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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     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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    20  *

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    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.AbstractSplittableGenerator;

    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 L64X256Random} 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 L64X256Random} 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 L64X256Random} 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 sum of one

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

    59  * (but {@link L64X256Random} does not use a mixing function).

    60  * <p>

    61  * The LCG subgenerator for {@link L64X256Random} has an update step of the

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

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

    64  * is fixed (the same for all instances of {@link L64X256Random}) and the addend

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

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

    67  * period, namely 2<sup>64</sup>); therefore there are 2<sup>63</sup> distinct choices

    68  * of parameter.

    69  * <p>

    70  * The Xorshift subgenerator for {@link L64X256Random} is the {@code xoshiro256} algorithm,

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

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

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

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

    75  * <p>

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

    77  * are relatively prime, the <em>period</em> of any single {@link L64X256Random} object

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

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

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

    81  * {@link L64X256Random} objects have different {@code a} parameters, then their

    82  * cycles of produced values will be different.

    83  * <p>

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

    85  * For any specific instance of {@link L64X256Random}, over the course of its cycle each

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

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

    88  * methods are likewise exactly equidistributed.

    89  * <p>

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

    91  * To be precise: for any specific instance of {@link L64X256Random}, consider

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

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

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

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

    96  * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>64</sup>)

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

    98  * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times.  So the ratio

    99  * of the probability of getting one of the less common subsequence values and the

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

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

   102  * one instance of {@link L64X256Random} to another, as a function of the additive

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

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

   105  * <p>

   106  * Method {@link #split} constructs and returns a new {@link L64X256Random}

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

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

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

   110  * generated by a single thread using a single {@link L64X256Random} object.

   111  * This is because, with high probability, distinct {@link L64X256Random} objects

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

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

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

   115  * cycle.

   116  * <p>

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

   118  * {@link L64X256Random} are <em>not</em> thread-safe.

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

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

   121  * computation using random numbers might include a construction

   122  * of the form {@code new Subtask(someL64X256Random.split()).fork()}.

   123  * <p>

   124  * This class provides additional methods for generating random

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

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

   127  * <p>

   128  * Instances of {@link L64X256Random} are not cryptographically

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

   130  * in security-sensitive applications. Additionally,

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

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

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

   134  *

   135  * @since 14

   136  */

   137 public final class L64X256Random extends AbstractSplittableGenerator {

   138 

   139     /*

   140      * Implementation Overview.

   141      *

   142      * The split() operation uses the current generator to choose six new 64-bit

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

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

   145      * generator.

   146      *

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

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

   149      * that the values generated by two instances of {@link L64X256Random}

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

   151      *

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

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

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

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

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

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

   158      * seed based on current time unless the

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

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

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

   162      *

   163      * File organization: First static fields, then instance

   164      * fields, then constructors, then instance methods.

   165      */

   166 

   167     /* ---------------- static fields ---------------- */

   168 

   169     /**

   170      * The seed generator for default constructors.

   171      */

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

   173 

   174     /*

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

   176      */

   177     private static final BigInteger PERIOD =

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

   179 

   180     /*

   181      * Multiplier used in the LCG portion of the algorithm, taken from

   182      * Pierre L'Ecuyer, Tables of linear congruential generators of

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

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

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

   186      */

   187 

   188     private static final long M = 2862933555777941757L;

   189 

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

   191 

   192     /**

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

   194      * Must be odd.

   195      */

   196     private final long a;

   197 

   198     /**

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

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

   201      */

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

   203 

   204     /* ---------------- constructors ---------------- */

   205 

   206     /**

   207      * Basic constructor that initializes all fields from parameters.

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

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

   210      *

   211      * @param a additive parameter for the LCG

   212      * @param s initial state for the LCG

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

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

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

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

   217      */

   218     public L64X256Random(long a, long s, long x0, long x1, long x2, long x3) {

   219         // Force a to be odd.

   220         this.a = a | 1;

   221         this.s = s;

   222         this.x0 = x0;

   223         this.x1 = x1;

   224         this.x2 = x2;

   225         this.x3 = x3;

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

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

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

   229             this.x0 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64);

   230             this.x1 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64);

   231             this.x2 = RandomSupport.mixStafford13(s += RandomSupport.GOLDEN_RATIO_64);

   232             this.x3 = RandomSupport.mixStafford13(s + RandomSupport.GOLDEN_RATIO_64);

   233         }

   234     }

   235 

   236     /**

   237      * Creates a new instance of {@link L64X256Random} using the

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

   239      * {@link L64X256Random} created with the same seed in the same

   240      * program execution generate identical sequences of values.

   241      *

   242      * @param seed the initial seed

   243      */

   244     public L64X256Random(long seed) {

   245         // Using a value with irregularly spaced 1-bit to xor the seed

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

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

   248         //

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

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

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

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

   253         // GOLDEN_RATIO_64 as the gamma value and Stafford13 as the mixer.

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

   255              1,

   256              RandomSupport.mixStafford13(seed),

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

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

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

   260     }

   261 

   262     /**

   263      * Creates a new instance of {@link L64X256Random} that is likely to

   264      * generate sequences of values that are statistically independent

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

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

   267      */

   268     public L64X256Random() {

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

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

   271     }

   272 

   273     /**

   274      * Creates a new instance of {@link L64X256Random} using the specified array of

   275      * initial seed bytes. Instances of {@link L64X256Random} created with the same

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

   277      *

   278      * @param seed the initial seed

   279      */

   280     public L64X256Random(byte[] seed) {

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

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

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

   284         // Force a to be odd.

   285         this.a = a | 1;

   286         this.s = s;

   287         this.x0 = x0;

   288         this.x1 = x1;

   289         this.x2 = x2;

   290         this.x3 = x3;

   291     }

   292 

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

   294 

   295     /**

   296      * Constructs and returns a new instance of {@link L64X256Random}

   297      * that shares no mutable state with this instance.

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

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

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

   301      * a single {@link L64X256Random} object.  Either or both of the two

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

   303      * and the same expected statistical properties apply to the

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

   305      *

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

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

   308      *               initialize the state of the new ones.

   309      *

   310      * @return a new instance of {@link L64X256Random}

   311      */

   312     public L64X256Random split(SplittableGenerator source) {

   313         // Literally pick a new instance "at random".

   314         return new L64X256Random(source.nextLong(), source.nextLong(),

   315                                  source.nextLong(), source.nextLong(),

   316                                  source.nextLong(), source.nextLong());

   317     }

   318 

   319     /**

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

   321      *

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

   323      */

   324     public long nextLong() {

   325         final long z = s + x0;

   326         s = M * s + a;  // LCG

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

   328         {   // xoshiro256 1.0

   329             long t = q1 << 17;

   330             q2 ^= q0;

   331             q3 ^= q1;

   332             q1 ^= q2;

   333             q0 ^= q3;

   334             q2 ^= t;

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

   336         }

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

   338         return z;

   339     }

   340 

   341     public BigInteger period() {

   342         return PERIOD;

   343     }

   344 }