author | jlaskey |
Thu, 14 Nov 2019 08:54:56 -0400 | |
branch | JDK-8193209-branch |
changeset 59080 | 1b314be4feb2 |
parent 57684 | 7cb325557832 |
permissions | -rw-r--r-- |
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/* |
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* Copyright (c) 2013, 2019, Oracle and/or its affiliates. All rights reserved. |
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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* |
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* This code is free software; you can redistribute it and/or modify it |
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* under the terms of the GNU General Public License version 2 only, as |
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* published by the Free Software Foundation. Oracle designates this |
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* particular file as subject to the "Classpath" exception as provided |
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* by Oracle in the LICENSE file that accompanied this code. |
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* |
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* This code is distributed in the hope that it will be useful, but WITHOUT |
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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* version 2 for more details (a copy is included in the LICENSE file that |
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* accompanied this code). |
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* |
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* You should have received a copy of the GNU General Public License version |
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* 2 along with this work; if not, write to the Free Software Foundation, |
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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* |
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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* or visit www.oracle.com if you need additional information or have any |
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* questions. |
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*/ |
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package java.util.random; |
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import java.math.BigInteger; |
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import java.util.concurrent.atomic.AtomicLong; |
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import java.util.random.RandomGenerator.SplittableGenerator; |
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import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator; |
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/** |
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* A generator of uniform pseudorandom values applicable for use in |
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* (among other contexts) isolated parallel computations that may |
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* generate subtasks. Class {@link L128X256MixRandom} implements |
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* interfaces {@link RandomGenerator} and {@link SplittableGenerator}, |
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* and therefore supports methods for producing pseudorandomly chosen |
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* numbers of type {@code int}, {@code long}, {@code float}, and {@code double} |
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* as well as creating new split-off {@link L128X256MixRandom} objects, |
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* with similar usages as for class {@link java.util.SplittableRandom}. |
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* <p> |
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* Series of generated values pass the TestU01 BigCrush and PractRand test suites |
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* that measure independence and uniformity properties of random number generators. |
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* (Most recently validated with |
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* <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a> |
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* and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>. |
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* Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()} |
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* method but also the result of bit-reversing each value produced by {@code nextLong()}.) |
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* These tests validate only the methods for certain |
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* types and ranges, but similar properties are expected to hold, at |
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* least approximately, for others as well. |
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* <p> |
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* {@link L128X256MixRandom} is a specific member of the LXM family of algorithms |
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* for pseudorandom number generators. Every LXM generator consists of two |
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* subgenerators; one is an LCG (Linear Congruential Generator) and the other is |
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* an Xorshift generator. Each output of an LXM generator is the result of |
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* combining state from the LCG with state from the Xorshift generator by |
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* using a Mixing function (and then the state of the LCG and the state of the |
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* Xorshift generator are advanced). |
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* <p> |
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* The LCG subgenerator for {@link L128X256MixRandom} has an update step of the |
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* form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all |
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* 128-bit integers; {@code s} is the mutable state, the multiplier {@code m} |
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* is fixed (the same for all instances of {@link L128X256MixRandom}) and the addend |
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* {@code a} is a parameter (a final field of the instance). The parameter |
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* {@code a} is required to be odd (this allows the LCG to have the maximal |
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* period, namely 2<sup>128</sup>); therefore there are 2<sup>127</sup> distinct choices |
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* of parameter. |
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* <p> |
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* The Xorshift subgenerator for {@link L128X256MixRandom} is the {@code xoshiro256} algorithm, |
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* version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**". |
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* Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, |
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* and {@code x3}, which can take on any values provided that they are not all zero. |
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* The period of this subgenerator is 2<sup>256</sup>-1. |
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* <p> |
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* The mixing function for {@link L128X256MixRandom} is {@link RandomSupport.mixLea64} |
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* applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}. |
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* <p> |
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* Because the periods 2<sup>128</sup> and 2<sup>256</sup>-1 of the two subgenerators |
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* are relatively prime, the <em>period</em> of any single {@link L128X256MixRandom} object |
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* (the length of the series of generated 64-bit values before it repeats) is the product |
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* of the periods of the subgenerators, that is, 2<sup>128</sup>(2<sup>256</sup>-1), |
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* which is just slightly smaller than 2<sup>384</sup>. Moreover, if two distinct |
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* {@link L128X256MixRandom} objects have different {@code a} parameters, then their |
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* cycles of produced values will be different. |
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* <p> |
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* The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. |
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* For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each |
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* of the 2<sup>64</sup> possible {@code long} values will be produced |
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* 2<sup>64</sup>(2<sup>256</sup>-1) times. The values produced by the {@code nextInt()}, |
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* {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. |
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* <p> |
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* Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be |
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* "very nearly" 4-equidistributed: all possible quadruples of 64-bit values are generated, |
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* and some pairs occur more often than others, but only very slightly more often. |
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* However, this conjecture has not yet been proven mathematically. |
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* If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()}, |
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* and {@code nextDouble()} methods are likewise approximately 4-equidistributed. |
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* <p> |
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* Method {@link #split} constructs and returns a new {@link L128X256MixRandom} |
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* instance that shares no mutable state with the current instance. However, with |
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* very high probability, the values collectively generated by the two objects |
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* have the same statistical properties as if the same quantity of values were |
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* generated by a single thread using a single {@link L128X256MixRandom} object. |
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* This is because, with high probability, distinct {@link L128X256MixRandom} objects |
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* have distinct {@code a} parameters and therefore use distinct members of the |
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* algorithmic family; and even if their {@code a} parameters are the same, with |
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* very high probability they will traverse different parts of their common state |
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* cycle. |
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* <p> |
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* As with {@link java.util.SplittableRandom}, instances of |
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* {@link L128X256MixRandom} are <em>not</em> thread-safe. |
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* They are designed to be split, not shared, across threads. For |
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* example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style |
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* computation using random numbers might include a construction |
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* of the form {@code new Subtask(someL128X256MixRandom.split()).fork()}. |
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* <p> |
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* This class provides additional methods for generating random |
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* streams, that employ the above techniques when used in |
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* {@code stream.parallel()} mode. |
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* <p> |
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* Instances of {@link L128X256MixRandom} are not cryptographically |
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* secure. Consider instead using {@link java.security.SecureRandom} |
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* in security-sensitive applications. Additionally, |
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* default-constructed instances do not use a cryptographically random |
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* seed unless the {@linkplain System#getProperty system property} |
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* {@code java.util.secureRandomSeed} is set to {@code true}. |
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* |
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* @since 14 |
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*/ |
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public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator { |
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/* |
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* Implementation Overview. |
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* |
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* The 128-bit parameter `a` is represented as two long fields `ah` and `al`. |
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* The 128-bit state variable `s` is represented as two long fields `sh` and `sl`. |
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* |
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* The split operation uses the current generator to choose eight |
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* new 64-bit long values that are then used to initialize the |
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* parameters `ah` and `al` and the state variables `sh`, `sl`, |
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* `x0`, `x1`, `x2`, and `x3` for a newly constructed generator. |
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* |
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* With extremely high probability, no two generators so chosen |
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* will have the same `a` parameter, and testing has indicated |
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* that the values generated by two instances of {@link L128X256MixRandom} |
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* will be (approximately) independent if have different values for `a`. |
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* |
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* The default (no-argument) constructor, in essence, uses |
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* "defaultGen" to generate eight new 64-bit values for the same |
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* purpose. Multiple generators created in this way will certainly |
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* differ in their `a` parameters. The defaultGen state must be accessed |
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* in a thread-safe manner, so we use an AtomicLong to represent |
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* this state. To bootstrap the defaultGen, we start off using a |
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* seed based on current time unless the |
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* java.util.secureRandomSeed property is set. This serves as a |
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* slimmed-down (and insecure) variant of SecureRandom that also |
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* avoids stalls that may occur when using /dev/random. |
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* |
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* File organization: First static fields, then instance |
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* fields, then constructors, then instance methods. |
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*/ |
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/* ---------------- static fields ---------------- */ |
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/** |
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* The seed generator for default constructors. |
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*/ |
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private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); |
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/* |
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* The period of this generator, which is (2**256 - 1) * 2**128. |
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*/ |
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private static final BigInteger PERIOD = |
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BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128); |
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/* |
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* Low half of multiplier used in the LCG portion of the algorithm; |
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* the overall multiplier is (2**64 + ML). |
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* Chosen based on research by Sebastiano Vigna and Guy Steele (2019). |
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* The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL |
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* are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493]. |
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*/ |
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private static final long ML = 0xd605bbb58c8abbfdL; |
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/* ---------------- instance fields ---------------- */ |
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/** |
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* The parameter that is used as an additive constant for the LCG. |
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* Must be odd (therefore al must be odd). |
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*/ |
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private final long ah, al; |
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/** |
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* The per-instance state: sh and sl for the LCG; x0, x1, x2, and x3 for the xorshift. |
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* At least one of the four fields x0, x1, x2, and x3 must be nonzero. |
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*/ |
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private long sh, sl, x0, x1, x2, x3; |
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/* ---------------- constructors ---------------- */ |
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/** |
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* Basic constructor that initializes all fields from parameters. |
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* It then adjusts the field values if necessary to ensure that |
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* all constraints on the values of fields are met. |
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* |
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* @param ah high half of the additive parameter for the LCG |
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* @param al low half of the additive parameter for the LCG |
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* @param sh high half of the initial state for the LCG |
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* @param sl low half of the initial state for the LCG |
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* @param x0 first word of the initial state for the xorshift generator |
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* @param x1 second word of the initial state for the xorshift generator |
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* @param x2 third word of the initial state for the xorshift generator |
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* @param x3 fourth word of the initial state for the xorshift generator |
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*/ |
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public L128X256MixRandom(long ah, long al, long sh, long sl, long x0, long x1, long x2, long x3) { |
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// Force a to be odd. |
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this.ah = ah; |
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this.al = al | 1; |
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this.sh = sh; |
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this.sl = sl; |
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this.x0 = x0; |
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this.x1 = x1; |
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this.x2 = x2; |
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this.x3 = x3; |
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// If x0, x1, x2, and x3 are all zero, we must choose nonzero values. |
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if ((x0 | x1 | x2 | x3) == 0) { |
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long v = sh; |
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// At least three of the four values generated here will be nonzero. |
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this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); |
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} |
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} |
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/** |
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* Creates a new instance of {@link L128X256MixRandom} using the |
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* specified {@code long} value as the initial seed. Instances of |
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* {@link L128X256MixRandom} created with the same seed in the same |
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* program generate identical sequences of values. |
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* |
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* @param seed the initial seed |
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*/ |
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public L128X256MixRandom(long seed) { |
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// Using a value with irregularly spaced 1-bits to xor the seed |
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// argument tends to improve "pedestrian" seeds such as 0 or |
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// other small integers. We may as well use SILVER_RATIO_64. |
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// |
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// The seed is hashed by mixMurmur64 to produce the `a` parameter. |
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// The seed is hashed by mixStafford13 to produce the initial `x0`, |
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// which will then be used to produce the first generated value. |
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// The other x values are filled in as if by a SplitMix PRNG with |
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// GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer. |
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this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
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RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64), |
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0, |
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1, |
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RandomSupport.mixStafford13(seed), |
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RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
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RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64)); |
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} |
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/** |
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* Creates a new instance of {@link L128X256MixRandom} that is likely to |
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* generate sequences of values that are statistically independent |
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* of those of any other instances in the current program execution, |
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* but may, and typically does, vary across program invocations. |
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*/ |
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public L128X256MixRandom() { |
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// Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
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this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); |
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} |
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||
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/** |
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* Creates a new instance of {@link L128X256MixRandom} using the specified array of |
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* initial seed bytes. Instances of {@link L128X256MixRandom} created with the same |
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* seed array in the same program execution generate identical sequences of values. |
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* |
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* @param seed the initial seed |
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*/ |
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public L128X256MixRandom(byte[] seed) { |
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// Convert the seed to 6 long values, of which the last 4 are not all zero. |
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long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 4); |
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long ah = data[0], al = data[1], sh = data[2], sl = data[3], |
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x0 = data[4], x1 = data[5], x2 = data[6], x3 = data[7]; |
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// Force a to be odd. |
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this.ah = ah; |
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this.al = al | 1; |
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this.sh = sh; |
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this.sl = sl; |
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this.x0 = x0; |
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this.x1 = x1; |
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this.x2 = x2; |
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this.x3 = x3; |
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} |
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/* ---------------- public methods ---------------- */ |
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/** |
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* Given 63 bits of "brine", constructs and returns a new instance of |
306 |
* {@code L128X256MixRandom} that shares no mutable state with this instance. |
|
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* However, with very high probability, the set of values collectively |
308 |
* generated by the two objects has the same statistical properties as if |
|
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* same the quantity of values were generated by a single thread using |
|
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* a single {@code L128X256MixRandom} object. Either or both of the two |
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* objects may be further split using the {@code split} method, |
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* and the same expected statistical properties apply to the |
|
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* entire set of generators constructed by such recursive splitting. |
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* |
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* @param source a {@code SplittableGenerator} instance to be used instead |
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* of this one as a source of pseudorandom bits used to |
317 |
* initialize the state of the new ones. |
|
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* @param brine a long value, of which the low 63 bits are used to choose |
319 |
* the {@code a} parameter for the new instance. |
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* @return a new instance of {@code L128X256MixRandom} |
|
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*/ |
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public SplittableGenerator split(SplittableGenerator source, long brine) { |
323 |
// Pick a new instance "at random", but use the brine for (the low half of) `a`. |
|
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return new L128X256MixRandom(source.nextLong(), brine << 1, |
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source.nextLong(), source.nextLong(), |
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source.nextLong(), source.nextLong(), |
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source.nextLong(), source.nextLong()); |
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} |
329 |
||
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/** |
|
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* Returns a pseudorandom {@code long} value. |
|
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* |
|
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* @return a pseudorandom {@code long} value |
|
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*/ |
|
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public long nextLong() { |
|
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// Compute the result based on current state information |
337 |
// (this allows the computation to be overlapped with state update). |
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final long result = RandomSupport.mixLea64(sh + x0); |
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// Update the LCG subgenerator |
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// The LCG is, in effect, s = ((1LL << 64) + ML) * s + a, if only we had 128-bit arithmetic. |
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final long u = ML * sl; |
|
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// Note that Math.multiplyHigh computes the high half of the product of signed values, |
|
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// but what we need is the high half of the product of unsigned values; for this we use the |
|
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// formula "unsignedMultiplyHigh(a, b) = multiplyHigh(a, b) + ((a >> 63) & b) + ((b >> 63) & a)"; |
|
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// in effect, each operand is added to the result iff the sign bit of the other operand is 1. |
|
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// (See Henry S. Warren, Jr., _Hacker's Delight_ (Second Edition), Addison-Wesley (2013), |
|
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// Section 8-3, p. 175; or see the First Edition, Addison-Wesley (2003), Section 8-3, p. 133.) |
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// If Math.unsignedMultiplyHigh(long, long) is ever implemented, the following line can become: |
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// sh = (ML * sh) + Math.unsignedMultiplyHigh(ML, sl) + sl + ah; |
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// and this entire comment can be deleted. |
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sh = (ML * sh) + (Math.multiplyHigh(ML, sl) + ((ML >> 63) & sl) + ((sl >> 63) & ML)) + sl + ah; |
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sl = u + al; |
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if (Long.compareUnsigned(sl, u) < 0) ++sh; // Handle the carry propagation from low half to high half. |
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// Update the Xorshift subgenerator |
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long q0 = x0, q1 = x1, q2 = x2, q3 = x3; |
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{ // xoshiro256 1.0 |
359 |
long t = q1 << 17; |
|
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q2 ^= q0; |
|
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q3 ^= q1; |
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q1 ^= q2; |
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q0 ^= q3; |
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q2 ^= t; |
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q3 = Long.rotateLeft(q3, 45); |
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} |
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x0 = q0; x1 = q1; x2 = q2; x3 = q3; |
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return result; |
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} |
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||
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/** |
372 |
* Returns the period of this random generator. |
|
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* |
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* @return a {@link BigInteger} whose value is the number of distinct possible states of this |
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* {@link RandomGenerator} object (2<sup>128</sup>(2<sup>256</sup>-1)). |
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*/ |
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public BigInteger period() { |
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return PERIOD; |
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} |
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} |