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.AbstractSplittableGenerator; |
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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 L64X1024Random} 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 L64X1024Random} 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 L64X1024Random} 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 sum of one |
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58 * output from each subgenerator, possibly processed by a final mixing function |
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59 * (but {@link L64X1024Random} does not use a mixing function). |
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60 * <p> |
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61 * The LCG subgenerator for {@link L64X1024Random} has an update step of the |
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62 * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all |
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63 * of type {@code long}; {@code s} is the mutable state, the multiplier {@code m} |
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64 * is fixed (the same for all instances of {@link L64X1024Random}) and the addend |
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65 * {@code a} is a parameter (a final field of the instance). The parameter |
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66 * {@code a} is required to be odd (this allows the LCG to have the maximal |
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67 * period, namely 2<sup>64</sup>); therefore there are 2<sup>63</sup> distinct choices |
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68 * of parameter. |
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69 * <p> |
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70 * The Xorshift subgenerator for {@link L64X1024Random} is the {@code xoroshiro1024} |
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71 * algorithm (parameters 25, 27, and 36), without any final scrambler such as "+" or "**". |
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72 * Its state consists of an array {@code x} of sixteen {@code long} values, |
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73 * which can take on any values provided that they are not all zero. |
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74 * The period of this subgenerator is 2<sup>1024</sup>-1. |
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75 * <p> |
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76 * Because the periods 2<sup>64</sup> and 2<sup>1024</sup>-1 of the two subgenerators |
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77 * are relatively prime, the <em>period</em> of any single {@link L64X1024Random} object |
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78 * (the length of the series of generated 64-bit values before it repeats) is the product |
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79 * of the periods of the subgenerators, that is, 2<sup>64</sup>(2<sup>1024</sup>-1), |
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80 * which is just slightly smaller than 2<sup>1088</sup>. Moreover, if two distinct |
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81 * {@link L64X1024Random} objects have different {@code a} parameters, then their |
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82 * cycles of produced values will be different. |
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83 * <p> |
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84 * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. |
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85 * For any specific instance of {@link L64X1024Random}, over the course of its cycle each |
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86 * of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>1024</sup>-1 times. |
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87 * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
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88 * methods are likewise exactly equidistributed. |
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89 * <p> |
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90 * In fact, the 64-bit values produced by the {@code nextLong()} method are 16-equidistributed. |
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91 * To be precise: for any specific instance of {@link L64X1024Random}, consider |
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92 * the (overlapping) length-16 subsequences of the cycle of 64-bit values produced by |
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93 * {@code nextLong()} (assuming no other methods are called that would affect the state). |
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94 * There are 2<sup>64</sup>(2<sup>1024</sup>-1) such subsequences, and each subsequence, |
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95 * which consists of 16 64-bit values, can have one of 2<sup>1024</sup> values. Of those |
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96 * 2<sup>1024</sup> subsequence values, nearly all of them (2<sup>1024</sup>-2<sup>64</sup>) |
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97 * occur 2<sup>64</sup> times over the course of the entire cycle, and the other |
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98 * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times. So the ratio |
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99 * of the probability of getting one of the less common subsequence values and the |
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100 * probability of getting one of the more common subsequence values is 1-2<sup>-64</sup>. |
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101 * (Note that the set of 2<sup>64</sup> less-common subsequence values will differ from |
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102 * one instance of {@link L64X1024Random} to another, as a function of the additive |
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103 * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, |
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104 * and {@code nextDouble()} methods are likewise 16-equidistributed. |
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105 * <p> |
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106 * Method {@link #split} constructs and returns a new {@link L64X1024Random} |
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107 * instance that shares no mutable state with the current instance. However, with |
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108 * very high probability, the values collectively generated by the two objects |
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109 * have the same statistical properties as if the same quantity of values were |
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110 * generated by a single thread using a single {@link L64X1024Random} object. |
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111 * This is because, with high probability, distinct {@link L64X1024Random} objects |
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112 * have distinct {@code a} parameters and therefore use distinct members of the |
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113 * algorithmic family; and even if their {@code a} parameters are the same, with |
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114 * very high probability they will traverse different parts of their common state |
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115 * cycle. |
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116 * <p> |
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117 * As with {@link java.util.SplittableRandom}, instances of |
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118 * {@link L64X1024Random} are <em>not</em> thread-safe. |
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119 * They are designed to be split, not shared, across threads. For |
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120 * example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style |
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121 * computation using random numbers might include a construction |
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122 * of the form {@code new Subtask(someL64X1024Random.split()).fork()}. |
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123 * <p> |
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124 * This class provides additional methods for generating random |
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125 * streams, that employ the above techniques when used in |
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126 * {@code stream.parallel()} mode. |
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127 * <p> |
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128 * Instances of {@link L64X1024Random} are not cryptographically |
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129 * secure. Consider instead using {@link java.security.SecureRandom} |
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130 * in security-sensitive applications. Additionally, |
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131 * default-constructed instances do not use a cryptographically random |
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132 * seed unless the {@linkplain System#getProperty system property} |
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133 * {@code java.util.secureRandomSeed} is set to {@code true}. |
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134 * |
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135 * @since 14 |
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136 */ |
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137 public final class L64X1024Random extends AbstractSplittableGenerator { |
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138 |
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139 /* |
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140 * Implementation Overview. |
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141 * |
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142 * The split() operation uses the current generator to choose 18 new 64-bit |
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143 * long values that are then used to initialize the parameter `a`, the |
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144 * state variable `s`, 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 L64X1024Random} |
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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 18 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**64. |
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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(64); |
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184 |
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185 /* |
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186 * Multiplier used in the LCG portion of the algorithm, taken from |
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187 * Pierre L'Ecuyer, Tables of linear congruential generators of |
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188 * different sizes and good lattice structure, <em>Mathematics of |
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189 * Computation</em> 68, 225 (January 1999), pages 249-260, |
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190 * Table 4 (first multiplier for size 2<sup>64</sup>). |
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191 */ |
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192 |
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193 private static final long M = 2862933555777941757L; |
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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. |
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200 */ |
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201 private final long a; |
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202 |
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203 /** |
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204 * The per-instance state: s 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 s; |
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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 a additive parameter for the LCG |
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220 * @param s initial state for the LCG |
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221 * @param x0 first word of the initial state for the xorshift generator |
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222 * @param x1 second word of the initial state for the xorshift generator |
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223 * @param x2 third word of the initial state for the xorshift generator |
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224 * @param x3 fourth word of the initial state for the xorshift generator |
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225 * @param x4 fifth word of the initial state for the xorshift generator |
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226 * @param x5 sixth word of the initial state for the xorshift generator |
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227 * @param x6 seventh word of the initial state for the xorshift generator |
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228 * @param x7 eight word of the initial state for the xorshift generator |
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229 * @param x8 ninth word of the initial state for the xorshift generator |
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230 * @param x9 tenth word of the initial state for the xorshift generator |
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231 * @param x10 eleventh word of the initial state for the xorshift generator |
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232 * @param x11 twelfth word of the initial state for the xorshift generator |
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233 * @param x12 thirteenth word of the initial state for the xorshift generator |
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234 * @param x13 fourteenth word of the initial state for the xorshift generator |
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235 * @param x14 fifteenth word of the initial state for the xorshift generator |
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236 * @param x15 sixteenth word of the initial state for the xorshift generator |
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237 */ |
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238 public L64X1024Random(long a, long s, |
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239 long x0, long x1, long x2, long x3, |
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240 long x4, long x5, long x6, long x7, |
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241 long x8, long x9, long x10, long x11, |
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242 long x12, long x13, long x14, long x15) { |
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243 // Force a to be odd. |
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244 this.a = a | 1; |
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245 this.s = s; |
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246 this.x = new long[N]; |
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247 this.x[0] = x0; |
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248 this.x[1] = x1; |
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249 this.x[2] = x2; |
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250 this.x[3] = x3; |
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251 this.x[4] = x4; |
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252 this.x[5] = x5; |
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253 this.x[6] = x6; |
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254 this.x[7] = x7; |
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255 this.x[8] = x8; |
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256 this.x[9] = x9; |
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257 this.x[10] = x10; |
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258 this.x[11] = x11; |
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259 this.x[12] = x12; |
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260 this.x[13] = x13; |
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261 this.x[14] = x14; |
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262 this.x[15] = x15; |
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263 // If x0, x1, ..., x15 are all zero (very unlikely), we must choose nonzero values. |
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264 if ((x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15) == 0) { |
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265 for (int j = 0; j < N; j++) { |
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266 this.x[j] = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64); |
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267 } |
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268 } |
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269 } |
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270 |
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271 /** |
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272 * Creates a new instance of {@link L64X1024Random} using the |
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273 * specified {@code long} value as the initial seed. Instances of |
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274 * {@link L64X1024Random} created with the same seed in the same |
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275 * program execution generate identical sequences of values. |
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276 * |
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277 * @param seed the initial seed |
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278 */ |
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279 public L64X1024Random(long seed) { |
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280 // Using a value with irregularly spaced 1-bits to xor the seed |
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281 // argument tends to improve "pedestrian" seeds such as 0 or |
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282 // other small integers. We may as well use SILVER_RATIO_64. |
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283 // |
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284 // The seed is hashed by mixMurmur64 to produce the `a` parameter. |
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285 // The seed is hashed by mixStafford13 to produce the initial `x[0]`, |
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286 // which will then be used to produce the first generated value. |
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287 // The other x values are filled in as if by a SplitMix PRNG with |
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288 // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer. |
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289 this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
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290 1, |
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291 RandomSupport.mixStafford13(seed), |
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292 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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293 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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294 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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295 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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296 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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297 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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298 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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299 RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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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 } |
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308 |
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309 /** |
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310 * Creates a new instance of {@link L64X1024Random} that is likely to |
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311 * generate sequences of values that are statistically independent |
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312 * of those of any other instances in the current program execution, |
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313 * but may, and typically does, vary across program invocations. |
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314 */ |
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315 public L64X1024Random() { |
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316 // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
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317 this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); |
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318 } |
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319 |
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320 /** |
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321 * Creates a new instance of {@link L64X1024Random} using the specified array of |
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322 * initial seed bytes. Instances of {@link L64X1024Random} created with the same |
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323 * seed array in the same program execution generate identical sequences of values. |
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324 * |
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325 * @param seed the initial seed |
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326 */ |
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327 public L64X1024Random(byte[] seed) { |
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328 // Convert the seed to 18 long values, of which the last 16 are not all zero. |
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329 long[] data = RandomSupport.convertSeedBytesToLongs(seed, 18, 16); |
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330 long a = data[0], s = data[1]; |
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331 // Force a to be odd. |
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332 this.a = a | 1; |
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333 this.s = s; |
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334 this.x = new long[N]; |
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335 for (int j = 0; j < N; j++) { |
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336 this.x[j] = data[2+j]; |
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337 } |
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338 } |
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339 |
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340 /* ---------------- public methods ---------------- */ |
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341 |
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342 /** |
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343 * Constructs and returns a new instance of {@link L64X1024Random} |
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344 * that shares no mutable state with this instance. |
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345 * However, with very high probability, the set of values collectively |
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346 * generated by the two objects has the same statistical properties as if |
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347 * same the quantity of values were generated by a single thread using |
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348 * a single {@link L64X1024Random} object. Either or both of the two |
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349 * objects may be further split using the {@code split} method, |
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350 * and the same expected statistical properties apply to the |
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351 * entire set of generators constructed by such recursive splitting. |
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352 * |
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353 * @param source a {@link SplittableGenerator} instance to be used instead |
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354 * of this one as a source of pseudorandom bits used to |
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355 * initialize the state of the new ones. |
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356 * @return a new instance of {@link L64X1024Random} |
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357 */ |
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358 public L64X1024Random split(SplittableGenerator source) { |
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359 // Literally pick a new instance "at random". |
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360 return new L64X1024Random(source.nextLong(), source.nextLong(), |
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361 source.nextLong(), source.nextLong(), |
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362 source.nextLong(), source.nextLong(), |
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363 source.nextLong(), source.nextLong(), |
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364 source.nextLong(), source.nextLong(), |
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365 source.nextLong(), source.nextLong(), |
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366 source.nextLong(), source.nextLong(), |
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367 source.nextLong(), source.nextLong(), |
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368 source.nextLong(), source.nextLong()); |
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369 } |
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370 |
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371 /** |
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372 * Returns a pseudorandom {@code long} value. |
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373 * |
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374 * @return a pseudorandom {@code long} value |
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375 */ |
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376 public long nextLong() { |
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377 // First part of xoroshiro1024: fetch array data |
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378 final int q = p; |
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379 final long s0 = x[p = (p + 1) & (N - 1)]; |
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380 long s15 = x[q]; |
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381 |
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382 final long z = s + s0; |
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383 s = M * s + a; // LCG |
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384 |
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385 // Second part of xoroshiro1024: update array data |
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386 s15 ^= s0; |
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387 x[q] = Long.rotateLeft(s0, 25) ^ s15 ^ (s15 << 27); |
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388 x[p] = Long.rotateLeft(s15, 36); |
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389 |
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390 return z; |
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391 } |
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392 |
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393 public BigInteger period() { |
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394 return PERIOD; |
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395 } |
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396 } |
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