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/*
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* Copyright (c) 2016, 2019, Oracle and/or its affiliates. All rights reserved.
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* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*
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*/
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// package java.util;
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import java.math.BigInteger;
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import java.util.concurrent.atomic.AtomicLong;
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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 {@code L32X64MixRandom} implements
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* interfaces {@link java.util.Rng} and {@link java.util.SplittableRng},
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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 {@code L32X64MixRandom} objects,
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* with similar usages as for class {@link java.util.SplittableRandom}.
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*
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* <p>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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*
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* <p>{@code L32X64MixRandom} 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 sum of one
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* output from each subgenerator, possibly processed by a final mixing function
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* (and {@code L32X64MixRandom} does use a mixing function).
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*
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* <p>The LCG subgenerator for {@code L32X64MixRandom} 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 int}; {@code s} is the mutable state, the multiplier {@code m}
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* is fixed (the same for all instances of {@code L32X64MixRandom}}) 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>32</sup>); therefore there are 2<sup>31</sup> distinct choices
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* of parameter.
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*
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* <p>The Xorshift subgenerator for {@code L32X64MixRandom} is the {@code xoroshiro64} algorithm,
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* version 1.0 (parameters 26, 9, 13), without any final scrambler such as "+" or "**".
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* Its state consists of two {@code int} 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>64</sup>-1.
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*
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* <p> The mixing function for {@code L32X64MixRandom} is the "starstar" mixing function.
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*
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* <p> Because the periods 2<sup>32</sup> and 2<sup>64</sup>-1 of the two subgenerators
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* are relatively prime, the <em>period</em> of any single {@code L32X64MixRandom} object
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* (the length of the series of generated 32-bit values before it repeats) is the product
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* of the periods of the subgenerators, that is, 2<sup>32</sup>(2<sup>64</sup>-1),
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* which is just slightly smaller than 2<sup>96</sup>. Moreover, if two distinct
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* {@code L32X64MixRandom} objects have different {@code a} parameters, then their
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* cycles of produced values will be different.
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*
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* <p>The 32-bit values produced by the {@code nextInt()} method are exactly equidistributed.
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* For any specific instance of {@code L32X64MixRandom}, over the course of its cycle each
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* of the 2<sup>32</sup> possible {@code int} values will be produced 2<sup>64</sup>-1 times.
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* The values produced by the {@code nextFloat()} method are likewise exactly equidistributed.
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*
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* <p>In fact, the 32-bit values produced by the {@code nextInt()} method are 2-equidistributed.
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* To be precise: for any specific instance of {@code L32X64MixRandom}, consider
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* the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by
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* {@code nextInt()} (assuming no other methods are called that would affect the state).
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* There are 2<sup>32</sup>(2<sup>64</sup>-1) such subsequences, and each subsequence,
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* which consists of 2 32-bit values, can have one of 2<sup>64</sup> values. Of those
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* 2<sup>64</sup> subsequence values, nearly all of them (2<sup>64</sup>-2<sup>32</sup>)
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* occur 2<sup>32</sup> times over the course of the entire cycle, and the other
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* 2<sup>32</sup> subsequence values occur only 2<sup>32</sup>-1 times. So the ratio
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* of the probability of getting one of the less common subsequence values and the
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* probability of getting one of the more common subsequence values is 1-2<sup>-32</sup>.
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* (Note that the set of 2<sup>32</sup> less-common subsequence values will differ from
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* one instance of {@code L32X64MixRandom} to another, as a function of the additive
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* parameter of the LCG.) As a consequence, the values produced by the {@code nextFloat()}
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* method are likewise 2-equidistributed, and the values produced by the {@code nextLong()}
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* and {@code nextDouble()} methods are equidistributed (but not 2-equidistributed).
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*
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* <p>Method {@link #split} constructs and returns a new {@code L32X64MixRandom}
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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 {@code L32X64MixRandom} object.
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* This is because, with high probability, distinct {@code L32X64MixRandom} 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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*
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* <p>As with {@link java.util.SplittableRandom}, instances of
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* {@code L32X64MixRandom} 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(someL32X64MixRandom.split()).fork()}.
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*
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* <p>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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*
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* <p>Instances of {@code L32X64MixRandom} 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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* @author Guy Steele
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* @since 1.9
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*/
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public final class L32X64MixRandom extends AbstractSplittableRng {
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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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* int 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 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 {@code L32X64MixRandom}
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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 32-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(RngSupport.initialSeed());
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/*
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* The period of this generator, which is (2**64 - 1) * 2**32.
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*/
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private static final BigInteger thePeriod =
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BigInteger.ONE.shiftLeft(64).subtract(BigInteger.ONE).shiftLeft(32);
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/*
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* Multiplier used in the LCG portion of the algorithm, taken from
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* Pierre L'Ecuyer, Tables of linear congruential generators of
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* different sizes and good lattice structure, <em>Mathematics of
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* Computation</em> 68, 225 (January 1999), pages 249–260,
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* Table 4 (third multiplier for size 2<sup>32</sup>).
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*/
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private static final int m = 32310901;
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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 int a;
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/**
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* The per-instance state: s 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 int s, 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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public L32X64MixRandom(int a, int s, int x0, int x1) {
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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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// If x0 and x1 are both zero, we must choose nonzero values.
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if ((x0 | x1) == 0) {
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// At least one of the two values generated here will be nonzero.
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this.x0 = RngSupport.mixMurmur32(s += RngSupport.GOLDEN_RATIO_32);
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this.x1 = RngSupport.mixMurmur32(s + RngSupport.GOLDEN_RATIO_32);
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}
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}
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/**
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* Creates a new instance of {@code L32X64MixRandom} using the
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* specified {@code long} value as the initial seed. Instances of
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* {@code L32X64MixRandom} 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 L32X64MixRandom(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 high half of the seed is hashed by mixMurmur32 to produce the `a` parameter.
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// The low half of the seed is hashed by mixMurmur32 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_32 as the gamma value and Murmur32 as the mixer.
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this(RngSupport.mixMurmur32((int)((seed ^= RngSupport.SILVER_RATIO_64) >>> 32)),
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1,
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RngSupport.mixLea32((int)(seed)),
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RngSupport.mixLea32((int)(seed) + RngSupport.GOLDEN_RATIO_32));
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}
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/**
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* Creates a new instance of {@code L32X64MixRandom} 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 L32X64MixRandom() {
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// Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.
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this(defaultGen.getAndAdd(RngSupport.GOLDEN_RATIO_64));
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}
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/**
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* Creates a new instance of {@code L32X64MixRandom} using the specified array of
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* initial seed bytes. Instances of {@code L32X64MixRandom} 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 L32X64MixRandom(byte[] seed) {
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// Convert the seed to 4 int values, of which the last 2 are not all zero.
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int[] data = RngSupport.convertSeedBytesToInts(seed, 4, 2);
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int a = data[0], s = data[1], x0 = data[2], x1 = data[3];
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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.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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* Constructs and returns a new instance of {@code L32X64MixRandom}
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* 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 L32X64MixRandom} 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 SplittableRng} 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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* @return a new instance of {@code L32X64MixRandom}
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*/
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public L32X64MixRandom split(SplittableRng source) {
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// Literally pick a new instance "at random".
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return new L32X64MixRandom(source.nextInt(), source.nextInt(),
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source.nextInt(), source.nextInt());
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}
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/**
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* Returns a pseudorandom {@code int} value.
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*
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* @return a pseudorandom {@code int} value
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*/
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public int nextInt() {
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final int z = s + x0;
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s = m * s + a; // LCG
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int q0 = x0, q1 = x1;
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{ q1 ^= q0; q0 = Integer.rotateLeft(q0, 26); q0 = q0 ^ q1 ^ (q1 << 9); q1 = Integer.rotateLeft(q1, 13); } // xoroshiro64
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x0 = q0; x1 = q1;
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return Integer.rotateLeft(z * 5, 7) * 9; // "starstar" mixing function
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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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return ((long)(nextInt()) << 32) | nextInt();
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}
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public BigInteger period() { return thePeriod; }
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}
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