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package java.util.random;
import java.math.BigInteger;
import java.util.concurrent.atomic.AtomicLong;
import java.util.random.RandomGenerator.SplittableGenerator;
import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator;
/**
* A generator of uniform pseudorandom values applicable for use in
* (among other contexts) isolated parallel computations that may
* generate subtasks. Class {@link L128X256MixRandom} implements
* interfaces {@link RandomGenerator} and {@link SplittableGenerator},
* 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 split-off {@link L128X256MixRandom} objects,
* with similar usages as for class {@link java.util.SplittableRandom}.
* <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>
* {@link L128X256MixRandom} 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 result of
* combining state from the LCG with state from the Xorshift generator by
* using a Mixing function (and then the state of the LCG and the state of the
* Xorshift generator are advanced).
* <p>
* The LCG subgenerator for {@link L128X256MixRandom} has an update step of the
* form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all
* 128-bit integers; {@code s} is the mutable state, the multiplier {@code m}
* is fixed (the same for all instances of {@link L128X256MixRandom}) 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 2<sup>128</sup>); therefore there are 2<sup>127</sup> distinct choices
* of parameter.
* <p>
* The Xorshift subgenerator for {@link L128X256MixRandom} is the {@code xoshiro256} algorithm,
* version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**".
* 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 subgenerator is 2<sup>256</sup>-1.
* <p>
* The mixing function for {@link L128X256MixRandom} is {@link RandomSupport.mixLea64}
* applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}.
* <p>
* Because the periods 2<sup>128</sup> and 2<sup>256</sup>-1 of the two subgenerators
* are relatively prime, the <em>period</em> of any single {@link L128X256MixRandom} 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, 2<sup>128</sup>(2<sup>256</sup>-1),
* which is just slightly smaller than 2<sup>384</sup>. Moreover, if two distinct
* {@link L128X256MixRandom} objects have different {@code a} parameters, then their
* cycles of produced values will be different.
* <p>
* The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed.
* For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each
* of the 2<sup>64</sup> possible {@code long} values will be produced
* 2<sup>64</sup>(2<sup>256</sup>-1) times. The values produced by the {@code nextInt()},
* {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed.
* <p>
* Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be
* "very nearly" 4-equidistributed: all possible quadruples of 64-bit values are generated,
* and some pairs occur more often than others, but only very slightly more often.
* However, this conjecture has not yet been proven mathematically.
* If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()},
* and {@code nextDouble()} methods are likewise approximately 4-equidistributed.
* <p>
* Method {@link #split} constructs and returns a new {@link L128X256MixRandom}
* 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 L128X256MixRandom} object.
* This is because, with high probability, distinct {@link L128X256MixRandom} 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.
* <p>
* As with {@link java.util.SplittableRandom}, instances of
* {@link L128X256MixRandom} are <em>not</em> 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(someL128X256MixRandom.split()).fork()}.
* <p>
* This class provides additional methods for generating random
* streams, that employ the above techniques when used in
* {@code stream.parallel()} mode.
* <p>
* Instances of {@link L128X256MixRandom} 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 L128X256MixRandom extends AbstractSplittableWithBrineGenerator {
/*
* Implementation Overview.
*
* The 128-bit parameter `a` is represented as two long fields `ah` and `al`.
* The 128-bit state variable `s` is represented as two long fields `sh` and `sl`.
*
* The split operation uses the current generator to choose eight
* new 64-bit long values that are then used to initialize the
* parameters `ah` and `al` and the state variables `sh`, `sl`,
* `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 L128X256MixRandom}
* will be (approximately) independent if have different values for `a`.
*
* The default (no-argument) constructor, in essence, uses
* "defaultGen" to generate eight 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());
/*
* The period of this generator, which is (2**256 - 1) * 2**128.
*/
private static final BigInteger PERIOD =
BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);
/*
* 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, x1, x2, and x3 for the xorshift.
* At least one of the four fields x0, x1, x2, and x3 must be nonzero.
*/
private long sh, sl, 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 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 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
*/
public L128X256MixRandom(long ah, long al, long sh, long sl, long x0, long x1, long x2, long x3) {
// Force a to be odd.
this.ah = ah;
this.al = al | 1;
this.sh = sh;
this.sl = sl;
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 = sh;
// 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 L128X256MixRandom} using the
* specified {@code long} value as the initial seed. Instances of
* {@link L128X256MixRandom} created with the same seed in the same
* program generate identical sequences of values.
*
* @param seed the initial seed
*/
public L128X256MixRandom(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),
RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64),
0,
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 L128X256MixRandom} 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 L128X256MixRandom() {
// 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 L128X256MixRandom} using the specified array of
* initial seed bytes. Instances of {@link L128X256MixRandom} created with the same
* seed array in the same program execution generate identical sequences of values.
*
* @param seed the initial seed
*/
public L128X256MixRandom(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 ah = data[0], al = data[1], sh = data[2], sl = data[3],
x0 = data[4], x1 = data[5], x2 = data[6], x3 = data[7];
// Force a to be odd.
this.ah = ah;
this.al = al | 1;
this.sh = sh;
this.sl = sl;
this.x0 = x0;
this.x1 = x1;
this.x2 = x2;
this.x3 = x3;
}
/* ---------------- public methods ---------------- */
/**
* Given 63 bits of "brine", constructs and returns a new instance of
* {@code L128X256MixRandom} 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 {@code L128X256MixRandom} 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 {@code SplittableGenerator} instance to be used instead
* of this one as a source of pseudorandom bits used to
* initialize the state of the new ones.
* @param brine a long value, of which the low 63 bits are used to choose
* the {@code a} parameter for the new instance.
* @return a new instance of {@code L128X256MixRandom}
*/
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 L128X256MixRandom(source.nextLong(), brine << 1,
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() {
// 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.
// Update the Xorshift 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;
}
/**
* Returns the period of this random generator.
*
* @return a {@link BigInteger} whose value is the number of distinct possible states of this
* {@link RandomGenerator} object (2<sup>128</sup>(2<sup>256</sup>-1)).
*/
public BigInteger period() {
return PERIOD;
}
}