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

     6  * under the terms of the GNU General Public License version 2 only, as

     7  * published by the Free Software Foundation.  Oracle designates this

     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

    18  * 2 along with this work; if not, write to the Free Software Foundation,

    19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

    20  *

    21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

    22  * or visit www.oracle.com if you need additional information or have any

    23  * questions.

    24  */

    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 /**

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

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

    37  * generate subtasks.  Class {@link L128X256MixRandom} implements

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

    39  * and therefore supports methods for producing pseudorandomly chosen

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

    41  * as well as creating new split-off {@link L128X256MixRandom} objects,

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

    43  * <p>

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

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

    46  * (Most recently validated with

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

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

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

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

    51  * These tests validate only the methods for certain

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

    53  * least approximately, for others as well.

    54  * <p>

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

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

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

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

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

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

    61  * Xorshift generator are advanced).

    62  * <p>

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

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

    65  * 128-bit integers; {@code s} is the mutable state, the multiplier {@code m}

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

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

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

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

    70  * of parameter.

    71  * <p>

    72  * The Xorshift subgenerator for {@link L128X256MixRandom} is the {@code xoshiro256} algorithm,

    73  * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**".

    74  * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2},

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

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

    77  * <p>

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

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

    80  * <p>

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

    82  * are relatively prime, the <em>period</em> of any single {@link L128X256MixRandom} 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>256</sup>-1),

    85  * which is just slightly smaller than 2<sup>384</sup>.  Moreover, if two distinct

    86  * {@link L128X256MixRandom} 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 L128X256MixRandom}, 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>256</sup>-1) times.  The values produced by the {@code nextInt()},

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

    94  * <p>

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

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

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

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

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

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

   101  * <p>

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

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

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

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

   106  * generated by a single thread using a single {@link L128X256MixRandom} object.

   107  * This is because, with high probability, distinct {@link L128X256MixRandom} objects

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

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

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

   111  * cycle.

   112  * <p>

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

   114  * {@link L128X256MixRandom} are <em>not</em> thread-safe.

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

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

   117  * computation using random numbers might include a construction

   118  * of the form {@code new Subtask(someL128X256MixRandom.split()).fork()}.

   119  * <p>

   120  * This class provides additional methods for generating random

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

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

   123  * <p>

   124  * Instances of {@link L128X256MixRandom} are not cryptographically

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

   126  * in security-sensitive applications. Additionally,

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

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

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

   130  *

   131  * @since 14

   132  */

   133 public final class L128X256MixRandom extends AbstractSplittableWithBrineGenerator {

   134 

   135     /*

   136      * Implementation Overview.

   137      *

   138      * The 128-bit parameter `a` is represented as two long fields `ah` and `al`.

   139      * The 128-bit state variable `s` is represented as two long fields `sh` and `sl`.

   140      *

   141      * The split operation uses the current generator to choose eight

   142      * new 64-bit long values that are then used to initialize the

   143      * parameters `ah` and `al` and the state variables `sh`, `sl`,

   144      * `x0`, `x1`, `x2`, and `x3` for a newly constructed generator.

   145      *

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

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

   148      * that the values generated by two instances of {@link L128X256MixRandom}

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

   150      *

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

   152      * "defaultGen" to generate eight new 64-bit values for the same

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

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

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

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

   157      * seed based on current time unless the

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

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

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

   161      *

   162      * File organization: First static fields, then instance

   163      * fields, then constructors, then instance methods.

   164      */

   165 

   166     /* ---------------- static fields ---------------- */

   167 

   168     /**

   169      * The seed generator for default constructors.

   170      */

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

   172 

   173     /*

   174      * The period of this generator, which is (2**256 - 1) * 2**128.

   175      */

   176     private static final BigInteger PERIOD =

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

   178 

   179     /*

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

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

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

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

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

   185      */

   186 

   187     private static final long ML = 0xd605bbb58c8abbfdL;

   188 

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

   190 

   191     /**

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

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

   194      */

   195     private final long ah, al;

   196 

   197     /**

   198      * The per-instance state: sh and sl for the LCG; x0, x1, x2, and x3 for the xorshift.

   199      * At least one of the four fields x0, x1, x2, and x3 must be nonzero.

   200      */

   201     private long sh, sl, x0, x1, x2, x3;

   202 

   203     /* ---------------- constructors ---------------- */

   204 

   205     /**

   206      * Basic constructor that initializes all fields from parameters.

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

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

   209      *

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

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

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

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

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

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

   216      * @param x2 third word of the initial state for the xorshift generator

   217      * @param x3 fourth word of the initial state for the xorshift generator

   218      */

   219     public L128X256MixRandom(long ah, long al, long sh, long sl, long x0, long x1, long x2, long x3) {

   220         // Force a to be odd.

   221         this.ah = ah;

   222         this.al = al | 1;

   223         this.sh = sh;

   224         this.sl = sl;

   225         this.x0 = x0;

   226         this.x1 = x1;

   227         this.x2 = x2;

   228         this.x3 = x3;

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

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

   231 	    long v = sh;

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

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

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

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

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

   237         }

   238     }

   239 

   240     /**

   241      * Creates a new instance of {@link L128X256MixRandom} using the

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

   243      * {@link L128X256MixRandom} created with the same seed in the same

   244      * program generate identical sequences of values.

   245      *

   246      * @param seed the initial seed

   247      */

   248     public L128X256MixRandom(long seed) {

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

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

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

   252         //

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

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

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

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

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

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

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

   260              0,

   261              1,

   262              RandomSupport.mixStafford13(seed),

   263              RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),

   264              RandomSupport.mixStafford13(seed += RandomSupport.GOLDEN_RATIO_64),

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

   266     }

   267 

   268     /**

   269      * Creates a new instance of {@link L128X256MixRandom} that is likely to

   270      * generate sequences of values that are statistically independent

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

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

   273      */

   274     public L128X256MixRandom() {

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

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

   277     }

   278 

   279     /**

   280      * Creates a new instance of {@link L128X256MixRandom} using the specified array of

   281      * initial seed bytes. Instances of {@link L128X256MixRandom} created with the same

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

   283      *

   284      * @param seed the initial seed

   285      */

   286     public L128X256MixRandom(byte[] seed) {

   287         // Convert the seed to 6 long values, of which the last 4 are not all zero.

   288         long[] data = RandomSupport.convertSeedBytesToLongs(seed, 6, 4);

   289         long ah = data[0], al = data[1], sh = data[2], sl = data[3],

   290              x0 = data[4], x1 = data[5], x2 = data[6], x3 = data[7];

   291         // Force a to be odd.

   292         this.ah = ah;

   293         this.al = al | 1;

   294         this.sh = sh;

   295         this.sl = sl;

   296         this.x0 = x0;

   297         this.x1 = x1;

   298         this.x2 = x2;

   299         this.x3 = x3;

   300     }

   301 

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

   303     

   304     /**

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

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

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

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

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

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

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

   312      * and the same expected statistical properties apply to the

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

   314      *

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

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

   317      *               initialize the state of the new ones.

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

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

   320      * @return a new instance of {@code L128X256MixRandom}

   321      */

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

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

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

   325 				     source.nextLong(), source.nextLong(),

   326 				     source.nextLong(), source.nextLong(),

   327 				     source.nextLong(), source.nextLong());

   328     }

   329 

   330     /**

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

   332      *

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

   334      */

   335     public long nextLong() {

   336 	// Compute the result based on current state information

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

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

   339 

   340 	// Update the LCG subgenerator

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

   342         final long u = ML * sl;

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

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

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

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

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

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

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

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

   351 	// and this entire comment can be deleted.

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

   353         sl = u + al;

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

   355 

   356 	// Update the Xorshift subgenerator

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

   358         {   // xoshiro256 1.0

   359             long t = q1 << 17;

   360             q2 ^= q0;

   361             q3 ^= q1;

   362             q1 ^= q2;

   363             q0 ^= q3;

   364             q2 ^= t;

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

   366         }

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

   368         return result;

   369     }

   370 

   371     /**

   372      * Returns the period of this random generator.

   373      *

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

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

   376      */

   377     public BigInteger period() {

   378         return PERIOD;

   379     }

   380 }