--- a/src/java.base/share/classes/java/util/random/L128X256MixRandom.java Thu Aug 29 11:33:26 2019 -0300
+++ b/src/java.base/share/classes/java/util/random/L128X256MixRandom.java Thu Nov 14 08:54:56 2019 -0400
@@ -28,7 +28,7 @@
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;
/**
@@ -55,9 +55,10 @@
* {@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
- * output from each subgenerator, possibly processed by a final mixing function
- * (and {@link L128X256MixRandom} does use a mixing function).
+ * 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
@@ -74,7 +75,8 @@
* 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
@@ -86,34 +88,16 @@
* <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.
- * The values produced by the {@code nextInt()}, {@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
- * 2-equidistributed. For any specific instance of {@link L128X256MixRandom}, 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>(2<sup>256</sup>-1) such subsequences, and each subsequence,
- * which consists of 2 64-bit values, can have one of 2<sup>128</sup> values, and each
- * 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.
+ * 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, 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.
+ * 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
@@ -146,7 +130,7 @@
*
* @since 14
*/
-public final class L128X256MixRandom extends AbstractSplittableGenerator {
+public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator {
/*
* Implementation Overview.
@@ -193,28 +177,20 @@
BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);
/*
- * The multiplier used in the LCG portion of the algorithm is 2**64 + m;
- * where m is taken from
- * Pierre L'Ecuyer, Tables of linear congruential generators of
- * different sizes and good lattice structure, <em>Mathematics of
- * Computation</em> 68, 225 (January 1999), pages 249-260,
- * Table 4 (first multiplier for size 2<sup>64</sup>).
- *
- * This is almost certainly not the best possible 128-bit multiplier
- * 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.
+ * 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 M = 2862933555777941757L;
+ private static final long ML = 0xd605bbb58c8abbfdL;
/* ---------------- 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;
@@ -252,11 +228,12 @@
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.x1 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);
- this.x2 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);
- this.x3 = RandomSupport.mixStafford13(sh + RandomSupport.GOLDEN_RATIO_64);
+ 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);
}
}
@@ -277,7 +254,7 @@
// 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,
@@ -323,29 +300,31 @@
}
/* ---------------- public methods ---------------- */
-
+
/**
- * Constructs and returns a new instance of {@link L128X256MixRandom}
- * that shares no mutable state with this instance.
+ * 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 {@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.
+ * @return a new instance of {@code L128X256MixRandom}
*/
- public L128X256MixRandom split(SplittableGenerator source) {
- // Literally pick a new instance "at random".
- return new L128X256MixRandom(source.nextLong(), source.nextLong(),
- source.nextLong(), source.nextLong(),
- source.nextLong(), source.nextLong(),
- source.nextLong(), source.nextLong());
+ 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());
}
/**
@@ -354,12 +333,27 @@
* @return a pseudorandom {@code long} value
*/
public long nextLong() {
- final long z = sh + x0;
- // The LCG: in effect, s = ((1LL << 64) + M) * s + a, if only we had 128-bit arithmetic.
- final long u = M * sl;
- sh = (M * sh) + Math.multiplyHigh(M, sl) + sl + ah;
+ // 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;
@@ -371,9 +365,15 @@
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;
}