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.LeapableGenerator;

    31 

    32 /**

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

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

    35  * generate subtasks.  Class {@link Xoroshiro128Plus} implements

    36  * interfaces {@link RandomGenerator} and {@link LeapableGenerator},

    37  * and therefore supports methods for producing pseudorandomly chosen

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

    39  * as well as creating new {@link Xoroshiro128Plus} objects

    40  * by "jumping" or "leaping".

    41  * <p>

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

    43  * that measure independence and uniformity properties of random number generators,

    44  * <em>except</em> that it does not pass the binary rank tests of PractRand,

    45  * which fail due to the lowest bit being an LFSR; all other bits pass all tests.

    46  * For this reason may be best for some purposes to use this generator to generate

    47  * pseudorandom {@code int}, {@code float}, and {@code double} values but not

    48  * {@code long} values.  For the same reason, it may be best not to use the

    49  * method {@code nextGaussian} or {@code nextExponential} with this generator.

    50  * <p>

    51  * The class {@link Xoroshiro128Plus} uses the {@code xoroshiro128} algorithm,

    52  * version 1.0 (parameters 24, 16, 37), with the "+" scrambler

    53  * (the returned value is the sum of the two state variables {@code x0} and {@code x1}).

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

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

    56  * The period of this generator is 2<sup>128</sup>-1.

    57  * <p>

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

    59  * To be precise, over the course of the cycle of length 2<sup>128</sup>-1,

    60  * each nonzero {@code long} value is generated 2<sup>64</sup> times,

    61  * but the value 0 is generated only 2<sup>64</sup>-1 times.

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

    63  * methods are likewise equidistributed.

    64  * <p>

    65  * Instances {@link Xoroshiro128Plus} are <em>not</em> thread-safe.

    66  * They are designed to be used so that each thread as its own instance.

    67  * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps}

    68  * can be used to construct new instances of {@link Xoroshiro128Plus} that traverse

    69  * other parts of the state cycle.

    70  * <p>

    71  * Instances of {@link Xoroshiro128Plus} are not cryptographically

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

    73  * in security-sensitive applications. Additionally,

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

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

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

    77  *

    78  * @since 14

    79  */

    80 public final class Xoroshiro128Plus implements LeapableGenerator {

    81 

    82     /*

    83      * Implementation Overview.

    84      *

    85      * This is an implementation of the xoroshiro128+ algorithm written

    86      * in 2016 by David Blackman and Sebastiano Vigna (vigna@acm.org),

    87      * and updated with improved parameters in 2018.

    88      * See http://xoshiro.di.unimi.it and these two papers:

    89      *

    90      *    Sebastiano Vigna. 2016. An Experimental Exploration of Marsaglia's

    91      *    xorshift Generators, Scrambled. ACM Transactions on Mathematical

    92      *    Software 42, 4, Article 30 (June 2016), 23 pages.

    93      *    https://doi.org/10.1145/2845077

    94      *

    95      *    David Blackman and Sebastiano Vigna.  2018.  Scrambled Linear

    96      *    Pseudorandom Number Generators.  Computing Research Repository (CoRR).

    97      *    http://arxiv.org/abs/1805.01407

    98      *

    99      * The jump operation moves the current generator forward by 2*64

   100      * steps; this has the same effect as calling nextLong() 2**64

   101      * times, but is much faster.  Similarly, the leap operation moves

   102      * the current generator forward by 2*96 steps; this has the same

   103      * effect as calling nextLong() 2**96 times, but is much faster.

   104      * The copy method may be used to make a copy of the current

   105      * generator.  Thus one may repeatedly and cumulatively copy and

   106      * jump to produce a sequence of generators whose states are well

   107      * spaced apart along the overall state cycle (indeed, the jumps()

   108      * and leaps() methods each produce a stream of such generators).

   109      * The generators can then be parceled out to other threads.

   110      *

   111      * File organization: First the non-public methods that constitute the

   112      * main algorithm, then the public methods.  Note that many methods are

   113      * defined by classes {@link AbstractJumpableGenerator} and {@link AbstractGenerator}.

   114      */

   115 

   116     /* ---------------- static fields ---------------- */

   117 

   118     /**

   119      * The seed generator for default constructors.

   120      */

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

   122 

   123     /*

   124      * The period of this generator, which is 2**128 - 1.

   125      */

   126     private static final BigInteger PERIOD =

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

   128 

   129     /* ---------------- instance fields ---------------- */

   130 

   131     /**

   132      * The per-instance state.

   133      * At least one of the two fields x0 and x1 must be nonzero.

   134      */

   135     private long x0, x1;

   136 

   137     /* ---------------- constructors ---------------- */

   138 

   139     /**

   140      * Basic constructor that initializes all fields from parameters.

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

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

   143      *

   144      * @param x0 first word of the initial state

   145      * @param x1 second word of the initial state

   146      */

   147     public Xoroshiro128Plus(long x0, long x1) {

   148         this.x0 = x0;

   149         this.x1 = x1;

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

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

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

   153             this.x0 = RandomSupport.mixStafford13(x0 += RandomSupport.GOLDEN_RATIO_64);

   154             this.x1 = (x0 += RandomSupport.GOLDEN_RATIO_64);

   155         }

   156     }

   157 

   158     /**

   159      * Creates a new instance of {@link Xoroshiro128Plus} using the

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

   161      * {@link Xoroshiro128Plus} created with the same seed in the same

   162      * program generate identical sequences of values.

   163      *

   164      * @param seed the initial seed

   165      */

   166     public Xoroshiro128Plus(long seed) {

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

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

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

   170         //

   171         // The x values are then filled in as if by a SplitMix PRNG with

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

   173         this(RandomSupport.mixStafford13(seed ^= RandomSupport.SILVER_RATIO_64),

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

   175     }

   176 

   177     /**

   178      * Creates a new instance of {@link Xoroshiro128Plus} that is likely to

   179      * generate sequences of values that are statistically independent

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

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

   182      */

   183     public Xoroshiro128Plus() {

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

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

   186     }

   187 

   188     /**

   189      * Creates a new instance of {@link Xoroshiro128Plus} using the specified array of

   190      * initial seed bytes. Instances of {@link Xoroshiro128Plus} created with the same

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

   192      *

   193      * @param seed the initial seed

   194      */

   195     public Xoroshiro128Plus(byte[] seed) {

   196         // Convert the seed to 2 long values, which are not both zero.

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

   198         long x0 = data[0], x1 = data[1];

   199         this.x0 = x0;

   200         this.x1 = x1;

   201     }

   202 

   203     /* ---------------- public methods ---------------- */

   204 

   205     public Xoroshiro128Plus copy() { return new Xoroshiro128Plus(x0, x1); }

   206 

   207 

   208     /*

   209      * To the extent possible under law, the author has dedicated all copyright and related and

   210      * neighboring rights to this software to the public domain worldwide. This software is distributed

   211      * without any warranty.

   212      * <p>

   213      * See <http://creativecommons.org/publicdomain/zero/1.0/>.

   214      */

   215 

   216     /*

   217      * This is the successor to xorshift128+. It is the fastest full-period generator passing

   218      * BigCrush without systematic failures, but due to the relatively short period it is acceptable

   219      * only for applications with a mild amount of parallelism; otherwise, use a xorshift1024*

   220      * generator.

   221      * <p>

   222      * Beside passing BigCrush, this generator passes the PractRand test suite up to (and included)

   223      * 16TB, with the exception of binary rank tests, which fail due to the lowest bit being an

   224      * LFSR; all other bits pass all tests. We suggest to use a sign test to extract a random

   225      * Boolean value.

   226      * <p>

   227      * Note that the generator uses a simulated rotate operation, which most C compilers will turn

   228      * into a single instruction. In Java, you can use Long.rotateLeft(). In languages that do not

   229      * make low-level rotation instructions accessible xorshift128+ could be faster.

   230      * <p>

   231      * The state must be seeded so that it is not everywhere zero. If you have a 64-bit seed, we

   232      * suggest to seed a splitmix64 generator and use its output to fill s.

   233      */

   234 

   235     /**

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

   237      *

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

   239      */

   240     public long nextLong() {

   241         final long s0 = x0;

   242         long s1 = x1;

   243         final long z = s0 + s1;

   244 

   245         s1 ^= s0;

   246         x0 = Long.rotateLeft(s0, 24) ^ s1 ^ (s1 << 16); // a, b

   247         x1 = Long.rotateLeft(s1, 37); // c

   248 

   249         return z;

   250     }

   251 

   252     public BigInteger period() {

   253         return PERIOD;

   254     }

   255 

   256     public double defaultJumpDistance() {

   257         return 0x1.0p64;

   258     }

   259 

   260     public double defaultLeapDistance() {

   261         return 0x1.0p96;

   262     }

   263 

   264     private static final long[] JUMP_TABLE = { 0xdf900294d8f554a5L, 0x170865df4b3201fcL };

   265 

   266     private static final long[] LEAP_TABLE = { 0xd2a98b26625eee7bL, 0xdddf9b1090aa7ac1L };

   267 

   268     /*

   269      * This is the jump function for the generator. It is equivalent

   270      * to 2**64 calls to nextLong(); it can be used to generate 2**64

   271      * non-overlapping subsequences for parallel computations.

   272      */

   273     public void jump() {

   274         jumpAlgorithm(JUMP_TABLE);

   275     }

   276 

   277     /**

   278      * This is the long-jump function for the generator. It is equivalent to 2**96 calls to next();

   279      * it can be used to generate 2**32 starting points, from each of which jump() will generate

   280      * 2**32 non-overlapping subsequences for parallel distributed computations.

   281      */

   282     public void leap() {

   283         jumpAlgorithm(LEAP_TABLE);

   284     }

   285 

   286     private void jumpAlgorithm(long[] table) {

   287         long s0 = 0, s1 = 0;

   288         for (int i = 0; i < table.length; i++) {

   289             for (int b = 0; b < 64; b++) {

   290                 if ((table[i] & (1L << b)) != 0) {

   291                     s0 ^= x0;

   292                     s1 ^= x1;

   293                 }

   294                 nextLong();

   295             }

   296             x0 = s0;

   297             x1 = s1;

   298         }

   299     }

   300 }