--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.base/share/classes/java/util/random/L128X1024MixRandom.java Thu Nov 14 12:50:08 2019 -0400
@@ -0,0 +1,432 @@
+/*
+ * Copyright (c) 2013, 2019, Oracle and/or its affiliates. All rights reserved.
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * This code is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 2 only, as
+ * published by the Free Software Foundation. Oracle designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Oracle in the LICENSE file that accompanied this code.
+ *
+ * This code is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+ * version 2 for more details (a copy is included in the LICENSE file that
+ * accompanied this code).
+ *
+ * You should have received a copy of the GNU General Public License version
+ * 2 along with this work; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+ * or visit www.oracle.com if you need additional information or have any
+ * questions.
+ */
+
+package java.util.random;
+
+import java.math.BigInteger;
+import java.util.concurrent.atomic.AtomicLong;
+import java.util.random.RandomGenerator.SplittableGenerator;
+import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator;
+
+/**
+ * A generator of uniform pseudorandom values applicable for use in
+ * (among other contexts) isolated parallel computations that may
+ * generate subtasks. Class {@link L128X1024MixRandom} implements
+ * interfaces {@link RandomGenerator} and {@link SplittableGenerator},
+ * 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 {@link L128X1024MixRandom} 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>
+ * {@link L128X1024MixRandom} 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 result of
+ * combining state from the LCG with state from the Xorshift generator by
+ * using a Mixing function (and then the state of the LCG and the state of the
+ * Xorshift generator are advanced).
+ * <p>
+ * The LCG subgenerator for {@link L128X256MixRandom} has an update step of the
+ * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all
+ * 128-bit integers; {@code s} is the mutable state, the multiplier {@code m}
+ * is fixed (the same for all instances of {@link L128X256MixRandom}) 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>128</sup>); therefore there are 2<sup>127</sup> distinct choices
+ * of parameter.
+ * <p>
+ * The Xorshift subgenerator for {@link L128X1024MixRandom} is the {@code xoroshiro1024}
+ * algorithm (parameters 25, 27, and 36), without any final scrambler such as "+" or "**".
+ * Its state consists of an array {@code x} of sixteen {@code long} values,
+ * which can take on any values provided that they are not all zero.
+ * The period of this subgenerator is 2<sup>1024</sup>-1.
+ * <p>
+ * The mixing function for {@link L128X1024MixRandom} is {@link RandomSupport.mixLea64}
+ * applied to the argument {@code (sh + s0)}, where {@code sh} is the high half of {@code s}
+ * and {@code s0} is the most recently computed element of {@code x}.
+ * <p>
+ * Because the periods 2<sup>128</sup> and 2<sup>1024</sup>-1 of the two subgenerators
+ * are relatively prime, the <em>period</em> of any single {@link L128X1024MixRandom} object
+ * (the length of the series of generated 64-bit values before it repeats) is the product
+ * of the periods of the subgenerators, that is, 2<sup>128</sup>(2<sup>1024</sup>-1),
+ * which is just slightly smaller than 2<sup>1152</sup>. Moreover, if two distinct
+ * {@link L128X1024MixRandom} objects have different {@code a} parameters, then their
+ * cycles of produced values will be different.
+ * <p>
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed.
+ * For any specific instance of {@link L128X1024MixRandom}, over the course of its cycle each
+ * of the 2<sup>64</sup> possible {@code long} values will be produced
+ * 2<sup>64</sup>(2<sup>1024</sup>-1 times. The values produced by the {@code nextInt()},
+ * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed.
+ * <p>
+ * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be
+ * "very nearly" 16-equidistributed: all possible 16-tuples of 64-bit values are generated,
+ * and some pairs occur more often than others, but only very slightly more often.
+ * However, this conjecture has not yet been proven mathematically.
+ * If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()},
+ * and {@code nextDouble()} methods are likewise approximately 16-equidistributed.
+ * <p>
+ * Method {@link #split} constructs and returns a new {@link L128X1024MixRandom}
+ * 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 {@link L128X1024MixRandom} object.
+ * This is because, with high probability, distinct {@link L128X1024MixRandom} 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
+ * {@link L128X1024MixRandom} 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(someL128X1024MixRandom.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 {@link L128X1024MixRandom} 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}.
+ *
+ * @since 14
+ */
+public final class L128X1024MixRandom extends AbstractSplittableWithBrineGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * The 128-bit parameter `a` is represented as two long fields `ah` and `al`.
+ * The 128-bit state variable `s` is represented as two long fields `sh` and `sl`.
+ *
+ * The split operation uses the current generator to choose 20
+ * new 64-bit long values that are then used to initialize the
+ * parameters `ah` and `al`, the state variables `sh`, `sl`,
+ * and the array `x` for a newly constructed generator.
+ *
+ * With extremely 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 {@link L128X1024MixRandom}
+ * will be (approximately) independent if have different values for `a`.
+ *
+ * The default (no-argument) constructor, in essence, uses
+ * "defaultGen" to generate 20 new 64-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 length of the array x.
+ */
+
+ private static final int N = 16;
+
+ /**
+ * The seed generator for default constructors.
+ */
+ private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed());
+
+ /*
+ * The period of this generator, which is (2**1024 - 1) * 2**128.
+ */
+ private static final BigInteger PERIOD =
+ BigInteger.ONE.shiftLeft(N*64).subtract(BigInteger.ONE).shiftLeft(128);
+
+ /*
+ * Low half of multiplier used in the LCG portion of the algorithm;
+ * the overall multiplier is (2**64 + ML).
+ * Chosen based on research by Sebastiano Vigna and Guy Steele (2019).
+ * The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL
+ * are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493].
+ */
+
+ private static final long ML = 0xd605bbb58c8abbfdL;
+
+ /* ---------------- instance fields ---------------- */
+
+ /**
+ * The parameter that is used as an additive constant for the LCG.
+ * Must be odd (therefore al must be odd).
+ */
+ private final long ah, al;
+
+ /**
+ * The per-instance state: sh and sl for the LCG; the array x for the xorshift;
+ * p is the rotating pointer into the array x.
+ * At least one of the 16 elements of the array x must be nonzero.
+ */
+ private long sh, sl;
+ private final long[] x;
+ private int p = N - 1;
+
+ /* ---------------- 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.
+ *
+ * @param ah high half of the additive parameter for the LCG
+ * @param al low half of the additive parameter for the LCG
+ * @param sh high half of the initial state for the LCG
+ * @param sl low half of the initial state for the LCG
+ * @param x0 first word of the initial state for the xorshift generator
+ * @param x1 second word of the initial state for the xorshift generator
+ * @param x2 third word of the initial state for the xorshift generator
+ * @param x3 fourth word of the initial state for the xorshift generator
+ * @param x4 fifth word of the initial state for the xorshift generator
+ * @param x5 sixth word of the initial state for the xorshift generator
+ * @param x6 seventh word of the initial state for the xorshift generator
+ * @param x7 eight word of the initial state for the xorshift generator
+ * @param x8 ninth word of the initial state for the xorshift generator
+ * @param x9 tenth word of the initial state for the xorshift generator
+ * @param x10 eleventh word of the initial state for the xorshift generator
+ * @param x11 twelfth word of the initial state for the xorshift generator
+ * @param x12 thirteenth word of the initial state for the xorshift generator
+ * @param x13 fourteenth word of the initial state for the xorshift generator
+ * @param x14 fifteenth word of the initial state for the xorshift generator
+ * @param x15 sixteenth word of the initial state for the xorshift generator
+ */
+ public L128X1024MixRandom(long ah, long al, long sh, long sl,
+ long x0, long x1, long x2, long x3,
+ long x4, long x5, long x6, long x7,
+ long x8, long x9, long x10, long x11,
+ long x12, long x13, long x14, long x15) {
+ // Force a to be odd.
+ this.ah = ah;
+ this.al = al | 1;
+ this.sh = sh;
+ this.sl = sl;
+ this.x = new long[N];
+ this.x[0] = x0;
+ this.x[1] = x1;
+ this.x[2] = x2;
+ this.x[3] = x3;
+ this.x[4] = x4;
+ this.x[5] = x5;
+ this.x[6] = x6;
+ this.x[7] = x7;
+ this.x[8] = x8;
+ this.x[9] = x9;
+ this.x[10] = x10;
+ this.x[11] = x11;
+ this.x[12] = x12;
+ this.x[13] = x13;
+ this.x[14] = x14;
+ this.x[15] = x15;
+ // If x0, x1, ..., x15 are all zero (very unlikely), we must choose nonzero values.
+ if ((x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15) == 0) {
+ long v = sh;
+ // At least fifteen of the sixteen values generated here will be nonzero.
+ for (int j = 0; j < N; j++) {
+ this.x[j] = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);
+ }
+ }
+ }
+
+ /**
+ * Creates a new instance of {@link L128X1024MixRandom} using the
+ * specified {@code long} value as the initial seed. Instances of
+ * {@link L128X1024MixRandom} created with the same seed in the same
+ * program execution generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public L128X1024MixRandom(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 seed is hashed by mixMurmur64 to produce the `a` parameter.
+ // The seed is hashed by mixStafford13 to produce the initial `x[0]`,
+ // which will then be used to produce the first generated value.
+ // The other x values are filled in as if by a SplitMix PRNG with
+ // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer.
+ this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64),
+ RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64),
+ 0,
+ 1,
+ RandomSupport.mixStafford13(seed),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
+ RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@link L128X1024MixRandom} 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 L128X1024MixRandom() {
+ // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.
+ this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@link L128X1024MixRandom} using the specified array of
+ * initial seed bytes. Instances of {@link L128X1024MixRandom} created with the same
+ * seed array in the same program execution generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public L128X1024MixRandom(byte[] seed) {
+ // Convert the seed to 20 long values, of which the last 16 are not all zero.
+ long[] data = RandomSupport.convertSeedBytesToLongs(seed, 20, 16);
+ long ah = data[0], al = data[1], sh = data[2], sl = data[3];
+ // Force a to be odd.
+ this.ah = ah;
+ this.al = al | 1;
+ this.sh = sh;
+ this.sl = sl;
+ this.x = new long[N];
+ for (int j = 0; j < N; j++) {
+ this.x[j] = data[4+j];
+ }
+ }
+
+ /* ---------------- public methods ---------------- */
+
+ /**
+ * Given 63 bits of "brine", constructs and returns a new instance of
+ * {@code L128X1024MixRandom} 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 L128X1024MixRandom} 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 SplittableGenerator} instance to be used instead
+ * of this one as a source of pseudorandom bits used to
+ * initialize the state of the new ones.
+ * @param brine a long value, of which the low 63 bits are used to choose
+ * the {@code a} parameter for the new instance.
+ * @return a new instance of {@code L128X1024MixRandom}
+ */
+ public SplittableGenerator split(SplittableGenerator source, long brine) {
+ // Pick a new instance "at random", but use the brine for (the low half of) `a`.
+ return new L128X1024MixRandom(source.nextLong(), brine << 1,
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong(),
+ source.nextLong(), source.nextLong());
+ }
+
+ /**
+ * Returns a pseudorandom {@code long} value.
+ *
+ * @return a pseudorandom {@code long} value
+ */
+ public long nextLong() {
+ // First part of xoroshiro1024: fetch array data
+ final int q = p;
+ final long s0 = x[p = (p + 1) & (N - 1)];
+ long s15 = x[q];
+
+ // Compute the result based on current state information
+ // (this allows the computation to be overlapped with state update).
+ final long result = RandomSupport.mixLea64(sh + s0);
+
+ // Update the LCG subgenerator
+ // The LCG is, in effect, s = ((1LL << 64) + ML) * s + a, if only we had 128-bit arithmetic.
+ final long u = ML * sl;
+ // Note that Math.multiplyHigh computes the high half of the product of signed values,
+ // but what we need is the high half of the product of unsigned values; for this we use the
+ // formula "unsignedMultiplyHigh(a, b) = multiplyHigh(a, b) + ((a >> 63) & b) + ((b >> 63) & a)";
+ // in effect, each operand is added to the result iff the sign bit of the other operand is 1.
+ // (See Henry S. Warren, Jr., _Hacker's Delight_ (Second Edition), Addison-Wesley (2013),
+ // Section 8-3, p. 175; or see the First Edition, Addison-Wesley (2003), Section 8-3, p. 133.)
+ // If Math.unsignedMultiplyHigh(long, long) is ever implemented, the following line can become:
+ // sh = (ML * sh) + Math.unsignedMultiplyHigh(ML, sl) + sl + ah;
+ // and this entire comment can be deleted.
+ sh = (ML * sh) + (Math.multiplyHigh(ML, sl) + ((ML >> 63) & sl) + ((sl >> 63) & ML)) + sl + ah;
+ sl = u + al;
+ if (Long.compareUnsigned(sl, u) < 0) ++sh; // Handle the carry propagation from low half to high half.
+
+ // Second part of xoroshiro1024: update array data
+ s15 ^= s0;
+ x[q] = Long.rotateLeft(s0, 25) ^ s15 ^ (s15 << 27);
+ x[p] = Long.rotateLeft(s15, 36);
+
+ return result;
+ }
+
+ /**
+ * Returns the period of this random generator.
+ *
+ * @return a {@link BigInteger} whose value is the number of distinct possible states of this
+ * {@link RandomGenerator} object (2<sup>128</sup>(2<sup>1024</sup>-1)).
+ */
+ public BigInteger period() {
+ return PERIOD;
+ }
+}