The {@link L32X64MixRandom} algorithm is a specific member of * the LXM family of algorithms for pseudorandom number generators; * for more information, see the documentation for package * {@link jdk.random}. Each instance of {@link L32X64MixRandom} * has 96 bits of state plus one 32-bit instance-specific parameter. * *
If two instances of {@link L32X64MixRandom} are created with * the same seed within the same program execution, and the same * sequence of method calls is made for each, they will generate and * return identical sequences of values. * *
As with {@link java.util.SplittableRandom}, instances of * {@link L32X64MixRandom} are not thread-safe. They are * designed to be split, not shared, across threads (see the {@link #split} * method). For example, a {@link java.util.concurrent.ForkJoinTask} * fork/join-style computation using random numbers might include a * construction of the form * {@code new Subtask(someL32X64MixRandom.split()).fork()}. * *
This class provides additional methods for generating random * streams, that employ the above techniques when used in * {@code stream.parallel()} mode. * *
Instances of {@link L32X64MixRandom} are not cryptographically * secure. Consider instead using {@link java.security.SecureRandom} * in security-sensitive applications. Additionally, * default-constructed instances do not use a cryptographically random * seed unless the {@linkplain System#getProperty system property} * {@code java.util.secureRandomSeed} is set to {@code true}. * * @since 17 * */ @RandomGeneratorProperties( name = "L32X64MixRandom", group = "LXM", i = 64, j = 1, k = 32, equidistribution = 1 ) public final class L32X64MixRandom extends AbstractSplittableWithBrineGenerator { /* * Implementation Overview. * * The split operation uses the current generator to choose four new 32-bit * int values that are then used to initialize the parameter `a` and the * state variables `s`, `x0`, and `x1` for a newly constructed generator. * * With high probability, no two generators so chosen will have the same * `a` parameter, and testing has indicated that the values generated by * two instances of {@link L32X64MixRandom} will be (approximately) * independent if the two instances have different values for `a`. * * The default (no-argument) constructor, in essence, uses * "defaultGen" to generate four new 32-bit values for the same * purpose. Multiple generators created in this way will certainly * differ in their `a` parameters. The defaultGen state must be accessed * in a thread-safe manner, so we use an AtomicLong to represent * this state. To bootstrap the defaultGen, we start off using a * seed based on current time unless the * java.util.secureRandomSeed property is set. This serves as a * slimmed-down (and insecure) variant of SecureRandom that also * avoids stalls that may occur when using /dev/random. * * File organization: First static fields, then instance * fields, then constructors, then instance methods. */ /* ---------------- static fields ---------------- */ /** * The seed generator for default constructors. */ private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed()); /* * 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 0xadb4a92d * are [0.975884, 0.936244, 0.755793, 0.877642, 0.751300, 0.789333, 0.728869]. */ private static final int M = 0xadb4a92d; /* ---------------- instance fields ---------------- */ /** * The parameter that is used as an additive constant for the LCG. * Must be odd. */ private final int a; /** * The per-instance state: s for the LCG; x0 and x1 for the XBG. * At least one of x0 and x1 must be nonzero. */ private int s, x0, x1; /* ---------------- constructors ---------------- */ /** * Basic constructor that initializes all fields from parameters. * It then adjusts the field values if necessary to ensure that * all constraints on the values of fields are met. * * @param a additive parameter for the LCG * @param s initial state for the LCG * @param x0 first word of the initial state for the XBG * @param x1 second word of the initial state for the XBG */ public L32X64MixRandom(int a, int s, int x0, int 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) { int v = s; // At least one of the two values generated here will be nonzero. this.x0 = RandomSupport.mixMurmur32(v += RandomSupport.GOLDEN_RATIO_32); this.x1 = RandomSupport.mixMurmur32(v + RandomSupport.GOLDEN_RATIO_32); } } /** * Creates a new instance of {@link L32X64MixRandom} using the * specified {@code long} value as the initial seed. Instances of * {@link L32X64MixRandom} created with the same seed in the same * program generate identical sequences of values. * * @param seed the initial seed */ public L32X64MixRandom(long seed) { // Using a value with irregularly spaced 1-bits to xor the seed // argument tends to improve "pedestrian" seeds such as 0 or // other small integers. We may as well use SILVER_RATIO_64. // // The high half of the seed is hashed by mixMurmur32 to produce the `a` parameter. // The low half of the seed is hashed by mixLea32 to produce the initial `x0`, // which will then be used to produce the first generated value. // Then x1 is filled in as if by a SplitMix PRNG with // GOLDEN_RATIO_32 as the gamma value and mixLea32 as the mixer. this(RandomSupport.mixMurmur32((int)((seed ^= RandomSupport.SILVER_RATIO_64) >>> 32)), 1, RandomSupport.mixLea32((int)(seed)), RandomSupport.mixLea32((int)(seed) + RandomSupport.GOLDEN_RATIO_32)); } /** * Creates a new instance of {@link L32X64MixRandom} that is likely to * generate sequences of values that are statistically independent * of those of any other instances in the current program execution, * but may, and typically does, vary across program invocations. */ public L32X64MixRandom() { // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values. this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64)); } /** * Creates a new instance of {@link L32X64MixRandom} using the specified array of * initial seed bytes. Instances of {@link L32X64MixRandom} created with the same * seed array in the same program execution generate identical sequences of values. * * @param seed the initial seed */ public L32X64MixRandom(byte[] seed) { // Convert the seed to 4 int values, of which the last 2 are not all zero. int[] data = RandomSupport.convertSeedBytesToInts(seed, 4, 2); int a = data[0], s = data[1], x0 = data[2], x1 = data[3]; // Force a to be odd. this.a = a | 1; this.s = s; this.x0 = x0; this.x1 = x1; } /* ---------------- public methods ---------------- */ @Override public SplittableGenerator split(SplittableGenerator source, long brine) { // Pick a new instance "at random", but use (the low 31 bits of) the brine for `a`. return new L32X64MixRandom((int)brine << 1, source.nextInt(), source.nextInt(), source.nextInt()); } @Override public int nextInt() { // Compute the result based on current state information // (this allows the computation to be overlapped with state update). final int result = RandomSupport.mixLea32(s + x0); // Update the LCG subgenerator s = M * s + a; // Update the XBG subgenerator int q0 = x0, q1 = x1; { // xoroshiro64 q1 ^= q0; q0 = Integer.rotateLeft(q0, 26); q0 = q0 ^ q1 ^ (q1 << 9); q1 = Integer.rotateLeft(q1, 13); } x0 = q0; x1 = q1; return result; } @Override public long nextLong() { return ((long)nextInt() << 32) ^ (long)nextInt(); } }