jdk-sandbox: comparison src/java.base/share/classes/java/util/random/L128X256MixRandom.java

equal deleted inserted replaced

-:7e791393cc4d
+:1b314be4feb2
 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.AbstractSplittableGenerator;
+import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator;
 /**
 * A generator of uniform pseudorandom values applicable for use in
 * (among other contexts) isolated parallel computations that may
 * 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 sum of one
+* an Xorshift generator.  Each output of an LXM generator is the result of
-* output from each subgenerator, possibly processed by a final mixing function
+* combining state from the LCG with state from the Xorshift generator by
-* (and {@link L128X256MixRandom} does use a mixing function).
+* 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
 * 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 the 64-bit MurmurHash3 finalizer.
+* 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),
 * {@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>256</sup>-1 times.
+* of the 2<sup>64</sup> possible {@code long} values will be produced
-* The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}
+* 2<sup>64</sup>(2<sup>256</sup>-1) times.  The values produced by the {@code nextInt()},
-* methods are likewise exactly equidistributed.
+* {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed.
 * <p>
-* In fact, the 64-bit values produced by the {@code nextLong()} method are exactly
+* Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be
-* 2-equidistributed.  For any specific instance of {@link L128X256MixRandom}, consider
+* "very nearly" 4-equidistributed: all possible quadruples of 64-bit values are generated,
-* the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by
+* and some pairs occur more often than others, but only very slightly more often.
-* {@code nextLong()} (assuming no other methods are called that would affect the state).
+* However, this conjecture has not yet been proven mathematically.
-* There are 2<sup>128</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,
+* If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()},
-* which consists of 2 64-bit values, can have one of 2<sup>128</sup> values, and each
+* and {@code nextDouble()} methods are likewise approximately 4-equidistributed.
-* such value occurs  2<sup>256</sup>-1 times.  The values produced by the {@code nextInt()},
-* {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly 2-equidistributed.
-* <p>
-* Moreover, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed.
-* To be precise: for any specific instance of {@link L128X256MixRandom}, 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 <sup>128</sup>(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, nearly all of them (2<sup>256</sup>-2<sup>128</sup>)
-* occur 2<sup>128</sup> times over the course of the entire cycle, and the other
-* 2<sup>128</sup> subsequence values occur only 2<sup>128</sup>-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<sup>-128</sup>.
-* (Note that the set of 2<sup>128</sup> less-common subsequence values will differ from
-* one instance of {@link L128X256MixRandom} 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 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
 * seed unless the {@linkplain System#getProperty system property}
 * {@code java.util.secureRandomSeed} is set to {@code true}.
 *
 * @since 14
 */
-public final class L128X256MixRandom extends AbstractSplittableGenerator {
+public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator {
 /*
 * Implementation Overview.
 *
 * The 128-bit parameter `a` is represented as two long fields `ah` and `al`.
 */
 private static final BigInteger PERIOD =
 BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);
 /*
-* The multiplier used in the LCG portion of the algorithm is 2**64 + m;
+* Low half of multiplier used in the LCG portion of the algorithm;
-* where m is taken from
+* the overall multiplier is (2**64 + ML).
-* Pierre L'Ecuyer, Tables of linear congruential generators of
+* Chosen based on research by Sebastiano Vigna and Guy Steele (2019).
-* different sizes and good lattice structure, <em>Mathematics of
+* The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL
-* Computation</em> 68, 225 (January 1999), pages 249-260,
+* are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493].
-* Table 4 (first multiplier for size 2<sup>64</sup>).
+*/
-*
-* This is almost certainly not the best possible 128-bit multiplier
+private static final long ML = 0xd605bbb58c8abbfdL;
-* for an LCG, but it is sufficient for our purposes here; because
-* is is larger than 2**64, the 64-bit values produced by nextLong()
-* are exactly 2-equidistributed, and the fact that it is of the
-* form (2**64 + m) simplifies the code, given that we have only
-* 64-bit arithmetic to work with.
-*/
-private static final long M = 2862933555777941757L;
 /* ---------------- instance fields ---------------- */
 /**
 * The parameter that is used as an additive constant for the LCG.
-* Must be odd.
+* 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.
 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(sh += RandomSupport.GOLDEN_RATIO_64);
+this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);
-this.x1 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);
+this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);
-this.x2 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);
+this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);
-this.x3 = RandomSupport.mixStafford13(sh + RandomSupport.GOLDEN_RATIO_64);
+this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64);
 }
 }
 /**
 * Creates a new instance of {@link L128X256MixRandom} using the
 //
 // 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 Stafford13 as the mixer.
+// 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),
 this.x2 = x2;
 this.x3 = x3;
 }
 /* ---------------- public methods ---------------- */
 /**
-* Constructs and returns a new instance of {@link L128X256MixRandom}
+* Given 63 bits of "brine", constructs and returns a new instance of
-* that shares no mutable state with this instance.
+* {@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 {@link L128X256MixRandom} object.  Either or both of the two
+* 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 {@link SplittableGenerator} instance to be used instead
+* @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.
-* @return a new instance of {@link L128X256MixRandom}
+* @param brine a long value, of which the low 63 bits are used to choose
-*/
+*              the {@code a} parameter for the new instance.
-public L128X256MixRandom split(SplittableGenerator source) {
+* @return a new instance of {@code L128X256MixRandom}
-// Literally pick a new instance "at random".
+*/
-return new L128X256MixRandom(source.nextLong(), source.nextLong(),
+public SplittableGenerator split(SplittableGenerator source, long brine) {
-source.nextLong(), source.nextLong(),
+	// Pick a new instance "at random", but use the brine for (the low half of) `a`.
-source.nextLong(), source.nextLong(),
+return new L128X256MixRandom(source.nextLong(), brine << 1,
-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() {
-final long z = sh + x0;
+	// Compute the result based on current state information
-// The LCG: in effect, s = ((1LL << 64) + M) * s + a, if only we had 128-bit arithmetic.
+	// (this allows the computation to be overlapped with state update).
-final long u = M * sl;
+final long result = RandomSupport.mixLea64(sh + x0);
-sh = (M * sh) + Math.multiplyHigh(M, sl) + sl + ah;
+	// 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;
 q0 ^= q3;
 q2 ^= t;
 q3 = Long.rotateLeft(q3, 45);
 }
 x0 = q0; x1 = q1; x2 = q2; x3 = q3;
-return RandomSupport.mixLea64(z);  // mixing function
+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;
 }
 }

branch	JDK-8193209-branch
changeset 59080	1b314be4feb2
parent 57684	7cb325557832