1 /*

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

     4  *

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     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).

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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 L64X128Random} 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 L64X128Random} 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 L64X128Random} 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 L64X128Random} does not use a mixing function).

    60  * <p>

    61  * The LCG subgenerator for {@link L64X128Random} 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 L64X128Random}) 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 L64X128Random} is the {@code xoroshiro128} algorithm,

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

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

    75  * <p>

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

    77  * are relatively prime, the <em>period</em> of any single {@link L64X128Random} 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>128</sup>-1),

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

    81  * {@link L64X128Random} 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 L64X128Random}, over the course of its cycle each

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

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

    92  * the (overlapping) length-2 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>128</sup>-1) such subsequences, and each subsequence,

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

    96  * 2<sup>128</sup> subsequence values, nearly all of them (2<sup>128</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 L64X128Random} 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 2-equidistributed.

   105  * <p>

   106  * Method {@link #split} constructs and returns a new {@link L64X128Random}

   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 L64X128Random} object.

   111  * This is because, with high probability, distinct {@link L64X128Random} 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 L64X128Random} 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(someL64X128Random.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 L64X128Random} 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 L64X128Random extends AbstractSplittableGenerator {

   138 

   139     /*

   140      * Implementation Overview.

   141      *

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

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

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

   145      *

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

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

   148      * that the values generated by two instances of {@link L64X128Random}

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

   150      *

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

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

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

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

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

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

   157      * seed based on current time unless the

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

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

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

   161      *

   162      * File organization: First static fields, then instance

   163      * fields, then constructors, then instance methods.

   164      */

   165 

   166     /* ---------------- static fields ---------------- */

   167 

   168     /**

   169      * The seed generator for default constructors.

   170      */

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

   172 

   173     /*

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

   175      */

   176     private static final BigInteger PERIOD =

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

   178 

   179     /*

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

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

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

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

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

   185      */

   186 

   187     private static final long M = 2862933555777941757L;

   188 

   189     /* ---------------- instance fields ---------------- */

   190 

   191     /**

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

   193      * Must be odd.

   194      */

   195     private final long a;

   196 

   197     /**

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

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

   200      */

   201     private long s, x0, x1;

   202 

   203     /* ---------------- constructors ---------------- */

   204 

   205     /**

   206      * Basic constructor that initializes all fields from parameters.

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

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

   209      *

   210      * @param a additive parameter for the LCG

   211      * @param s initial state for the LCG

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

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

   214      */

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

   216         // Force a to be odd.

   217         this.a = a | 1;

   218         this.s = s;

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

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

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

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

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

   224         }

   225     }

   226 

   227     /**

   228      * Creates a new instance of {@link L64X128Random} using the

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

   230      * {@link L64X128Random} created with the same seed in the same

   231      * program generate identical sequences of values.

   232      *

   233      * @param seed the initial seed

   234      */

   235     public L64X128Random(long seed) {

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

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

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

   239         //

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

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

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

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

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

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

   246              1,

   247              RandomSupport.mixStafford13(seed),

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

   249     }

   250 

   251     /**

   252      * Creates a new instance of {@link L64X128Random} that is likely to

   253      * generate sequences of values that are statistically independent

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

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

   256      */

   257     public L64X128Random() {

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

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

   260     }

   261 

   262     /**

   263      * Creates a new instance of {@link L64X128MixRandom} using the specified array of

   264      * initial seed bytes. Instances of {@link L64X128MixRandom} created with the same

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

   266      *

   267      * @param seed the initial seed

   268      */

   269     public L64X128Random(byte[] seed) {

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

   271         long[] data = RandomSupport.convertSeedBytesToLongs(seed, 4, 2);

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

   273         // Force a to be odd.

   274         this.a = a | 1;

   275         this.s = s;

   276         this.x0 = x0;

   277         this.x1 = x1;

   278     }

   279 

   280     /* ---------------- public methods ---------------- */

   281 

   282     /**

   283      * Constructs and returns a new instance of {@link L64X128Random}

   284      * that shares no mutable state with this instance.

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

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

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

   288      * a single {@link L64X128Random} object.  Either or both of the two

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

   290      * and the same expected statistical properties apply to the

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

   292      *

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

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

   295      *               initialize the state of the new ones.

   296      *

   297      * @return a new instance of {@link L64X128Random}

   298      */

   299     public L64X128Random split(SplittableGenerator source) {

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

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

   302                                  source.nextLong(), source.nextLong());

   303     }

   304 

   305     /**

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

   307      *

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

   309      */

   310     public long nextLong() {

   311         final long z = s + x0;

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

   313         long q0 = x0, q1 = x1;

   314         {   // xoroshiro128v1_0

   315             q1 ^= q0;

   316             q0 = Long.rotateLeft(q0, 24);

   317             q0 = q0 ^ q1 ^ (q1 << 16);

   318             q1 = Long.rotateLeft(q1, 37);

   319         }

   320         x0 = q0; x1 = q1;

   321         return z;

   322     }

   323 

   324     public BigInteger period() {

   325         return PERIOD;

   326     }

   327 }