1 /*

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

     4  *

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     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

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    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

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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.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 L32X64MixRandom} 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 L32X64MixRandom} 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 L32X64MixRandom} 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  * (and {@link L32X64MixRandom} does use a mixing function).

    60  * <p>

    61  * The LCG subgenerator for {@link L32X64MixRandom} 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 int}; {@code s} is the mutable state, the multiplier {@code m}

    64  * is fixed (the same for all instances of {@link L32X64MixRandom}) 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>32</sup>); therefore there are 2<sup>31</sup> distinct choices

    68  * of parameter.

    69  * <p>

    70  * The Xorshift subgenerator for {@link L32X64MixRandom} is the {@code xoroshiro64} algorithm,

    71  * version 1.0 (parameters 26, 9, 13), without any final scrambler such as "+" or "**".

    72  * Its state consists of two {@code int} fields {@code x0} and {@code x1},

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

    74  * The period of this subgenerator is 2<sup>64</sup>-1.

    75  * <p>

    76  * The mixing function for {@link L32X64MixRandom} is the "starstar" mixing function.

    77  * <p>

    78  * Because the periods 2<sup>32</sup> and 2<sup>64</sup>-1 of the two subgenerators

    79  * are relatively prime, the <em>period</em> of any single {@link L32X64MixRandom} object

    80  * (the length of the series of generated 32-bit values before it repeats) is the product

    81  * of the periods of the subgenerators, that is, 2<sup>32</sup>(2<sup>64</sup>-1),

    82  * which is just slightly smaller than 2<sup>96</sup>.  Moreover, if two distinct

    83  * {@link L32X64MixRandom} objects have different {@code a} parameters, then their

    84  * cycles of produced values will be different.

    85  * <p>

    86  * The 32-bit values produced by the {@code nextInt()} method are exactly equidistributed.

    87  * For any specific instance of {@link L32X64MixRandom}, over the course of its cycle each

    88  * of the 2<sup>32</sup> possible {@code int} values will be produced 2<sup>64</sup>-1 times.

    89  * The values produced by the {@code nextFloat()} method are likewise exactly equidistributed.

    90  * <p>

    91  * In fact, the 32-bit values produced by the {@code nextInt()} method are 2-equidistributed.

    92  * To be precise: for any specific instance of {@link L32X64MixRandom}, consider

    93  * the (overlapping) length-2 subsequences of the cycle of 64-bit values produced by

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

    95  * There are 2<sup>32</sup>(2<sup>64</sup>-1) such subsequences, and each subsequence,

    96  * which consists of 2 32-bit values, can have one of 2<sup>64</sup> values. Of those

    97  * 2<sup>64</sup> subsequence values, nearly all of them (2<sup>64</sup>-2<sup>32</sup>)

    98  * occur 2<sup>32</sup> times over the course of the entire cycle, and the other

    99  * 2<sup>32</sup> subsequence values occur only 2<sup>32</sup>-1 times.  So the ratio

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

   101  * probability of getting one of the more common subsequence values is 1-2<sup>-32</sup>.

   102  * (Note that the set of 2<sup>32</sup> less-common subsequence values will differ from

   103  * one instance of {@link L32X64MixRandom} to another, as a function of the additive

   104  * parameter of the LCG.)  As a consequence, the values produced by the {@code nextFloat()}

   105  * method are likewise 2-equidistributed, and the values produced by the {@code nextLong()}

   106  * and {@code nextDouble()} methods are equidistributed (but not 2-equidistributed).

   107  * <p>

   108  * Method {@link #split} constructs and returns a new {@link L32X64MixRandom}

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

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

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

   112  * generated by a single thread using a single {@link L32X64MixRandom} object.

   113  * This is because, with high probability, distinct {@link L32X64MixRandom} objects

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

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

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

   117  * cycle.

   118  * <p>

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

   120  * {@link L32X64MixRandom} are <em>not</em> thread-safe.

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

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

   123  * computation using random numbers might include a construction

   124  * of the form {@code new Subtask(someL32X64MixRandom.split()).fork()}.

   125  * <p>

   126  * This class provides additional methods for generating random

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

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

   129  * <p>

   130  * Instances of {@link L32X64MixRandom} are not cryptographically

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

   132  * in security-sensitive applications. Additionally,

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

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

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

   136  *

   137   * @since 14

   138  */

   139 public final class L32X64MixRandom extends AbstractSplittableGenerator {

   140 

   141     /*

   142      * Implementation Overview.

   143      *

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

   145      * int values that are then used to initialize the parameter `a` and the

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

   147      *

   148      * With high probability, no two generators so chosen

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

   150      * that the values generated by two instances of {@link L32X64MixRandom}

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

   152      *

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

   154      * "defaultGen" to generate four new 32-bit values for the same

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

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

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

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

   159      * seed based on current time unless the

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

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

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

   163      *

   164      * File organization: First static fields, then instance

   165      * fields, then constructors, then instance methods.

   166      */

   167 

   168     /* ---------------- static fields ---------------- */

   169 

   170     /**

   171      * The seed generator for default constructors.

   172      */

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

   174 

   175     /*

   176      * The period of this generator, which is (2**64 - 1) * 2**32.

   177      */

   178     private static final BigInteger PERIOD =

   179         BigInteger.ONE.shiftLeft(64).subtract(BigInteger.ONE).shiftLeft(32);

   180 

   181     /*

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

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

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

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

   186      * Table 4 (third multiplier for size 2<sup>32</sup>).

   187      */

   188 

   189     private static final int M = 32310901;

   190 

   191     /* ---------------- instance fields ---------------- */

   192 

   193     /**

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

   195      * Must be odd.

   196      */

   197     private final int a;

   198 

   199     /**

   200      * The per-instance state: s for the LCG; x0 and x1 for the xorshift.

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

   202      */

   203     private int s, x0, x1;

   204 

   205     /* ---------------- constructors ---------------- */

   206 

   207     /**

   208      * Basic constructor that initializes all fields from parameters.

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

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

   211      *

   212      * @param a additive parameter for the LCG

   213      * @param s 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      */

   217     public L32X64MixRandom(int a, int s, int x0, int x1) {

   218         // Force a to be odd.

   219         this.a = a | 1;

   220         this.s = s;

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

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

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

   224             this.x0 = RandomSupport.mixMurmur32(s += RandomSupport.GOLDEN_RATIO_32);

   225             this.x1 = RandomSupport.mixMurmur32(s + RandomSupport.GOLDEN_RATIO_32);

   226         }

   227     }

   228 

   229     /**

   230      * Creates a new instance of {@link L32X64MixRandom} using the

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

   232      * {@link L32X64MixRandom} created with the same seed in the same

   233      * program generate identical sequences of values.

   234      *

   235      * @param seed the initial seed

   236      */

   237     public L32X64MixRandom(long seed) {

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

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

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

   241         //

   242         // The high half of the seed is hashed by mixMurmur32 to produce the `a` parameter.

   243         // The low half of the seed is hashed by mixMurmur32 to produce the initial `x0`,

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

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

   246         // GOLDEN_RATIO_32 as the gamma value and Murmur32 as the mixer.

   247         this(RandomSupport.mixMurmur32((int)((seed ^= RandomSupport.SILVER_RATIO_64) >>> 32)),

   248              1,

   249              RandomSupport.mixLea32((int)(seed)),

   250              RandomSupport.mixLea32((int)(seed) + RandomSupport.GOLDEN_RATIO_32));

   251     }

   252 

   253     /**

   254      * Creates a new instance of {@link L32X64MixRandom} that is likely to

   255      * generate sequences of values that are statistically independent

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

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

   258      */

   259     public L32X64MixRandom() {

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

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

   262     }

   263 

   264     /**

   265      * Creates a new instance of {@link L32X64MixRandom} using the specified array of

   266      * initial seed bytes. Instances of {@link L32X64MixRandom} created with the same

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

   268      *

   269      * @param seed the initial seed

   270      */

   271     public L32X64MixRandom(byte[] seed) {

   272         // Convert the seed to 4 int values, of which the last 2 are not all zero.

   273         int[] data = RandomSupport.convertSeedBytesToInts(seed, 4, 2);

   274         int a = data[0], s = data[1], x0 = data[2], x1 = data[3];

   275         // Force a to be odd.

   276         this.a = a | 1;

   277         this.s = s;

   278         this.x0 = x0;

   279         this.x1 = x1;

   280     }

   281 

   282     /* ---------------- public methods ---------------- */

   283 

   284     /**

   285      * Constructs and returns a new instance of {@link L32X64MixRandom} that shares no mutable state

   286      * with this instance. However, with very high probability, the set of values collectively

   287      * generated by the two objects has the same statistical properties as if same the quantity of

   288      * values were generated by a single thread using a single {@link L32X64MixRandom} object.

   289      * Either or both of the two objects may be further split using the {@code split} method, and

   290      * the same expected statistical properties apply to the entire set of generators constructed by

   291      * such recursive splitting.

   292      *

   293      * @param source a {@link SplittableGenerator} instance to be used instead of this one as

   294      *               a source of pseudorandom bits used to initialize the state of the new ones.

   295      *

   296      * @return a new instance of {@link L32X64MixRandom}

   297      */

   298     public L32X64MixRandom split(SplittableGenerator source) {

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

   300         return new L32X64MixRandom(source.nextInt(), source.nextInt(),

   301                                    source.nextInt(), source.nextInt());

   302     }

   303 

   304     /**

   305      * Returns a pseudorandom {@code int} value.

   306      *

   307      * @return a pseudorandom {@code int} value

   308      */

   309     public int nextInt() {

   310         final int z = s + x0;

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

   312         int q0 = x0, q1 = x1;

   313         {   // xoroshiro64

   314             q1 ^= q0;

   315             q0 = Integer.rotateLeft(q0, 26);

   316             q0 = q0 ^ q1 ^ (q1 << 9);

   317             q1 = Integer.rotateLeft(q1, 13);

   318         }

   319         x0 = q0; x1 = q1;

   320         return Integer.rotateLeft(z * 5, 7) * 9;  // "starstar" mixing function

   321     }

   322 

   323     /**

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

   325      *

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

   327      */

   328     public long nextLong() {

   329         return ((long)(nextInt()) << 32) | nextInt();

   330     }

   331 

   332     public BigInteger period() {

   333         return PERIOD;

   334     }

   335 }