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 L64X1024MixRandom} 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 L64X1024MixRandom} 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 L64X1024MixRandom} 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 L64X1024MixRandom} 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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* of type {@code long}; {@code s} is the mutable state, the multiplier {@code m} |
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* is fixed (the same for all instances of {@link L64X1024MixRandom}) 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>64</sup>); therefore there are 2<sup>63</sup> distinct choices |
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* of parameter. |
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* <p> |
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* The Xorshift subgenerator for {@link L64X1024MixRandom} is the {@code xoroshiro1024} |
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* algorithm (parameters 25, 27, and 36), without any final scrambler such as "+" or "**". |
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* Its state consists of an array {@code x} of sixteen {@code long} values, |
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* 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>1024</sup>-1. |
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* <p> |
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* The mixing function for {@link L64X1024MixRandom} is {@link RandomSupport.mixLea64} |
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* applied to the argument {@code (s + s0)}, where {@code s0} is the most recently computed |
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* element of {@code x}. |
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* <p> |
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* Because the periods 2<sup>64</sup> and 2<sup>1024</sup>-1 of the two subgenerators |
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* are relatively prime, the <em>period</em> of any single {@link L64X1024MixRandom} 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>64</sup>(2<sup>1024</sup>-1), |
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* which is just slightly smaller than 2<sup>1088</sup>. Moreover, if two distinct |
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* {@link L64X1024MixRandom} 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 L64X1024MixRandom}, over the course of its cycle each |
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* of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>1024</sup>-1 times. |
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* The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} |
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* methods are likewise exactly equidistributed. |
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* <p> |
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* In fact, the 64-bit values produced by the {@code nextLong()} method are 16-equidistributed. |
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* To be precise: for any specific instance of {@link L64X1024MixRandom}, consider |
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* the (overlapping) length-16 subsequences of the cycle of 64-bit values produced by |
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* {@code nextLong()} (assuming no other methods are called that would affect the state). |
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* There are 2<sup>64</sup>(2<sup>1024</sup>-1) such subsequences, and each subsequence, |
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* which consists of 16 64-bit values, can have one of 2<sup>1024</sup> values. Of those |
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* 2<sup>1024</sup> subsequence values, nearly all of them (2<sup>1024</sup>-2<sup>64</sup>) |
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* occur 2<sup>64</sup> times over the course of the entire cycle, and the other |
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* 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times. So the ratio |
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* of the probability of getting any specific one of the less common subsequence values and the |
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* probability of getting any specific one of the more common subsequence values is 1-2<sup>-64</sup>. |
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* (Note that the set of 2<sup>64</sup> less-common subsequence values will differ from |
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* one instance of {@link L64X1024MixRandom} to another, as a function of the additive |
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* parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, |
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* and {@code nextDouble()} methods are likewise 16-equidistributed. |
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* <p> |
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* Method {@link #split} constructs and returns a new {@link L64X1024MixRandom} |
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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 L64X1024MixRandom} object. |
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* This is because, with high probability, distinct {@link L64X1024MixRandom} 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 L64X1024MixRandom} 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(someL64X1024MixRandom.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 L64X1024MixRandom} 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 L64X1024MixRandom extends AbstractSplittableWithBrineGenerator { |
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/* |
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* Implementation Overview. |
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* |
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* The split() operation uses the current generator to choose 18 new 64-bit |
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* long values that are then used to initialize the parameter `a`, the |
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* state variable `s`, and the array `x` 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 L64X1024MixRandom} |
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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 18 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 length of the array x. |
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*/ |
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private static final int N = 16; |
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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**1024 - 1) * 2**64. |
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*/ |
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private static final BigInteger PERIOD = |
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BigInteger.ONE.shiftLeft(N*64).subtract(BigInteger.ONE).shiftLeft(64); |
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/* |
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* Multiplier used in the LCG portion of the algorithm. |
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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 0xd1342543de82ef95 |
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* are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215]. |
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*/ |
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private static final long M = 0xd1342543de82ef95L; |
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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. |
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*/ |
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private final long a; |
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/** |
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* The per-instance state: s for the LCG; the array x for the xorshift; |
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* p is the rotating pointer into the array x. |
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* At least one of the 16 elements of the array x must be nonzero. |
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*/ |
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private long s; |
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private final long[] x; |
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private int p = N - 1; |
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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 a additive parameter for the LCG |
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* @param s 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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* @param x4 fifth word of the initial state for the xorshift generator |
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* @param x5 sixth word of the initial state for the xorshift generator |
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* @param x6 seventh word of the initial state for the xorshift generator |
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* @param x7 eight word of the initial state for the xorshift generator |
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* @param x8 ninth word of the initial state for the xorshift generator |
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* @param x9 tenth word of the initial state for the xorshift generator |
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* @param x10 eleventh word of the initial state for the xorshift generator |
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* @param x11 twelfth word of the initial state for the xorshift generator |
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* @param x12 thirteenth word of the initial state for the xorshift generator |
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* @param x13 fourteenth word of the initial state for the xorshift generator |
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* @param x14 fifteenth word of the initial state for the xorshift generator |
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* @param x15 sixteenth word of the initial state for the xorshift generator |
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*/ |
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public L64X1024MixRandom(long a, long s, |
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long x0, long x1, long x2, long x3, |
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long x4, long x5, long x6, long x7, |
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long x8, long x9, long x10, long x11, |
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long x12, long x13, long x14, long x15) { |
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// Force a to be odd. |
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this.a = a | 1; |
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this.s = s; |
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this.x = new long[N]; |
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this.x[0] = x0; |
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this.x[1] = x1; |
57388 | 253 |
this.x[2] = x2; |
254 |
this.x[3] = x3; |
|
255 |
this.x[4] = x4; |
|
256 |
this.x[5] = x5; |
|
257 |
this.x[6] = x6; |
|
258 |
this.x[7] = x7; |
|
259 |
this.x[8] = x8; |
|
260 |
this.x[9] = x9; |
|
261 |
this.x[10] = x10; |
|
262 |
this.x[11] = x11; |
|
263 |
this.x[12] = x12; |
|
264 |
this.x[13] = x13; |
|
265 |
this.x[14] = x14; |
|
266 |
this.x[15] = x15; |
|
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// If x0, x1, ..., x15 are all zero (very unlikely), we must choose nonzero values. |
57388 | 268 |
if ((x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15) == 0) { |
59080 | 269 |
long v = s; |
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// At least fifteen of the sixteen values generated here will be nonzero. |
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for (int j = 0; j < N; j++) { |
59080 | 272 |
this.x[j] = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); |
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273 |
} |
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274 |
} |
57388 | 275 |
} |
276 |
||
277 |
/** |
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* Creates a new instance of {@link L64X1024MixRandom} using the |
57388 | 279 |
* specified {@code long} value as the initial seed. Instances of |
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280 |
* {@link L64X1024MixRandom} created with the same seed in the same |
57388 | 281 |
* program execution generate identical sequences of values. |
282 |
* |
|
283 |
* @param seed the initial seed |
|
284 |
*/ |
|
285 |
public L64X1024MixRandom(long seed) { |
|
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286 |
// Using a value with irregularly spaced 1-bits to xor the seed |
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287 |
// argument tends to improve "pedestrian" seeds such as 0 or |
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288 |
// other small integers. We may as well use SILVER_RATIO_64. |
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289 |
// |
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290 |
// The seed is hashed by mixMurmur64 to produce the `a` parameter. |
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291 |
// The seed is hashed by mixStafford13 to produce the initial `x[0]`, |
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292 |
// which will then be used to produce the first generated value. |
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// The other x values are filled in as if by a SplitMix PRNG with |
59080 | 294 |
// GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer. |
57547 | 295 |
this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), |
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296 |
1, |
57547 | 297 |
RandomSupport.mixStafford13(seed), |
298 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
299 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
300 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
301 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
302 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
303 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
304 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
305 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
306 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
307 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
308 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
309 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
310 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
311 |
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64), |
|
312 |
RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64)); |
|
57388 | 313 |
} |
314 |
||
315 |
/** |
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316 |
* Creates a new instance of {@link L64X1024MixRandom} that is likely to |
57388 | 317 |
* generate sequences of values that are statistically independent |
318 |
* of those of any other instances in the current program execution, |
|
319 |
* but may, and typically does, vary across program invocations. |
|
320 |
*/ |
|
321 |
public L64X1024MixRandom() { |
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// Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. |
57547 | 323 |
this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); |
57388 | 324 |
} |
325 |
||
326 |
/** |
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327 |
* Creates a new instance of {@link L64X1024MixRandom} using the specified array of |
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328 |
* initial seed bytes. Instances of {@link L64X1024MixRandom} created with the same |
57388 | 329 |
* seed array in the same program execution generate identical sequences of values. |
330 |
* |
|
331 |
* @param seed the initial seed |
|
332 |
*/ |
|
333 |
public L64X1024MixRandom(byte[] seed) { |
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334 |
// Convert the seed to 18 long values, of which the last 16 are not all zero. |
57547 | 335 |
long[] data = RandomSupport.convertSeedBytesToLongs(seed, 18, 16); |
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336 |
long a = data[0], s = data[1]; |
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337 |
// Force a to be odd. |
57388 | 338 |
this.a = a | 1; |
339 |
this.s = s; |
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340 |
this.x = new long[N]; |
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341 |
for (int j = 0; j < N; j++) { |
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342 |
this.x[j] = data[2+j]; |
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343 |
} |
57388 | 344 |
} |
345 |
||
346 |
/* ---------------- public methods ---------------- */ |
|
347 |
/** |
|
59080 | 348 |
* Given 63 bits of "brine", constructs and returns a new instance of |
349 |
* {@code L64X1024MixRandom} that shares no mutable state with this instance. |
|
57388 | 350 |
* However, with very high probability, the set of values collectively |
351 |
* generated by the two objects has the same statistical properties as if |
|
352 |
* same the quantity of values were generated by a single thread using |
|
59080 | 353 |
* a single {@code L64X1024MixRandom} object. Either or both of the two |
57388 | 354 |
* objects may be further split using the {@code split} method, |
355 |
* and the same expected statistical properties apply to the |
|
356 |
* entire set of generators constructed by such recursive splitting. |
|
357 |
* |
|
59080 | 358 |
* @param source a {@code SplittableGenerator} instance to be used instead |
57388 | 359 |
* of this one as a source of pseudorandom bits used to |
360 |
* initialize the state of the new ones. |
|
59080 | 361 |
* @param brine a long value, of which the low 63 bits are used to choose |
362 |
* the {@code a} parameter for the new instance. |
|
363 |
* @return a new instance of {@code L64X1024MixRandom} |
|
57388 | 364 |
*/ |
59080 | 365 |
public SplittableGenerator split(SplittableGenerator source, long brine) { |
366 |
// Pick a new instance "at random", but use the brine for `a`. |
|
367 |
return new L64X1024MixRandom(brine << 1, source.nextLong(), |
|
368 |
source.nextLong(), source.nextLong(), |
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369 |
source.nextLong(), source.nextLong(), |
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370 |
source.nextLong(), source.nextLong(), |
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371 |
source.nextLong(), source.nextLong(), |
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372 |
source.nextLong(), source.nextLong(), |
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373 |
source.nextLong(), source.nextLong(), |
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374 |
source.nextLong(), source.nextLong(), |
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375 |
source.nextLong(), source.nextLong()); |
57388 | 376 |
} |
377 |
||
378 |
/** |
|
379 |
* Returns a pseudorandom {@code long} value. |
|
380 |
* |
|
381 |
* @return a pseudorandom {@code long} value |
|
382 |
*/ |
|
383 |
public long nextLong() { |
|
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384 |
// First part of xoroshiro1024: fetch array data |
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385 |
final int q = p; |
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386 |
final long s0 = x[p = (p + 1) & (N - 1)]; |
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387 |
long s15 = x[q]; |
57388 | 388 |
|
59080 | 389 |
// Compute the result based on current state information |
390 |
// (this allows the computation to be overlapped with state update). |
|
391 |
||
392 |
final long result = RandomSupport.mixLea64(s + s0); |
|
393 |
||
394 |
// Update the LCG subgenerator |
|
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395 |
s = M * s + a; // LCG |
57388 | 396 |
|
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397 |
// Second part of xoroshiro1024: update array data |
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398 |
s15 ^= s0; |
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399 |
x[q] = Long.rotateLeft(s0, 25) ^ s15 ^ (s15 << 27); |
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400 |
x[p] = Long.rotateLeft(s15, 36); |
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|
401 |
|
59080 | 402 |
return result; |
57388 | 403 |
} |
404 |
||
59080 | 405 |
/** |
406 |
* Returns the period of this random generator. |
|
407 |
* |
|
408 |
* @return a {@link BigInteger} whose value is the number of distinct possible states of this |
|
409 |
* {@link RandomGenerator} object (2<sup>64</sup>(2<sup>1024</sup>-1)). |
|
410 |
*/ |
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411 |
public BigInteger period() { |
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412 |
return PERIOD; |
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413 |
} |
57388 | 414 |
} |