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

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

    20  *

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

    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 L64X256MixRandom} 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 L64X256MixRandom} 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 L64X256MixRandom} 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 L64X256MixRandom} has an update step of the

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

    64  * of type {@code long}; {@code s} is the mutable state, the multiplier {@code m}

    65  * is fixed (the same for all instances of {@link L64X256MixRandom}) 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>64</sup>); therefore there are 2<sup>63</sup> distinct choices

    69  * of parameter.

    70  * <p>

    71  * The Xorshift subgenerator for {@link L64X256MixRandom} is the {@code xoshiro256} algorithm,

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

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

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

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

    76  * <p>

    77  * The mixing function for {@link L64X256MixRandom} is {@link RandomSupport.mixLea64}

    78  * applied to the argument {@code (s + x0)}.

    79  * <p>

    80  * Because the periods 2<sup>64</sup> and 2<sup>256</sup>-1 of the two subgenerators

    81  * are relatively prime, the <em>period</em> of any single {@link L64X256MixRandom} object

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

    83  * of the periods of the subgenerators, that is, 2<sup>64</sup>(2<sup>256</sup>-1),

    84  * which is just slightly smaller than 2<sup>320</sup>.  Moreover, if two distinct

    85  * {@link L64X256MixRandom} objects have different {@code a} parameters, then their

    86  * cycles of produced values will be different.

    87  * <p>

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

    89  * For any specific instance of {@link L64X256MixRandom}, over the course of its cycle each

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

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

    92  * methods are likewise exactly equidistributed.

    93  * <p>

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

    95  * To be precise: for any specific instance of {@link L64X256MixRandom}, consider

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

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

    98  * There are 2<sup>64</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,

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

   100  * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>64</sup>)

   101  * occur 2<sup>64</sup> times over the course of the entire cycle, and the other

   102  * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times.  So the ratio

   103  * of the probability of getting any specific one of the less common subsequence values and the

   104  * probability of getting any specific one of the more common subsequence values is 1-2<sup>-64</sup>.

   105  * (Note that the set of 2<sup>64</sup> less-common subsequence values will differ from

   106  * one instance of {@link L64X256MixRandom} to another, as a function of the additive

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

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

   109  * <p>

   110  * Method {@link #split} constructs and returns a new {@link L64X256MixRandom}

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

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

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

   114  * generated by a single thread using a single {@link L64X256MixRandom} object.

   115  * This is because, with high probability, distinct {@link L64X256MixRandom} objects

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

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

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

   119  * cycle.

   120  * <p>

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

   122  * {@link L64X256MixRandom} are <em>not</em> thread-safe.

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

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

   125  * computation using random numbers might include a construction

   126  * of the form {@code new Subtask(someL64X256MixRandom.split()).fork()}.

   127  * <p>

   128  * This class provides additional methods for generating random

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

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

   131  * <p>

   132  * Instances of {@link L64X256MixRandom} are not cryptographically

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

   134  * in security-sensitive applications. Additionally,

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

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

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

   138  *

   139  * @since 14

   140  */

   141 public final class L64X256MixRandom extends AbstractSplittableWithBrineGenerator {

   142 

   143     /*

   144      * Implementation Overview.

   145      *

   146      * The split operation uses the current generator to choose six new 64-bit

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

   148      * state variables `s`, `x0`, `x1`, `x2`, and `x3` for a newly constructed

   149      * generator.

   150      *

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

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

   153      * that the values generated by two instances of {@link L64X256MixRandom}

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

   155      *

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

   157      * "defaultGen" to generate six new 64-bit values for the same

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

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

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

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

   162      * seed based on current time unless the

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

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

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

   166      *

   167      * File organization: First static fields, then instance

   168      * fields, then constructors, then instance methods.

   169      */

   170 

   171     /* ---------------- static fields ---------------- */

   172 

   173     /**

   174      * The seed generator for default constructors.

   175      */

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

   177 

   178     /*

   179      * The period of this generator, which is (2**256 - 1) * 2**64.

   180      */

   181     private static final BigInteger PERIOD =

   182         BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(64);

   183 

   184     /*

   185      * Multiplier used in the LCG portion of the algorithm.

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

   187      * The spectral scores for dimensions 2 through 8 for the multiplier 0xd1342543de82ef95

   188      * are [0.958602, 0.937479, 0.870757, 0.822326, 0.820405, 0.813065, 0.760215].

   189      */

   190 

   191     private static final long M = 0xd1342543de82ef95L;

   192 

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

   194 

   195     /**

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

   197      * Must be odd.

   198      */

   199     private final long a;

   200 

   201     /**

   202      * The per-instance state: s for the LCG; x0, x1, x2, and x3 for the xorshift.

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

   204      */

   205     private long s, x0, x1, x2, x3;

   206 

   207     /* ---------------- constructors ---------------- */

   208 

   209     /**

   210      * Basic constructor that initializes all fields from parameters.

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

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

   213      *

   214      * @param a additive parameter for the LCG

   215      * @param s initial state for the LCG

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

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

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

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

   220      */

   221     public L64X256MixRandom(long a, long s, long x0, long x1, long x2, long x3) {

   222         // Force a to be odd.

   223         this.a = a | 1;

   224         this.s = s;

   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 = s;

   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 L64X256MixRandom} using the

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

   243      * {@link L64X256MixRandom} 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 L64X256MixRandom(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              1,

   260              RandomSupport.mixStafford13(seed),

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

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

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

   264     }

   265 

   266     /**

   267      * Creates a new instance of {@link L64X256MixRandom} that is likely to

   268      * generate sequences of values that are statistically independent

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

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

   271      */

   272     public L64X256MixRandom() {

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

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

   275     }

   276 

   277     /**

   278      * Creates a new instance of {@link L64X256MixRandom} using the specified array of

   279      * initial seed bytes. Instances of {@link L64X256MixRandom} created with the same

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

   281      *

   282      * @param seed the initial seed

   283      */

   284     public L64X256MixRandom(byte[] seed) {

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

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

   287         long a = data[0], s = data[1], x0 = data[2], x1 = data[3], x2 = data[4], x3 = data[5];

   288         // Force a to be odd.

   289         this.a = a | 1;

   290         this.s = s;

   291         this.x0 = x0;

   292         this.x1 = x1;

   293         this.x2 = x2;

   294         this.x3 = x3;

   295     }

   296 

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

   298 

   299     /**

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

   301      * {@code L64X256MixRandom} that shares no mutable state with this instance.

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

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

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

   305      * a single {@code L64X256MixRandom} object.  Either or both of the two

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

   307      * and the same expected statistical properties apply to the

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

   309      *

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

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

   312      *               initialize the state of the new ones.

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

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

   315      * @return a new instance of {@code L64X256MixRandom}

   316      */

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

   318 	// Pick a new instance "at random", but use the brine for `a`.

   319         return new L64X256MixRandom(brine << 1, source.nextLong(),

   320 				    source.nextLong(), source.nextLong(),

   321 				    source.nextLong(), source.nextLong());

   322     }

   323 

   324     /**

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

   326      *

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

   328      */

   329     public long nextLong() {

   330 	// Compute the result based on current state information

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

   332         final long result = RandomSupport.mixLea64(s + x0);

   333 	// Update the LCG subgenerator

   334         s = M * s + a;

   335 	// Update the Xorshift subgenerator

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

   337         {   // xoshiro256 1.0

   338             long t = q1 << 17;

   339             q2 ^= q0;

   340             q3 ^= q1;

   341             q1 ^= q2;

   342             q0 ^= q3;

   343             q2 ^= t;

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

   345         }

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

   347         return result;

   348     }

   349 

   350     /**

   351      * Returns the period of this random generator.

   352      *

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

   354      *         {@link RandomGenerator} object (2<sup>64</sup>(2<sup>256</sup>-1)).

   355      */

   356     public BigInteger period() {

   357         return PERIOD;

   358     }

   359 }