***************

*** 28,34 ****

  import java.math.BigInteger;

  import java.util.concurrent.atomic.AtomicLong;

  import java.util.random.RandomGenerator.SplittableGenerator;

- import java.util.random.RandomSupport.AbstractSplittableGenerator;

  /**

--- 28,34 ----

  import java.math.BigInteger;

  import java.util.concurrent.atomic.AtomicLong;

  import java.util.random.RandomGenerator.SplittableGenerator;

+ import java.util.random.RandomSupport.AbstractSplittableWithBrineGenerator;

  /**

***************

*** 55,63 ****

   * {@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).

   * <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

--- 55,64 ----

   * {@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

***************

*** 74,80 ****

   * 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.

   * <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

--- 75,82 ----

   * 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

***************

*** 86,119 ****

   * <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.

   * <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

--- 88,103 ----

   * <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

***************

*** 146,152 ****

   *

   * @since 14

   */

- public final class L128X256MixRandom extends AbstractSplittableGenerator {

      /*

       * Implementation Overview.

--- 130,136 ----

   *

   * @since 14

   */

+ public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator {

      /*

       * Implementation Overview.

***************

*** 193,220 ****

          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.

       */

-     private static final long M = 2862933555777941757L;

      /* ---------------- instance fields ---------------- */

      /**

       * The parameter that is used as an additive constant for the LCG.

-      * Must be odd.

       */

      private final long ah, al;

--- 177,196 ----

          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;

***************

*** 252,262 ****

          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(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);

          }

      }

--- 228,239 ----

          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);

          }

      }

***************

*** 277,283 ****

          // 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.

          this(RandomSupport.mixMurmur64(seed ^= RandomSupport.SILVER_RATIO_64),

               RandomSupport.mixMurmur64(seed += RandomSupport.GOLDEN_RATIO_64),

               0,

--- 254,260 ----

          // 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,

***************

*** 323,351 ****

      }

      /* ---------------- public methods ---------------- */

- 

      /**

-      * Constructs and returns a new instance of {@link 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

       * 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

       *               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}

       */

-     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());

      }

      /**

--- 300,330 ----

      }

      /* ---------------- 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());

      }

      /**

***************

*** 354,365 ****

       * @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;

          sl = u + al;

          if (Long.compareUnsigned(sl, u) < 0) ++sh;  // Handle the carry propagation from low half to high half.

          long q0 = x0, q1 = x1, q2 = x2, q3 = x3;

          {   // xoshiro256 1.0

              long t = q1 << 17;

--- 333,359 ----

       * @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;

***************

*** 371,379 ****

              q3 = Long.rotateLeft(q3, 45);

          }

          x0 = q0; x1 = q1; x2 = q2; x3 = q3;

-         return RandomSupport.mixLea64(z);  // mixing function

      }

      public BigInteger period() {

          return PERIOD;

      }

--- 365,379 ----

              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;

      }