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 L64X128Random} 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 L64X128Random} 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 L64X128Random} 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  * (but {@code L64X128Random} does not use a mixing function).

    58  *

    59  * <p>The LCG subgenerator for {@code L64X128Random} 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 long}; {@code s} is the mutable state, the multiplier {@code m}

    62  * is fixed (the same for all instances of {@code L64X128Random}}) 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>64</sup>); therefore there are 2<sup>63</sup> distinct choices

    66  * of parameter.

    67  *

    68  * <p>The Xorshift subgenerator for {@code L64X128Random} is the {@code xoroshiro128} algorithm,

    69  * version 1.0 (parameters 24, 16, 37), without any final scrambler such as "+" or "**".

    70  * Its state consists of two {@code long} 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>128</sup>-1.

    73  * 

    74  * <p> Because the periods 2<sup>64</sup> and 2<sup>128</sup>-1 of the two subgenerators

    75  * are relatively prime, the <em>period</em> of any single {@code L64X128Random} object 

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

    77  * of the periods of the subgenerators, that is, 2<sup>64</sup>(2<sup>128</sup>-1),

    78  * which is just slightly smaller than 2<sup>192</sup>.  Moreover, if two distinct

    79  * {@code L64X128Random} objects have different {@code a} parameters, then their

    80  * cycles of produced values will be different.

    81  *

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

    83  * For any specific instance of {@code L64X128Random}, over the course of its cycle each

    84  * of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>128</sup>-1 times.

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

    86  * methods are likewise exactly equidistributed.

    87  *

    88  * <p>In fact, the 64-bit values produced by the {@code nextLong()} method are 2-equidistributed.

    89  * To be precise: for any specific instance of {@code L64X128Random}, consider

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

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

    92  * There are 2<sup>64</sup>(2<sup>128</sup>-1) such subsequences, and each subsequence,

    93  * which consists of 2 64-bit values, can have one of 2<sup>128</sup> values. Of those

    94  * 2<sup>128</sup> subsequence values, nearly all of them (2<sup>128</sup>-2<sup>64</sup>)

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

    96  * 2<sup>64</sup> subsequence values occur only 2<sup>64</sup>-1 times.  So the ratio

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

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

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

   100  * one instance of {@code L64X128Random} to another, as a function of the additive

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

   102  * and {@code nextDouble()} methods are likewise 2-equidistributed.

   103  *

   104  * <p>Method {@link #split} constructs and returns a new {@code L64X128Random}

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

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

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

   108  * generated by a single thread using a single {@code L64X128Random} object.

   109  * This is because, with high probability, distinct {@code L64X128Random} objects

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

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

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

   113  * cycle.

   114  *

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

   116  * {@code L64X128Random} are <em>not</em> thread-safe.

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

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

   119  * computation using random numbers might include a construction

   120  * of the form {@code new Subtask(someL64X128Random.split()).fork()}.

   121  *

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

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

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

   125  *

   126  * <p>Instances of {@code L64X128Random} are not cryptographically

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

   128  * in security-sensitive applications. Additionally,

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

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

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

   132  *

   133  * @author  Guy Steele

   134  * @since   1.9

   135  */

   136 public final class L64X128Random extends AbstractSplittableRng {

   137 

   138     /*

   139      * Implementation Overview.

   140      *

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

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

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

   144      *

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

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

   147      * that the values generated by two instances of {@code L64X128Random}

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

   149      *

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

   151      * "defaultGen" to generate four new 64-bit values for the same

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

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

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

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

   156      * seed based on current time unless the

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

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

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

   160      *

   161      * File organization: First static fields, then instance

   162      * fields, then constructors, then instance methods.

   163      */

   164 

   165     /* ---------------- static fields ---------------- */

   166 

   167     /**

   168      * The seed generator for default constructors.

   169      */

   170     private static final AtomicLong defaultGen = new AtomicLong(RngSupport.initialSeed());

   171     

   172     /*

   173      * The period of this generator, which is (2**128 - 1) * 2**64.

   174      */

   175     private static final BigInteger thePeriod =

   176 	BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE).shiftLeft(64);

   177 

   178     /*

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

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

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

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

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

   184      */

   185 

   186     private static final long m = 2862933555777941757L;

   187 

   188     /* ---------------- instance fields ---------------- */

   189 

   190     /**

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

   192      * Must be odd.

   193      */

   194     private final long a;

   195 

   196     /**

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

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

   199      */

   200     private long s, x0, x1;

   201 

   202     /* ---------------- constructors ---------------- */

   203 

   204     /**

   205      * Basic constructor that initializes all fields from parameters.

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

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

   208      */

   209     public L64X128Random(long a, long s, long x0, long x1) {

   210 	// Force a to be odd.

   211         this.a = a | 1;

   212         this.s = s;

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

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

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

   216 	    this.x0 = RngSupport.mixStafford13(s += RngSupport.GOLDEN_RATIO_64);

   217 	    this.x1 = RngSupport.mixStafford13(s + RngSupport.GOLDEN_RATIO_64);

   218 	}

   219     }

   220 

   221     /**

   222      * Creates a new instance of {@code L64X128Random} using the

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

   224      * {@code L64X128Random} created with the same seed in the same

   225      * program generate identical sequences of values.

   226      *

   227      * @param seed the initial seed

   228      */

   229     public L64X128Random(long seed) {

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

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

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

   233 	//

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

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

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

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

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

   239         this(RngSupport.mixMurmur64(seed ^= RngSupport.SILVER_RATIO_64),

   240 	     1,

   241 	     RngSupport.mixStafford13(seed),

   242 	     RngSupport.mixStafford13(seed + RngSupport.GOLDEN_RATIO_64));

   243     }

   244 

   245     /**

   246      * Creates a new instance of {@code L64X128Random} that is likely to

   247      * generate sequences of values that are statistically independent

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

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

   250      */

   251     public L64X128Random() {

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

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

   254     }

   255 

   256     /**

   257      * Creates a new instance of {@code L64X128MixRandom} using the specified array of

   258      * initial seed bytes. Instances of {@code L64X128MixRandom} created with the same

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

   260      *

   261      * @param seed the initial seed

   262      */

   263     public L64X128Random(byte[] seed) {

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

   265 	long[] data = RngSupport.convertSeedBytesToLongs(seed, 4, 2);

   266 	long a = data[0], s = data[1], x0 = data[2], x1 = data[3];

   267 	// Force a to be odd.

   268         this.a = a | 1;

   269         this.s = s;

   270         this.x0 = x0;

   271         this.x1 = x1;

   272     }

   273 

   274     /* ---------------- public methods ---------------- */

   275 

   276     /**

   277      * Constructs and returns a new instance of {@code L64X128Random}

   278      * that shares no mutable state with this instance.

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

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

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

   282      * a single {@code L64X128Random} object.  Either or both of the two

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

   284      * and the same expected statistical properties apply to the

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

   286      *

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

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

   289      *               initialize the state of the new ones.

   290      * @return a new instance of {@code L64X128Random}

   291      */

   292     public L64X128Random split(SplittableRng source) {

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

   294         return new L64X128Random(source.nextLong(), source.nextLong(),

   295 				 source.nextLong(), source.nextLong());

   296     }

   297 

   298     /**

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

   300      *

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

   302      */

   303 

   304     public long nextLong() {

   305 	final long z = s + x0;

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

   307 	long q0 = x0, q1 = x1;

   308 	{ q1 ^= q0; q0 = Long.rotateLeft(q0, 24); q0 = q0 ^ q1 ^ (q1 << 16); q1 = Long.rotateLeft(q1, 37); }  // xoroshiro128v1_0

   309 	x0 = q0; x1 = q1;

   310 	return z;

   311     }

   312 

   313     public BigInteger period() { return thePeriod; }

   314 }