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+++ b/newrandom/L32X64MixRandom.java Thu May 23 16:45:56 2019 -0400
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+/*
+ * Copyright (c) 2016, 2019, Oracle and/or its affiliates. All rights reserved.
+ * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ */
+
+// package java.util;
+
+import java.math.BigInteger;
+import java.util.concurrent.atomic.AtomicLong;
+
+/**
+ * A generator of uniform pseudorandom values applicable for use in
+ * (among other contexts) isolated parallel computations that may
+ * generate subtasks. Class {@code L32X64MixRandom} implements
+ * interfaces {@link java.util.Rng} and {@link java.util.SplittableRng},
+ * and therefore supports methods for producing pseudorandomly chosen
+ * numbers of type {@code int}, {@code long}, {@code float}, and {@code double}
+ * as well as creating new split-off {@code L32X64MixRandom} objects,
+ * with similar usages as for class {@link java.util.SplittableRandom}.
+ *
+ * <p>Series of generated values pass the TestU01 BigCrush and PractRand test suites
+ * that measure independence and uniformity properties of random number generators.
+ * (Most recently validated with
+ * <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a>
+ * and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>.
+ * Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()}
+ * method but also the result of bit-reversing each value produced by {@code nextLong()}.)
+ * These tests validate only the methods for certain
+ * types and ranges, but similar properties are expected to hold, at
+ * least approximately, for others as well.
+ *
+ * <p>{@code L32X64MixRandom} is a specific member of the LXM family of algorithms
+ * for pseudorandom number generators. Every LXM generator consists of two
+ * subgenerators; one is an LCG (Linear Congruential Generator) and the other is
+ * an Xorshift generator. Each output of an LXM generator is the sum of one
+ * output from each subgenerator, possibly processed by a final mixing function
+ * (and {@code L32X64MixRandom} does use a mixing function).
+ *
+ * <p>The LCG subgenerator for {@code L32X64MixRandom} has an update step of the
+ * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all
+ * of type {@code int}; {@code s} is the mutable state, the multiplier {@code m}
+ * is fixed (the same for all instances of {@code L32X64MixRandom}}) and the addend
+ * {@code a} is a parameter (a final field of the instance). The parameter
+ * {@code a} is required to be odd (this allows the LCG to have the maximal
+ * period, namely 2<sup>32</sup>); therefore there are 2<sup>31</sup> distinct choices
+ * of parameter.
+ *
+ * <p>The Xorshift subgenerator for {@code L32X64MixRandom} is the {@code xoroshiro64} algorithm,
+ * version 1.0 (parameters 26, 9, 13), without any final scrambler such as "+" or "**".
+ * Its state consists of two {@code int} fields {@code x0} and {@code x1},
+ * which can take on any values provided that they are not both zero.
+ * The period of this subgenerator is 2<sup>64</sup>-1.
+ *
+ * <p> The mixing function for {@code L32X64MixRandom} is the "starstar" mixing function.
+ *
+ * <p> Because the periods 2<sup>32</sup> and 2<sup>64</sup>-1 of the two subgenerators
+ * are relatively prime, the <em>period</em> of any single {@code L32X64MixRandom} object
+ * (the length of the series of generated 32-bit values before it repeats) is the product
+ * of the periods of the subgenerators, that is, 2<sup>32</sup>(2<sup>64</sup>-1),
+ * which is just slightly smaller than 2<sup>96</sup>. Moreover, if two distinct
+ * {@code L32X64MixRandom} objects have different {@code a} parameters, then their
+ * cycles of produced values will be different.
+ *
+ * <p>The 32-bit values produced by the {@code nextInt()} method are exactly equidistributed.
+ * For any specific instance of {@code L32X64MixRandom}, over the course of its cycle each
+ * of the 2<sup>32</sup> possible {@code int} values will be produced 2<sup>64</sup>-1 times.
+ * The values produced by the {@code nextFloat()} method are likewise exactly equidistributed.
+ *
+ * <p>In fact, the 32-bit values produced by the {@code nextInt()} method are 2-equidistributed.
+ * To be precise: for any specific instance of {@code L32X64MixRandom}, consider
+ * the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by
+ * {@code nextInt()} (assuming no other methods are called that would affect the state).
+ * There are 2<sup>32</sup>(2<sup>64</sup>-1) such subsequences, and each subsequence,
+ * which consists of 2 32-bit values, can have one of 2<sup>64</sup> values. Of those
+ * 2<sup>64</sup> subsequence values, nearly all of them (2<sup>64</sup>-2<sup>32</sup>)
+ * occur 2<sup>32</sup> times over the course of the entire cycle, and the other
+ * 2<sup>32</sup> subsequence values occur only 2<sup>32</sup>-1 times. So the ratio
+ * of the probability of getting one of the less common subsequence values and the
+ * probability of getting one of the more common subsequence values is 1-2<sup>-32</sup>.
+ * (Note that the set of 2<sup>32</sup> less-common subsequence values will differ from
+ * one instance of {@code L32X64MixRandom} to another, as a function of the additive
+ * parameter of the LCG.) As a consequence, the values produced by the {@code nextFloat()}
+ * method are likewise 2-equidistributed, and the values produced by the {@code nextLong()}
+ * and {@code nextDouble()} methods are equidistributed (but not 2-equidistributed).
+ *
+ * <p>Method {@link #split} constructs and returns a new {@code L32X64MixRandom}
+ * instance that shares no mutable state with the current instance. However, with
+ * very high probability, the values collectively generated by the two objects
+ * have the same statistical properties as if the same quantity of values were
+ * generated by a single thread using a single {@code L32X64MixRandom} object.
+ * This is because, with high probability, distinct {@code L32X64MixRandom} objects
+ * have distinct {@code a} parameters and therefore use distinct members of the
+ * algorithmic family; and even if their {@code a} parameters are the same, with
+ * very high probability they will traverse different parts of their common state
+ * cycle.
+ *
+ * <p>As with {@link java.util.SplittableRandom}, instances of
+ * {@code L32X64MixRandom} are <em>not</em> thread-safe.
+ * They are designed to be split, not shared, across threads. For
+ * example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style
+ * computation using random numbers might include a construction
+ * of the form {@code new Subtask(someL32X64MixRandom.split()).fork()}.
+ *
+ * <p>This class provides additional methods for generating random
+ * streams, that employ the above techniques when used in
+ * {@code stream.parallel()} mode.
+ *
+ * <p>Instances of {@code L32X64MixRandom} are not cryptographically
+ * secure. Consider instead using {@link java.security.SecureRandom}
+ * in security-sensitive applications. Additionally,
+ * default-constructed instances do not use a cryptographically random
+ * seed unless the {@linkplain System#getProperty system property}
+ * {@code java.util.secureRandomSeed} is set to {@code true}.
+ *
+ * @author Guy Steele
+ * @since 1.9
+ */
+public final class L32X64MixRandom extends AbstractSplittableRng {
+
+ /*
+ * Implementation Overview.
+ *
+ * The split operation uses the current generator to choose four new 64-bit
+ * int values that are then used to initialize the parameter `a` and the
+ * state variables `s`, `x0`, and `x1` for a newly constructed generator.
+ *
+ * With high probability, no two generators so chosen
+ * will have the same `a` parameter, and testing has indicated
+ * that the values generated by two instances of {@code L32X64MixRandom}
+ * will be (approximately) independent if have different values for `a`.
+ *
+ * The default (no-argument) constructor, in essence, uses
+ * "defaultGen" to generate four new 32-bit values for the same
+ * purpose. Multiple generators created in this way will certainly
+ * differ in their `a` parameters. The defaultGen state must be accessed
+ * in a thread-safe manner, so we use an AtomicLong to represent
+ * this state. To bootstrap the defaultGen, we start off using a
+ * seed based on current time unless the
+ * java.util.secureRandomSeed property is set. This serves as a
+ * slimmed-down (and insecure) variant of SecureRandom that also
+ * avoids stalls that may occur when using /dev/random.
+ *
+ * File organization: First static fields, then instance
+ * fields, then constructors, then instance methods.
+ */
+
+ /* ---------------- static fields ---------------- */
+
+ /**
+ * The seed generator for default constructors.
+ */
+ private static final AtomicLong defaultGen = new AtomicLong(RngSupport.initialSeed());
+
+ /*
+ * The period of this generator, which is (2**64 - 1) * 2**32.
+ */
+ private static final BigInteger thePeriod =
+ BigInteger.ONE.shiftLeft(64).subtract(BigInteger.ONE).shiftLeft(32);
+
+ /*
+ * Multiplier used in the LCG portion of the algorithm, taken from
+ * Pierre L'Ecuyer, Tables of linear congruential generators of
+ * different sizes and good lattice structure, <em>Mathematics of
+ * Computation</em> 68, 225 (January 1999), pages 249–260,
+ * Table 4 (third multiplier for size 2<sup>32</sup>).
+ */
+
+ private static final int m = 32310901;
+
+ /* ---------------- instance fields ---------------- */
+
+ /**
+ * The parameter that is used as an additive constant for the LCG.
+ * Must be odd.
+ */
+ private final int a;
+
+ /**
+ * The per-instance state: s for the LCG; x0 and x1 for the xorshift.
+ * At least one of x0 and x1 must be nonzero.
+ */
+ private int s, x0, x1;
+
+ /* ---------------- constructors ---------------- */
+
+ /**
+ * Basic constructor that initializes all fields from parameters.
+ * It then adjusts the field values if necessary to ensure that
+ * all constraints on the values of fields are met.
+ */
+ public L32X64MixRandom(int a, int s, int x0, int x1) {
+ // Force a to be odd.
+ this.a = a | 1;
+ this.s = s;
+ // If x0 and x1 are both zero, we must choose nonzero values.
+ if ((x0 | x1) == 0) {
+ // At least one of the two values generated here will be nonzero.
+ this.x0 = RngSupport.mixMurmur32(s += RngSupport.GOLDEN_RATIO_32);
+ this.x1 = RngSupport.mixMurmur32(s + RngSupport.GOLDEN_RATIO_32);
+ }
+ }
+
+ /**
+ * Creates a new instance of {@code L32X64MixRandom} using the
+ * specified {@code long} value as the initial seed. Instances of
+ * {@code L32X64MixRandom} created with the same seed in the same
+ * program generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public L32X64MixRandom(long seed) {
+ // Using a value with irregularly spaced 1-bits to xor the seed
+ // argument tends to improve "pedestrian" seeds such as 0 or
+ // other small integers. We may as well use SILVER_RATIO_64.
+ //
+ // The high half of the seed is hashed by mixMurmur32 to produce the `a` parameter.
+ // The low half of the seed is hashed by mixMurmur32 to produce the initial `x0`,
+ // which will then be used to produce the first generated value.
+ // Then x1 is filled in as if by a SplitMix PRNG with
+ // GOLDEN_RATIO_32 as the gamma value and Murmur32 as the mixer.
+ this(RngSupport.mixMurmur32((int)((seed ^= RngSupport.SILVER_RATIO_64) >>> 32)),
+ 1,
+ RngSupport.mixLea32((int)(seed)),
+ RngSupport.mixLea32((int)(seed) + RngSupport.GOLDEN_RATIO_32));
+ }
+
+ /**
+ * Creates a new instance of {@code L32X64MixRandom} that is likely to
+ * generate sequences of values that are statistically independent
+ * of those of any other instances in the current program execution,
+ * but may, and typically does, vary across program invocations.
+ */
+ public L32X64MixRandom() {
+ // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.
+ this(defaultGen.getAndAdd(RngSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@code L32X64MixRandom} using the specified array of
+ * initial seed bytes. Instances of {@code L32X64MixRandom} created with the same
+ * seed array in the same program execution generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public L32X64MixRandom(byte[] seed) {
+ // Convert the seed to 4 int values, of which the last 2 are not all zero.
+ int[] data = RngSupport.convertSeedBytesToInts(seed, 4, 2);
+ int a = data[0], s = data[1], x0 = data[2], x1 = data[3];
+ // Force a to be odd.
+ this.a = a | 1;
+ this.s = s;
+ this.x0 = x0;
+ this.x1 = x1;
+ }
+
+ /* ---------------- public methods ---------------- */
+
+ /**
+ * Constructs and returns a new instance of {@code L32X64MixRandom}
+ * that shares no mutable state with this instance.
+ * However, with very high probability, the set of values collectively
+ * generated by the two objects has the same statistical properties as if
+ * same the quantity of values were generated by a single thread using
+ * a single {@code L32X64MixRandom} object. Either or both of the two
+ * objects may be further split using the {@code split} method,
+ * and the same expected statistical properties apply to the
+ * entire set of generators constructed by such recursive splitting.
+ *
+ * @param source a {@code SplittableRng} instance to be used instead
+ * of this one as a source of pseudorandom bits used to
+ * initialize the state of the new ones.
+ * @return a new instance of {@code L32X64MixRandom}
+ */
+ public L32X64MixRandom split(SplittableRng source) {
+ // Literally pick a new instance "at random".
+ return new L32X64MixRandom(source.nextInt(), source.nextInt(),
+ source.nextInt(), source.nextInt());
+ }
+
+ /**
+ * Returns a pseudorandom {@code int} value.
+ *
+ * @return a pseudorandom {@code int} value
+ */
+ public int nextInt() {
+ final int z = s + x0;
+ s = m * s + a; // LCG
+ int q0 = x0, q1 = x1;
+ { q1 ^= q0; q0 = Integer.rotateLeft(q0, 26); q0 = q0 ^ q1 ^ (q1 << 9); q1 = Integer.rotateLeft(q1, 13); } // xoroshiro64
+ x0 = q0; x1 = q1;
+ return Integer.rotateLeft(z * 5, 7) * 9; // "starstar" mixing function
+ }
+
+ /**
+ * Returns a pseudorandom {@code long} value.
+ *
+ * @return a pseudorandom {@code long} value
+ */
+
+ public long nextLong() {
+ return ((long)(nextInt()) << 32) | nextInt();
+ }
+
+ public BigInteger period() { return thePeriod; }
+}