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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 Xoshiro256StarStar} 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 Xoshiro256StarStar} 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.
* (Most recently validated with
* <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a>
* and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>.
* 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.
* <p>
* The class {@link Xoshiro256StarStar} uses the {@code xoshiro256} algorithm,
* version 1.0 (parameters 17, 45), with the "**" scrambler (a mixing function).
* Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2},
* and {@code x3}, which can take on any values provided that they are not all zero.
* The period of this generator is 2<sup>256</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>256</sup>-1,
* each nonzero {@code long} value is generated 2<sup>192</sup> times,
* but the value 0 is generated only 2<sup>192</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 4-equidistributed.
* To be precise: consider the (overlapping) length-4 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>256</sup>-1 such subsequences, and each subsequence,
* which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those
* 2<sup>256</sup> subsequence values, each one is generated exactly once over the course
* of the entire cycle, except that the subsequence (0, 0, 0, 0) never appears.
* The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
* methods are likewise 4-equidistributed, but note that that the subsequence (0, 0, 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 Xoshiro256StarStar} 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 Xoshiro256StarStar} that traverse
* other parts of the state cycle.
* <p>
* Instances of {@link Xoshiro256StarStar} 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 Xoshiro256StarStar implements LeapableGenerator {
/*
* Implementation Overview.
*
* This is an implementation of the xoroshiro128** algorithm written
* in 2018 by David Blackman and Sebastiano Vigna (vigna@acm.org).
* 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*128
* steps; this has the same effect as calling nextLong() 2**128
* times, but is much faster. Similarly, the leap operation moves
* the current generator forward by 2*192 steps; this has the same
* effect as calling nextLong() 2**192 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 static fields, then instance
* fields, then constructors, then instance methods.
*/
/* ---------------- 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**256 - 1.
*/
private static final BigInteger PERIOD =
BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE);
/* ---------------- instance fields ---------------- */
/**
* The per-instance state.
* At least one of the four fields x0, x1, x2, and x3 must be nonzero.
*/
private long 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 x0 first word of the initial state
* @param x1 second word of the initial state
* @param x2 third word of the initial state
* @param x3 fourth word of the initial state
*/
public Xoshiro256StarStar(long x0, long x1, long x2, long x3) {
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) {
// At least three of the four values generated here will be nonzero.
this.x0 = RandomSupport.mixStafford13(x0 += RandomSupport.GOLDEN_RATIO_64);
this.x1 = (x0 += RandomSupport.GOLDEN_RATIO_64);
this.x2 = (x0 += RandomSupport.GOLDEN_RATIO_64);
this.x3 = (x0 += RandomSupport.GOLDEN_RATIO_64);
}
}
/**
* Creates a new instance of {@link Xoshiro256StarStar} using the
* specified {@code long} value as the initial seed. Instances of
* {@link Xoshiro256StarStar} created with the same seed in the same
* program generate identical sequences of values.
*
* @param seed the initial seed
*/
public Xoshiro256StarStar(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),
RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),
RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64));
}
/**
* Creates a new instance of {@link Xoshiro256StarStar} 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 Xoshiro256StarStar() {
// 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 Xoshiro256StarStar} using the specified array of
* initial seed bytes. Instances of {@link Xoshiro256StarStar} created with the same
* seed array in the same program execution generate identical sequences of values.
*
* @param seed the initial seed
*/
public Xoshiro256StarStar(byte[] seed) {
// Convert the seed to 4 long values, which are not all zero.
long[] data = RandomSupport.convertSeedBytesToLongs(seed, 4, 4);
long x0 = data[0], x1 = data[1], x2 = data[2], x3 = data[3];
this.x0 = x0;
this.x1 = x1;
this.x2 = x2;
this.x3 = x3;
}
/* ---------------- public methods ---------------- */
public Xoshiro256StarStar copy() {
return new Xoshiro256StarStar(x0, x1, x2, x3);
}
/**
* Returns a pseudorandom {@code long} value.
*
* @return a pseudorandom {@code long} value
*/
public long nextLong() {
// Compute the result based on current state information
// (this allows the computation to be overlapped with state update).
final long result = Long.rotateLeft(x0 * 5, 7) * 9; // "starstar" mixing function
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;
}
public BigInteger period() {
return PERIOD;
}
public double defaultJumpDistance() {
return 0x1.0p64;
}
public double defaultLeapDistance() {
return 0x1.0p96;
}
private static final long[] JUMP_TABLE = {
0x180ec6d33cfd0abaL, 0xd5a61266f0c9392cL, 0xa9582618e03fc9aaL, 0x39abdc4529b1661cL };
private static final long[] LEAP_TABLE = {
0x76e15d3efefdcbbfL, 0xc5004e441c522fb3L, 0x77710069854ee241L, 0x39109bb02acbe635L };
/**
* This is the jump function for the generator. It is equivalent to 2**128 calls to next(); it
* can be used to generate 2**128 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**192 calls to next();
* it can be used to generate 2**64 starting points, from each of which jump() will generate
* 2**64 non-overlapping subsequences for parallel distributed computations.
*/
public void leap() {
jumpAlgorithm(LEAP_TABLE);
}
private void jumpAlgorithm(long[] table) {
long s0 = 0, s1 = 0, s2 = 0, s3 = 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;
s2 ^= x2;
s3 ^= x3;
}
nextLong();
}
x0 = s0;
x1 = s1;
x2 = s2;
x3 = s3;
}
}
}