The {@link L64X256MixRandom} 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 L64X256MixRandom} * has 320 bits of state plus one 64-bit instance-specific parameter. * *
If two instances of {@link L64X256MixRandom} 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 L64X256MixRandom} 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(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 17 * */ @RandomGeneratorProperties( name = "L64X256MixRandom", group = "LXM", i = 256, j = 1, k = 64, equidistribution = 4 ) 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()); /* * 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 XBG. * 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 XBG * @param x1 second word of the initial state for the XBG * @param x2 third word of the initial state for the XBG * @param x3 fourth word of the initial state for the XBG */ 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 ---------------- */ @Override 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()); } @Override 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 XBG 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; } }