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 L64X256Random} 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 L64X256Random} 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 L64X256Random} 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 L64X256Random} does not use a mixing function).

    58  *

    59  * <p>The LCG subgenerator for {@code L64X256Random} 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 L64X256Random}}) 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 L64X256Random} is the {@code xoshiro256} algorithm,

    69  * version 1.0 (parameters 17, 45), without any final scrambler such as "+" or "**".

    70  * Its state consists of four {@code long} fields {@code x0}, {@code x1}, {@code x2},

    71  * and {@code x3}, which can take on any values provided that they are not all zero.

    72  * The period of this subgenerator is 2<sup>256</sup>-1.

    73  *

    74  * <p> Because the periods 2<sup>64</sup> and 2<sup>256</sup>-1 of the two subgenerators

    75  * are relatively prime, the <em>period</em> of any single {@code L64X256Random} 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>256</sup>-1),

    78  * which is just slightly smaller than 2<sup>320</sup>.  Moreover, if two distinct

    79  * {@code L64X256Random} 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 L64X256Random}, over the course of its cycle each

    84  * of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>256</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 4-equidistributed.

    89  * To be precise: for any specific instance of {@code L64X256Random}, consider

    90  * the (overlapping) length-4 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>256</sup>-1) such subsequences, and each subsequence,

    93  * which consists of 4 64-bit values, can have one of 2<sup>256</sup> values. Of those

    94  * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</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 L64X256Random} 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 4-equidistributed.

   103  *

   104  * <p>Method {@link #split} constructs and returns a new {@code L64X256Random}

   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 L64X256Random} object.

   109  * This is because, with high probability, distinct {@code L64X256Random} 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 L64X256Random} 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(someL64X256Random.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 L64X256Random} 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 L64X256Random extends AbstractSplittableRng {

   137 

   138     /*

   139      * Implementation Overview.

   140      *

   141      * The split() operation uses the current generator to choose six new 64-bit

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

   143      * state variables `s`, `x0`, `x1`, `x2`, and `x3` for a newly constructed

   144      * 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 {@code L64X256Random}

   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 six 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(RngSupport.initialSeed());

   172 

   173     /*

   174      * The period of this generator, which is (2**256 - 1) * 2**64.

   175      */

   176     private static final BigInteger thePeriod =

   177 	BigInteger.ONE.shiftLeft(256).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, x1, x2, and x3 for the xorshift.

   199      * At least one of the four fields x0, x1, x2, and x3 must be nonzero.

   200      */

   201     private long s, x0, x1, x2, x3;

   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     public L64X256Random(long a, long s, long x0, long x1, long x2, long x3) {

   211 	// Force a to be odd.

   212         this.a = a | 1;

   213         this.s = s;

   214         this.x0 = x0;

   215         this.x1 = x1;

   216         this.x2 = x2;

   217         this.x3 = x3;

   218 	// If x0, x1, x2, and x3 are all zero, we must choose nonzero values.

   219         if ((x0 | x1 | x2 | x3) == 0) {

   220 	    // At least three of the four values generated here will be nonzero.

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

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

   223 	    this.x2 = RngSupport.mixStafford13(s += RngSupport.GOLDEN_RATIO_64);

   224 	    this.x3 = RngSupport.mixStafford13(s + RngSupport.GOLDEN_RATIO_64);

   225 	}

   226     }

   227 

   228     /**

   229      * Creates a new instance of {@code L64X256Random} using the

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

   231      * {@code L64X256Random} created with the same seed in the same

   232      * program execution generate identical sequences of values.

   233      *

   234      * @param seed the initial seed

   235      */

   236     public L64X256Random(long seed) {

   237 	// Using a value with irregularly spaced 1-bit to xor the seed

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

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

   240 	//

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

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

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

   244 	// The other x values are filled in as if by a SplitMix PRNG with

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

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

   247 	     1,

   248 	     RngSupport.mixStafford13(seed),

   249 	     RngSupport.mixStafford13(seed += RngSupport.GOLDEN_RATIO_64),

   250 	     RngSupport.mixStafford13(seed += RngSupport.GOLDEN_RATIO_64),

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

   252     }

   253 

   254     /**

   255      * Creates a new instance of {@code L64X256Random} that is likely to

   256      * generate sequences of values that are statistically independent

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

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

   259      */

   260     public L64X256Random() {

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

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

   263     }

   264 

   265     /**

   266      * Creates a new instance of {@code L64X256Random} using the specified array of

   267      * initial seed bytes. Instances of {@code L64X256Random} created with the same

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

   269      *

   270      * @param seed the initial seed

   271      */

   272     public L64X256Random(byte[] seed) {

   273 	// Convert the seed to 6 long values, of which the last 4 are not all zero.

   274 	long[] data = RngSupport.convertSeedBytesToLongs(seed, 6, 4);

   275 	long a = data[0], s = data[1], x0 = data[2], x1 = data[3], x2 = data[4], x3 = data[5];

   276 	// Force a to be odd.

   277         this.a = a | 1;

   278         this.s = s;

   279         this.x0 = x0;

   280         this.x1 = x1;

   281         this.x2 = x2;

   282         this.x3 = x3;

   283     }

   284 

   285     /* ---------------- public methods ---------------- */

   286 

   287     /**

   288      * Constructs and returns a new instance of {@code L64X256Random}

   289      * that shares no mutable state with this instance.

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

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

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

   293      * a single {@code L64X256Random} object.  Either or both of the two

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

   295      * and the same expected statistical properties apply to the

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

   297      *

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

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

   300      *               initialize the state of the new ones.

   301      * @return a new instance of {@code L64X256Random}

   302      */

   303     public L64X256Random split(SplittableRng source) {

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

   305         return new L64X256Random(source.nextLong(), source.nextLong(), 

   306 				 source.nextLong(), source.nextLong(),

   307 				 source.nextLong(), source.nextLong());

   308     }

   309 

   310     /**

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

   312      *

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

   314      */

   315 

   316     public long nextLong() {

   317 	final long z = s + x0;

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

   319 	long q0 = x0, q1 = x1, q2 = x2, q3 = x3;	

   320 	{ long t = q1 << 17; q2 ^= q0; q3 ^= q1; q1 ^= q2; q0 ^= q3; q2 ^= t; q3 = Long.rotateLeft(q3, 45); }  // xoshiro256 1.0

   321 	x0 = q0; x1 = q1; x2 = q2; x3 = q3;

   322 	return z;

   323     }

   324 

   325     public BigInteger period() { return thePeriod; }

   326 }