- * 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 L64X1024Random} 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 - * (but {@link L64X1024Random} does not use a mixing function). - *
- * The LCG subgenerator for {@link L64X1024Random} 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 L64X1024Random}) 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 L64X1024Random} 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. - *
- * Because the periods 264 and 21024-1 of the two subgenerators - * are relatively prime, the period of any single {@link L64X1024Random} 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 L64X1024Random} 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 L64X1024Random}, 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 L64X1024Random}, 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 one of the less common subsequence values and the - * probability of getting 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 L64X1024Random} 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 L64X1024Random} - * 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 L64X1024Random} object. - * This is because, with high probability, distinct {@link L64X1024Random} 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 L64X1024Random} 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(someL64X1024Random.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 L64X1024Random} 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 L64X1024Random extends AbstractSplittableGenerator { - - /* - * 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 L64X1024Random} - * 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, 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). - */ - - 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 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 L64X1024Random(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) { - for (int j = 0; j < N; j++) { - this.x[j] = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64); - } - } - } - - /** - * Creates a new instance of {@link L64X1024Random} using the - * specified {@code long} value as the initial seed. Instances of - * {@link L64X1024Random} created with the same seed in the same - * program execution generate identical sequences of values. - * - * @param seed the initial seed - */ - public L64X1024Random(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 Stafford13 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 L64X1024Random} 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 L64X1024Random() { - // 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 L64X1024Random} using the specified array of - * initial seed bytes. Instances of {@link L64X1024Random} created with the same - * seed array in the same program execution generate identical sequences of values. - * - * @param seed the initial seed - */ - public L64X1024Random(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 ---------------- */ - - /** - * Constructs and returns a new instance of {@link L64X1024Random} - * 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 L64X1024Random} 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 L64X1024Random} - */ - public L64X1024Random split(SplittableGenerator source) { - // Literally pick a new instance "at random". - return new L64X1024Random(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]; - - final long z = s + s0; - 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 z; - } - - public BigInteger period() { - return PERIOD; - } -}