * Basic constructor that initializes all fields from parameters. |
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202 * It then adjusts the field values if necessary to ensure that |
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203 * all constraints on the values of fields are met. |
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204 * |
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205 * @param ah high half of the additive parameter for the LCG |
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206 * @param al low half of the additive parameter for the LCG |
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207 * @param sh high half of the initial state for the LCG |
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208 * @param sl low half of the initial state for the LCG |
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209 * @param x0 first word of the initial state for the xorshift generator |
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210 * @param x1 second word of the initial state for the xorshift generator |
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211 */ |
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212 public L128X128MixRandom(long ah, long al, long sh, long sl, long x0, long x1) { |
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213 // Force a to be odd. |
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214 this.ah = ah; |
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215 this.al = al | 1; |
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216 this.sh = sh; |
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217 this.sl = sl; |
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218 this.x0 = x0; |
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219 this.x1 = x1; |
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220 // If x0 and x1 are both zero, we must choose nonzero values. |
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221 if ((x0 | x1) == 0) { |
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222 long v = sh; |
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223 // At least one of the two values generated here will be nonzero. |
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224 this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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225 this.x1 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); |
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226 } |
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227 } |
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228 |
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229 /** |
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230 * Creates a new instance of {@link L128X128MixRandom} using the |
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231 * specified {@code long} value as the initial seed. Instances of |
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232 * {@link L128X128MixRandom} created with the same seed in the same |
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233 * program generate identical sequences of values. |
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234 * |
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235 * @param seed the initial seed |
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236 */ |
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237 public L128X128MixRandom(long seed) { |
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238 // Using a value with irregularly spaced 1-bits to xor the seed |
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239 // argument tends to improve "pedestrian" seeds such as 0 or |
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240 // other small integers. We may as well use SILVER_RATIO_64. |
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241 // |
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242 // The seed is hashed by mixMurmur64 to produce the `a` parameter. |
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243 // The seed is hashed by mixStafford13 to produce the initial `x0`, |
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244 // which will then be used to produce the first generated value. |
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245 // Then x1 is filled in as if by a SplitMix PRNG with |
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246 // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer. |
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247 this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
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248 RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64), |
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249 0, |
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250 1, |
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251 RandomSupport.mixStafford13(seed), |
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252 RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64)); |
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253 } |
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254 |
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255 /** |
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256 * Creates a new instance of {@link L128X128MixRandom} that is likely to |
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257 * generate sequences of values that are statistically independent |
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258 * of those of any other instances in the current program execution, |
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259 * but may, and typically does, vary across program invocations. |
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260 */ |
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261 public L128X128MixRandom() { |
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262 // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
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263 this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); |
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264 } |
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265 |
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266 /** |
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267 * Creates a new instance of {@link L128X128MixRandom} using the specified array of |
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268 * initial seed bytes. Instances of {@link L128X128MixRandom} created with the same |
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269 * seed array in the same program execution generate identical sequences of values. |
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270 * |
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271 * @param seed the initial seed |
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272 */ |
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273 public L128X128MixRandom(byte[] seed) { |
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274 // Convert the seed to 6 long values, of which the last 2 are not all zero. |
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275 long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2); |
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276 long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5]; |
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277 // Force a to be odd. |
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278 this.ah = ah; |
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279 this.al = al | 1; |
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280 this.sh = sh; |
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281 this.sl = sl; |
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282 this.x0 = x0; |
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283 this.x1 = x1; |
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284 } |
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285 |
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286 /* ---------------- public methods ---------------- */ |
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287 |
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288 /** |
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289 * Given 63 bits of "brine", constructs and returns a new instance of |
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290 * {@code L128X128MixRandom} that shares no mutable state with this instance. |
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291 * However, with very high probability, the set of values collectively |
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292 * generated by the two objects has the same statistical properties as if |
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293 * same the quantity of values were generated by a single thread using |
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294 * a single {@code L128X128MixRandom} object. Either or both of the two |
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295 * objects may be further split using the {@code split} method, |
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296 * and the same expected statistical properties apply to the |
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297 * entire set of generators constructed by such recursive splitting. |
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298 * |
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299 * @param source a {@code SplittableGenerator} instance to be used instead |
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300 * of this one as a source of pseudorandom bits used to |
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301 * initialize the state of the new ones. |
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302 * @param brine a long value, of which the low 63 bits are used to choose |
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303 * the {@code a} parameter for the new instance. |
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304 * @return a new instance of {@code L128X128MixRandom} |
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305 */ |
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306 public SplittableGenerator split(SplittableGenerator source, long brine) { |
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307 // Pick a new instance "at random", but use the brine for (the low half of) `a`. |
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308 return new L128X128MixRandom(source.nextLong(), brine << 1, |
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309 source.nextLong(), source.nextLong(), |
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310 source.nextLong(), source.nextLong()); |
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311 } |
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312 |
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313 /** |
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314 * Returns a pseudorandom {@code long} value. |
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315 * |
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316 * @return a pseudorandom {@code long} value |
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317 */ |
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318 public long nextLong() { |
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319 // Compute the result based on current state information |
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320 // (this allows the computation to be overlapped with state update). |
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321 final long result = RandomSupport.mixLea64(sh + x0); |
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322 |
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323 // Update the LCG subgenerator |
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324 // The LCG is, in effect, s = ((1LL << 64) + ML) * s + a, if only we had 128-bit arithmetic. |
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325 final long u = ML * sl; |
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326 // Note that Math.multiplyHigh computes the high half of the product of signed values, |
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327 // but what we need is the high half of the product of unsigned values; for this we use the |
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328 // formula "unsignedMultiplyHigh(a, b) = multiplyHigh(a, b) + ((a >> 63) & b) + ((b >> 63) & a)"; |
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329 // in effect, each operand is added to the result iff the sign bit of the other operand is 1. |
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330 // (See Henry S. Warren, Jr., _Hacker's Delight_ (Second Edition), Addison-Wesley (2013), |
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331 // Section 8-3, p. 175; or see the First Edition, Addison-Wesley (2003), Section 8-3, p. 133.) |
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332 // If Math.unsignedMultiplyHigh(long, long) is ever implemented, the following line can become: |
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333 // sh = (ML * sh) + Math.unsignedMultiplyHigh(ML, sl) + sl + ah; |
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334 // and this entire comment can be deleted. |
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335 sh = (ML * sh) + (Math.multiplyHigh(ML, sl) + ((ML >> 63) & sl) + ((sl >> 63) & ML)) + sl + ah; |
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336 sl = u + al; |
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337 if (Long.compareUnsigned(sl, u) < 0) ++sh; // Handle the carry propagation from low half to high half. |
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338 |
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339 long q0 = x0, q1 = x1; |
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340 // Update the Xorshift subgenerator |
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341 { // xoroshiro128v1_0 |
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342 q1 ^= q0; |
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343 q0 = Long.rotateLeft(q0, 24); |
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344 q0 = q0 ^ q1 ^ (q1 << 16); |
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345 q1 = Long.rotateLeft(q1, 37); |
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346 } |
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347 x0 = q0; x1 = q1; |
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348 return result; |
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349 } |
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350 |
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351 /** |
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352 * Returns the period of this random generator. |
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353 * |
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354 * @return a {@link BigInteger} whose value is the number of distinct possible states of this |
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355 * {@link RandomGenerator} object (2<sup>128</sup>(2<sup>128</sup>-1)). |
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356 */ |
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357 public BigInteger period() { |
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358 return PERIOD; |
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359 } |
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360 } |