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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 Xoroshiro128StarStar} 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 Xoroshiro128StarStar} objects
* by "jumping" or "leaping".
* <p>
* Series of generated values pass the TestU01 BigCrush and PractRand test suites
* that measure independence and uniformity properties of random number generators.
* <p>
* 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 2<sup>128</sup>-1.
* <p>
* The 64-bit values produced by the {@code nextLong()} method are equidistributed.
* To be precise, over the course of the cycle of length 2<sup>128</sup>-1,
* each nonzero {@code long} value is generated 2<sup>64</sup> times,
* but the value 0 is generated only 2<sup>64</sup>-1 times.
* The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
* methods are likewise equidistributed.
* <p>
* 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 2<sup>128</sup>-1 such subsequences, and each subsequence,
* which consists of 2 64-bit values, can have one of 2<sup>128</sup> values. Of those
* 2<sup>128</sup> 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.
* <p>
* Instances {@link Xoroshiro128StarStar} are <em>not</em> 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.
* <p>
* 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.
* <p>
* See <http://creativecommons.org/publicdomain/zero/1.0/>.
*/
/*
* This is the successor to xorshift128+. It is the fastest full-period generator passing
* BigCrush without systematic failures, but due to the relatively short period it is acceptable
* only for applications with a mild amount of parallelism; otherwise, use a xorshift1024*
* generator.
* <p>
* 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.
* <p>
* 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.
* <p>
* 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;
}
}
}