The {@link L128X128MixRandom} 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 L128X128MixRandom} * has 256 bits of state plus one 128-bit instance-specific parameter. * *
If two instances of {@link L128X128MixRandom} 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 L128X128MixRandom} 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(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 17 * */ @RandomGeneratorProperties( name = "L128X128MixRandom", group = "LXM", i = 128, j = 1, k = 128, equidistribution = 1 ) 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()); /* * 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 XBG. * 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 XBG * @param x1 second word of the initial state for the XBG */ 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 ---------------- */ @Override 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()); } @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(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 XBG 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; } }