1 /*

     2  * Copyright (c) 2013, 2019, Oracle and/or its affiliates. All rights reserved.

     3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

     4  *

     5  * This code is free software; you can redistribute it and/or modify it

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     8  * particular file as subject to the "Classpath" exception as provided

     9  * by Oracle in the LICENSE file that accompanied this code.

    10  *

    11  * This code is distributed in the hope that it will be useful, but WITHOUT

    12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

    13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

    14  * version 2 for more details (a copy is included in the LICENSE file that

    15  * accompanied this code).

    16  *

    17  * You should have received a copy of the GNU General Public License version

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    20  *

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    23  * questions.

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    25 

    26 package java.util.random;

    27 

    28 import java.math.BigInteger;

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

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

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

    32 

    33 /**

    34  * A generator of uniform pseudorandom values applicable for use in

    35  * (among other contexts) isolated parallel computations that may

    36  * generate subtasks.  Class {@link L128X128PlusPlusRandom} implements

    37  * interfaces {@link RandomGenerator} and {@link SplittableGenerator},

    38  * and therefore supports methods for producing pseudorandomly chosen

    39  * numbers of type {@code int}, {@code long}, {@code float}, and {@code double}

    40  * as well as creating new split-off {@link L128X128PlusPlusRandom} objects,

    41  * with similar usages as for class {@link java.util.SplittableRandom}.

    42  * <p>

    43  * Series of generated values pass the TestU01 BigCrush and PractRand test suites

    44  * that measure independence and uniformity properties of random number generators.

    45  * (Most recently validated with

    46  * <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">version 1.2.3 of TestU01</a>

    47  * and <a href="http://pracrand.sourceforge.net">version 0.90 of PractRand</a>.

    48  * Note that TestU01 BigCrush was used to test not only values produced by the {@code nextLong()}

    49  * method but also the result of bit-reversing each value produced by {@code nextLong()}.)

    50  * These tests validate only the methods for certain

    51  * types and ranges, but similar properties are expected to hold, at

    52  * least approximately, for others as well.

    53  * <p>

    54  * {@link L128X128PlusPlusRandom} is a specific member of the LXM family of algorithms

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

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

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

    58  * combining state from the LCG with state from the Xorshift generator by

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

    60  * Xorshift generator are advanced).

    61  * <p>

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

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

    64  * 128-bit integers; {@code s} is the mutable state, the multiplier {@code m}

    65  * is fixed (the same for all instances of {@link L128X256MixRandom}) and the addend

    66  * {@code a} is a parameter (a final field of the instance).  The parameter

    67  * {@code a} is required to be odd (this allows the LCG to have the maximal

    68  * period, namely 2<sup>128</sup>); therefore there are 2<sup>127</sup> distinct choices

    69  * of parameter.

    70  * <p>

    71  * The Xorshift subgenerator for {@link L128X128PlusPlusRandom} is the {@code xoroshiro128} algorithm,

    72  * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**".

    73  * Its state consists of two {@code long} fields {@code x0} and {@code x1},

    74  * which can take on any values provided that they are not both zero.

    75  * The period of this subgenerator is 2<sup>128</sup>-1.

    76  * <p>

    77  * The mixing function for {@link L128X128PlusPlusRandom} is the 64-bit "plusplus(17)"

    78  * scrambler that computes {@code Long.rotateLeft((sh + x0), 17) + x1}, where {@code sh}

    79  * is the high half of {@code s}.

    80  * <p>

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

    82  * are relatively prime, the <em>period</em> of any single {@link L128X128PlusPlusRandom} object

    83  * (the length of the series of generated 64-bit values before it repeats) is the product

    84  * of the periods of the subgenerators, that is, 2<sup>128</sup>(2<sup>128</sup>-1),

    85  * which is just slightly smaller than 2<sup>256</sup>.  Moreover, if two distinct

    86  * {@link L128X128PlusPlusRandom} objects have different {@code a} parameters, then their

    87  * cycles of produced values will be different.

    88  * <p>

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

    90  * For any specific instance of {@link L128X128PlusPlusRandom}, over the course of its cycle each

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

    92  * 2<sup>64</sup>(2<sup>128</sup>-1) times.  The values produced by the {@code nextInt()},

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

    94  * <p>

    95  * Method {@link #split} constructs and returns a new {@link L128X128PlusPlusRandom}

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

    97  * very high probability, the values collectively generated by the two objects

    98  * have the same statistical properties as if the same quantity of values were

    99  * generated by a single thread using a single {@link L128X128PlusPlusRandom} object.

   100  * This is because, with high probability, distinct {@link L128X128PlusPlusRandom} objects

   101  * have distinct {@code a} parameters and therefore use distinct members of the

   102  * algorithmic family; and even if their {@code a} parameters are the same, with

   103  * very high probability they will traverse different parts of their common state

   104  * cycle.

   105  * <p>

   106  * As with {@link java.util.SplittableRandom}, instances of

   107  * {@link L128X128PlusPlusRandom} are <em>not</em> thread-safe.

   108  * They are designed to be split, not shared, across threads. For

   109  * example, a {@link java.util.concurrent.ForkJoinTask} fork/join-style

   110  * computation using random numbers might include a construction

   111  * of the form {@code new Subtask(someL128X128PlusPlusRandom.split()).fork()}.

   112  * <p>

   113  * This class provides additional methods for generating random

   114  * streams, that employ the above techniques when used in

   115  * {@code stream.parallel()} mode.

   116  * <p>

   117  * Instances of {@link L128X128PlusPlusRandom} are not cryptographically

   118  * secure.  Consider instead using {@link java.security.SecureRandom}

   119  * in security-sensitive applications. Additionally,

   120  * default-constructed instances do not use a cryptographically random

   121  * seed unless the {@linkplain System#getProperty system property}

   122  * {@code java.util.secureRandomSeed} is set to {@code true}.

   123  *

   124  * @since 14

   125  */

   126 public final class L128X128PlusPlusRandom extends AbstractSplittableWithBrineGenerator {

   127 

   128     /*

   129      * Implementation Overview.

   130      *

   131      * The split operation uses the current generator to choose four new 64-bit

   132      * long values that are then used to initialize the parameter `a` and the

   133      * state variables `s`, `x0`, and `x1` for a newly constructed generator.

   134      *

   135      * With extremely high probability, no two generators so chosen

   136      * will have the same `a` parameter, and testing has indicated

   137      * that the values generated by two instances of {@link L128X128PlusPlusRandom}

   138      * will be (approximately) independent if have different values for `a`.

   139      *

   140      * The default (no-argument) constructor, in essence, uses

   141      * "defaultGen" to generate four new 64-bit values for the same

   142      * purpose.  Multiple generators created in this way will certainly

   143      * differ in their `a` parameters.  The defaultGen state must be accessed

   144      * in a thread-safe manner, so we use an AtomicLong to represent

   145      * this state.  To bootstrap the defaultGen, we start off using a

   146      * seed based on current time unless the

   147      * java.util.secureRandomSeed property is set. This serves as a

   148      * slimmed-down (and insecure) variant of SecureRandom that also

   149      * avoids stalls that may occur when using /dev/random.

   150      *

   151      * File organization: First static fields, then instance

   152      * fields, then constructors, then instance methods.

   153      */

   154 

   155     /* ---------------- static fields ---------------- */

   156 

   157     /**

   158      * The seed generator for default constructors.

   159      */

   160     private static final AtomicLong defaultGen = new AtomicLong(RandomSupport.initialSeed());

   161 

   162     /*

   163      * The period of this generator, which is (2**128 - 1) * 2**128.

   164      */

   165     private static final BigInteger PERIOD =

   166         BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE).shiftLeft(128);

   167 

   168     /*

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

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

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

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

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

   174      */

   175 

   176     private static final long ML = 0xd605bbb58c8abbfdL;

   177 

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

   179 

   180     /**

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

   182      * Must be odd (therefore al must be odd).

   183      */

   184     private final long ah, al;

   185 

   186     /**

   187      * The per-instance state: sh and sl for the LCG; x0 and x1 for the xorshift.

   188      * At least one of x0 and x1 must be nonzero.

   189      */

   190     private long sh, sl, x0, x1;

   191 

   192     /* ---------------- constructors ---------------- */

   193 

   194     /**

   195      * Basic constructor that initializes all fields from parameters.

   196      * It then adjusts the field values if necessary to ensure that

   197      * all constraints on the values of fields are met.

   198      *

   199      * @param ah high half of the additive parameter for the LCG

   200      * @param al low half of the additive parameter for the LCG

   201      * @param sh high half of the initial state for the LCG

   202      * @param sl low half of the initial state for the LCG

   203      * @param x0 first word of the initial state for the xorshift generator

   204      * @param x1 second word of the initial state for the xorshift generator

   205      */

   206     public L128X128PlusPlusRandom(long ah, long al, long sh, long sl, long x0, long x1) {

   207         // Force a to be odd.

   208         this.ah = ah;

   209         this.al = al | 1;

   210         this.sh = sh;

   211         this.sl = sl;

   212         this.x0 = x0;

   213         this.x1 = x1;

   214         // If x0 and x1 are both zero, we must choose nonzero values.

   215         if ((x0 | x1) == 0) {

   216 	    long v = sh;

   217             // At least one of the two values generated here will be nonzero.

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

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

   220         }

   221     }

   222 

   223     /**

   224      * Creates a new instance of {@link L128X128PlusPlusRandom} using the

   225      * specified {@code long} value as the initial seed. Instances of

   226      * {@link L128X128PlusPlusRandom} created with the same seed in the same

   227      * program generate identical sequences of values.

   228      *

   229      * @param seed the initial seed

   230      */

   231     public L128X128PlusPlusRandom(long seed) {

   232         // Using a value with irregularly spaced 1-bits to xor the seed

   233         // argument tends to improve "pedestrian" seeds such as 0 or

   234         // other small integers.  We may as well use SILVER_RATIO_64.

   235         //

   236         // The seed is hashed by mixMurmur64 to produce the `a` parameter.

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

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

   239         // Then x1 is filled in as if by a SplitMix PRNG with

   240         // GOLDEN_RATIO_64 as the gamma value and mixStafford13 as the mixer.

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

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

   243              0,

   244              1,

   245              RandomSupport.mixStafford13(seed),

   246              RandomSupport.mixStafford13(seed + RandomSupport.GOLDEN_RATIO_64));

   247     }

   248 

   249     /**

   250      * Creates a new instance of {@link L128X128PlusPlusRandom} that is likely to

   251      * generate sequences of values that are statistically independent

   252      * of those of any other instances in the current program execution,

   253      * but may, and typically does, vary across program invocations.

   254      */

   255     public L128X128PlusPlusRandom() {

   256         // Using GOLDEN_RATIO_64 here gives us a good Weyl sequence of values.

   257         this(defaultGen.getAndAdd(RandomSupport.GOLDEN_RATIO_64));

   258     }

   259 

   260     /**

   261      * Creates a new instance of {@link L128X128PlusPlusRandom} using the specified array of

   262      * initial seed bytes. Instances of {@link L128X128PlusPlusRandom} created with the same

   263      * seed array in the same program execution generate identical sequences of values.

   264      *

   265      * @param seed the initial seed

   266      */

   267     public L128X128PlusPlusRandom(byte[] seed) {

   268         // Convert the seed to 6 long values, of which the last 2 are not all zero.

   269         long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 2);

   270         long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5];

   271         // Force a to be odd.

   272         this.ah = ah;

   273         this.al = al | 1;

   274         this.sh = sh;

   275         this.sl = sl;

   276         this.x0 = x0;

   277         this.x1 = x1;

   278     }

   279 

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

   281 

   282     /**

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

   284      * {@code L128X128PlusPlusRandom} that shares no mutable state with this instance.

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

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

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

   288      * a single {@code L128X128PlusPlusRandom} object.  Either or both of the two

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

   290      * and the same expected statistical properties apply to the

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

   292      *

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

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

   295      *               initialize the state of the new ones.

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

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

   298      * @return a new instance of {@code L128X128PlusPlusRandom}

   299      */

   300     public SplittableGenerator split(SplittableGenerator source, long brine) {

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

   302         return new L128X128PlusPlusRandom(source.nextLong(), brine << 1,

   303 					  source.nextLong(), source.nextLong(),

   304 					  source.nextLong(), source.nextLong());

   305     }

   306 

   307     /**

   308      * Returns a pseudorandom {@code long} value.

   309      *

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

   311      */

   312     public long nextLong() {

   313 	// Compute the result based on current state information

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

   315 	final long result = Long.rotateLeft((sh + x0), 17) + x1;  // "plusplus" scrambler

   316 

   317 	// Update the LCG subgenerator

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

   319         final long u = ML * sl;

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

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

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

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

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

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

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

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

   328 	// and this entire comment can be deleted.

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

   330         sl = u + al;

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

   332 

   333         long q0 = x0, q1 = x1;

   334 	// Update the Xorshift subgenerator

   335         {   // xoroshiro128v1_0

   336             q1 ^= q0;

   337             q0 = Long.rotateLeft(q0, 24);

   338             q0 = q0 ^ q1 ^ (q1 << 16);

   339             q1 = Long.rotateLeft(q1, 37);

   340         }

   341         x0 = q0; x1 = q1;

   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>128</sup>-1)).

   350      */

   351     public BigInteger period() {

   352         return PERIOD;

   353     }

   354 }