+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@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). + *
+ * 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 2128); therefore there are 2127 distinct choices + * of parameter. + *
+ * 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 21024-1. + *
+ * 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}. + *
+ * Because the periods 2128 and 21024-1 of the two subgenerators + * are relatively prime, the period 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, 2128(21024-1), + * which is just slightly smaller than 21152. Moreover, if two distinct + * {@link L128X1024MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * 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 264 possible {@code long} values will be produced + * 264(21024-1 times. The values produced by the {@code nextInt()}, + * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
+ * 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. + *
+ * 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L128X1024MixRandom} are not 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()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * 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 (2128(21024-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L128X128MixRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L128X128MixRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,360 @@ +/* + * 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 L128X128MixRandom} 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 L128X128MixRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L128X128MixRandom} 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). + *
+ * 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 2128); therefore there are 2127 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L128X128MixRandom} is the {@code xoroshiro128} algorithm, + * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**". + * Its state consists of two {@code long} 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 2128-1. + *
+ * The mixing function for {@link L128X128MixRandom} is {@link RandomSupport.mixLea64} + * applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}. + *
+ * Because the periods 2128 and 2128-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X128MixRandom} 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, 2128(2128-1), + * which is just slightly smaller than 2256. Moreover, if two distinct + * {@link L128X128MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X128MixRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced + * 264(2128-1) times. The values produced by the {@code nextInt()}, + * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
+ * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be + * "very nearly" 2-equidistributed: all possible pairs 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 2-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X128MixRandom} + * 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 L128X128MixRandom} object. + * This is because, with high probability, distinct {@link L128X128MixRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L128X128MixRandom} are not 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(someL128X128MixRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L128X128MixRandom} 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 L128X128MixRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split operation uses the current generator to choose four new 64-bit + * long values that are then used to initialize the parameter `a` and the + * state variables `s`, `x0`, and `x1` 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 L128X128MixRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate four 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**128 - 1) * 2**128. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(128).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; x0 and x1 for the xorshift. + * At least one of x0 and x1 must be nonzero. + */ + private long sh, sl, 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. + * + * @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 + */ + public L128X128MixRandom(long ah, long al, long sh, long sl, long x0, long x1) { + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + // If x0 and x1 are both zero, we must choose nonzero values. + if ((x0 | x1) == 0) { + long v = sh; + // At least one of the two values generated here will be nonzero. + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L128X128MixRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L128X128MixRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128MixRandom(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 `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_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)); + } + + /** + * Creates a new instance of {@link L128X128MixRandom} 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 L128X128MixRandom() { + // 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 L128X128MixRandom} using the specified array of + * initial seed bytes. Instances of {@link L128X128MixRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128MixRandom(byte[] seed) { + // Convert the seed to 6 long values, of which the last 2 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2); + long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5]; + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + } + + /* ---------------- public methods ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L128X128MixRandom} 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 L128X128MixRandom} 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 L128X128MixRandom} + */ + 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 L128X128MixRandom(source.nextLong(), brine << 1, + source.nextLong(), source.nextLong(), + source.nextLong(), source.nextLong()); + } + + /** + * Returns a pseudorandom {@code long} value. + * + * @return a pseudorandom {@code long} value + */ + public long nextLong() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = RandomSupport.mixLea64(sh + x0); + + // 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. + + long q0 = x0, q1 = x1; + // Update the Xorshift subgenerator + { // xoroshiro128v1_0 + q1 ^= q0; + q0 = Long.rotateLeft(q0, 24); + q0 = q0 ^ q1 ^ (q1 << 16); + q1 = Long.rotateLeft(q1, 37); + } + x0 = q0; x1 = q1; + 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 (2128(2128-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L128X128PlusPlusRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L128X128PlusPlusRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,354 @@ +/* + * 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 L128X128PlusPlusRandom} 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 L128X128PlusPlusRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L128X128PlusPlusRandom} 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). + *
+ * 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 2128); therefore there are 2127 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L128X128PlusPlusRandom} is the {@code xoroshiro128} algorithm, + * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**". + * Its state consists of two {@code long} 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 2128-1. + *
+ * The mixing function for {@link L128X128PlusPlusRandom} is the 64-bit "plusplus(17)" + * scrambler that computes {@code Long.rotateLeft((sh + x0), 17) + x1}, where {@code sh} + * is the high half of {@code s}. + *
+ * Because the periods 2128 and 2128-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X128PlusPlusRandom} 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, 2128(2128-1), + * which is just slightly smaller than 2256. Moreover, if two distinct + * {@link L128X128PlusPlusRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X128PlusPlusRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced + * 264(2128-1) times. The values produced by the {@code nextInt()}, + * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X128PlusPlusRandom} + * 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 L128X128PlusPlusRandom} object. + * This is because, with high probability, distinct {@link L128X128PlusPlusRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L128X128PlusPlusRandom} are not 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(someL128X128PlusPlusRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L128X128PlusPlusRandom} 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 L128X128PlusPlusRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split operation uses the current generator to choose four new 64-bit + * long values that are then used to initialize the parameter `a` and the + * state variables `s`, `x0`, and `x1` 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 L128X128PlusPlusRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate four 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**128 - 1) * 2**128. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(128).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; x0 and x1 for the xorshift. + * At least one of x0 and x1 must be nonzero. + */ + private long sh, sl, 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. + * + * @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 + */ + public L128X128PlusPlusRandom(long ah, long al, long sh, long sl, long x0, long x1) { + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + // If x0 and x1 are both zero, we must choose nonzero values. + if ((x0 | x1) == 0) { + long v = sh; + // At least one of the two values generated here will be nonzero. + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L128X128PlusPlusRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L128X128PlusPlusRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128PlusPlusRandom(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 `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_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)); + } + + /** + * Creates a new instance of {@link L128X128PlusPlusRandom} 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 L128X128PlusPlusRandom() { + // 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 L128X128PlusPlusRandom} using the specified array of + * initial seed bytes. Instances of {@link L128X128PlusPlusRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128PlusPlusRandom(byte[] seed) { + // Convert the seed to 6 long values, of which the last 2 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2); + long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5]; + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + } + + /* ---------------- public methods ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L128X128PlusPlusRandom} 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 L128X128PlusPlusRandom} 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 L128X128PlusPlusRandom} + */ + 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 L128X128PlusPlusRandom(source.nextLong(), brine << 1, + source.nextLong(), source.nextLong(), + source.nextLong(), source.nextLong()); + } + + /** + * Returns a pseudorandom {@code long} value. + * + * @return a pseudorandom {@code long} value + */ + public long nextLong() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = Long.rotateLeft((sh + x0), 17) + x1; // "plusplus" scrambler + + // 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. + + long q0 = x0, q1 = x1; + // Update the Xorshift subgenerator + { // xoroshiro128v1_0 + q1 ^= q0; + q0 = Long.rotateLeft(q0, 24); + q0 = q0 ^ q1 ^ (q1 << 16); + q1 = Long.rotateLeft(q1, 37); + } + x0 = q0; x1 = q1; + 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 (2128(2128-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L128X128StarStarRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L128X128StarStarRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,361 @@ +/* + * 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 L128X128StarStarRandom} 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 L128X128StarStarRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L128X128StarStarRandom} 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). + *
+ * 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 2128); therefore there are 2127 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L128X128StarStarRandom} is the {@code xoroshiro128} algorithm, + * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**". + * Its state consists of two {@code long} 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 2128-1. + *
+ * The mixing function for {@link L128X128StarStarRandom} is the 64-bit "starstar(5,7,9)" + * scrambler that computes {@code Long.rotateLeft((sh + x0) * 5, 7) * 9}, where {@code sh} + * is the high half of {@code s}. + *
+ * Because the periods 2128 and 2128-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X128StarStarRandom} 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, 2128(2128-1), + * which is just slightly smaller than 2256. Moreover, if two distinct + * {@link L128X128StarStarRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X128StarStarRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced + * 264(2128-1) times. The values produced by the {@code nextInt()}, + * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
+ * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be + * "very nearly" 2-equidistributed: all possible pairs 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 2-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X128StarStarRandom} + * 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 L128X128StarStarRandom} object. + * This is because, with high probability, distinct {@link L128X128StarStarRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L128X128StarStarRandom} are not 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(someL128X128StarStarRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L128X128StarStarRandom} 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 L128X128StarStarRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split operation uses the current generator to choose four new 64-bit + * long values that are then used to initialize the parameter `a` and the + * state variables `s`, `x0`, and `x1` 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 L128X128StarStarRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate four 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**128 - 1) * 2**128. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(128).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; x0 and x1 for the xorshift. + * At least one of x0 and x1 must be nonzero. + */ + private long sh, sl, 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. + * + * @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 + */ + public L128X128StarStarRandom(long ah, long al, long sh, long sl, long x0, long x1) { + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + // 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. + long v = sh; + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L128X128StarStarRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L128X128StarStarRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128StarStarRandom(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 `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_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)); + } + + /** + * Creates a new instance of {@link L128X128StarStarRandom} 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 L128X128StarStarRandom() { + // 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 L128X128StarStarRandom} using the specified array of + * initial seed bytes. Instances of {@link L128X128StarStarRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X128StarStarRandom(byte[] seed) { + // Convert the seed to 6 long values, of which the last 2 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2); + long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5]; + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + } + + /* ---------------- public methods ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L128X128StarStarRandom} 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 L128X128StarStarRandom} 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 L128X128StarStarRandom} + */ + 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 L128X128StarStarRandom(source.nextLong(), brine << 1, + source.nextLong(), source.nextLong(), + source.nextLong(), source.nextLong()); + } + + /** + * Returns a pseudorandom {@code long} value. + * + * @return a pseudorandom {@code long} value + */ + public long nextLong() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = Long.rotateLeft((sh + x0) * 5, 7) * 9; // "starstar" scrambler + + // 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. + + long q0 = x0, q1 = x1; + // Update the Xorshift subgenerator + { // xoroshiro128v1_0 + q1 ^= q0; + q0 = Long.rotateLeft(q0, 24); + q0 = q0 ^ q1 ^ (q1 << 16); + q1 = Long.rotateLeft(q1, 37); + } + x0 = q0; x1 = q1; + 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 (2128(2128-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L128X256MixRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L128X256MixRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,380 @@ +/* + * 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 L128X256MixRandom} 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 L128X256MixRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L128X256MixRandom} 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). + *
+ * 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 2128); therefore there are 2127 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L128X256MixRandom} is the {@code xoshiro256} algorithm, + * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**". + * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, + * and {@code x3}, which can take on any values provided that they are not all zero. + * The period of this subgenerator is 2256-1. + *
+ * The mixing function for {@link L128X256MixRandom} is {@link RandomSupport.mixLea64} + * applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}. + *
+ * Because the periods 2128 and 2256-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X256MixRandom} 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, 2128(2256-1), + * which is just slightly smaller than 2384. Moreover, if two distinct + * {@link L128X256MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced + * 264(2256-1) times. The values produced by the {@code nextInt()}, + * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
+ * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be + * "very nearly" 4-equidistributed: all possible quadruples 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 4-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X256MixRandom} + * 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 L128X256MixRandom} object. + * This is because, with high probability, distinct {@link L128X256MixRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L128X256MixRandom} are not 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(someL128X256MixRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L128X256MixRandom} 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 L128X256MixRandom 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 eight + * new 64-bit long values that are then used to initialize the + * parameters `ah` and `al` and the state variables `sh`, `sl`, + * `x0`, `x1`, `x2`, and `x3` 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 L128X256MixRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate eight 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**256 - 1) * 2**128. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(256).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; x0, x1, x2, and x3 for the xorshift. + * At least one of the four fields x0, x1, x2, and x3 must be nonzero. + */ + private long sh, sl, x0, x1, x2, x3; + + /* ---------------- 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 + */ + public L128X256MixRandom(long ah, long al, long sh, long sl, long x0, long x1, long x2, long x3) { + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + this.x2 = x2; + this.x3 = x3; + // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. + if ((x0 | x1 | x2 | x3) == 0) { + long v = sh; + // At least three of the four values generated here will be nonzero. + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L128X256MixRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L128X256MixRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X256MixRandom(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 `x0`, + // 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)); + } + + /** + * Creates a new instance of {@link L128X256MixRandom} 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 L128X256MixRandom() { + // 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 L128X256MixRandom} using the specified array of + * initial seed bytes. Instances of {@link L128X256MixRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L128X256MixRandom(byte[] seed) { + // Convert the seed to 6 long values, of which the last 4 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 4); + long ah = data[0], al = data[1], sh = data[2], sl = data[3], + x0 = data[4], x1 = data[5], x2 = data[6], x3 = data[7]; + // Force a to be odd. + this.ah = ah; + this.al = al | 1; + this.sh = sh; + this.sl = sl; + this.x0 = x0; + this.x1 = x1; + this.x2 = x2; + this.x3 = x3; + } + + /* ---------------- public methods ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L128X256MixRandom} 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 L128X256MixRandom} 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 L128X256MixRandom} + */ + 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 L128X256MixRandom(source.nextLong(), brine << 1, + 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() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = RandomSupport.mixLea64(sh + x0); + + // 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. + + // Update the Xorshift subgenerator + long q0 = x0, q1 = x1, q2 = x2, q3 = x3; + { // xoshiro256 1.0 + long t = q1 << 17; + q2 ^= q0; + q3 ^= q1; + q1 ^= q2; + q0 ^= q3; + q2 ^= t; + q3 = Long.rotateLeft(q3, 45); + } + x0 = q0; x1 = q1; x2 = q2; x3 = q3; + 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 (2128(2256-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L128X256MixRandom.java.rej --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L128X256MixRandom.java.rej Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,353 @@ +*************** +*** 28,34 **** + import java.math.BigInteger; + import java.util.concurrent.atomic.AtomicLong; + import java.util.random.RandomGenerator.SplittableGenerator; +- import java.util.random.RandomSupport.AbstractSplittableGenerator; + + + /** +--- 28,34 ---- + import java.math.BigInteger; + import java.util.concurrent.atomic.AtomicLong; + import java.util.random.RandomGenerator.SplittableGenerator; ++ import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator; + + + /** +*************** +*** 55,63 **** + * {@link L128X256MixRandom} 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 {@link L128X256MixRandom} does use a mixing function). + *
+ * 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 +--- 55,64 ---- + * {@link L128X256MixRandom} 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). + *
+ * 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 +*************** +*** 74,80 **** + * and {@code x3}, which can take on any values provided that they are not all zero. + * The period of this subgenerator is 2256-1. + *
+- * The mixing function for {@link L128X256MixRandom} is the 64-bit MurmurHash3 finalizer. + *
+ * Because the periods 2128 and 2256-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X256MixRandom} object +--- 75,82 ---- + * and {@code x3}, which can take on any values provided that they are not all zero. + * The period of this subgenerator is 2256-1. + *
++ * The mixing function for {@link L128X256MixRandom} is {@link RandomSupport.mixLea64} ++ * applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}. + *
+ * Because the periods 2128 and 2256-1 of the two subgenerators + * are relatively prime, the period of any single {@link L128X256MixRandom} object +*************** +*** 86,119 **** + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each +- * of the 264 possible {@code long} values will be produced 2256-1 times. +- * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} +- * methods are likewise exactly equidistributed. +- *
+- * In fact, the 64-bit values produced by the {@code nextLong()} method are exactly +- * 2-equidistributed. For any specific instance of {@link L128X256MixRandom}, consider +- * the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by +- * {@code nextLong()} (assuming no other methods are called that would affect the state). +- * There are 2128(2256-1) such subsequences, and each subsequence, +- * which consists of 2 64-bit values, can have one of 2128 values, and each +- * such value occurs 2256-1 times. The values produced by the {@code nextInt()}, +- * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly 2-equidistributed. + *
+- * Moreover, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed. +- * To be precise: for any specific instance of {@link L128X256MixRandom}, consider +- * the (overlapping) length-4 subsequences of the cycle of 64-bit values produced by +- * {@code nextLong()} (assuming no other methods are called that would affect the state). +- * There are 128(2256-1) such subsequences, and each subsequence, +- * which consists of 4 64-bit values, can have one of 2256 values. Of those +- * 2256 subsequence values, nearly all of them (2256-2128) +- * occur 2128 times over the course of the entire cycle, and the other +- * 2128 subsequence values occur only 2128-1 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 1-2-128. +- * (Note that the set of 2128 less-common subsequence values will differ from +- * one instance of {@link L128X256MixRandom} to another, as a function of the additive +- * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, +- * and {@code nextDouble()} methods are likewise 4-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X256MixRandom} + * instance that shares no mutable state with the current instance. However, with +--- 88,103 ---- + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each ++ * of the 264 possible {@code long} values will be produced ++ * 264(2256-1) times. The values produced by the {@code nextInt()}, ++ * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed. + *
++ * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be ++ * "very nearly" 4-equidistributed: all possible quadruples 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 4-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L128X256MixRandom} + * instance that shares no mutable state with the current instance. However, with +*************** +*** 146,152 **** + * + * @since 14 + */ +- public final class L128X256MixRandom extends AbstractSplittableGenerator { + + /* + * Implementation Overview. +--- 130,136 ---- + * + * @since 14 + */ ++ public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. +*************** +*** 193,220 **** + BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128); + + /* +- * The multiplier used in the LCG portion of the algorithm is 2**64 + m; +- * where m is taken from +- * Pierre L'Ecuyer, Tables of linear congruential generators of +- * different sizes and good lattice structure, Mathematics of +- * Computation 68, 225 (January 1999), pages 249-260, +- * Table 4 (first multiplier for size 264). +- * +- * This is almost certainly not the best possible 128-bit multiplier +- * for an LCG, but it is sufficient for our purposes here; because +- * is is larger than 2**64, the 64-bit values produced by nextLong() +- * are exactly 2-equidistributed, and the fact that it is of the +- * form (2**64 + m) simplifies the code, given that we have only +- * 64-bit arithmetic to work with. + */ + +- private static final long M = 2862933555777941757L; + + /* ---------------- instance fields ---------------- */ + + /** + * The parameter that is used as an additive constant for the LCG. +- * Must be odd. + */ + private final long ah, al; + +--- 177,196 ---- + BigInteger.ONE.shiftLeft(256).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; + +*************** +*** 252,262 **** + this.x3 = x3; + // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. + if ((x0 | x1 | x2 | x3) == 0) { + // At least three of the four values generated here will be nonzero. +- this.x0 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64); +- this.x1 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64); +- this.x2 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64); +- this.x3 = RandomSupport.mixStafford13(sh + RandomSupport.GOLDEN_RATIO_64); + } + } + +--- 228,239 ---- + this.x3 = x3; + // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. + if ((x0 | x1 | x2 | x3) == 0) { ++ long v = sh; + // At least three of the four values generated here will be nonzero. ++ this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); ++ this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); ++ this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); ++ this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + +*************** +*** 277,283 **** + // The seed is hashed by mixStafford13 to produce the initial `x0`, + // 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 Stafford13 as the mixer. + this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), + RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64), + 0, +--- 254,260 ---- + // The seed is hashed by mixStafford13 to produce the initial `x0`, + // 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, +*************** +*** 323,351 **** + } + + /* ---------------- public methods ---------------- */ +- + /** +- * Constructs and returns a new instance of {@link L128X256MixRandom} +- * 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 {@link L128X256MixRandom} 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 {@link SplittableGenerator} 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 {@link L128X256MixRandom} + */ +- public L128X256MixRandom split(SplittableGenerator source) { +- // Literally pick a new instance "at random". +- return new L128X256MixRandom(source.nextLong(), source.nextLong(), +- source.nextLong(), source.nextLong(), +- source.nextLong(), source.nextLong(), +- source.nextLong(), source.nextLong()); + } + + /** +--- 300,330 ---- + } + + /* ---------------- public methods ---------------- */ ++ + /** ++ * Given 63 bits of "brine", constructs and returns a new instance of ++ * {@code L128X256MixRandom} 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 L128X256MixRandom} 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 L128X256MixRandom} + */ ++ 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 L128X256MixRandom(source.nextLong(), brine << 1, ++ source.nextLong(), source.nextLong(), ++ source.nextLong(), source.nextLong(), ++ source.nextLong(), source.nextLong()); + } + + /** +*************** +*** 354,365 **** + * @return a pseudorandom {@code long} value + */ + public long nextLong() { +- final long z = sh + x0; +- // The LCG: in effect, s = ((1LL << 64) + M) * s + a, if only we had 128-bit arithmetic. +- final long u = M * sl; +- sh = (M * sh) + Math.multiplyHigh(M, sl) + sl + ah; + sl = u + al; + if (Long.compareUnsigned(sl, u) < 0) ++sh; // Handle the carry propagation from low half to high half. + long q0 = x0, q1 = x1, q2 = x2, q3 = x3; + { // xoshiro256 1.0 + long t = q1 << 17; +--- 333,359 ---- + * @return a pseudorandom {@code long} value + */ + public long nextLong() { ++ // Compute the result based on current state information ++ // (this allows the computation to be overlapped with state update). ++ final long result = RandomSupport.mixLea64(sh + x0); ++ ++ // 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. ++ ++ // Update the Xorshift subgenerator + long q0 = x0, q1 = x1, q2 = x2, q3 = x3; + { // xoshiro256 1.0 + long t = q1 << 17; +*************** +*** 371,379 **** + q3 = Long.rotateLeft(q3, 45); + } + x0 = q0; x1 = q1; x2 = q2; x3 = q3; +- return RandomSupport.mixLea64(z); // mixing function + } + + public BigInteger period() { + return PERIOD; + } +--- 365,379 ---- + q3 = Long.rotateLeft(q3, 45); + } + x0 = q0; x1 = q1; x2 = q2; x3 = q3; ++ 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 (2128(2256-1)). ++ */ + public BigInteger period() { + return PERIOD; + } diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L64X1024MixRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L64X1024MixRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,414 @@ +/* + * 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 L64X1024MixRandom} 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 L64X1024MixRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L64X1024MixRandom} 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). + *
+ * The LCG subgenerator for {@link L64X1024MixRandom} 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 long}; {@code s} is the mutable state, the multiplier {@code m} + * is fixed (the same for all instances of {@link L64X1024MixRandom}) 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 264); therefore there are 263 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L64X1024MixRandom} 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 21024-1. + *
+ * The mixing function for {@link L64X1024MixRandom} is {@link RandomSupport.mixLea64} + * applied to the argument {@code (s + s0)}, where {@code s0} is the most recently computed + * element of {@code x}. + *
+ * Because the periods 264 and 21024-1 of the two subgenerators + * are relatively prime, the period of any single {@link L64X1024MixRandom} 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, 264(21024-1), + * which is just slightly smaller than 21088. Moreover, if two distinct + * {@link L64X1024MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L64X1024MixRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced 21024-1 times. + * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} + * methods are likewise exactly equidistributed. + *
+ * In fact, the 64-bit values produced by the {@code nextLong()} method are 16-equidistributed. + * To be precise: for any specific instance of {@link L64X1024MixRandom}, consider + * the (overlapping) length-16 subsequences of the cycle of 64-bit values produced by + * {@code nextLong()} (assuming no other methods are called that would affect the state). + * There are 264(21024-1) such subsequences, and each subsequence, + * which consists of 16 64-bit values, can have one of 21024 values. Of those + * 21024 subsequence values, nearly all of them (21024-264) + * occur 264 times over the course of the entire cycle, and the other + * 264 subsequence values occur only 264-1 times. So the ratio + * of the probability of getting any specific one of the less common subsequence values and the + * probability of getting any specific one of the more common subsequence values is 1-2-64. + * (Note that the set of 264 less-common subsequence values will differ from + * one instance of {@link L64X1024MixRandom} to another, as a function of the additive + * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, + * and {@code nextDouble()} methods are likewise 16-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L64X1024MixRandom} + * 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 L64X1024MixRandom} object. + * This is because, with high probability, distinct {@link L64X1024MixRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L64X1024MixRandom} are not 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(someL64X1024MixRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L64X1024MixRandom} 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 L64X1024MixRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split() operation uses the current generator to choose 18 new 64-bit + * long values that are then used to initialize the parameter `a`, the + * state variable `s`, 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 L64X1024MixRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate 18 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**64. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(N*64).subtract(BigInteger.ONE).shiftLeft(64); + + /* + * Multiplier used in the LCG portion of the algorithm. + * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). + * The spectral scores for dimensions 2 through 8 for the multiplier 0xd1342543de82ef95 + * are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215]. + */ + + private static final long M = 0xd1342543de82ef95L; + + /* ---------------- instance fields ---------------- */ + + /** + * The parameter that is used as an additive constant for the LCG. + * Must be odd. + */ + private final long a; + + /** + * The per-instance state: s 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 s; + 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 a additive parameter for the LCG + * @param s 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 L64X1024MixRandom(long a, long s, + 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.a = a | 1; + this.s = s; + 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 = s; + // 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 L64X1024MixRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L64X1024MixRandom} created with the same seed in the same + * program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X1024MixRandom(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), + 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 L64X1024MixRandom} 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 L64X1024MixRandom() { + // 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 L64X1024MixRandom} using the specified array of + * initial seed bytes. Instances of {@link L64X1024MixRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X1024MixRandom(byte[] seed) { + // Convert the seed to 18 long values, of which the last 16 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 18, 16); + long a = data[0], s = data[1]; + // Force a to be odd. + this.a = a | 1; + this.s = s; + this.x = new long[N]; + for (int j = 0; j < N; j++) { + this.x[j] = data[2+j]; + } + } + + /* ---------------- public methods ---------------- */ + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L64X1024MixRandom} 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 L64X1024MixRandom} 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 L64X1024MixRandom} + */ + public SplittableGenerator split(SplittableGenerator source, long brine) { + // Pick a new instance "at random", but use the brine for `a`. + return new L64X1024MixRandom(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()); + } + + /** + * 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(s + s0); + + // Update the LCG subgenerator + s = M * s + a; // LCG + + // 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 (264(21024-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L64X128MixRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L64X128MixRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,344 @@ +/* + * 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 L64X128MixRandom} 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 L64X128MixRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L64X128MixRandom} 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). + *
+ * The LCG subgenerator for {@link L64X128MixRandom} 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 long}; {@code s} is the mutable state, the multiplier {@code m} + * is fixed (the same for all instances of {@link L64X128MixRandom}}) 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 264); therefore there are 263 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L64X128MixRandom} is the {@code xoroshiro128} algorithm, + * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**". + * Its state consists of two {@code long} 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 2128-1. + *
+ * The mixing function for {@link L64X128MixRandom} is {@link RandomSupport.mixLea64} + * applied to the argument {@code (s + x0)}. + *
+ * Because the periods 264 and 2128-1 of the two subgenerators + * are relatively prime, the period of any single {@link L64X128MixRandom} 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, 264(2128-1), + * which is just slightly smaller than 2192. Moreover, if two distinct + * {@link L64X128MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L64X128MixRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced 2128-1 times. + * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} + * methods are likewise exactly equidistributed. + *
+ * In fact, the 64-bit values produced by the {@code nextLong()} method are 2-equidistributed. + * To be precise: for any specific instance of {@link L64X128MixRandom}, consider + * the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by + * {@code nextLong()} (assuming no other methods are called that would affect the state). + * There are 264(2128-1) such subsequences, and each subsequence, + * which consists of 2 64-bit values, can have one of 2128 values. Of those + * 2128 subsequence values, nearly all of them (2128-264) + * occur 264 times over the course of the entire cycle, and the other + * 264 subsequence values occur only 264-1 times. So the ratio + * of the probability of getting any specific one of the less common subsequence values and the + * probability of getting any specific one of the more common subsequence values is 1-2-64. + * (Note that the set of 264 less-common subsequence values will differ from + * one instance of {@link L64X128MixRandom} to another, as a function of the additive + * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, + * and {@code nextDouble()} methods are likewise 2-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L64X128MixRandom} + * 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 L64X128MixRandom} object. + * This is because, with high probability, distinct {@link L64X128MixRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L64X128MixRandom} are not 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(someL64X128MixRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L64X128MixRandom} 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 L64X128MixRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split operation uses the current generator to choose four new 64-bit + * long values that are then used to initialize the parameter `a` and the + * state variables `s`, `x0`, and `x1` 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 L64X128MixRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate four 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**128 - 1) * 2**64. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE).shiftLeft(64); + + /* + * Multiplier used in the LCG portion of the algorithm. + * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). + * The spectral scores for dimensions 2 through 8 for the multiplier 0xd1342543de82ef95 + * are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215]. + */ + + private static final long M = 0xd1342543de82ef95L; + + /* ---------------- instance fields ---------------- */ + + /** + * The parameter that is used as an additive constant for the LCG. + * Must be odd. + */ + private final long 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 long 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. + * + * @param a additive parameter for the LCG + * @param s 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 + */ + public L64X128MixRandom(long a, long s, long x0, long x1) { + // Force a to be odd. + this.a = a | 1; + this.s = s; + this.x0 = x0; + this.x1 = x1; + // If x0 and x1 are both zero, we must choose nonzero values. + if ((x0 | x1) == 0) { + long v = s; + // At least one of the two values generated here will be nonzero. + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L64X128MixRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L64X128MixRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X128MixRandom(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 `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_64 as the gamma value and mixStafford13 as the mixer. + this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64), + 1, + RandomSupport.mixStafford13(seed), + RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64)); + } + + /** + * Creates a new instance of {@link L64X128MixRandom} 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 L64X128MixRandom() { + // 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 L64X128MixRandom} using the specified array of + * initial seed bytes. Instances of {@link L64X128MixRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X128MixRandom(byte[] seed) { + // Convert the seed to 4 long values, of which the last 2 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 4, 2); + long 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 ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L64X128MixRandom} 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 L64X128MixRandom} 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 L64X128MixRandom} + */ + public SplittableGenerator split(SplittableGenerator source, long brine) { + // Pick a new instance "at random", but use the brine for `a`. + return new L64X128MixRandom(brine << 1, source.nextLong(), + source.nextLong(), source.nextLong()); + } + + /** + * Returns a pseudorandom {@code long} value. + * + * @return a pseudorandom {@code long} value + */ + public long nextLong() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = RandomSupport.mixLea64(s + x0); + // Update the LCG subgenerator + s = M * s + a; + // Update the Xorshift subgenerator + long q0 = x0, q1 = x1; + { // xoroshiro128v1_0 + q1 ^= q0; + q0 = Long.rotateLeft(q0, 24); + q0 = q0 ^ q1 ^ (q1 << 16); + q1 = Long.rotateLeft(q1, 37); + } + x0 = q0; x1 = q1; + 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 (264(2128-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/L64X256MixRandom.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/L64X256MixRandom.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,359 @@ +/* + * 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 L64X256MixRandom} 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 L64X256MixRandom} objects, + * with similar usages as for class {@link java.util.SplittableRandom}. + *
+ * 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 + * version 1.2.3 of TestU01 + * and version 0.90 of PractRand. + * 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. + *
+ * {@link L64X256MixRandom} 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). + *
+ * The LCG subgenerator for {@link L64X256MixRandom} 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 long}; {@code s} is the mutable state, the multiplier {@code m} + * is fixed (the same for all instances of {@link L64X256MixRandom}) 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 264); therefore there are 263 distinct choices + * of parameter. + *
+ * The Xorshift subgenerator for {@link L64X256MixRandom} is the {@code xoshiro256} algorithm, + * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**". + * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2}, + * and {@code x3}, which can take on any values provided that they are not all zero. + * The period of this subgenerator is 2256-1. + *
+ * The mixing function for {@link L64X256MixRandom} is {@link RandomSupport.mixLea64} + * applied to the argument {@code (s + x0)}. + *
+ * Because the periods 264 and 2256-1 of the two subgenerators + * are relatively prime, the period of any single {@link L64X256MixRandom} 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, 264(2256-1), + * which is just slightly smaller than 2320. Moreover, if two distinct + * {@link L64X256MixRandom} objects have different {@code a} parameters, then their + * cycles of produced values will be different. + *
+ * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed. + * For any specific instance of {@link L64X256MixRandom}, over the course of its cycle each + * of the 264 possible {@code long} values will be produced 2256-1 times. + * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()} + * methods are likewise exactly equidistributed. + *
+ * In fact, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed. + * To be precise: for any specific instance of {@link L64X256MixRandom}, consider + * the (overlapping) length-4 subsequences of the cycle of 64-bit values produced by + * {@code nextLong()} (assuming no other methods are called that would affect the state). + * There are 264(2256-1) such subsequences, and each subsequence, + * which consists of 4 64-bit values, can have one of 2256 values. Of those + * 2256 subsequence values, nearly all of them (2256-264) + * occur 264 times over the course of the entire cycle, and the other + * 264 subsequence values occur only 264-1 times. So the ratio + * of the probability of getting any specific one of the less common subsequence values and the + * probability of getting any specific one of the more common subsequence values is 1-2-64. + * (Note that the set of 264 less-common subsequence values will differ from + * one instance of {@link L64X256MixRandom} to another, as a function of the additive + * parameter of the LCG.) The values produced by the {@code nextInt()}, {@code nextFloat()}, + * and {@code nextDouble()} methods are likewise 4-equidistributed. + *
+ * Method {@link #split} constructs and returns a new {@link L64X256MixRandom} + * 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 L64X256MixRandom} object. + * This is because, with high probability, distinct {@link L64X256MixRandom} 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. + *
+ * As with {@link java.util.SplittableRandom}, instances of + * {@link L64X256MixRandom} are not 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(someL64X256MixRandom.split()).fork()}. + *
+ * This class provides additional methods for generating random + * streams, that employ the above techniques when used in + * {@code stream.parallel()} mode. + *
+ * Instances of {@link L64X256MixRandom} 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 L64X256MixRandom extends AbstractSplittableWithBrineGenerator { + + /* + * Implementation Overview. + * + * The split operation uses the current generator to choose six new 64-bit + * long values that are then used to initialize the parameter `a` and the + * state variables `s`, `x0`, `x1`, `x2`, and `x3` 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 L64X256MixRandom} + * will be (approximately) independent if have different values for `a`. + * + * The default (no-argument) constructor, in essence, uses + * "defaultGen" to generate six 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 seed generator for default constructors. + */ + private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); + + /* + * The period of this generator, which is (2**256 - 1) * 2**64. + */ + private static final BigInteger PERIOD = + BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(64); + + /* + * Multiplier used in the LCG portion of the algorithm. + * Chosen based on research by Sebastiano Vigna and Guy Steele (2019). + * The spectral scores for dimensions 2 through 8 for the multiplier 0xd1342543de82ef95 + * are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215]. + */ + + private static final long M = 0xd1342543de82ef95L; + + /* ---------------- instance fields ---------------- */ + + /** + * The parameter that is used as an additive constant for the LCG. + * Must be odd. + */ + private final long a; + + /** + * The per-instance state: s for the LCG; x0, x1, x2, and x3 for the xorshift. + * At least one of the four fields x0, x1, x2, and x3 must be nonzero. + */ + private long s, x0, x1, x2, x3; + + /* ---------------- 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 a additive parameter for the LCG + * @param s 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 + */ + public L64X256MixRandom(long a, long s, long x0, long x1, long x2, long x3) { + // Force a to be odd. + this.a = a | 1; + this.s = s; + this.x0 = x0; + this.x1 = x1; + this.x2 = x2; + this.x3 = x3; + // If x0, x1, x2, and x3 are all zero, we must choose nonzero values. + if ((x0 | x1 | x2 | x3) == 0) { + long v = s; + // At least three of the four values generated here will be nonzero. + this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64); + this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64); + } + } + + /** + * Creates a new instance of {@link L64X256MixRandom} using the + * specified {@code long} value as the initial seed. Instances of + * {@link L64X256MixRandom} created with the same seed in the same + * program generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X256MixRandom(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 `x0`, + // 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), + 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)); + } + + /** + * Creates a new instance of {@link L64X256MixRandom} 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 L64X256MixRandom() { + // 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 L64X256MixRandom} using the specified array of + * initial seed bytes. Instances of {@link L64X256MixRandom} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public L64X256MixRandom(byte[] seed) { + // Convert the seed to 6 long values, of which the last 4 are not all zero. + long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 4); + long a = data[0], s = data[1], x0 = data[2], x1 = data[3], x2 = data[4], x3 = data[5]; + // Force a to be odd. + this.a = a | 1; + this.s = s; + this.x0 = x0; + this.x1 = x1; + this.x2 = x2; + this.x3 = x3; + } + + /* ---------------- public methods ---------------- */ + + /** + * Given 63 bits of "brine", constructs and returns a new instance of + * {@code L64X256MixRandom} 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 L64X256MixRandom} 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 L64X256MixRandom} + */ + public SplittableGenerator split(SplittableGenerator source, long brine) { + // Pick a new instance "at random", but use the brine for `a`. + return new L64X256MixRandom(brine << 1, 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() { + // Compute the result based on current state information + // (this allows the computation to be overlapped with state update). + final long result = RandomSupport.mixLea64(s + x0); + // Update the LCG subgenerator + s = M * s + a; + // Update the Xorshift subgenerator + long q0 = x0, q1 = x1, q2 = x2, q3 = x3; + { // xoshiro256 1.0 + long t = q1 << 17; + q2 ^= q0; + q3 ^= q1; + q1 ^= q2; + q0 ^= q3; + q2 ^= t; + q3 = Long.rotateLeft(q3, 45); + } + x0 = q0; x1 = q1; x2 = q2; x3 = q3; + 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 (264(2256-1)). + */ + public BigInteger period() { + return PERIOD; + } +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/MRG32k3a.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/MRG32k3a.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,485 @@ +/* + * 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.LeapableGenerator; +import java.util.random.RandomSupport.AbstractArbitrarilyJumpableGenerator; + +/** + * A generator of uniform pseudorandom values applicable for use in + * (among other contexts) isolated parallel computations that may + * generate subtasks. Class {@link MRG32k3a} implements + * interfaces {@link RandomGenerator} and {@link AbstractArbitrarilyJumpableGenerator}, + * 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 {@link Xoroshiro128PlusMRG32k3a} objects + * by "jumping" or "leaping". + *
+ * Instances {@link Xoroshiro128Plus} are not thread-safe. + * They are designed to be used so that each thread as its own instance. + * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps} + * can be used to construct new instances of {@link Xoroshiro128Plus} that traverse + * other parts of the state cycle. + *
+ * Instances of {@link MRG32k3a} 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 MRG32k3a extends AbstractArbitrarilyJumpableGenerator { + + /* + * Implementation Overview. + * + * See http://simul.iro.umontreal.ca/rng/MRG32k3a.c . + * + * File organization: First the non-public methods that constitute + * the main algorithm, then the main public methods, followed by + * some custom spliterator classes needed for stream methods. + */ + + private final static double NORM1 = 2.328306549295728e-10; + private final static double NORM2 = 2.328318824698632e-10; + private final static double M1 = 4294967087.0; + private final static double M2 = 4294944443.0; + private final static double A12 = 1403580.0; + private final static double A13N = 810728.0; + private final static double A21 = 527612.0; + private final static double A23N = 1370589.0; + private final static int M1_DEFICIT = 209; + + /** + * The per-instance state. + The seeds for s10, s11, s12 must be integers in [0, m1 - 1] and not all 0. + The seeds for s20, s21, s22 must be integers in [0, m2 - 1] and not all 0. + */ + private double s10, s11, s12, + s20, s21, s22; + + /** + * The seed generator for default constructors. + */ + private static final AtomicLong DEFAULT_GEN = + new AtomicLong(RandomSupport.initialSeed()); + + /* + 32-bits Random number generator U(0,1): MRG32k3a + Author: Pierre L'Ecuyer, + Source: Good Parameter Sets for Combined Multiple Recursive Random + Number Generators, + Shorter version in Operations Research, + 47, 1 (1999), 159--164. + --------------------------------------------------------- + */ + + private void nextState() { + /* Component 1 */ + double p1 = A12 * s11 - A13N * s10; + double k1 = p1 / M1; p1 -= k1 * M1; if (p1 < 0.0) p1 += M1; + s10 = s11; s11 = s12; s12 = p1; + /* Component 2 */ + double p2 = A21 * s22 - A23N * s20; + double k2 = p2 / M2; p2 -= k2 * M2; if (p2 < 0.0) p2 += M2; + s20 = s21; s21 = s22; s22 = p2; + } + + + /** + * The form of nextInt used by IntStream Spliterators. + * Exactly the same as long version, except for types. + * + * @param origin the least value, unless greater than bound + * @param bound the upper bound (exclusive), must not equal origin + * + * @return a pseudorandom value + */ + private int internalNextInt(int origin, int bound) { + if (origin < bound) { + final int n = bound - origin; + final int m = n - 1; + if (n > 0) { + int r; + for (int u = (int)nextDouble() >>> 1; + u + m + ((M1_DEFICIT + 1) >>> 1) - (r = u % n) < 0; + u = (int)nextDouble() >>> 1) + ; + return (r + origin); + } else { + return RandomSupport.boundedNextInt(this, origin, bound); + } + } else { + return nextInt(); + } + } + + private int internalNextInt(int bound) { + // Specialize internalNextInt for origin == 0, bound > 0 + final int n = bound; + final int m = n - 1; + int r; + for (int u = (int)nextDouble() >>> 1; + u + m + ((M1_DEFICIT + 1) >>> 1) - (r = u % n) < 0; + u = (int)nextDouble() >>> 1) + ; + return r; + } + + /** + * All arguments must be known to be nonnegative integral values + * less than the appropriate modulus. + */ + private MRG32k3a(double s10, double s11, double s12, + double s20, double s21, double s22) { + this.s10 = s10; this.s11 = s11; this.s12 = s12; + this.s20 = s20; this.s21 = s21; this.s22 = s22; + if ((s10 == 0.0) && (s11 == 0.0) && (s12 == 0.0)) { + this.s10 = this.s11 = this.s12 = 12345.0; + } + if ((s20 == 0.0) && (s21 == 0.0) && (s22 == 0.0)) { + this.s20 = this.s21 = this.s21 = 12345.0; + } + } + + /* ---------------- public methods ---------------- */ + + /** + * Creates a new MRG32k3a instance using six specified {@code int} + * initial seed values. MRG32k3a instances created with the same + * seeds in the same program generate identical sequences of values. + * If all six seed values are zero, the generator is seeded to a + * widely used initialization of MRG32k3a: all six state variables + * are set to 12345. + * + * @param s10 the first seed value for the first subgenerator + * @param s11 the second seed value for the first subgenerator + * @param s12 the third seed value for the first subgenerator + * @param s20 the first seed value for the second subgenerator + * @param s21 the second seed value for the second subgenerator + * @param s22 the third seed value for the second subgenerator + */ + public MRG32k3a(int s10, int s11, int s12, + int s20, int s21, int s22) { + this(((double)(((long)s10) & 0x00000000ffffffffL)) % M1, + ((double)(((long)s11) & 0x00000000ffffffffL)) % M1, + ((double)(((long)s12) & 0x00000000ffffffffL)) % M1, + ((double)(((long)s20) & 0x00000000ffffffffL)) % M2, + ((double)(((long)s21) & 0x00000000ffffffffL)) % M2, + ((double)(((long)s22) & 0x00000000ffffffffL)) % M2); + } + + /** + * Creates a new MRG32k3a instance using the specified + * initial seed. MRG32k3a instances created with the same + * seed in the same program generate identical sequences of values. + * An argument of 0 seeds the generator to a widely used initialization + * of MRG32k3a: all six state variables are set to 12345. + * + * @param seed the initial seed + */ + public MRG32k3a(long seed) { + this((double)((seed & 0x7FF) + 12345), + (double)(((seed >>> 11) & 0x7FF) + 12345), + (double)(((seed >>> 22) & 0x7FF) + 12345), + (double)(((seed >>> 33) & 0x7FF) + 12345), + (double)(((seed >>> 44) & 0x7FF) + 12345), + (double)((seed >>> 55) + 12345)); + } + + /** + * Creates a new MRG32k3a instance that is likely to + * generate sequences of values that are statistically independent + * of those of any other instances in the current program; and + * may, and typically does, vary across program invocations. + */ + public MRG32k3a() { + this(DEFAULT_GEN.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); + } + + /** + * Creates a new instance of {@link Xoshiro256StarStar} using the specified array of + * initial seed bytes. Instances of {@link Xoshiro256StarStar} created with the same + * seed array in the same program execution generate identical sequences of values. + * + * @param seed the initial seed + */ + public MRG32k3a(byte[] seed) { + // Convert the seed to 6 int values. + int[] data = RandomSupport.convertSeedBytesToInts(seed, 6, 0); + int s10 = data[0], s11 = data[1], s12 = data[2]; + int s20 = data[3], s21 = data[4], s22 = data[5]; + this.s10 = ((double)(((long)s10) & 0x00000000ffffffffL)) % M1; + this.s11 = ((double)(((long)s11) & 0x00000000ffffffffL)) % M1; + this.s12 = ((double)(((long)s12) & 0x00000000ffffffffL)) % M1; + this.s20 = ((double)(((long)s20) & 0x00000000ffffffffL)) % M2; + this.s21 = ((double)(((long)s21) & 0x00000000ffffffffL)) % M2; + this.s22 = ((double)(((long)s22) & 0x00000000ffffffffL)) % M2; + if ((s10 == 0.0) && (s11 == 0.0) && (s12 == 0.0)) { + this.s10 = this.s11 = this.s12 = 12345.0; + } + if ((s20 == 0.0) && (s21 == 0.0) && (s22 == 0.0)) { + this.s20 = this.s21 = this.s21 = 12345.0; + } + } + + public MRG32k3a copy() { + return new MRG32k3a(s10, s11, s12, s20, s21, s22); + } + + /** + * Returns a pseudorandom {@code double} value between zero + * (exclusive) and one (exclusive). + * + * @return a pseudorandom {@code double} value between zero + * (exclusive) and one (exclusive) + */ + public double nextOpenDouble() { + nextState(); + double p1 = s12, p2 = s22; + if (p1 <= p2) + return ((p1 - p2 + M1) * NORM1); + else + return ((p1 - p2) * NORM1); + } + + /** + * Returns a pseudorandom {@code double} value between zero + * (inclusive) and one (exclusive). + * + * @return a pseudorandom {@code double} value between zero + * (inclusive) and one (exclusive) + */ + public double nextDouble() { + nextState(); + double p1 = s12, p2 = s22; + final double p = p1 * NORM1 - p2 * NORM2; + if (p < 0.0) return (p + 1.0); + else return p; + } + + + /** + * Returns a pseudorandom {@code float} value between zero + * (inclusive) and one (exclusive). + * + * @return a pseudorandom {@code float} value between zero + * (inclusive) and one (exclusive) + */ + public float nextFloat() { + return (float)nextDouble(); + } + + /** + * Returns a pseudorandom {@code int} value. + * + * @return a pseudorandom {@code int} value + */ + public int nextInt() { + return (internalNextInt(0x10000) << 16) | internalNextInt(0x10000); + } + + /** + * Returns a pseudorandom {@code long} value. + * + * @return a pseudorandom {@code long} value + */ + + public long nextLong() { + return (((long)internalNextInt(0x200000) << 43) | + ((long)internalNextInt(0x200000) << 22) | + ((long)internalNextInt(0x400000))); + } + + // Period is (m1**3 - 1)(m2**3 - 1)/2, or approximately 2**191. + static BigInteger calculateThePeriod() { + BigInteger bigm1 = BigInteger.valueOf((long)M1); + BigInteger bigm2 = BigInteger.valueOf((long)M2); + BigInteger t1 = bigm1.multiply(bigm1).multiply(bigm1).subtract(BigInteger.ONE); + BigInteger t2 = bigm2.multiply(bigm2).multiply(bigm2).subtract(BigInteger.ONE); + return t1.shiftRight(1).multiply(t2); + } + + static final BigInteger PERIOD = calculateThePeriod(); + + public BigInteger period() { + return PERIOD; + } + + // Jump and leap distances recommended in Section 1.3 of this paper: + // Pierre L'Ecuyer, Richard Simard, E. Jack Chen, and W. David Kelton. + // An Object-Oriented Random-Number Package with Many Long Streams and Substreams. + // Operations Research 50, 6 (Nov--Dec 2002), 1073--1075. + + public double defaultJumpDistance() { + return 0x1.0p76; // 2**76 + } + + public double defaultLeapDistance() { + return 0x1.0p127; // 2**127 + } + + public void jump(double distance) { + if (distance < 0.0 || Double.isInfinite(distance) || distance != Math.floor(distance)) + throw new IllegalArgumentException("jump distance must be a nonnegative finite integer"); + // We will compute a jump transformation (s => M s) for each LCG. + // We initialize each transformation to the identity transformation. + // Each will be turned into the d'th power of the corresponding base transformation. + long m1_00 = 1, m1_01 = 0, m1_02 = 0, + m1_10 = 0, m1_11 = 1, m1_12 = 0, + m1_20 = 0, m1_21 = 0, m1_22 = 1; + long m2_00 = 1, m2_01 = 0, m2_02 = 0, + m2_10 = 0, m2_11 = 1, m2_12 = 0, + m2_20 = 0, m2_21 = 0, m2_22 = 1; + // These are the base transformations, which will be repeatedly squared, + // and composed with the computed transformations for each 1-bit in distance. + long t1_00 = 0, t1_01 = 1, t1_02 = 0, + t1_10 = 0, t1_11 = 0, t1_12 = 1, + t1_20 = -(long)A13N, t1_21 = (long)A12, t1_22 = 0; + long t2_00 = 0, t2_01 = 1, t2_02 = 0, + t2_10 = 0, t2_11 = 0, t2_12 = 1, + t2_20 = -(long)A23N, t2_21 = (long)A21, t2_22 = 0; + while (distance > 0.0) { + final double dhalf = 0.5 * distance; + if (Math.floor(dhalf) != dhalf) { + // distance is odd: accumulate current squaring + final long n1_00 = m1_00 * t1_00 + m1_01 * t1_10 + m1_02 * t1_20; + final long n1_01 = m1_00 * t1_01 + m1_01 * t1_11 + m1_02 * t1_21; + final long n1_02 = m1_00 * t1_02 + m1_01 * t1_12 + m1_02 * t1_22; + final long n1_10 = m1_10 * t1_00 + m1_11 * t1_10 + m1_12 * t1_20; + final long n1_11 = m1_10 * t1_01 + m1_11 * t1_11 + m1_12 * t1_21; + final long n1_12 = m1_10 * t1_02 + m1_11 * t1_12 + m1_12 * t1_22; + final long n1_20 = m1_20 * t1_00 + m1_21 * t1_10 + m1_22 * t1_20; + final long n1_21 = m1_20 * t1_01 + m1_21 * t1_11 + m1_22 * t1_21; + final long n1_22 = m1_20 * t1_02 + m1_21 * t1_12 + m1_22 * t1_22; + m1_00 = Math.floorMod(n1_00, (long)M1); + m1_01 = Math.floorMod(n1_01, (long)M1); + m1_02 = Math.floorMod(n1_02, (long)M1); + m1_10 = Math.floorMod(n1_10, (long)M1); + m1_11 = Math.floorMod(n1_11, (long)M1); + m1_12 = Math.floorMod(n1_12, (long)M1); + m1_20 = Math.floorMod(n1_20, (long)M1); + m1_21 = Math.floorMod(n1_21, (long)M1); + m1_22 = Math.floorMod(n1_22, (long)M1); + final long n2_00 = m2_00 * t2_00 + m2_01 * t2_10 + m2_02 * t2_20; + final long n2_01 = m2_00 * t2_01 + m2_01 * t2_11 + m2_02 * t2_21; + final long n2_02 = m2_00 * t2_02 + m2_01 * t2_12 + m2_02 * t2_22; + final long n2_10 = m2_10 * t2_00 + m2_11 * t2_10 + m2_12 * t2_20; + final long n2_11 = m2_10 * t2_01 + m2_11 * t2_11 + m2_12 * t2_21; + final long n2_12 = m2_10 * t2_02 + m2_11 * t2_12 + m2_12 * t2_22; + final long n2_20 = m2_20 * t2_00 + m2_21 * t2_10 + m2_22 * t2_20; + final long n2_21 = m2_20 * t2_01 + m2_21 * t2_11 + m2_22 * t2_21; + final long n2_22 = m2_20 * t2_02 + m2_21 * t2_12 + m2_22 * t2_22; + m2_00 = Math.floorMod(n2_00, (long)M2); + m2_01 = Math.floorMod(n2_01, (long)M2); + m2_02 = Math.floorMod(n2_02, (long)M2); + m2_10 = Math.floorMod(n2_10, (long)M2); + m2_11 = Math.floorMod(n2_11, (long)M2); + m2_12 = Math.floorMod(n2_12, (long)M2); + m2_20 = Math.floorMod(n2_20, (long)M2); + m2_21 = Math.floorMod(n2_21, (long)M2); + m2_22 = Math.floorMod(n2_22, (long)M2); + } + // Square the base transformations. + { + final long z1_00 = m1_00 * m1_00 + m1_01 * m1_10 + m1_02 * m1_20; + final long z1_01 = m1_00 * m1_01 + m1_01 * m1_11 + m1_02 * m1_21; + final long z1_02 = m1_00 * m1_02 + m1_01 * m1_12 + m1_02 * m1_22; + final long z1_10 = m1_10 * m1_00 + m1_11 * m1_10 + m1_12 * m1_20; + final long z1_11 = m1_10 * m1_01 + m1_11 * m1_11 + m1_12 * m1_21; + final long z1_12 = m1_10 * m1_02 + m1_11 * m1_12 + m1_12 * m1_22; + final long z1_20 = m1_20 * m1_00 + m1_21 * m1_10 + m1_22 * m1_20; + final long z1_21 = m1_20 * m1_01 + m1_21 * m1_11 + m1_22 * m1_21; + final long z1_22 = m1_20 * m1_02 + m1_21 * m1_12 + m1_22 * m1_22; + m1_00 = Math.floorMod(z1_00, (long)M1); + m1_01 = Math.floorMod(z1_01, (long)M1); + m1_02 = Math.floorMod(z1_02, (long)M1); + m1_10 = Math.floorMod(z1_10, (long)M1); + m1_11 = Math.floorMod(z1_11, (long)M1); + m1_12 = Math.floorMod(z1_12, (long)M1); + m1_20 = Math.floorMod(z1_20, (long)M1); + m1_21 = Math.floorMod(z1_21, (long)M1); + m1_22 = Math.floorMod(z1_22, (long)M1); + final long z2_00 = m2_00 * m2_00 + m2_01 * m2_10 + m2_02 * m2_20; + final long z2_01 = m2_00 * m2_01 + m2_01 * m2_11 + m2_02 * m2_21; + final long z2_02 = m2_00 * m2_02 + m2_01 * m2_12 + m2_02 * m2_22; + final long z2_10 = m2_10 * m2_00 + m2_11 * m2_10 + m2_12 * m2_20; + final long z2_11 = m2_10 * m2_01 + m2_11 * m2_11 + m2_12 * m2_21; + final long z2_12 = m2_10 * m2_02 + m2_11 * m2_12 + m2_12 * m2_22; + final long z2_20 = m2_20 * m2_00 + m2_21 * m2_10 + m2_22 * m2_20; + final long z2_21 = m2_20 * m2_01 + m2_21 * m2_11 + m2_22 * m2_21; + final long z2_22 = m2_20 * m2_02 + m2_21 * m2_12 + m2_22 * m2_22; + m2_00 = Math.floorMod(z2_00, (long)M2); + m2_01 = Math.floorMod(z2_01, (long)M2); + m2_02 = Math.floorMod(z2_02, (long)M2); + m2_10 = Math.floorMod(z2_10, (long)M2); + m2_11 = Math.floorMod(z2_11, (long)M2); + m2_12 = Math.floorMod(z2_12, (long)M2); + m2_20 = Math.floorMod(z2_20, (long)M2); + m2_21 = Math.floorMod(z2_21, (long)M2); + m2_22 = Math.floorMod(z2_22, (long)M2); + } + // Divide distance by 2. + distance = dhalf; + } + final long w10 = m1_00 * (long)s10 + m1_01 * (long)s11 + m1_02 * (long)s12; + final long w11 = m1_10 * (long)s10 + m1_11 * (long)s11 + m1_12 * (long)s12; + final long w12 = m1_20 * (long)s10 + m1_21 * (long)s11 + m1_22 * (long)s12; + s10 = Math.floorMod(w10, (long)M1); + s11 = Math.floorMod(w11, (long)M1); + s12 = Math.floorMod(w12, (long)M1); + final long w20 = m2_00 * (long)s20 + m2_01 * (long)s21 + m2_02 * (long)s22; + final long w21 = m2_10 * (long)s20 + m2_11 * (long)s21 + m2_12 * (long)s22; + final long w22 = m2_20 * (long)s20 + m2_21 * (long)s21 + m2_22 * (long)s22; + s20 = Math.floorMod(w20, (long)M2); + s21 = Math.floorMod(w21, (long)M2); + s22 = Math.floorMod(w22, (long)M2); + } + + /** + * Alter the state of this pseudorandom number generator so as to + * jump forward a distance equal to 2{@code logDistance} + * within its state cycle. + * + * @param logDistance the base-2 logarithm of the distance to jump + * forward within the state cycle. Must be non-negative and + * not greater than 192. + * + * @throws IllegalArgumentException if {@code logDistance} is + * less than zero or 2{@code logDistance} is + * greater than the period of this generator + */ + public void jumpPowerOfTwo(int logDistance) { + if (logDistance < 0 || logDistance > 192) + throw new IllegalArgumentException("logDistance must be non-negative and not greater than 192"); + jump(Math.scalb(1.0, logDistance)); + } + +} diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/RandomGenerator.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/java.base/share/classes/java/util/random/RandomGenerator.java Thu Nov 14 12:50:08 2019 -0400 @@ -0,0 +1,1651 @@ +/* + * Copyright (c) 2016, 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.Objects; +import java.util.stream.DoubleStream; +import java.util.stream.IntStream; +import java.util.stream.LongStream; +import java.util.stream.Stream; + +/** + * The {@link RandomGenerator} interface is designed to provide a common protocol for objects that + * generate random or (more typically) pseudorandom sequences of numbers (or Boolean values). + * Such a sequence may be obtained by either repeatedly invoking a method that returns a single + * (pseudo)randomly chosen value, or by invoking a method that returns a stream of (pseudo)randomly + * chosen values. + *
+ * Ideally, given an implicitly or explicitly specified range of values, each value would be chosen + * independently and uniformly from that range. In practice, one may have to settle for some + * approximation to independence and uniformity. + *
+ * In the case of {@code int}, {@code long}, and {@link Boolean} values, if there is no explicit + * specification of range, then the range includes all possible values of the type. In the case of + * {@code float} and {@code double} values, a value is always chosen from the set of + * 2w values between 0.0 (inclusive) and 1.0 (exclusive), where w is 23 for + * {@code float} values and 52 for {@code double} values, such that adjacent values differ by + * 2−w; if an explicit range is specified, then the chosen number is + * computationally scaled and translated so as to appear to have been chosen from that range. + *
+ * Each method that returns a stream produces a stream of values each of which is chosen in the same + * manner as for a method that returns a single (pseudo)randomly chosen value. For example, if + * {@code r} implements {@link RandomGenerator}, then the method call {@code r.ints(100)} returns a + * stream of 100 {@code int} values. These are not necessarily the exact same values that would + * have been returned if instead {@code r.nextInt()} had been called 100 times; all that is + * guaranteed is that each value in the stream is chosen in a similar (pseudo)random manner from the + * same range. + *
+ * Every object that implements the {@link RandomNumberGenerator} interface by using a + * pseudorandom algorithm is assumed to contain a finite amount of state. Using such an object to + * generate a pseudorandomly chosen value alters its state by computing a new state as a function + * of the current state, without reference to any information other than the current state. + * The number of distinct possible states of such an object is called its period. + * (Some implementations of the {@link RandomNumberGenerator} interface may be truly random + * rather than pseudorandom, for example relying on the statistical behavior of a physical + * object to derive chosen values. Such implementations do not have a fixed period.) + *
+ * As a rule, objects that implement the {@link RandomGenerator} interface need not be thread-safe. + * It is recommended that multithreaded applications use either {@link ThreadLocalRandom} or + * (preferably) pseudorandom number generators that implement the {@link SplittableGenerator} or + * {@link JumpableGenerator} interface. + *
+ * To implement this interface, a class only needs to provide concrete definitions for the methods + * {@code nextLong()} and {@code period()}. Default implementations are provided for all other + * methods (but it may be desirable to override some of them, especially {@code nextInt()} if the + * underlying algorithm is {@code int}-based). Moreover, it may be preferable instead to implement + * a more specialized interface such as {@link JumpableGenerator} or {@link LeapableGenerator}, + * or to extend an abstract implementation-support class such as {@link AbstractSplittableGenerator} + * or {@link AbstractArbitrarilyJumpableGenerator}. + *
+ * Objects that implement {@link RandomGenerator} are typically not cryptographically secure.
+ * Consider instead using {@link java.security.SecureRandom} to get a cryptographically secure
+ * pseudorandom number generator for use by security-sensitive applications. Note, however, that
+ * {@code java.security.SecureRandom} does implement the {@link RandomGenerator} interface, so that
+ * instances of {@code java.security.SecureRandom} may be used interchangeably with other types of
+ * pseudorandom generators in applications that do not require a secure generator.
+ *
+ * @since 14
+ */
+public interface RandomGenerator {
+
+ /**
+ * Supported random number Algorithms.
+ */
+ public enum Algorithm {
+ /**
+ * L64X128MixRandom algorithm
+ */
+ L64X128MixRandom("L64X128MixRandom"),
+ /**
+ * L64X256MixRandom algorithm
+ */
+ L64X256MixRandom("L64X256MixRandom"),
+ /**
+ * L64X1024MixRandom algorithm
+ */
+ L64X1024MixRandom("L64X1024MixRandom"),
+ /**
+ * L128X256MixRandom algorithm
+ */
+ L128X256MixRandom("L128X256MixRandom"),
+ /**
+ * MRG32k3a algorithm
+ */
+ MRG32k3a("MRG32k3a"),
+ /**
+ * Legacy Random algorithm
+ */
+ @Deprecated
+ Random("Random"),
+ /**
+ * Legacy SecureRandom algorithm
+ */
+ @Deprecated
+ SecureRandom("SecureRandom"),
+ /**
+ * Xoroshiro128StarStar algorithm
+ */
+ Xoroshiro128StarStar("Xoroshiro128StarStar"),
+ /**
+ * Xoshiro256StarStar algorithm
+ */
+ Xoshiro256StarStar("Xoshiro256StarStar");
+
+ private String name;
+
+ private Algorithm(String name) {
+ this.name = name;
+ }
+
+ public String toString() {
+ return name;
+ }
+
+ /**
+ * Returns an instance of {@link RandomGenerator} that utilizes this algorithm.
+ *
+ * @return An instance of {@link RandomGenerator}
+ */
+ public RandomGenerator instance() {
+ return RandomGeneratorFactory.of(name, RandomGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link RandomGenerator} that utilizes this algorithm.
+ *
+ * @return {@link RandomGeneratorFactory} of {@link RandomGenerator}
+ */
+ public RandomGeneratorFactory
+ * The default implementation tests the high-order bit (sign bit) of a value produced by
+ * {@code nextInt()}, on the grounds that some algorithms for pseudorandom number generation
+ * produce values whose high-order bits have better statistical quality than the low-order bits.
+ *
+ * @return a pseudorandomly chosen {@code boolean} value
+ */
+ default boolean nextBoolean() {
+ return nextInt() < 0;
+ }
+
+ /**
+ * Returns a pseudorandom {@code float} value between zero (inclusive) and one (exclusive).
+ *
+ * The default implementation uses the 24 high-order bits from a call to {@code nextInt()}.
+ *
+ * @return a pseudorandom {@code float} value between zero (inclusive) and one (exclusive)
+ */
+ default float nextFloat() {
+ return (nextInt() >>> 8) * 0x1.0p-24f;
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code float} value between zero
+ * (inclusive) and the specified bound (exclusive).
+ *
+ * @param bound the upper bound (exclusive) for the returned value.
+ * Must be positive and finite
+ *
+ * @return a pseudorandomly chosen {@code float} value between
+ * zero (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code bound} is not
+ * both positive and finite
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkBound(bound)} and then
+ * {@code RandomSupport.boundedNextFloat(this, bound)}.
+ */
+ default float nextFloat(float bound) {
+ RandomSupport.checkBound(bound);
+ return RandomSupport.boundedNextFloat(this, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code float} value between the
+ * specified origin (inclusive) and the specified bound (exclusive).
+ *
+ * @param origin the least value that can be returned
+ * @param bound the upper bound (exclusive)
+ *
+ * @return a pseudorandomly chosen {@code float} value between the
+ * origin (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code origin} is not finite,
+ * or {@code bound} is not finite, or {@code origin}
+ * is greater than or equal to {@code bound}
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkRange(origin, bound)} and then
+ * {@code RandomSupport.boundedNextFloat(this, origin, bound)}.
+ */
+ default float nextFloat(float origin, float bound) {
+ RandomSupport.checkRange(origin, bound);
+ return RandomSupport.boundedNextFloat(this, origin, bound);
+ }
+
+ /**
+ * Returns a pseudorandom {@code double} value between zero (inclusive) and one (exclusive).
+ *
+ * The default implementation uses the 53 high-order bits from a call to {@code nextLong()}.
+ *
+ * @return a pseudorandom {@code double} value between zero (inclusive) and one (exclusive)
+ */
+ default double nextDouble() {
+ return (nextLong() >>> 11) * 0x1.0p-53;
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code double} value between zero
+ * (inclusive) and the specified bound (exclusive).
+ *
+ * @param bound the upper bound (exclusive) for the returned value.
+ * Must be positive and finite
+ *
+ * @return a pseudorandomly chosen {@code double} value between
+ * zero (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code bound} is not
+ * both positive and finite
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkBound(bound)} and then
+ * {@code RandomSupport.boundedNextDouble(this, bound)}.
+ */
+ default double nextDouble(double bound) {
+ RandomSupport.checkBound(bound);
+ return RandomSupport.boundedNextDouble(this, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code double} value between the
+ * specified origin (inclusive) and the specified bound (exclusive).
+ *
+ * @param origin the least value that can be returned
+ * @param bound the upper bound (exclusive) for the returned value
+ *
+ * @return a pseudorandomly chosen {@code double} value between the
+ * origin (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code origin} is not finite,
+ * or {@code bound} is not finite, or {@code origin}
+ * is greater than or equal to {@code bound}
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkRange(origin, bound)} and then
+ * {@code RandomSupport.boundedNextDouble(this, origin, bound)}.
+ */
+ default double nextDouble(double origin, double bound) {
+ RandomSupport.checkRange(origin, bound);
+ return RandomSupport.boundedNextDouble(this, origin, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code int} value.
+ *
+ * The default implementation uses the 32 high-order bits from a call to {@code nextLong()}.
+ *
+ * @return a pseudorandomly chosen {@code int} value
+ */
+ default public int nextInt() {
+ return (int)(nextLong() >>> 32);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code int} value between
+ * zero (inclusive) and the specified bound (exclusive).
+ *
+ * @param bound the upper bound (exclusive) for the returned value. Must be positive.
+ *
+ * @return a pseudorandomly chosen {@code int} value between
+ * zero (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code bound} is not positive
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkBound(bound)} and then
+ * {@code RandomSupport.boundedNextInt(this, bound)}.
+ */
+ default int nextInt(int bound) {
+ RandomSupport.checkBound(bound);
+ return RandomSupport.boundedNextInt(this, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code int} value between the
+ * specified origin (inclusive) and the specified bound (exclusive).
+ *
+ * @param origin the least value that can be returned
+ * @param bound the upper bound (exclusive) for the returned value
+ *
+ * @return a pseudorandomly chosen {@code int} value between the
+ * origin (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code origin} is greater than
+ * or equal to {@code bound}
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkRange(origin, bound)} and then
+ * {@code RandomSupport.boundedNextInt(this, origin, bound)}.
+ */
+ default int nextInt(int origin, int bound) {
+ RandomSupport.checkRange(origin, bound);
+ return RandomSupport.boundedNextInt(this, origin, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code long} value.
+ *
+ * @return a pseudorandomly chosen {@code long} value
+ */
+ long nextLong();
+
+ /**
+ * Returns a pseudorandomly chosen {@code long} value between
+ * zero (inclusive) and the specified bound (exclusive).
+ *
+ * @param bound the upper bound (exclusive) for the returned value. Must be positive.
+ *
+ * @return a pseudorandomly chosen {@code long} value between
+ * zero (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code bound} is not positive
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkBound(bound)} and then
+ * {@code RandomSupport.boundedNextLong(this, bound)}.
+ */
+ default long nextLong(long bound) {
+ RandomSupport.checkBound(bound);
+ return RandomSupport.boundedNextLong(this, bound);
+ }
+
+ /**
+ * Returns a pseudorandomly chosen {@code long} value between the
+ * specified origin (inclusive) and the specified bound (exclusive).
+ *
+ * @param origin the least value that can be returned
+ * @param bound the upper bound (exclusive) for the returned value
+ *
+ * @return a pseudorandomly chosen {@code long} value between the
+ * origin (inclusive) and the bound (exclusive)
+ *
+ * @throws IllegalArgumentException if {@code origin} is greater than
+ * or equal to {@code bound}
+ *
+ * @implNote The default implementation simply calls
+ * {@code RandomSupport.checkRange(origin, bound)} and then
+ * {@code RandomSupport.boundedNextInt(this, origin, bound)}.
+ *
+ */
+ default long nextLong(long origin, long bound) {
+ RandomSupport.checkRange(origin, bound);
+ return RandomSupport.boundedNextLong(this, origin, bound);
+ }
+
+ /**
+ * Returns a {@code double} value pseudorandomly chosen from
+ * a Gaussian (normal) distribution whose mean is 0 and whose
+ * standard deviation is 1.
+ *
+ * @return a {@code double} value pseudorandomly chosen from a
+ * Gaussian distribution
+ */
+ default double nextGaussian() {
+ return RandomSupport.computeNextGaussian(this);
+ }
+
+ /**
+ * Returns a {@code double} value pseudorandomly chosen from
+ * a Gaussian (normal) distribution with a mean and
+ * standard deviation specified by the arguments.
+ *
+ * @param mean the mean of the Gaussian distribution to be drawn from
+ * @param stddev the standard deviation (square root of the variance)
+ * of the Gaussian distribution to be drawn from
+ *
+ * @return a {@code double} value pseudorandomly chosen from the
+ * specified Gaussian distribution
+ *
+ * @throws IllegalArgumentException if {@code stddev} is negative
+ */
+ default double nextGaussian(double mean, double stddev) {
+ if (stddev < 0.0) throw new IllegalArgumentException("standard deviation must be non-negative");
+ return mean + stddev * RandomSupport.computeNextGaussian(this);
+ }
+
+ /**
+ * Returns a nonnegative {@code double} value pseudorandomly chosen
+ * from an exponential distribution whose mean is 1.
+ *
+ * @return a nonnegative {@code double} value pseudorandomly chosen from an
+ * exponential distribution
+ */
+ default double nextExponential() {
+ return RandomSupport.computeNextExponential(this);
+ }
+
+ /**
+ * Returns the period of this {@link RandomGenerator} object.
+ *
+ * @return a {@link BigInteger} whose value is the number of distinct possible states of this
+ * {@link RandomGenerator} object, or 0 if unknown, or negative if extremely
+ * large.
+ */
+ BigInteger period();
+
+ /**
+ * The value (0) returned by the {@code period()} method if the period is unknown.
+ */
+ static final BigInteger UNKNOWN_PERIOD = BigInteger.ZERO;
+
+ /**
+ * The (negative) value returned by the {@code period()} method if this generator
+ * has no period because it is truly random rather than just pseudorandom.
+ */
+ static final BigInteger TRULY_RANDOM = BigInteger.valueOf(-1);
+
+ /**
+ * The (negative) value that may be returned by the {@code period()} method
+ * if this generator has a huge period (larger than 2**(2**16)).
+ */
+ static final BigInteger HUGE_PERIOD = BigInteger.valueOf(-2);
+
+ /**
+ * The {@link StreamableGenerator} interface augments the {@link RandomGenerator} interface
+ * to provide methods that return streams of {@link RandomGenerator} objects.
+ * Ideally, such a stream of objects would have the property that the
+ * behavior of each object is statistically independent of all the others.
+ * In practice, one may have to settle for some approximation to this property.
+ *
+ * A generator that implements interface {@link SplittableGenerator}
+ * may choose to use its {@code splits} method to implement the {@code rngs}
+ * method required by this interface.
+ *
+ * A generator that implements interface {@link JumpableGenerator}
+ * may choose to use its {@code jumps} method to implement the {@code rngs}
+ * method required by this interface.
+ *
+ * A generator that implements interface {@link LeapableGenerator}
+ * may choose to use its {@code leaps} method to implement the {@code rngs}
+ * method required by this interface.
+ *
+ * An implementation of the {@link StreamableGenerator} interface must provide
+ * concrete definitions for the methods {@code nextInt()}, {@code nextLong},
+ * {@code period()}, and {@code rngs()}.
+ * Default implementations are provided for all other methods.
+ *
+ * Objects that implement {@link StreamableGenerator} are typically
+ * not cryptographically secure. Consider instead using
+ * {@link java.security.SecureRandom} to get a cryptographically
+ * secure pseudo-random number generator for use by
+ * security-sensitive applications.
+ *
+ * @since 14
+ */
+ public interface StreamableGenerator extends RandomGenerator {
+
+ /**
+ * Returns an instance of {@link StreamableGenerator} that utilizes the
+ * {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return An instance of {@link StreamableGenerator}
+ */
+ public static StreamableGenerator of(String name) {
+ Objects.requireNonNull(name);
+ return RandomGeneratorFactory.of(name, StreamableGenerator.class);
+ }
+
+ /**
+ * Returns an instance of {@link StreamableGenerator} that utilizes the
+ * specified {@code algorithm}.
+ *
+ * @param algorithm Random number generator algorithm
+ *
+ * @return An instance of {@link StreamableGenerator}
+ */
+ public static StreamableGenerator of(Algorithm algorithm) {
+ Objects.requireNonNull(algorithm);
+ return RandomGeneratorFactory.of(algorithm.toString(), StreamableGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link StreamableGenerator} that utilizes the {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return {@link RandomGeneratorFactory} of {@link StreamableGenerator}
+ */
+ public static RandomGeneratorFactory
+ * Ideally, all {@link SplittableGenerator} objects produced by recursive
+ * splitting from a single original {@link SplittableGenerator} object are
+ * statistically independent of one another and individually uniform.
+ * Therefore we would expect the set of values collectively generated
+ * by a set of such objects to have the same statistical properties as
+ * if the same quantity of values were generated by a single thread
+ * using a single {@link SplittableGenerator} object. In practice, one must
+ * settle for some approximation to independence and uniformity.
+ *
+ * Methods are provided to perform a single splitting operation and
+ * also to produce a stream of generators split off from the original
+ * (by either iterative or recursive splitting, or a combination).
+ *
+ * An implementation of the {@link SplittableGenerator} interface must provide
+ * concrete definitions for the methods {@code nextInt()}, {@code nextLong},
+ * {@code period()}, {@code split()}, {@code split(SplittableGenerator)},
+ * {@code splits()}, {@code splits(long)}, {@code splits(SplittableGenerator)},
+ * and {@code splits(long, SplittableGenerator)}. Perhaps the most convenient
+ * way to implement this interface is to extend the abstract class
+ * {@link AbstractSplittableGenerator}.
+ *
+ * Objects that implement {@link SplittableGenerator} are
+ * typically not cryptographically secure. Consider instead using
+ * {@link java.security.SecureRandom} to get a cryptographically
+ * secure pseudo-random number generator for use by
+ * security-sensitive applications.
+ *
+ * @since 14
+ */
+ public interface SplittableGenerator extends StreamableGenerator {
+
+ /**
+ * Returns an instance of {@link SplittableGenerator} that utilizes the
+ * {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return An instance of {@link SplittableGenerator}
+ */
+ public static SplittableGenerator of(String name) {
+ Objects.requireNonNull(name);
+ return RandomGeneratorFactory.of(name, SplittableGenerator.class);
+ }
+
+ /**
+ * Returns an instance of {@link SplittableGenerator} that utilizes the
+ * specified {@code algorithm}.
+ *
+ * @param algorithm Random number generator algorithm
+ *
+ * @return An instance of {@link SplittableGenerator}
+ */
+ public static SplittableGenerator of(Algorithm algorithm) {
+ Objects.requireNonNull(algorithm);
+ return RandomGeneratorFactory.of(algorithm.toString(), SplittableGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link SplittableGenerator} that utilizes the {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return {@link RandomGeneratorFactory} of {@link SplittableGenerator}
+ */
+ public static RandomGeneratorFactory
+ * Ideally, all {@link JumpableGenerator} objects produced by iterative jumping from a single
+ * original {@link JumpableGenerator} object are statistically independent of one another and
+ * individually uniform. In practice, one must settle for some approximation to independence and
+ * uniformity. In particular, a specific implementation may assume that each generator in a
+ * stream produced by the {@code jumps} method is used to produce a number of values no larger
+ * than either 264 or the square root of its period. Implementors are advised to use
+ * algorithms whose period is at least 2127.
+ *
+ * Methods are provided to perform a single jump operation and also to produce a stream of
+ * generators produced from the original by iterative copying and jumping of internal state. A
+ * typical strategy for a multithreaded application is to create a single {@link
+ * JumpableGenerator} object, calls its {@code jumps} method exactly once, and then parcel out
+ * generators from the resulting stream, one to each thread. It is generally not a good idea to
+ * call {@code jump} on a generator that was itself produced by the {@code jumps} method,
+ * because the result may be a generator identical to another generator already produce by that
+ * call to the {@code jumps} method. For this reason, the return type of the {@code jumps}
+ * method is {@code Stream
+ * An implementation of the {@link JumpableGenerator} interface must provide concrete
+ * definitions for the methods {@code nextInt()}, {@code nextLong}, {@code period()}, {@code
+ * copy()}, {@code jump()}, and {@code defaultJumpDistance()}. Default implementations are
+ * provided for all other methods.
+ *
+ * Objects that implement {@link JumpableGenerator} are typically not cryptographically secure.
+ * Consider instead using {@link java.security.SecureRandom} to get a cryptographically secure
+ * pseudo-random number generator for use by security-sensitive applications.
+ *
+ * @since 14
+ */
+ public interface JumpableGenerator extends StreamableGenerator {
+
+ /**
+ * Returns an instance of {@link JumpableGenerator} that utilizes the
+ * {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return An instance of {@link JumpableGenerator}
+ */
+ public static JumpableGenerator of(String name) {
+ Objects.requireNonNull(name);
+ return RandomGeneratorFactory.of(name, JumpableGenerator.class);
+ }
+
+ /**
+ * Returns an instance of {@link JumpableGenerator} that utilizes the
+ * specified {@code algorithm}.
+ *
+ * @param algorithm Random number generator algorithm
+ *
+ * @return An instance of {@link JumpableGenerator}
+ */
+ public static JumpableGenerator of(Algorithm algorithm) {
+ Objects.requireNonNull(algorithm);
+ return RandomGeneratorFactory.of(algorithm.toString(), JumpableGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link JumpableGenerator} that utilizes the {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return {@link RandomGeneratorFactory} of {@link JumpableGenerator}
+ */
+ public static RandomGeneratorFactory
+ * Typically one will construct a series of {@link LeapableGenerator} objects by iterative
+ * leaping from a single original {@link LeapableGenerator} object, and then for each such
+ * object produce a subseries of objects by iterative jumping. There is little conceptual
+ * difference between leaping and jumping, but typically a leap will be a very long jump in the
+ * state cycle (perhaps distance 2128 or so).
+ *
+ * Ideally, all {@link LeapableGenerator} objects produced by iterative leaping and jumping from
+ * a single original {@link LeapableGenerator} object are statistically independent of one
+ * another and individually uniform. In practice, one must settle for some approximation to
+ * independence and uniformity. In particular, a specific implementation may assume that each
+ * generator in a stream produced by the {@code leaps} method is used to produce (by jumping) a
+ * number of objects no larger than 264. Implementors are advised to use algorithms
+ * whose period is at least 2191.
+ *
+ * Methods are provided to perform a single leap operation and also to produce a stream of
+ * generators produced from the original by iterative copying and leaping of internal state.
+ * The generators produced must implement the {@link JumpableGenerator} interface but need not
+ * also implement the {@link LeapableGenerator} interface. A typical strategy for a
+ * multithreaded application is to create a single {@link LeapableGenerator} object, calls its
+ * {@code leaps} method exactly once, and then parcel out generators from the resulting stream,
+ * one to each thread. Then the {@code jumps} method of each such generator be called to
+ * produce a substream of generator objects.
+ *
+ * An implementation of the {@link LeapableGenerator} interface must provide concrete
+ * definitions for the methods {@code nextInt()}, {@code nextLong}, {@code period()},
+ * {@code copy()}, {@code jump()}, {@code defaultJumpDistance()}, {@code leap()},
+ * and {@code defaultLeapDistance()}. Default implementations are provided for all other
+ * methods.
+ *
+ * Objects that implement {@link LeapableGenerator} are typically not cryptographically secure.
+ * Consider instead using {@link java.security.SecureRandom} to get a cryptographically secure
+ * pseudo-random number generator for use by security-sensitive applications.
+ *
+ * @since 14
+ */
+ public interface LeapableGenerator extends JumpableGenerator {
+
+ /**
+ * Returns an instance of {@link LeapableGenerator} that utilizes the
+ * {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return An instance of {@link LeapableGenerator}
+ */
+ public static LeapableGenerator of(String name) {
+ Objects.requireNonNull(name);
+ return RandomGeneratorFactory.of(name, LeapableGenerator.class);
+ }
+
+ /**
+ * Returns an instance of {@link LeapableGenerator} that utilizes the
+ * specified {@code algorithm}.
+ *
+ * @param algorithm Random number generator algorithm
+ *
+ * @return An instance of {@link LeapableGenerator}
+ */
+ public static LeapableGenerator of(Algorithm algorithm) {
+ Objects.requireNonNull(algorithm);
+ return RandomGeneratorFactory.of(algorithm.toString(), LeapableGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link LeapableGenerator} that utilizes the {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return {@link RandomGeneratorFactory} of {@link LeapableGenerator}
+ */
+ public static RandomGeneratorFactory
+ * Ideally, all {@link ArbitrarilyJumpableGenerator} objects produced by iterative jumping from
+ * a single original {@link ArbitrarilyJumpableGenerator} object are statistically independent
+ * of one another and individually uniform, provided that they do not traverse overlapping
+ * portions of the state cycle. In practice, one must settle for some approximation to
+ * independence and uniformity. In particular, a specific implementation may assume that each
+ * generator in a stream produced by the {@code jumps} method is used to produce a number of
+ * values no larger than the jump distance specified. Implementors are advised to use
+ * algorithms whose period is at least 2127.
+ *
+ * For many applications, it suffices to jump forward by a power of two or some small multiple
+ * of a power of two, but this power of two may not be representable as a {@code long} value.
+ * To avoid the use of {@link java.math.BigInteger} values as jump distances, {@code double}
+ * values are used instead.
+ *
+ * Methods are provided to perform a single jump operation and also to produce a stream of
+ * generators produced from the original by iterative copying and jumping of internal state. A
+ * typical strategy for a multithreaded application is to create a single
+ * {@link ArbitrarilyJumpableGenerator} object, call its {@code jumps} method exactly once, and
+ * then parcel out generators from the resulting stream, one to each thread. However, each
+ * generator produced also has type {@link ArbitrarilyJumpableGenerator}; with care, different
+ * jump distances can be used to traverse the entire state cycle in various ways.
+ *
+ * An implementation of the {@link ArbitrarilyJumpableGenerator} interface must provide concrete
+ * definitions for the methods {@code nextInt()}, {@code nextLong}, {@code period()},
+ * {@code copy()}, {@code jump(double)}, {@code defaultJumpDistance()}, and
+ * {@code defaultLeapDistance()}. Default implementations are provided for all other methods.
+ * Perhaps the most convenient way to implement this interface is to extend the abstract class
+ * {@link ArbitrarilyJumpableGenerator}, which provides spliterator-based implementations of the
+ * methods {@code ints}, {@code longs}, {@code doubles}, {@code rngs}, {@code jumps}, and
+ * {@code leaps}.
+ *
+ * Objects that implement {@link ArbitrarilyJumpableGenerator} are typically not
+ * cryptographically secure. Consider instead using {@link java.security.SecureRandom} to get a
+ * cryptographically secure pseudo-random number generator for use by security-sensitive
+ * applications.
+ *
+ * @since 14
+ */
+ public interface ArbitrarilyJumpableGenerator extends LeapableGenerator {
+
+ /**
+ * Returns an instance of {@link ArbitrarilyJumpableGenerator} that utilizes the
+ * {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return An instance of {@link ArbitrarilyJumpableGenerator}
+ */
+ public static ArbitrarilyJumpableGenerator of(String name) {
+ Objects.requireNonNull(name);
+ return RandomGeneratorFactory.of(name, ArbitrarilyJumpableGenerator.class);
+ }
+
+ /**
+ * Returns an instance of {@link ArbitrarilyJumpableGenerator} that utilizes the
+ * specified {@code algorithm}.
+ *
+ * @param algorithm Random number generator algorithm
+ *
+ * @return An instance of {@link ArbitrarilyJumpableGenerator}
+ */
+ public static ArbitrarilyJumpableGenerator of(Algorithm algorithm) {
+ Objects.requireNonNull(algorithm);
+ return RandomGeneratorFactory.of(algorithm.toString(), ArbitrarilyJumpableGenerator.class);
+ }
+
+ /**
+ * Returns a {@link RandomGeneratorFactory} that can produce instances
+ * of {@link ArbitrarilyJumpableGenerator} that utilizes the {@code name} algorithm.
+ *
+ * @param name Name of random number generator algorithm
+ *
+ * @return {@link RandomGeneratorFactory} of {@link ArbitrarilyJumpableGenerator}
+ */
+ public static RandomGeneratorFactory
+ * The implementation considers four cases:
+ *
+ * The implementation considers two cases:
+ * An implementation of the {@link AbstractArbitrarilyJumpableGenerator} class
+ * must provide concrete definitions for the methods {@code nextInt()},
+ * {@code nextLong}, {@code period()}, {@code copy()}, {@code jump(double)},
+ * {@code defaultJumpDistance()}, and {@code defaultLeapDistance()}.
+ * Default implementations are provided for all other methods.
+ *
+ * The documentation for each non-abstract method in this class
+ * describes its implementation in detail. Each of these methods may
+ * be overridden if the pseudorandom number generator being
+ * implemented admits a more efficient implementation.
+ *
+ * @since 14
+ */
+ public abstract static class AbstractArbitrarilyJumpableGenerator
+ extends AbstractSpliteratorGenerator implements RandomGenerator.ArbitrarilyJumpableGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * This class provides most of the "user API" methods needed to satisfy
+ * the interface ArbitrarilyJumpableGenerator. Most of these methods
+ * are in turn inherited from AbstractGenerator and the non-public class
+ * AbstractSpliteratorGenerator; this file implements four versions of the
+ * jumps method and defines the spliterators necessary to support them.
+ *
+ * File organization: First the non-public methods needed by the class
+ * AbstractSpliteratorGenerator, then the main public methods, followed by some
+ * custom spliterator classes needed for stream methods.
+ */
+
+ // IllegalArgumentException messages
+ static final String BadLogDistance = "logDistance must be non-negative";
+
+ // Methods required by class AbstractSpliteratorGenerator
+ public Spliterator.OfInt makeIntsSpliterator(long index, long fence, int origin, int bound) {
+ return new RandomIntsSpliterator(this, index, fence, origin, bound);
+ }
+ public Spliterator.OfLong makeLongsSpliterator(long index, long fence, long origin, long bound) {
+ return new RandomLongsSpliterator(this, index, fence, origin, bound);
+ }
+ public Spliterator.OfDouble makeDoublesSpliterator(long index, long fence, double origin, double bound) {
+ return new RandomDoublesSpliterator(this, index, fence, origin, bound);
+ }
+
+ // Similar methods used by this class
+ Spliterator
+ * To implement a pseudorandom number generator, the programmer needs only to extend this class and
+ * provide implementations for the methods {@code nextInt()}, {@code nextLong()}, {@code period()},
+ * and {@code split(SplittableGenerator)}.
+ *
+ * (If the pseudorandom number generator also has the ability to jump an arbitrary
+ * specified distance, then the programmer may wish to consider instead extending the
+ * class {@link AbstractArbitrarilyJumpableGenerator}. See also the class
+ * {@link AbstractSplittableWithBrineGenerator}.)
+ *
+ * The programmer should generally provide at least three constructors: one that takes no arguments,
+ * one that accepts a {@code long} seed value, and one that accepts an array of seed {@code byte}
+ * values. This class provides a public {@code initialSeed()} method that may be useful in
+ * initializing some static state from which to derive defaults seeds for use by the no-argument
+ * constructor.
+ *
+ * For the stream methods (such as {@code ints()} and {@code splits()}), this class provides
+ * {@link Spliterator}-based implementations that allow parallel execution when appropriate.
+ *
+ * The documentation for each non-abstract method in this class describes its implementation in
+ * detail. Each of these methods may be overridden if the pseudorandom number generator being
+ * implemented admits a more efficient implementation.
+ *
+ * @since 14
+ */
+ public abstract static class AbstractSplittableGenerator extends AbstractSpliteratorGenerator implements SplittableGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * This class provides most of the "user API" methods needed to
+ * satisfy the interface SplittableGenerator. Most of these methods
+ * are in turn inherited from AbstractGenerator and the non-public class
+ * AbstractSpliteratorGenerator; this class provides two versions of the
+ * splits method and defines the spliterators necessary to support
+ * them.
+ *
+ * File organization: First the non-public methods needed by the class
+ * AbstractSpliteratorGenerator, then the main public methods, followed by some
+ * custom spliterator classes.
+ */
+
+ public Spliterator.OfInt makeIntsSpliterator(long index, long fence, int origin, int bound) {
+ return new RandomIntsSpliterator(this, index, fence, origin, bound);
+ }
+
+ public Spliterator.OfLong makeLongsSpliterator(long index, long fence, long origin, long bound) {
+ return new RandomLongsSpliterator(this, index, fence, origin, bound);
+ }
+
+ public Spliterator.OfDouble makeDoublesSpliterator(long index, long fence, double origin, double bound) {
+ return new RandomDoublesSpliterator(this, index, fence, origin, bound);
+ }
+
+ Spliterator
+ * This pseudorandom number generator provides the entropy used to seed the new ones.
+ *
+ * @return a stream of {@link SplittableGenerator} objects
+ *
+ * @implNote This method is implemented to be equivalent to {@code splits(Long.MAX_VALUE)}.
+ */
+ public Stream
+ * This pseudorandom number generator provides the entropy used to seed the new ones.
+ *
+ * @param streamSize the number of values to generate
+ *
+ * @return a stream of {@link SplittableGenerator} objects
+ *
+ * @throws IllegalArgumentException if {@code streamSize} is less than zero
+ */
+ public Stream
+ * To implement a pseudorandom number generator, the programmer needs only to extend this class and
+ * provide implementations for the methods {@code nextInt()}, {@code nextLong()}, {@code period()},
+ * and {@code split(SplittableGenerator, long)}.
+ *
+ * The programmer should generally provide at least three constructors: one that takes no arguments,
+ * one that accepts a {@code long} seed value, and one that accepts an array of seed {@code byte}
+ * values. This class provides a public {@code initialSeed()} method that may be useful in
+ * initializing some static state from which to derive defaults seeds for use by the no-argument
+ * constructor.
+ *
+ * For the stream methods (such as {@code ints()} and {@code splits()}), this class provides
+ * {@link Spliterator}-based implementations that allow parallel execution when appropriate.
+ *
+ * The documentation for each non-abstract method in this class describes its implementation in
+ * detail. Each of these methods may be overridden if the pseudorandom number generator being
+ * implemented admits a more efficient implementation.
+ *
+ * @since 14
+ */
+ public abstract static class AbstractSplittableWithBrineGenerator
+ extends AbstractSplittableGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * This class provides most of the "user API" methods needed to
+ * satisfy the interface SplittableGenerator. Most of these methods
+ * are in turn inherited from AbstractSplittableGenerator and the non-public class
+ * AbstractSpliteratorGenerator; this class provides four versions of the
+ * splits method and defines the spliterators necessary to support
+ * them.
+ *
+ * File organization: First the non-public methods needed by the class
+ * AbstractSplittableWithBrineGenerator, then the main public methods,
+ * followed by some custom spliterator classes needed for stream methods.
+ */
+
+ // The salt consists groups of bits each SALT_SHIFT in size, starting from
+ // the left-hand (high-order) end of the word. We can regard them as
+ // digits base (1 << SALT_SHIFT). If SALT_SHIFT does not divide 64
+ // evenly, then any leftover bits at the low end of the word are zero.
+ // The lowest digit of the salt is set to the largest possible digit
+ // (all 1-bits, or ((1 << SALT_SHIFT) - 1)); all other digits are set
+ // to a randomly chosen value less than that largest possible digit.
+ // The salt may be shifted left by SALT_SHIFT any number of times.
+ // If any salt remains in the word, its right-hand end can be identified
+ // by searching from left to right for an occurrence of a digit that is
+ // all 1-bits (not that we ever do that; this is simply a proof that one
+ // can identify the boundary between the salt and the index if any salt
+ // remains in the word). The idea is that before computing the bitwise OR
+ // of an index and the salt, one can first check to see whether the
+ // bitwise AND is nonzero; if so, one can shift the salt left by
+ // SALT_SHIFT and try again. In this way, when the bitwise OR is
+ // computed, if the salt is nonzero then its rightmost 1-bit is to the
+ // left of the leftmost 1-bit of the index.
+
+ // We need 2 <= SALT_SHIFT <= 63 (3 through 8 are good values; 4 is probably best)
+ static final int SALT_SHIFT = 4;
+
+ // Methods required by class AbstractSpliteratorGenerator (override)
+ Spliterator
+ * Series of generated values pass the TestU01 BigCrush and PractRand test suites
+ * that measure independence and uniformity properties of random number generators.
+ *
+ * The class {@link Xoroshiro128StarStar} uses the {@code xoroshiro128} algorithm,
+ * version 1.0 (parameters 24, 16, 37), with the "**" scrambler (a mixing function).
+ * Its state consists of two {@code long} fields {@code x0} and {@code x1},
+ * which can take on any values provided that they are not both zero.
+ * The period of this generator is 2128-1.
+ *
+ * The 64-bit values produced by the {@code nextLong()} method are equidistributed.
+ * To be precise, over the course of the cycle of length 2128-1,
+ * each nonzero {@code long} value is generated 264 times,
+ * but the value 0 is generated only 264-1 times.
+ * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
+ * methods are likewise equidistributed.
+ *
+ * In fact, the 64-bit values produced by the {@code nextLong()} method are 2-equidistributed.
+ * To be precise: consider the (overlapping) length-2 subsequences of the cycle of 64-bit
+ * values produced by {@code nextLong()} (assuming no other methods are called that would
+ * affect the state). There are 2128-1 such subsequences, and each subsequence,
+ * which consists of 2 64-bit values, can have one of 2128 values. Of those
+ * 2128 subsequence values, each one is generated exactly once over the course
+ * of the entire cycle, except that the subsequence (0, 0) never appears.
+ * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
+ * methods are likewise 2-equidistributed, but note that that the subsequence (0, 0)
+ * can also appear (but occurring somewhat less frequently than all other subsequences),
+ * because the values produced by those methods have fewer than 64 randomly chosen bits.
+ *
+ * Instances {@link Xoroshiro128StarStar} are not thread-safe.
+ * They are designed to be used so that each thread as its own instance.
+ * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps}
+ * can be used to construct new instances of {@link Xoroshiro128StarStar} that traverse
+ * other parts of the state cycle.
+ *
+ * Instances of {@link Xoroshiro128StarStar} 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 Xoroshiro128StarStar implements LeapableGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * This is an implementation of the xoroshiro128** algorithm written
+ * in 2016 by David Blackman and Sebastiano Vigna (vigna@acm.org),
+ * and updated with improved parameters in 2018.
+ * See http://xoshiro.di.unimi.it and these two papers:
+ *
+ * Sebastiano Vigna. 2016. An Experimental Exploration of Marsaglia's
+ * xorshift Generators, Scrambled. ACM Transactions on Mathematical
+ * Software 42, 4, Article 30 (June 2016), 23 pages.
+ * https://doi.org/10.1145/2845077
+ *
+ * David Blackman and Sebastiano Vigna. 2018. Scrambled Linear
+ * Pseudorandom Number Generators. Computing Research Repository (CoRR).
+ * http://arxiv.org/abs/1805.01407
+ *
+ * The jump operation moves the current generator forward by 2*64
+ * steps; this has the same effect as calling nextLong() 2**64
+ * times, but is much faster. Similarly, the leap operation moves
+ * the current generator forward by 2*96 steps; this has the same
+ * effect as calling nextLong() 2**96 times, but is much faster.
+ * The copy method may be used to make a copy of the current
+ * generator. Thus one may repeatedly and cumulatively copy and
+ * jump to produce a sequence of generators whose states are well
+ * spaced apart along the overall state cycle (indeed, the jumps()
+ * and leaps() methods each produce a stream of such generators).
+ * The generators can then be parceled out to other threads.
+ *
+ * File organization: First the non-public methods that constitute the
+ * main algorithm, then the public methods. Note that many methods are
+ * defined by classes {@link AbstractJumpableGenerator} and {@link AbstractGenerator}.
+ */
+
+ /* ---------------- static fields ---------------- */
+
+ /**
+ * The seed generator for default constructors.
+ */
+ private static final AtomicLong DEFAULT_GEN = new AtomicLong(RandomSupport.initialSeed());
+
+ /*
+ * The period of this generator, which is 2**128 - 1.
+ */
+ private static final BigInteger PERIOD =
+ BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE);
+
+ /* ---------------- instance fields ---------------- */
+
+ /**
+ * The per-instance state.
+ * At least one of the two fields x0 and x1 must be nonzero.
+ */
+ private long 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.
+ *
+ * @param x0 first word of the initial state
+ * @param x1 second word of the initial state
+ */
+ public Xoroshiro128StarStar(long x0, long x1) {
+ this.x0 = x0;
+ this.x1 = x1;
+ // If x0 and x1 are both zero, we must choose nonzero values.
+ if ((x0 | x1) == 0) {
+ this.x0 = RandomSupport.GOLDEN_RATIO_64;
+ this.x1 = RandomSupport.SILVER_RATIO_64;
+ }
+ }
+
+ /**
+ * Creates a new instance of {@link Xoroshiro128StarStar} using the
+ * specified {@code long} value as the initial seed. Instances of
+ * {@link Xoroshiro128StarStar} created with the same seed in the same
+ * program generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public Xoroshiro128StarStar(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 x values are then filled in as if by a SplitMix PRNG with
+ // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer.
+ this(RandomSupport.mixStafford13(seed ^= RandomSupport.SILVER_RATIO_64),
+ RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@link Xoroshiro128StarStar} 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 Xoroshiro128StarStar() {
+ // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.
+ this(DEFAULT_GEN.getAndAdd(RandomSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@link Xoroshiro128StarStar} using the specified array of
+ * initial seed bytes. Instances of {@link Xoroshiro128StarStar} created with the same
+ * seed array in the same program execution generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public Xoroshiro128StarStar(byte[] seed) {
+ // Convert the seed to 2 long values, which are not both zero.
+ long[] data = RandomSupport.convertSeedBytesToLongs(seed, 2, 2);
+ long x0 = data[0], x1 = data[1];
+ this.x0 = x0;
+ this.x1 = x1;
+ }
+
+ /* ---------------- public methods ---------------- */
+
+ public Xoroshiro128StarStar copy() { return new Xoroshiro128StarStar(x0, x1); }
+
+ /*
+ * To the extent possible under law, the author has dedicated all copyright and related and
+ * neighboring rights to this software to the public domain worldwide. This software is
+ * distributed without any warranty.
+ *
+ * See
+ * Beside passing BigCrush, this generator passes the PractRand test suite up to (and included)
+ * 16TB, with the exception of binary rank tests, which fail due to the lowest bit being an
+ * LFSR; all other bits pass all tests. We suggest to use a sign test to extract a random
+ * Boolean value.
+ *
+ * Note that the generator uses a simulated rotate operation, which most C compilers will turn
+ * into a single instruction. In Java, you can use Long.rotateLeft(). In languages that do not
+ * make low-level rotation instructions accessible xorshift128+ could be faster.
+ *
+ * The state must be seeded so that it is not everywhere zero. If you have a 64-bit seed, we
+ * suggest to seed a splitmix64 generator and use its output to fill s.
+ */
+
+ /**
+ * Returns a pseudorandom {@code long} value.
+ *
+ * @return a pseudorandom {@code long} value
+ */
+ public long nextLong() {
+ final long s0 = x0;
+ long s1 = x1;
+ // Compute the result based on current state information
+ // (this allows the computation to be overlapped with state update).
+ final long result = Long.rotateLeft(s0 * 5, 7) * 9; // "starstar" mixing function
+
+ s1 ^= s0;
+ x0 = Long.rotateLeft(s0, 24) ^ s1 ^ (s1 << 16); // a, b
+ x1 = Long.rotateLeft(s1, 37); // c
+
+ return result;
+ }
+
+ public BigInteger period() {
+ return PERIOD;
+ }
+
+ public double defaultJumpDistance() {
+ return 0x1.0p64;
+ }
+
+ public double defaultLeapDistance() {
+ return 0x1.0p96;
+ }
+
+ private static final long[] JUMP_TABLE = { 0xdf900294d8f554a5L, 0x170865df4b3201fcL };
+
+ private static final long[] LEAP_TABLE = { 0xd2a98b26625eee7bL, 0xdddf9b1090aa7ac1L };
+
+ /**
+ * This is the jump function for the generator. It is equivalent to 2**64 calls to nextLong();
+ * it can be used to generate 2**64 non-overlapping subsequences for parallel computations.
+ */
+ public void jump() {
+ jumpAlgorithm(JUMP_TABLE);
+ }
+
+ /**
+ * This is the long-jump function for the generator. It is equivalent to 2**96 calls to next();
+ * it can be used to generate 2**32 starting points, from each of which jump() will generate
+ * 2**32 non-overlapping subsequences for parallel distributed computations.
+ */
+ public void leap() {
+ jumpAlgorithm(LEAP_TABLE);
+ }
+
+ private void jumpAlgorithm(long[] table) {
+ long s0 = 0, s1 = 0;
+ for (int i = 0; i < table.length; i++) {
+ for (int b = 0; b < 64; b++) {
+ if ((table[i] & (1L << b)) != 0) {
+ s0 ^= x0;
+ s1 ^= x1;
+ }
+ nextLong();
+ }
+ x0 = s0;
+ x1 = s1;
+ }
+ }
+}
diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/Xoshiro256StarStar.java
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.base/share/classes/java/util/random/Xoshiro256StarStar.java Thu Nov 14 12:50:08 2019 -0400
@@ -0,0 +1,308 @@
+/*
+ * 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.LeapableGenerator;
+
+/**
+ * A generator of uniform pseudorandom values applicable for use in
+ * (among other contexts) isolated parallel computations that may
+ * generate subtasks. Class {@link Xoshiro256StarStar} implements
+ * interfaces {@link RandomGenerator} and {@link LeapableGenerator},
+ * 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 {@link Xoshiro256StarStar} objects
+ * by "jumping" or "leaping".
+ *
+ * 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
+ * version 1.2.3 of TestU01
+ * and version 0.90 of PractRand.
+ * 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.
+ *
+ * The class {@link Xoshiro256StarStar} uses the {@code xoshiro256} algorithm,
+ * version 1.0 (parameters 17, 45), with the "**" scrambler (a mixing function).
+ * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2},
+ * and {@code x3}, which can take on any values provided that they are not all zero.
+ * The period of this generator is 2256-1.
+ *
+ * The 64-bit values produced by the {@code nextLong()} method are equidistributed.
+ * To be precise, over the course of the cycle of length 2256-1,
+ * each nonzero {@code long} value is generated 2192 times,
+ * but the value 0 is generated only 2192-1 times.
+ * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
+ * methods are likewise equidistributed.
+ *
+ * In fact, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed.
+ * To be precise: consider the (overlapping) length-4 subsequences of the cycle of 64-bit
+ * values produced by {@code nextLong()} (assuming no other methods are called that would
+ * affect the state). There are 2256-1 such subsequences, and each subsequence,
+ * which consists of 4 64-bit values, can have one of 2256 values. Of those
+ * 2256 subsequence values, each one is generated exactly once over the course
+ * of the entire cycle, except that the subsequence (0, 0, 0, 0) never appears.
+ * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
+ * methods are likewise 4-equidistributed, but note that that the subsequence (0, 0, 0, 0)
+ * can also appear (but occurring somewhat less frequently than all other subsequences),
+ * because the values produced by those methods have fewer than 64 randomly chosen bits.
+ *
+ * Instances {@link Xoshiro256StarStar} are not thread-safe.
+ * They are designed to be used so that each thread as its own instance.
+ * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps}
+ * can be used to construct new instances of {@link Xoshiro256StarStar} that traverse
+ * other parts of the state cycle.
+ *
+ * Instances of {@link Xoshiro256StarStar} 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 Xoshiro256StarStar implements LeapableGenerator {
+
+ /*
+ * Implementation Overview.
+ *
+ * This is an implementation of the xoroshiro128** algorithm written
+ * in 2018 by David Blackman and Sebastiano Vigna (vigna@acm.org).
+ * See http://xoshiro.di.unimi.it and these two papers:
+ *
+ * Sebastiano Vigna. 2016. An Experimental Exploration of Marsaglia's
+ * xorshift Generators, Scrambled. ACM Transactions on Mathematical
+ * Software 42, 4, Article 30 (June 2016), 23 pages.
+ * https://doi.org/10.1145/2845077
+ *
+ * David Blackman and Sebastiano Vigna. 2018. Scrambled Linear
+ * Pseudorandom Number Generators. Computing Research Repository (CoRR).
+ * http://arxiv.org/abs/1805.01407
+ *
+ * The jump operation moves the current generator forward by 2*128
+ * steps; this has the same effect as calling nextLong() 2**128
+ * times, but is much faster. Similarly, the leap operation moves
+ * the current generator forward by 2*192 steps; this has the same
+ * effect as calling nextLong() 2**192 times, but is much faster.
+ * The copy method may be used to make a copy of the current
+ * generator. Thus one may repeatedly and cumulatively copy and
+ * jump to produce a sequence of generators whose states are well
+ * spaced apart along the overall state cycle (indeed, the jumps()
+ * and leaps() methods each produce a stream of such generators).
+ * The generators can then be parceled out to other threads.
+ *
+ * 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 DEFAULT_GEN = new AtomicLong(RandomSupport.initialSeed());
+
+ /*
+ * The period of this generator, which is 2**256 - 1.
+ */
+ private static final BigInteger PERIOD =
+ BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE);
+
+ /* ---------------- instance fields ---------------- */
+
+ /**
+ * The per-instance state.
+ * At least one of the four fields x0, x1, x2, and x3 must be nonzero.
+ */
+ private long x0, x1, x2, x3;
+
+ /* ---------------- 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 x0 first word of the initial state
+ * @param x1 second word of the initial state
+ * @param x2 third word of the initial state
+ * @param x3 fourth word of the initial state
+ */
+ public Xoshiro256StarStar(long x0, long x1, long x2, long x3) {
+ this.x0 = x0;
+ this.x1 = x1;
+ this.x2 = x2;
+ this.x3 = x3;
+ // If x0, x1, x2, and x3 are all zero, we must choose nonzero values.
+ if ((x0 | x1 | x2 | x3) == 0) {
+ // At least three of the four values generated here will be nonzero.
+ this.x0 = RandomSupport.mixStafford13(x0 += RandomSupport.GOLDEN_RATIO_64);
+ this.x1 = (x0 += RandomSupport.GOLDEN_RATIO_64);
+ this.x2 = (x0 += RandomSupport.GOLDEN_RATIO_64);
+ this.x3 = (x0 += RandomSupport.GOLDEN_RATIO_64);
+ }
+ }
+
+ /**
+ * Creates a new instance of {@link Xoshiro256StarStar} using the
+ * specified {@code long} value as the initial seed. Instances of
+ * {@link Xoshiro256StarStar} created with the same seed in the same
+ * program generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public Xoshiro256StarStar(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 x values are then filled in as if by a SplitMix PRNG with
+ // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer.
+ this(RandomSupport.mixStafford13(seed ^= RandomSupport.SILVER_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 Xoshiro256StarStar} 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 Xoshiro256StarStar() {
+ // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.
+ this(DEFAULT_GEN.getAndAdd(RandomSupport.GOLDEN_RATIO_64));
+ }
+
+ /**
+ * Creates a new instance of {@link Xoshiro256StarStar} using the specified array of
+ * initial seed bytes. Instances of {@link Xoshiro256StarStar} created with the same
+ * seed array in the same program execution generate identical sequences of values.
+ *
+ * @param seed the initial seed
+ */
+ public Xoshiro256StarStar(byte[] seed) {
+ // Convert the seed to 4 long values, which are not all zero.
+ long[] data = RandomSupport.convertSeedBytesToLongs(seed, 4, 4);
+ long x0 = data[0], x1 = data[1], x2 = data[2], x3 = data[3];
+ this.x0 = x0;
+ this.x1 = x1;
+ this.x2 = x2;
+ this.x3 = x3;
+ }
+
+ /* ---------------- public methods ---------------- */
+
+ public Xoshiro256StarStar copy() {
+ return new Xoshiro256StarStar(x0, x1, x2, x3);
+ }
+
+ /**
+ * Returns a pseudorandom {@code long} value.
+ *
+ * @return a pseudorandom {@code long} value
+ */
+ public long nextLong() {
+ // Compute the result based on current state information
+ // (this allows the computation to be overlapped with state update).
+ final long result = Long.rotateLeft(x0 * 5, 7) * 9; // "starstar" mixing function
+
+ long q0 = x0, q1 = x1, q2 = x2, q3 = x3;
+ { // xoshiro256 1.0
+ long t = q1 << 17;
+ q2 ^= q0;
+ q3 ^= q1;
+ q1 ^= q2;
+ q0 ^= q3;
+ q2 ^= t;
+ q3 = Long.rotateLeft(q3, 45);
+ }
+ x0 = q0; x1 = q1; x2 = q2; x3 = q3;
+ return result;
+ }
+
+ public BigInteger period() {
+ return PERIOD;
+ }
+
+ public double defaultJumpDistance() {
+ return 0x1.0p64;
+ }
+
+ public double defaultLeapDistance() {
+ return 0x1.0p96;
+ }
+
+ private static final long[] JUMP_TABLE = {
+ 0x180ec6d33cfd0abaL, 0xd5a61266f0c9392cL, 0xa9582618e03fc9aaL, 0x39abdc4529b1661cL };
+
+ private static final long[] LEAP_TABLE = {
+ 0x76e15d3efefdcbbfL, 0xc5004e441c522fb3L, 0x77710069854ee241L, 0x39109bb02acbe635L };
+
+ /**
+ * This is the jump function for the generator. It is equivalent to 2**128 calls to next(); it
+ * can be used to generate 2**128 non-overlapping subsequences for parallel computations.
+ */
+ public void jump() {
+ jumpAlgorithm(JUMP_TABLE);
+ }
+
+ /**
+ * This is the long-jump function for the generator. It is equivalent to 2**192 calls to next();
+ * it can be used to generate 2**64 starting points, from each of which jump() will generate
+ * 2**64 non-overlapping subsequences for parallel distributed computations.
+ */
+ public void leap() {
+ jumpAlgorithm(LEAP_TABLE);
+ }
+
+ private void jumpAlgorithm(long[] table) {
+ long s0 = 0, s1 = 0, s2 = 0, s3 = 0;
+ for (int i = 0; i < table.length; i++) {
+ for (int b = 0; b < 64; b++) {
+ if ((table[i] & (1L << b)) != 0) {
+ s0 ^= x0;
+ s1 ^= x1;
+ s2 ^= x2;
+ s3 ^= x3;
+ }
+ nextLong();
+ }
+ x0 = s0;
+ x1 = s1;
+ x2 = s2;
+ x3 = s3;
+ }
+ }
+
+}
diff -r effb66aab08b -r da026c172c1e src/java.base/share/classes/java/util/random/package-info.java
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.base/share/classes/java/util/random/package-info.java Thu Nov 14 12:50:08 2019 -0400
@@ -0,0 +1,104 @@
+/*
+ * Copyright (c) 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.
+ */
+
+ /**
+ * Classes and interfaces that support the definition and use of "random generators", a term that
+ * is meant to cover what have traditionally been called "random number generators" as well as
+ * generators of other sorts of randomly chosen values, and also to cover not only deterministic
+ * (pseudorandom) algorithms but also generators of values that use some "truly random" physical
+ * source (perhaps making use of thermal noise, for example, or quantum-mechanical effects).
+ *
+ * The principal interface is {@link java.util.random.RandomGenerator}, which provides methods
+ * for requesting individual values of type {@code int}, {@code long}, {@code float}, {@code double}, or {@code boolean}
+ * chosen (pseudo)randomly from a uniform distribution; methods for requesting values of type {@code double}
+ * chosen (pseudo)randomly from a normal distribution or from an exponential distribution;
+ * and methods for creating streams of (pseudo)randomly chosen values of type {@code int}, {@code long}, or {@code double}.
+ * These streams are spliterator-based, allowing for parallel processing of their elements.
+ *
+ * An important subsidiary interface is {@link java.util.random.RandomGenerator.StreamableGenerator},
+ * which provides methods for creating spliterator-based streams of {@code RandomGenerator} objects,
+ * allowing for allowing for parallel processing of these objects using multiple threads.
+ * Unlike {@link java.util.Random}, most implementations of {@code java.util.random.RandomGenerator}
+ * are not thread-safe. The intent is that instances should not be shared among threads;
+ * rather, each thread should have its own random generator(s) to use. The various pseudorandom algorithms
+ * provided by this package are designed so that multiple instances will (with very high probability) behave as
+ * if statistically independent.
+ *
+ * Historically, most pseudorandom generator algorithms have been based on some sort of
+ * finite-state machine with a single, large cycle of states; when it is necessary to have
+ * multiple threads use the same algorithm simultaneously, the usual technique is to arrange for
+ * each thread to traverse a different region of the state cycle. These regions may be doled out
+ * to threads by starting with a single initial state and then using a "jump function" that
+ * travels a long distance around the cycle (perhaps 264 steps or more); the jump function is applied repeatedly
+ * and sequentially, to identify widely spaced initial states for each thread's generator. This strategy is
+ * supported by the interface {@link java.util.random.RandomGenerator.JumpableGenerator}.
+ * Sometimes it is desirable to support two levels of jumping (by long distances and
+ * by really long distances); this strategy is supported by the interface
+ * {@link java.util.random.RandomGenerator.LeapableGenerator}. There is also an interface
+ * {@link java.util.random.RandomGenerator.ArbitrarilyJumpableGenerator} for algorithms that
+ * allow jumping along the state cycle by any user-specified distance.
+ * In this package, implementations of these interfaces include
+ * {@link java.util.random.Xoroshiro128PlusPlus},
+ * {@link java.util.random.Xoroshiro128StarStar},
+ * {@link java.util.random.Xoshiro256StarStar},
+ * and {@link java.util.random.MRG32K3A}.
+ *
+ * A more recent category of "splittable" pseudorandom generator algorithms uses a large family
+ * of state cycles and makes some attempt to ensure that distinct instances use different state
+ * cycles; but even if two instances "accidentally" use the same state cycle, they are highly
+ * likely to traverse different regions parts of that shared state cycle. This strategy is
+ * supported by the interface {@link java.util.random.RandomGenerator.SplittableGenerator}.
+ * In this package, implementations of this interface include
+ * {@link java.util.random.L32X64MixRandom},
+ * {@link java.util.random.L64X128MixRandom},
+ * {@link java.util.random.L64X128PlusPlusRandom},
+ * {@link java.util.random.L64X128StarStarMixRandom},
+ * {@link java.util.random.L64X256MixRandom},
+ * {@link java.util.random.L64X1024MixRandom},
+ * {@link java.util.random.L128X128MixRandom},
+ * {@link java.util.random.L128X128PlusPlusRandom},
+ * {@link java.util.random.L128X128StarStarMixRandom},
+ * {@link java.util.random.L128X256MixRandom},
+ * {@link java.util.random.L128X1024MixRandom},
+ * and {@link java.util.SplittableRandom}.
+ * Generally speaking, among the "{@code LmmmXnnn}" generators, the state size of the generator is
+ * {@code (mmm - 1 + nnn)} bits and the memory required for an instance is {@code (2 * mmm + nnn)} bits;
+ * larger values of "{@code mmm}" imply a lower probability that two instances will traverse the
+ * same state cycle; and larger values of "{@code nnn}" imply that the generator is equidistributed
+ * in a larger number of dimensions. A class with "{@code Mix}" in its name uses a strong mixing
+ * function with excellent avalanche characteristics; a class with "{@code StarStar}" or "{@code PlusPlus}"
+ * in its name uses a weaker but faster mixing function. See the documentation for individual classes
+ * for details about their specific characteristics.
+ *
+ * The class {@link java.util.random.RandomSupport} provides utility methods, constants, and
+ * abstract classes frequently useful in the implementation of pseudorandom number generators
+ * that satisfy the interface {@link RandomGenerator}.
+ *
+ * @since 14
+ */
+
+ package java.util.random;
+
+
+ *
+ *
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code long} values
+ * @param origin the least value that can be produced,
+ * unless greater than or equal to {@code bound}
+ * @param bound the upper bound (exclusive), unless {@code origin}
+ * is greater than or equal to {@code bound}
+ *
+ * @return a pseudorandomly chosen {@code long} value,
+ * which will be between {@code origin} (inclusive) and
+ * {@code bound} exclusive unless {@code origin}
+ * is greater than or equal to {@code bound}
+ */
+ public static long boundedNextLong(RandomGenerator rng, long origin, long bound) {
+ long r = rng.nextLong();
+ if (origin < bound) {
+ // It's not case (1).
+ final long n = bound - origin;
+ final long m = n - 1;
+ if ((n & m) == 0L) {
+ // It is case (2): length of range is a power of 2.
+ r = (r & m) + origin;
+ } else if (n > 0L) {
+ // It is case (3): need to reject over-represented candidates.
+ /* This loop takes an unlovable form (but it works):
+ because the first candidate is already available,
+ we need a break-in-the-middle construction,
+ which is concisely but cryptically performed
+ within the while-condition of a body-less for loop. */
+ for (long u = r >>> 1; // ensure nonnegative
+ u + m - (r = u % n) < 0L; // rejection check
+ u = rng.nextLong() >>> 1) // retry
+ ;
+ r += origin;
+ }
+ else {
+ // It is case (4): length of range not representable as long.
+ while (r < origin || r >= bound)
+ r = rng.nextLong();
+ }
+ }
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextLong} used by the public method
+ * {@code nextLong(bound)}. This is essentially a version of
+ * {@code boundedNextLong(origin, bound)} that has been
+ * specialized for the case where the {@code origin} is zero
+ * and the {@code bound} is greater than zero. The value
+ * returned is chosen pseudorandomly from nonnegative integer
+ * values less than {@code bound}.
+ *
+ * @implNote This method first calls {@code nextLong()} to obtain
+ * a {@code long} value that is assumed to be pseudorandomly
+ * chosen uniformly and independently from the 264
+ * possible {@code long} values (that is, each of the 264
+ * possible long values is equally likely to be chosen).
+ * Under some circumstances (when the specified range is not
+ * a power of 2), {@code nextLong()} may be called additional times
+ * to ensure that that the values in the specified range are
+ * equally likely to be chosen (provided the assumption holds).
+ *
+ *
+ *
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code long} values
+ * @param bound the upper bound (exclusive); must be greater than zero
+ *
+ * @return a pseudorandomly chosen {@code long} value
+ */
+ public static long boundedNextLong(RandomGenerator rng, long bound) {
+ // Specialize boundedNextLong for origin == 0, bound > 0
+ final long m = bound - 1;
+ long r = rng.nextLong();
+ if ((bound & m) == 0L) {
+ // The bound is a power of 2.
+ r &= m;
+ } else {
+ // Must reject over-represented candidates
+ /* This loop takes an unlovable form (but it works):
+ because the first candidate is already available,
+ we need a break-in-the-middle construction,
+ which is concisely but cryptically performed
+ within the while-condition of a body-less for loop. */
+ for (long u = r >>> 1;
+ u + m - (r = u % bound) < 0L;
+ u = rng.nextLong() >>> 1)
+ ;
+ }
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextInt} used by an {@link IntStream}
+ * {@link Spliterator} and by the public method
+ * {@code nextInt(origin, bound)}. If {@code origin} is greater
+ * than {@code bound}, then this method simply calls the unbounded
+ * version of {@code nextInt()}, choosing pseudorandomly from
+ * among all 264 possible {@code int} values}, and
+ * otherwise uses one or more calls to {@code nextInt()} to
+ * choose a value pseudorandomly from the possible values
+ * between {@code origin} (inclusive) and {@code bound} (exclusive).
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code int} values
+ * @param origin the least value that can be produced,
+ * unless greater than or equal to {@code bound}
+ * @param bound the upper bound (exclusive), unless {@code origin}
+ * is greater than or equal to {@code bound}
+ *
+ * @return a pseudorandomly chosen {@code int} value,
+ * which will be between {@code origin} (inclusive) and
+ * {@code bound} exclusive unless {@code origin}
+ * is greater than or equal to {@code bound}
+ *
+ * @implNote The implementation of this method is identical to
+ * the implementation of {@code nextLong(origin, bound)}
+ * except that {@code int} values and the {@code nextInt()}
+ * method are used rather than {@code long} values and the
+ * {@code nextLong()} method.
+ */
+ public static int boundedNextInt(RandomGenerator rng, int origin, int bound) {
+ int r = rng.nextInt();
+ if (origin < bound) {
+ // It's not case (1).
+ final int n = bound - origin;
+ final int m = n - 1;
+ if ((n & m) == 0) {
+ // It is case (2): length of range is a power of 2.
+ r = (r & m) + origin;
+ } else if (n > 0) {
+ // It is case (3): need to reject over-represented candidates.
+ for (int u = r >>> 1;
+ u + m - (r = u % n) < 0;
+ u = rng.nextInt() >>> 1)
+ ;
+ r += origin;
+ }
+ else {
+ // It is case (4): length of range not representable as long.
+ while (r < origin || r >= bound) {
+ r = rng.nextInt();
+ }
+ }
+ }
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextInt} used by the public method
+ * {@code nextInt(bound)}. This is essentially a version of
+ * {@code boundedNextInt(origin, bound)} that has been
+ * specialized for the case where the {@code origin} is zero
+ * and the {@code bound} is greater than zero. The value
+ * returned is chosen pseudorandomly from nonnegative integer
+ * values less than {@code bound}.
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code long} values
+ * @param bound the upper bound (exclusive); must be greater than zero
+ *
+ * @return a pseudorandomly chosen {@code long} value
+ *
+ * @implNote The implementation of this method is identical to
+ * the implementation of {@code nextLong(bound)}
+ * except that {@code int} values and the {@code nextInt()}
+ * method are used rather than {@code long} values and the
+ * {@code nextLong()} method.
+ */
+ public static int boundedNextInt(RandomGenerator rng, int bound) {
+ // Specialize boundedNextInt for origin == 0, bound > 0
+ final int m = bound - 1;
+ int r = rng.nextInt();
+ if ((bound & m) == 0) {
+ // The bound is a power of 2.
+ r &= m;
+ } else {
+ // Must reject over-represented candidates
+ for (int u = r >>> 1;
+ u + m - (r = u % bound) < 0;
+ u = rng.nextInt() >>> 1)
+ ;
+ }
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextDouble} used by a {@link DoubleStream}
+ * {@link Spliterator} and by the public method
+ * {@code nextDouble(origin, bound)}. If {@code origin} is greater
+ * than {@code bound}, then this method simply calls the unbounded
+ * version of {@code nextDouble()}, and otherwise scales and translates
+ * the result of a call to {@code nextDouble()} so that it lies
+ * between {@code origin} (inclusive) and {@code bound} (exclusive).
+ *
+ * @implNote The implementation considers two cases:
+ *
+ *
+ *
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code double} values
+ * @param origin the least value that can be produced,
+ * unless greater than or equal to {@code bound}; must be finite
+ * @param bound the upper bound (exclusive), unless {@code origin}
+ * is greater than or equal to {@code bound}; must be finite
+ * @return a pseudorandomly chosen {@code double} value,
+ * which will be between {@code origin} (inclusive) and
+ * {@code bound} exclusive unless {@code origin}
+ * is greater than or equal to {@code bound},
+ * in which case it will be between 0.0 (inclusive)
+ * and 1.0 (exclusive)
+ */
+ public static double boundedNextDouble(RandomGenerator rng, double origin, double bound) {
+ double r = rng.nextDouble();
+ if (origin < bound) {
+ r = r * (bound - origin) + origin;
+ if (r >= bound) // may need to correct a rounding problem
+ r = Double.longBitsToDouble(Double.doubleToLongBits(bound) - 1);
+ }
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextDouble} used by the public method
+ * {@code nextDouble(bound)}. This is essentially a version of
+ * {@code boundedNextDouble(origin, bound)} that has been
+ * specialized for the case where the {@code origin} is zero
+ * and the {@code bound} is greater than zero.
+ *
+ * @implNote The result of a call to {@code nextDouble} is
+ * multiplied by {@code bound}, and then if this result is
+ * not less than {@code bound} (which can sometimes occur
+ * because of rounding), it is replaced with the largest
+ * {@code double} value that is less than {@code bound}.
+ *
+ * @param rng a random number generator to be used as a
+ * source of pseudorandom {@code double} values
+ * @param bound the upper bound (exclusive); must be finite and
+ * greater than zero
+ * @return a pseudorandomly chosen {@code double} value
+ * between zero (inclusive) and {@code bound} (exclusive)
+ */
+ public static double boundedNextDouble(RandomGenerator rng, double bound) {
+ // Specialize boundedNextDouble for origin == 0, bound > 0
+ double r = rng.nextDouble();
+ r = r * bound;
+ if (r >= bound) // may need to correct a rounding problem
+ r = Double.longBitsToDouble(Double.doubleToLongBits(bound) - 1);
+ return r;
+ }
+
+ /**
+ * This is the form of {@code nextFloat} used by a {@code Stream