1 ***************

     2 *** 28,34 ****

     3   import java.math.BigInteger;

     4   import java.util.concurrent.atomic.AtomicLong;

     5   import java.util.random.RandomGenerator.SplittableGenerator;

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

     7   

     8   

     9   /**

    10 --- 28,34 ----

    11   import java.math.BigInteger;

    12   import java.util.concurrent.atomic.AtomicLong;

    13   import java.util.random.RandomGenerator.SplittableGenerator;

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

    15   

    16   

    17   /**

    18 ***************

    19 *** 55,63 ****

    20    * {@link L128X256MixRandom} is a specific member of the LXM family of algorithms

    21    * for pseudorandom number generators.  Every LXM generator consists of two

    22    * subgenerators; one is an LCG (Linear Congruential Generator) and the other is

    23 -  * an Xorshift generator.  Each output of an LXM generator is the sum of one

    24 -  * output from each subgenerator, possibly processed by a final mixing function

    25 -  * (and {@link L128X256MixRandom} does use a mixing function).

    26    * <p>

    27    * The LCG subgenerator for {@link L128X256MixRandom} has an update step of the

    28    * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all

    29 --- 55,64 ----

    30    * {@link L128X256MixRandom} is a specific member of the LXM family of algorithms

    31    * for pseudorandom number generators.  Every LXM generator consists of two

    32    * subgenerators; one is an LCG (Linear Congruential Generator) and the other is

    33 +  * an Xorshift generator.  Each output of an LXM generator is the result of

    34 +  * combining state from the LCG with state from the Xorshift generator by

    35 +  * using a Mixing function (and then the state of the LCG and the state of the

    36 +  * Xorshift generator are advanced).

    37    * <p>

    38    * The LCG subgenerator for {@link L128X256MixRandom} has an update step of the

    39    * form {@code s = m * s + a}, where {@code s}, {@code m}, and {@code a} are all

    40 ***************

    41 *** 74,80 ****

    42    * and {@code x3}, which can take on any values provided that they are not all zero.

    43    * The period of this subgenerator is 2<sup>256</sup>-1.

    44    * <p>

    45 -  * The mixing function for {@link L128X256MixRandom} is the 64-bit MurmurHash3 finalizer.

    46    * <p>

    47    * Because the periods 2<sup>128</sup> and 2<sup>256</sup>-1 of the two subgenerators

    48    * are relatively prime, the <em>period</em> of any single {@link L128X256MixRandom} object

    49 --- 75,82 ----

    50    * and {@code x3}, which can take on any values provided that they are not all zero.

    51    * The period of this subgenerator is 2<sup>256</sup>-1.

    52    * <p>

    53 +  * The mixing function for {@link L128X256MixRandom} is {@link RandomSupport.mixLea64}

    54 +  * applied to the argument {@code (sh + x0)}, where {@code sh} is the high half of {@code s}.

    55    * <p>

    56    * Because the periods 2<sup>128</sup> and 2<sup>256</sup>-1 of the two subgenerators

    57    * are relatively prime, the <em>period</em> of any single {@link L128X256MixRandom} object

    58 ***************

    59 *** 86,119 ****

    60    * <p>

    61    * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed.

    62    * For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each

    63 -  * of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>256</sup>-1 times.

    64 -  * The values produced by the {@code nextInt()}, {@code nextFloat()}, and {@code nextDouble()}

    65 -  * methods are likewise exactly equidistributed.

    66 -  * <p>

    67 -  * In fact, the 64-bit values produced by the {@code nextLong()} method are exactly

    68 -  * 2-equidistributed.  For any specific instance of {@link L128X256MixRandom}, consider

    69 -  * the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by

    70 -  * {@code nextLong()} (assuming no other methods are called that would affect the state).

    71 -  * There are 2<sup>128</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,

    72 -  * which consists of 2 64-bit values, can have one of 2<sup>128</sup> values, and each

    73 -  * such value occurs  2<sup>256</sup>-1 times.  The values produced by the {@code nextInt()},

    74 -  * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly 2-equidistributed.

    75    * <p>

    76 -  * Moreover, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed.

    77 -  * To be precise: for any specific instance of {@link L128X256MixRandom}, consider

    78 -  * the (overlapping) length-4 subsequences of the cycle of 64-bit values produced by

    79 -  * {@code nextLong()} (assuming no other methods are called that would affect the state).

    80 -  * There are <sup>128</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,

    81 -  * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those

    82 -  * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>128</sup>)

    83 -  * occur 2<sup>128</sup> times over the course of the entire cycle, and the other

    84 -  * 2<sup>128</sup> subsequence values occur only 2<sup>128</sup>-1 times.  So the ratio

    85 -  * of the probability of getting one of the less common subsequence values and the

    86 -  * probability of getting one of the more common subsequence values is 1-2<sup>-128</sup>.

    87 -  * (Note that the set of 2<sup>128</sup> less-common subsequence values will differ from

    88 -  * one instance of {@link L128X256MixRandom} to another, as a function of the additive

    89 -  * parameter of the LCG.)  The values produced by the {@code nextInt()}, {@code nextFloat()},

    90 -  * and {@code nextDouble()} methods are likewise 4-equidistributed.

    91    * <p>

    92    * Method {@link #split} constructs and returns a new {@link L128X256MixRandom}

    93    * instance that shares no mutable state with the current instance. However, with

    94 --- 88,103 ----

    95    * <p>

    96    * The 64-bit values produced by the {@code nextLong()} method are exactly equidistributed.

    97    * For any specific instance of {@link L128X256MixRandom}, over the course of its cycle each

    98 +  * of the 2<sup>64</sup> possible {@code long} values will be produced

    99 +  * 2<sup>64</sup>(2<sup>256</sup>-1) times.  The values produced by the {@code nextInt()},

   100 +  * {@code nextFloat()}, and {@code nextDouble()} methods are likewise exactly equidistributed.

   101    * <p>

   102 +  * Moreover, 64-bit values produced by the {@code nextLong()} method are conjectured to be

   103 +  * "very nearly" 4-equidistributed: all possible quadruples of 64-bit values are generated,

   104 +  * and some pairs occur more often than others, but only very slightly more often.

   105 +  * However, this conjecture has not yet been proven mathematically.

   106 +  * If this conjecture is true, then the values produced by the {@code nextInt()}, {@code nextFloat()},

   107 +  * and {@code nextDouble()} methods are likewise approximately 4-equidistributed.

   108    * <p>

   109    * Method {@link #split} constructs and returns a new {@link L128X256MixRandom}

   110    * instance that shares no mutable state with the current instance. However, with

   111 ***************

   112 *** 146,152 ****

   113    *

   114    * @since 14

   115    */

   116 - public final class L128X256MixRandom extends AbstractSplittableGenerator {

   117   

   118       /*

   119        * Implementation Overview.

   120 --- 130,136 ----

   121    *

   122    * @since 14

   123    */

   124 + public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator {

   125   

   126       /*

   127        * Implementation Overview.

   128 ***************

   129 *** 193,220 ****

   130           BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);

   131   

   132       /*

   133 -      * The multiplier used in the LCG portion of the algorithm is 2**64 + m;

   134 -      * where m is taken from

   135 -      * Pierre L'Ecuyer, Tables of linear congruential generators of

   136 -      * different sizes and good lattice structure, <em>Mathematics of

   137 -      * Computation</em> 68, 225 (January 1999), pages 249-260,

   138 -      * Table 4 (first multiplier for size 2<sup>64</sup>).

   139 -      *

   140 -      * This is almost certainly not the best possible 128-bit multiplier

   141 -      * for an LCG, but it is sufficient for our purposes here; because

   142 -      * is is larger than 2**64, the 64-bit values produced by nextLong()

   143 -      * are exactly 2-equidistributed, and the fact that it is of the

   144 -      * form (2**64 + m) simplifies the code, given that we have only

   145 -      * 64-bit arithmetic to work with.

   146        */

   147   

   148 -     private static final long M = 2862933555777941757L;

   149   

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

   151   

   152       /**

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

   154 -      * Must be odd.

   155        */

   156       private final long ah, al;

   157   

   158 --- 177,196 ----

   159           BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);

   160   

   161       /*

   162 +      * Low half of multiplier used in the LCG portion of the algorithm;

   163 +      * the overall multiplier is (2**64 + ML).

   164 +      * Chosen based on research by Sebastiano Vigna and Guy Steele (2019).

   165 +      * The spectral scores for dimensions 2 through 8 for the multiplier 0x1d605bbb58c8abbfdLL

   166 +      * are [0.991889, 0.907938, 0.830964, 0.837980, 0.780378, 0.797464, 0.761493].

   167        */

   168   

   169 +     private static final long ML = 0xd605bbb58c8abbfdL;

   170   

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

   172   

   173       /**

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

   175 +      * Must be odd (therefore al must be odd).

   176        */

   177       private final long ah, al;

   178   

   179 ***************

   180 *** 252,262 ****

   181           this.x3 = x3;

   182           // If x0, x1, x2, and x3 are all zero, we must choose nonzero values.

   183           if ((x0 | x1 | x2 | x3) == 0) {

   184               // At least three of the four values generated here will be nonzero.

   185 -             this.x0 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);

   186 -             this.x1 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);

   187 -             this.x2 = RandomSupport.mixStafford13(sh += RandomSupport.GOLDEN_RATIO_64);

   188 -             this.x3 = RandomSupport.mixStafford13(sh + RandomSupport.GOLDEN_RATIO_64);

   189           }

   190       }

   191   

   192 --- 228,239 ----

   193           this.x3 = x3;

   194           // If x0, x1, x2, and x3 are all zero, we must choose nonzero values.

   195           if ((x0 | x1 | x2 | x3) == 0) {

   196 + 	    long v = sh;

   197               // At least three of the four values generated here will be nonzero.

   198 +             this.x0 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);

   199 +             this.x1 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);

   200 +             this.x2 = RandomSupport.mixStafford13(v += RandomSupport.GOLDEN_RATIO_64);

   201 +             this.x3 = RandomSupport.mixStafford13(v + RandomSupport.GOLDEN_RATIO_64);

   202           }

   203       }

   204   

   205 ***************

   206 *** 277,283 ****

   207           // The seed is hashed by mixStafford13 to produce the initial `x0`,

   208           // which will then be used to produce the first generated value.

   209           // The other x values are filled in as if by a SplitMix PRNG with

   210 -         // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer.

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

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

   213                0,

   214 --- 254,260 ----

   215           // The seed is hashed by mixStafford13 to produce the initial `x0`,

   216           // which will then be used to produce the first generated value.

   217           // The other x values are filled in as if by a SplitMix PRNG with

   218 +         // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer.

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

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

   221                0,

   222 ***************

   223 *** 323,351 ****

   224       }

   225   

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

   227 - 

   228       /**

   229 -      * Constructs and returns a new instance of {@link L128X256MixRandom}

   230 -      * that shares no mutable state with this instance.

   231        * However, with very high probability, the set of values collectively

   232        * generated by the two objects has the same statistical properties as if

   233        * same the quantity of values were generated by a single thread using

   234 -      * a single {@link L128X256MixRandom} object.  Either or both of the two

   235        * objects may be further split using the {@code split} method,

   236        * and the same expected statistical properties apply to the

   237        * entire set of generators constructed by such recursive splitting.

   238        *

   239 -      * @param source a {@link SplittableGenerator} instance to be used instead

   240        *               of this one as a source of pseudorandom bits used to

   241        *               initialize the state of the new ones.

   242 -      * @return a new instance of {@link L128X256MixRandom}

   243        */

   244 -     public L128X256MixRandom split(SplittableGenerator source) {

   245 -         // Literally pick a new instance "at random".

   246 -         return new L128X256MixRandom(source.nextLong(), source.nextLong(),

   247 -                                      source.nextLong(), source.nextLong(),

   248 -                                      source.nextLong(), source.nextLong(),

   249 -                                      source.nextLong(), source.nextLong());

   250       }

   251   

   252       /**

   253 --- 300,330 ----

   254       }

   255   

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

   257 +     

   258       /**

   259 +      * Given 63 bits of "brine", constructs and returns a new instance of

   260 +      * {@code L128X256MixRandom} that shares no mutable state with this instance.

   261        * However, with very high probability, the set of values collectively

   262        * generated by the two objects has the same statistical properties as if

   263        * same the quantity of values were generated by a single thread using

   264 +      * a single {@code L128X256MixRandom} object.  Either or both of the two

   265        * objects may be further split using the {@code split} method,

   266        * and the same expected statistical properties apply to the

   267        * entire set of generators constructed by such recursive splitting.

   268        *

   269 +      * @param source a {@code SplittableGenerator} instance to be used instead

   270        *               of this one as a source of pseudorandom bits used to

   271        *               initialize the state of the new ones.

   272 +      * @param brine a long value, of which the low 63 bits are used to choose

   273 +      *              the {@code a} parameter for the new instance.

   274 +      * @return a new instance of {@code L128X256MixRandom}

   275        */

   276 +     public SplittableGenerator split(SplittableGenerator source, long brine) {

   277 + 	// Pick a new instance "at random", but use the brine for (the low half of) `a`.

   278 +         return new L128X256MixRandom(source.nextLong(), brine << 1,

   279 + 				     source.nextLong(), source.nextLong(),

   280 + 				     source.nextLong(), source.nextLong(),

   281 + 				     source.nextLong(), source.nextLong());

   282       }

   283   

   284       /**

   285 ***************

   286 *** 354,365 ****

   287        * @return a pseudorandom {@code long} value

   288        */

   289       public long nextLong() {

   290 -         final long z = sh + x0;

   291 -         // The LCG: in effect, s = ((1LL << 64) + M) * s + a, if only we had 128-bit arithmetic.

   292 -         final long u = M * sl;

   293 -         sh = (M * sh) + Math.multiplyHigh(M, sl) + sl + ah;

   294           sl = u + al;

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

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

   297           {   // xoshiro256 1.0

   298               long t = q1 << 17;

   299 --- 333,359 ----

   300        * @return a pseudorandom {@code long} value

   301        */

   302       public long nextLong() {

   303 + 	// Compute the result based on current state information

   304 + 	// (this allows the computation to be overlapped with state update).

   305 +         final long result = RandomSupport.mixLea64(sh + x0);

   306 + 

   307 + 	// Update the LCG subgenerator

   308 +         // The LCG is, in effect, s = ((1LL << 64) + ML) * s + a, if only we had 128-bit arithmetic.

   309 +         final long u = ML * sl;

   310 + 	// Note that Math.multiplyHigh computes the high half of the product of signed values,

   311 + 	// but what we need is the high half of the product of unsigned values; for this we use the

   312 + 	// formula "unsignedMultiplyHigh(a, b) = multiplyHigh(a, b) + ((a >> 63) & b) + ((b >> 63) & a)";

   313 + 	// in effect, each operand is added to the result iff the sign bit of the other operand is 1.

   314 + 	// (See Henry S. Warren, Jr., _Hacker's Delight_ (Second Edition), Addison-Wesley (2013),

   315 + 	// Section 8-3, p. 175; or see the First Edition, Addison-Wesley (2003), Section 8-3, p. 133.)

   316 + 	// If Math.unsignedMultiplyHigh(long, long) is ever implemented, the following line can become:

   317 + 	//         sh = (ML * sh) + Math.unsignedMultiplyHigh(ML, sl) + sl + ah;

   318 + 	// and this entire comment can be deleted.

   319 +         sh = (ML * sh) + (Math.multiplyHigh(ML, sl) + ((ML >> 63) & sl) + ((sl >> 63) & ML)) + sl + ah;

   320           sl = u + al;

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

   322 + 

   323 + 	// Update the Xorshift subgenerator

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

   325           {   // xoshiro256 1.0

   326               long t = q1 << 17;

   327 ***************

   328 *** 371,379 ****

   329               q3 = Long.rotateLeft(q3, 45);

   330           }

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

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

   333       }

   334   

   335       public BigInteger period() {

   336           return PERIOD;

   337       }

   338 --- 365,379 ----

   339               q3 = Long.rotateLeft(q3, 45);

   340           }

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

   342 +         return result;

   343       }

   344   

   345 +     /**

   346 +      * Returns the period of this random generator.

   347 +      *

   348 +      * @return a {@link BigInteger} whose value is the number of distinct possible states of this

   349 +      *         {@link RandomGenerator} object (2<sup>128</sup>(2<sup>256</sup>-1)).

   350 +      */

   351       public BigInteger period() {

   352           return PERIOD;

   353       }