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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 L128X128MixRandom} 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 L128X128MixRandom} 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 L128X128MixRandom} 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 L128X128MixRandom} is the {@code xoroshiro128} algorithm,
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* version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**".
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* Its state consists of two {@code long} fields {@code x0} and {@code x1},
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* which can take on any values provided that they are not both zero.
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* The period of this subgenerator is 2<sup>128</sup>-1.
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* <p>
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* The mixing function for {@link L128X128MixRandom} 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>128</sup>-1 of the two subgenerators
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* are relatively prime, the <em>period</em> of any single {@link L128X128MixRandom} 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>128</sup>-1),
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* which is just slightly smaller than 2<sup>256</sup>. Moreover, if two distinct
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* {@link L128X128MixRandom} 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 L128X128MixRandom}, 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>128</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" 2-equidistributed: all possible pairs 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 2-equidistributed.
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* <p>
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* Method {@link #split} constructs and returns a new {@link L128X128MixRandom}
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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 L128X128MixRandom} object.
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* This is because, with high probability, distinct {@link L128X128MixRandom} 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 L128X128MixRandom} 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(someL128X128MixRandom.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 L128X128MixRandom} 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 L128X128MixRandom 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 four new 64-bit
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* long values that are then used to initialize the parameter `a` and the
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* state variables `s`, `x0`, and `x1` 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 L128X128MixRandom}
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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 four 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**128 - 1) * 2**128.
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*/
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private static final BigInteger PERIOD =
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BigInteger.ONE.shiftLeft(128).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 and x1 for the xorshift.
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* At least one of x0 and x1 must be nonzero.
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*/
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private long sh, sl, x0, x1;
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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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*/
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public L128X128MixRandom(long ah, long al, long sh, long sl, long x0, long x1) {
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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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// If x0 and x1 are both zero, we must choose nonzero values.
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if ((x0 | x1) == 0) {
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long v = sh;
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// At least one of the two 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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}
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}
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/**
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* Creates a new instance of {@link L128X128MixRandom} using the
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* specified {@code long} value as the initial seed. Instances of
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* {@link L128X128MixRandom} 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 L128X128MixRandom(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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// Then x1 is 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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}
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/**
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* Creates a new instance of {@link L128X128MixRandom} 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 L128X128MixRandom() {
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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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* Creates a new instance of {@link L128X128MixRandom} using the specified array of
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* initial seed bytes. Instances of {@link L128X128MixRandom} 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 L128X128MixRandom(byte[] seed) {
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// Convert the seed to 6 long values, of which the last 2 are not all zero.
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long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2);
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long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5];
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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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}
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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
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* {@code L128X128MixRandom} that shares no mutable state with this instance.
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* However, with very high probability, the set of values collectively
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* 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 L128X128MixRandom} 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
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* 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
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* the {@code a} parameter for the new instance.
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* @return a new instance of {@code L128X128MixRandom}
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*/
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public SplittableGenerator split(SplittableGenerator source, long brine) {
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// Pick a new instance "at random", but use the brine for (the low half of) `a`.
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return new L128X128MixRandom(source.nextLong(), brine << 1,
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source.nextLong(), source.nextLong(),
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source.nextLong(), source.nextLong());
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}
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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
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// (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.
|
|
338 |
|
|
339 |
long q0 = x0, q1 = x1;
|
|
340 |
// Update the Xorshift subgenerator
|
|
341 |
{ // xoroshiro128v1_0
|
|
342 |
q1 ^= q0;
|
|
343 |
q0 = Long.rotateLeft(q0, 24);
|
|
344 |
q0 = q0 ^ q1 ^ (q1 << 16);
|
|
345 |
q1 = Long.rotateLeft(q1, 37);
|
|
346 |
}
|
|
347 |
x0 = q0; x1 = q1;
|
|
348 |
return result;
|
|
349 |
}
|
|
350 |
|
|
351 |
/**
|
|
352 |
* Returns the period of this random generator.
|
|
353 |
*
|
|
354 |
* @return a {@link BigInteger} whose value is the number of distinct possible states of this
|
|
355 |
* {@link RandomGenerator} object (2<sup>128</sup>(2<sup>128</sup>-1)).
|
|
356 |
*/
|
|
357 |
public BigInteger period() {
|
|
358 |
return PERIOD;
|
|
359 |
}
|
|
360 |
}
|