1 /*

     2  * Copyright (c) 2016, 2019, Oracle and/or its affiliates. All rights reserved.

     3  * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.

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    25 

    26 // package java.util;

    27 

    28 import java.math.BigInteger;

    29 import java.util.concurrent.atomic.AtomicLong;

    30 

    31 /**

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

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

    34  * generate subtasks.  Class {@code L32X64MixRandom} implements

    35  * interfaces {@link java.util.Rng} and {@link java.util.SplittableRng},

    36  * and therefore supports methods for producing pseudorandomly chosen

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

    38  * as well as creating new split-off {@code L32X64MixRandom} objects,

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

    40  *

    41  * <p>Series of generated values pass the TestU01 BigCrush and PractRand test suites

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

    43  * (Most recently validated with

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

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

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

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

    48  * These tests validate only the methods for certain

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

    50  * least approximately, for others as well.

    51  *

    52  * <p>{@code L32X64MixRandom} is a specific member of the LXM family of algorithms

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

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

    55  * an Xorshift generator.  Each output of an LXM generator is the sum of one

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

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

    58  *

    59  * <p>The LCG subgenerator for {@code L32X64MixRandom} has an update step of the

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

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

    62  * is fixed (the same for all instances of {@code L32X64MixRandom}}) and the addend

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

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

    65  * period, namely 2<sup>32</sup>); therefore there are 2<sup>31</sup> distinct choices

    66  * of parameter.

    67  *

    68  * <p>The Xorshift subgenerator for {@code L32X64MixRandom} is the {@code xoroshiro64} algorithm,

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

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

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

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

    73  * 

    74  * <p> The mixing function for {@code L32X64MixRandom} is the "starstar" mixing function.

    75  *

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

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

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

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

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

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

    82  * cycles of produced values will be different.

    83  *

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

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

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

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

    88  *

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

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

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

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

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

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

    95  * 2<sup>64</sup> subsequence values, nearly all of them (2<sup>64</sup>-2<sup>32</sup>)

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

    97  * 2<sup>32</sup> subsequence values occur only 2<sup>32</sup>-1 times.  So the ratio

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

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

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

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

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

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

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

   105  *

   106  * <p>Method {@link #split} constructs and returns a new {@code L32X64MixRandom}

   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 {@code L32X64MixRandom} object.

   111  * This is because, with high probability, distinct {@code L32X64MixRandom} 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  *

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

   118  * {@code L32X64MixRandom} 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(someL32X64MixRandom.split()).fork()}.

   123  *

   124  * <p>This class provides additional methods for generating random

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

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

   127  *

   128  * <p>Instances of {@code L32X64MixRandom} 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  * @author  Guy Steele

   136  * @since   1.9

   137  */

   138 public final class L32X64MixRandom extends AbstractSplittableRng {

   139 

   140     /*

   141      * Implementation Overview.

   142      *

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

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

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

   146      *

   147      * With 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 {@code L32X64MixRandom}

   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 four new 32-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(RngSupport.initialSeed());

   173 

   174     /*

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

   176      */

   177     private static final BigInteger thePeriod =

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

   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 (third multiplier for size 2<sup>32</sup>).

   186      */

   187 

   188     private static final int m = 32310901;

   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 int a;

   197 

   198     /**

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

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

   201      */

   202     private int s, x0, x1;

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

   212 	// Force a to be odd.

   213         this.a = a | 1;

   214         this.s = s;

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

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

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

   218 	    this.x0 = RngSupport.mixMurmur32(s += RngSupport.GOLDEN_RATIO_32);

   219 	    this.x1 = RngSupport.mixMurmur32(s + RngSupport.GOLDEN_RATIO_32);

   220 	}

   221     }

   222 

   223     /**

   224      * Creates a new instance of {@code L32X64MixRandom} using the

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

   226      * {@code L32X64MixRandom} created with the same seed in the same

   227      * program generate identical sequences of values.

   228      *

   229      * @param seed the initial seed

   230      */

   231     public L32X64MixRandom(long seed) {

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

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

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

   235 	//

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

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

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

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

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

   241         this(RngSupport.mixMurmur32((int)((seed ^= RngSupport.SILVER_RATIO_64) >>> 32)),

   242 	     1,

   243 	     RngSupport.mixLea32((int)(seed)),

   244 	     RngSupport.mixLea32((int)(seed) + RngSupport.GOLDEN_RATIO_32));

   245     }

   246 

   247     /**

   248      * Creates a new instance of {@code L32X64MixRandom} that is likely to

   249      * generate sequences of values that are statistically independent

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

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

   252      */

   253     public L32X64MixRandom() {

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

   255         this(defaultGen.getAndAdd(RngSupport.GOLDEN_RATIO_64));

   256     }

   257 

   258     /**

   259      * Creates a new instance of {@code L32X64MixRandom} using the specified array of

   260      * initial seed bytes. Instances of {@code L32X64MixRandom} created with the same

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

   262      *

   263      * @param seed the initial seed

   264      */

   265     public L32X64MixRandom(byte[] seed) {

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

   267 	int[] data = RngSupport.convertSeedBytesToInts(seed, 4, 2);

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

   269 	// Force a to be odd.

   270         this.a = a | 1;

   271         this.s = s;

   272         this.x0 = x0;

   273         this.x1 = x1;

   274     }

   275 

   276     /* ---------------- public methods ---------------- */

   277 

   278     /**

   279      * Constructs and returns a new instance of {@code L32X64MixRandom}

   280      * that shares no mutable state with this instance.

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

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

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

   284      * a single {@code L32X64MixRandom} object.  Either or both of the two

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

   286      * and the same expected statistical properties apply to the

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

   288      *

   289      * @param source a {@code SplittableRng} instance to be used instead

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

   291      *               initialize the state of the new ones.

   292      * @return a new instance of {@code L32X64MixRandom}

   293      */

   294     public L32X64MixRandom split(SplittableRng source) {

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

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

   297 				   source.nextInt(), source.nextInt());

   298     }

   299 

   300     /**

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

   302      *

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

   304      */

   305     public int nextInt() {

   306 	final int z = s + x0;

   307 	s = m * s + a;  // LCG

   308 	int q0 = x0, q1 = x1;

   309 	{ q1 ^= q0; q0 = Integer.rotateLeft(q0, 26); q0 = q0 ^ q1 ^ (q1 << 9); q1 = Integer.rotateLeft(q1, 13); }  // xoroshiro64

   310 	x0 = q0; x1 = q1;

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

   312     }

   313 

   314     /**

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

   316      *

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

   318      */

   319 

   320     public long nextLong() {

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

   322     }

   323 

   324     public BigInteger period() { return thePeriod; }

   325 }