1 /*

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

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

     4  *

     5  *

     6  *

     7  *

     8  *

     9  *

    10  *

    11  *

    12  *

    13  *

    14  *

    15  *

    16  *

    17  *

    18  *

    19  *

    20  *

    21  *

    22  *

    23  *

    24  */

    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 MRG32k3a} implements

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

    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 {@code Xoroshiro128PlusMRG32k3a} objects

    39  * by "jumping" or "leaping".

    40  *

    41  * <p>Instances {@code Xoroshiro128Plus} are <em>not</em> thread-safe.

    42  * They are designed to be used so that each thread as its own instance.

    43  * The methods {@link #jump} and {@link #leap} and {@link #jumps} and {@link #leaps}

    44  * can be used to construct new instances of {@code Xoroshiro128Plus} that traverse

    45  * other parts of the state cycle.

    46  *

    47  * <p>Instances of {@code MRG32k3a} are not cryptographically

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

    49  * in security-sensitive applications. Additionally,

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

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

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

    53  *

    54  * @author  Guy Steele

    55  * @since   1.9

    56  */

    57 public final class MRG32k3a extends AbstractArbitrarilyJumpableRng {

    58 

    59     /*

    60      * Implementation Overview.

    61      *

    62      * xxxx

    63      *

    64      * File organization: First the non-public methods that constitute

    65      * the main algorithm, then the main public methods, followed by

    66      * some custom spliterator classes needed for stream methods.

    67      */

    68 

    69     private final static double norm1 = 2.328306549295728e-10;

    70     private final static double norm2 = 2.328318824698632e-10;

    71     private final static double m1 =   4294967087.0;

    72     private final static double m2 =   4294944443.0;

    73     private final static double a12 =     1403580.0;

    74     private final static double a13n =     810728.0;

    75     private final static double a21 =      527612.0;

    76     private final static double a23n =    1370589.0;

    77     private final static int m1_deficit = 209;

    78     

    79     // IllegalArgumentException messages

    80     private static final String BadLogDistance  = "logDistance must be non-negative and not greater than 192";

    81 

    82     /**

    83      * The per-instance state.

    84      The seeds for s10, s11, s12 must be integers in [0, m1 - 1] and not all 0. 

    85      The seeds for s20, s21, s22 must be integers in [0, m2 - 1] and not all 0. 

    86      */

    87     private double s10, s11, s12,

    88 	           s20, s21, s22;

    89 

    90     /**

    91      * The seed generator for default constructors.

    92      */

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

    94 

    95     /*

    96       32-bits Random number generator U(0,1): MRG32k3a

    97       Author: Pierre L'Ecuyer,

    98       Source: Good Parameter Sets for Combined Multiple Recursive Random

    99            Number Generators,

   100            Shorter version in Operations Research,

   101            47, 1 (1999), 159--164.

   102 	   ---------------------------------------------------------

   103     */

   104 

   105     private void nextState() {

   106 	/* Component 1 */

   107 	double p1 = a12 * s11 - a13n * s10;

   108 	double k1 = p1 / m1;   p1 -= k1 * m1;   if (p1 < 0.0) p1 += m1;

   109 	s10 = s11;   s11 = s12;   s12 = p1;

   110 	/* Component 2 */

   111 	double p2 = a21 * s22 - a23n * s20;

   112 	double k2 = p2 / m2;   p2 -= k2 * m2;   if (p2 < 0.0) p2 += m2;

   113 	s20 = s21;   s21 = s22;   s22 = p2;

   114     }

   115 

   116     

   117     /**

   118      * The form of nextInt used by IntStream Spliterators.

   119      * Exactly the same as long version, except for types.

   120      *

   121      * @param origin the least value, unless greater than bound

   122      * @param bound the upper bound (exclusive), must not equal origin

   123      * @return a pseudorandom value

   124      */

   125     protected int internalNextInt(int origin, int bound) {

   126         if (origin < bound) {

   127             final int n = bound - origin;

   128 	    final int m = n - 1;

   129 	    if (n > 0) {

   130 		int r;

   131                 for (int u = (int)nextDouble() >>> 1;

   132                      u + m + ((m1_deficit + 1) >>> 1) - (r = u % n) < 0;

   133                      u = (int)nextDouble() >>> 1)

   134                     ;

   135                 return (r + origin);

   136             } else {

   137 		return RngSupport.boundedNextInt(this, origin, bound);

   138             }

   139         } else {

   140 	    return nextInt();

   141 	}

   142     }

   143 

   144     protected int internalNextInt(int bound) {

   145         // Specialize internalNextInt for origin == 0, bound > 0

   146 	final int n = bound;

   147 	final int m = n - 1;

   148 	int r;

   149 	for (int u = (int)nextDouble() >>> 1;

   150 	     u + m + ((m1_deficit + 1) >>> 1) - (r = u % n) < 0;

   151 	     u = (int)nextDouble() >>> 1)

   152 	    ;

   153 	return r;

   154     }

   155 

   156     /**

   157      * Constructor used by all others except default constructor.

   158      * All arguments must be known to be nonnegative integral values.

   159      */

   160     private MRG32k3a(double s10, double s11, double s12,

   161 		     double s20, double s21, double s22) {

   162 	this.s10 = s10; this.s11 = s11; this.s12 = s12;

   163 	this.s20 = s20; this.s21 = s21; this.s22 = s22;

   164 	if ((s10 == 0.0) && (s11 == 0.0) && (s12 == 0.0)) this.s10 = 12345.0;

   165 	if ((s20 == 0.0) && (s21 == 0.0) && (s22 == 0.0)) this.s20 = 12345.0;

   166     }

   167 

   168     /* ---------------- public methods ---------------- */

   169 

   170     public MRG32k3a(int s10, int s11, int s12,

   171 		    int s20, int s21, int s22) {

   172 	this(((double)(((long)s10) & 0x00000000ffffffffL)) % m1,

   173 	     ((double)(((long)s11) & 0x00000000ffffffffL)) % m1,

   174 	     ((double)(((long)s12) & 0x00000000ffffffffL)) % m1,

   175 	     ((double)(((long)s20) & 0x00000000ffffffffL)) % m2,

   176 	     ((double)(((long)s21) & 0x00000000ffffffffL)) % m2,

   177 	     ((double)(((long)s22) & 0x00000000ffffffffL)) % m2);

   178     }

   179 

   180     /**

   181      * Creates a new MRG32k3a instance using the specified

   182      * initial seed. MRG32k3a instances created with the same

   183      * seed in the same program generate identical sequences of values.

   184      * An argument of 0 seeds the generator to a widely used initialization

   185      * of MRG32k3a: all six state variables are set to 12345.

   186      *

   187      * @param seed the initial seed

   188      */

   189     public MRG32k3a(long seed) {

   190         this((double)((seed & 0x7FF) + 12345),

   191 	     (double)(((seed >>> 11) & 0x7FF) + 12345),

   192 	     (double)(((seed >>> 22) & 0x7FF) + 12345),

   193 	     (double)(((seed >>> 33) & 0x7FF) + 12345),

   194 	     (double)(((seed >>> 44) & 0x7FF) + 12345),

   195 	     (double)((seed >>> 55) + 12345));

   196     }

   197 

   198     /**

   199      * Creates a new MRG32k3a instance that is likely to

   200      * generate sequences of values that are statistically independent

   201      * of those of any other instances in the current program; and

   202      * may, and typically does, vary across program invocations.

   203      */

   204     public MRG32k3a() {

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

   206     }

   207 

   208     /**

   209      * Creates a new instance of {@code Xoshiro256StarStar} using the specified array of

   210      * initial seed bytes. Instances of {@code Xoshiro256StarStar} created with the same

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

   212      *

   213      * @param seed the initial seed

   214      */

   215     public MRG32k3a(byte[] seed) {

   216 	// Convert the seed to 6 int values.

   217 	int[] data = RngSupport.convertSeedBytesToInts(seed, 6, 0);

   218 	int s10 = data[0], s11 = data[1], s12 = data[2];

   219 	int s20 = data[3], s21 = data[4], s22 = data[5];

   220 	this.s10 = ((double)(((long)s10) & 0x00000000ffffffffL)) % m1;

   221 	this.s11 = ((double)(((long)s11) & 0x00000000ffffffffL)) % m1;

   222 	this.s12 = ((double)(((long)s12) & 0x00000000ffffffffL)) % m1;

   223 	this.s20 = ((double)(((long)s20) & 0x00000000ffffffffL)) % m2;

   224 	this.s21 = ((double)(((long)s21) & 0x00000000ffffffffL)) % m2;

   225 	this.s22 = ((double)(((long)s22) & 0x00000000ffffffffL)) % m2;

   226 	if ((s10 == 0.0) && (s11 == 0.0) && (s12 == 0.0)) this.s10 = 12345.0;

   227 	if ((s20 == 0.0) && (s21 == 0.0) && (s22 == 0.0)) this.s20 = 12345.0;

   228     }

   229 

   230     public MRG32k3a copy() { return new MRG32k3a(s10, s11, s12, s20, s21, s22); }

   231 

   232     /**

   233      * Returns a pseudorandom {@code double} value between zero

   234      * (exclusive) and one (exclusive).

   235      *

   236      * @return a pseudorandom {@code double} value between zero

   237      *         (exclusive) and one (exclusive)

   238      */

   239     public double nextOpenDouble() {

   240 	nextState();

   241 	double p1 = s12, p2 = s22;

   242 	if (p1 <= p2)

   243 	    return ((p1 - p2 + m1) * norm1);

   244 	else

   245 	    return ((p1 - p2) * norm1);

   246     }

   247 

   248     /**

   249      * Returns a pseudorandom {@code double} value between zero

   250      * (inclusive) and one (exclusive).

   251      *

   252      * @return a pseudorandom {@code double} value between zero

   253      *         (inclusive) and one (exclusive)

   254      */

   255     public double nextDouble() {

   256 	nextState();

   257 	double p1 = s12, p2 = s22;

   258 	final double p = p1 * norm1 - p2 * norm2;

   259 	if (p < 0.0) return (p + 1.0);

   260 	else return p;

   261     }

   262 

   263     

   264     /**

   265      * Returns a pseudorandom {@code float} value between zero

   266      * (inclusive) and one (exclusive).

   267      *

   268      * @return a pseudorandom {@code float} value between zero

   269      *         (inclusive) and one (exclusive)

   270      */

   271     public float nextFloat() {

   272         return (float)nextDouble();

   273     }

   274 

   275     /**

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

   277      *

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

   279      */

   280     public int nextInt() {

   281 	return (internalNextInt(0x10000) << 16) | internalNextInt(0x10000);

   282     }

   283 

   284     /**

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

   286      *

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

   288      */

   289 

   290     public long nextLong() {

   291  	return (((long)internalNextInt(0x200000) << 43) |

   292 		((long)internalNextInt(0x200000) << 22) |

   293 		((long)internalNextInt(0x400000)));

   294     }

   295 

   296     // Period is (m1**3 - 1)(m2**3 - 1)/2, or approximately 2**191.

   297     static BigInteger calculateThePeriod() {

   298 	BigInteger bigm1 = BigInteger.valueOf((long)m1);

   299 	BigInteger bigm2 = BigInteger.valueOf((long)m2);

   300 	BigInteger t1 = bigm1.multiply(bigm1).multiply(bigm1).subtract(BigInteger.ONE);

   301 	BigInteger t2 = bigm2.multiply(bigm2).multiply(bigm2).subtract(BigInteger.ONE);

   302 	return t1.shiftRight(1).multiply(t2);

   303     }

   304     static final BigInteger thePeriod = calculateThePeriod();

   305     public BigInteger period() { return thePeriod; }

   306 

   307     // Jump and leap distances recommended in Section 1.3 of this paper:

   308     // Pierre L'Ecuyer, Richard Simard, E. Jack Chen, and W. David Kelton.

   309     // An Object-Oriented Random-Number Package with Many Long Streams and Substreams.

   310     // Operations Research 50, 6 (Nov--Dec 2002), 1073--1075.

   311 

   312     public double defaultJumpDistance() { return 0x1.0p76; }  // 2**76

   313     public double defaultLeapDistance() { return 0x1.0p127; }  // 2**127

   314         

   315     public void jump(double distance) {

   316         if (distance < 0.0 || Double.isInfinite(distance) || distance != Math.floor(distance))

   317             throw new IllegalArgumentException("jump distance must be a nonnegative finite integer");

   318     	// We will compute a jump transformation (s => M s) for each LCG.

   319     	// We initialize each transformation to the identity transformation.

   320     	// Each will be turned into the d'th power of the corresponding base transformation.

   321 	long m1_00 = 1, m1_01 = 0, m1_02 = 0,

   322 	     m1_10 = 0, m1_11 = 1, m1_12 = 0,

   323 	     m1_20 = 0, m1_21 = 0, m1_22 = 1;

   324 	long m2_00 = 1, m2_01 = 0, m2_02 = 0,

   325 	     m2_10 = 0, m2_11 = 1, m2_12 = 0,

   326 	     m2_20 = 0, m2_21 = 0, m2_22 = 1;

   327 	// These are the base transformations, which will be repeatedly squared,

   328 	// and composed with the computed transformations for each 1-bit in distance.

   329 	long t1_00 = 0,           t1_01 = 1,         t1_02 = 0,

   330 	     t1_10 = 0,           t1_11 = 0,         t1_12 = 1,

   331 	     t1_20 = -(long)a13n, t1_21 = (long)a12, t1_22 = 0;

   332 	long t2_00 = 0,           t2_01 = 1,         t2_02 = 0,

   333 	     t2_10 = 0,           t2_11 = 0,         t2_12 = 1,

   334 	     t2_20 = -(long)a23n, t2_21 = (long)a21, t2_22 = 0;

   335 	while (distance > 0.0) {

   336 	    final double dhalf = 0.5 * distance;

   337 	    if (Math.floor(dhalf) != dhalf) {

   338 		// distance is odd: accumulate current squaring

   339 		final long n1_00 = m1_00 * t1_00 + m1_01 * t1_10 + m1_02 * t1_20;

   340 		final long n1_01 = m1_00 * t1_01 + m1_01 * t1_11 + m1_02 * t1_21;

   341 		final long n1_02 = m1_00 * t1_02 + m1_01 * t1_12 + m1_02 * t1_22;

   342 		final long n1_10 = m1_10 * t1_00 + m1_11 * t1_10 + m1_12 * t1_20;

   343 		final long n1_11 = m1_10 * t1_01 + m1_11 * t1_11 + m1_12 * t1_21;

   344 		final long n1_12 = m1_10 * t1_02 + m1_11 * t1_12 + m1_12 * t1_22;

   345 		final long n1_20 = m1_20 * t1_00 + m1_21 * t1_10 + m1_22 * t1_20;

   346 		final long n1_21 = m1_20 * t1_01 + m1_21 * t1_11 + m1_22 * t1_21;

   347 		final long n1_22 = m1_20 * t1_02 + m1_21 * t1_12 + m1_22 * t1_22;

   348 		m1_00 = Math.floorMod(n1_00, (long)m1);

   349 		m1_01 = Math.floorMod(n1_01, (long)m1);

   350 		m1_02 = Math.floorMod(n1_02, (long)m1);

   351 		m1_10 = Math.floorMod(n1_10, (long)m1);

   352 		m1_11 = Math.floorMod(n1_11, (long)m1);

   353 		m1_12 = Math.floorMod(n1_12, (long)m1);

   354 		m1_20 = Math.floorMod(n1_20, (long)m1);

   355 		m1_21 = Math.floorMod(n1_21, (long)m1);

   356 		m1_22 = Math.floorMod(n1_22, (long)m1);

   357 		final long n2_00 = m2_00 * t2_00 + m2_01 * t2_10 + m2_02 * t2_20;

   358 		final long n2_01 = m2_00 * t2_01 + m2_01 * t2_11 + m2_02 * t2_21;

   359 		final long n2_02 = m2_00 * t2_02 + m2_01 * t2_12 + m2_02 * t2_22;

   360 		final long n2_10 = m2_10 * t2_00 + m2_11 * t2_10 + m2_12 * t2_20;

   361 		final long n2_11 = m2_10 * t2_01 + m2_11 * t2_11 + m2_12 * t2_21;

   362 		final long n2_12 = m2_10 * t2_02 + m2_11 * t2_12 + m2_12 * t2_22;

   363 		final long n2_20 = m2_20 * t2_00 + m2_21 * t2_10 + m2_22 * t2_20;

   364 		final long n2_21 = m2_20 * t2_01 + m2_21 * t2_11 + m2_22 * t2_21;

   365 		final long n2_22 = m2_20 * t2_02 + m2_21 * t2_12 + m2_22 * t2_22;

   366 		m2_00 = Math.floorMod(n2_00, (long)m2);

   367 		m2_01 = Math.floorMod(n2_01, (long)m2);

   368 		m2_02 = Math.floorMod(n2_02, (long)m2);

   369 		m2_10 = Math.floorMod(n2_10, (long)m2);

   370 		m2_11 = Math.floorMod(n2_11, (long)m2);

   371 		m2_12 = Math.floorMod(n2_12, (long)m2);

   372 		m2_20 = Math.floorMod(n2_20, (long)m2);

   373 		m2_21 = Math.floorMod(n2_21, (long)m2);

   374 		m2_22 = Math.floorMod(n2_22, (long)m2);

   375 	    }

   376 	    // Square the base transformations.

   377 	    {

   378 		final long z1_00 = m1_00 * m1_00 + m1_01 * m1_10 + m1_02 * m1_20;

   379 		final long z1_01 = m1_00 * m1_01 + m1_01 * m1_11 + m1_02 * m1_21;

   380 		final long z1_02 = m1_00 * m1_02 + m1_01 * m1_12 + m1_02 * m1_22;

   381 		final long z1_10 = m1_10 * m1_00 + m1_11 * m1_10 + m1_12 * m1_20;

   382 		final long z1_11 = m1_10 * m1_01 + m1_11 * m1_11 + m1_12 * m1_21;

   383 		final long z1_12 = m1_10 * m1_02 + m1_11 * m1_12 + m1_12 * m1_22;

   384 		final long z1_20 = m1_20 * m1_00 + m1_21 * m1_10 + m1_22 * m1_20;

   385 		final long z1_21 = m1_20 * m1_01 + m1_21 * m1_11 + m1_22 * m1_21;

   386 		final long z1_22 = m1_20 * m1_02 + m1_21 * m1_12 + m1_22 * m1_22;

   387 		m1_00 = Math.floorMod(z1_00, (long)m1);

   388 		m1_01 = Math.floorMod(z1_01, (long)m1);

   389 		m1_02 = Math.floorMod(z1_02, (long)m1);

   390 		m1_10 = Math.floorMod(z1_10, (long)m1);

   391 		m1_11 = Math.floorMod(z1_11, (long)m1);

   392 		m1_12 = Math.floorMod(z1_12, (long)m1);

   393 		m1_20 = Math.floorMod(z1_20, (long)m1);

   394 		m1_21 = Math.floorMod(z1_21, (long)m1);

   395 		m1_22 = Math.floorMod(z1_22, (long)m1);

   396 		final long z2_00 = m2_00 * m2_00 + m2_01 * m2_10 + m2_02 * m2_20;

   397 		final long z2_01 = m2_00 * m2_01 + m2_01 * m2_11 + m2_02 * m2_21;

   398 		final long z2_02 = m2_00 * m2_02 + m2_01 * m2_12 + m2_02 * m2_22;

   399 		final long z2_10 = m2_10 * m2_00 + m2_11 * m2_10 + m2_12 * m2_20;

   400 		final long z2_11 = m2_10 * m2_01 + m2_11 * m2_11 + m2_12 * m2_21;

   401 		final long z2_12 = m2_10 * m2_02 + m2_11 * m2_12 + m2_12 * m2_22;

   402 		final long z2_20 = m2_20 * m2_00 + m2_21 * m2_10 + m2_22 * m2_20;

   403 		final long z2_21 = m2_20 * m2_01 + m2_21 * m2_11 + m2_22 * m2_21;

   404 		final long z2_22 = m2_20 * m2_02 + m2_21 * m2_12 + m2_22 * m2_22;

   405 		m2_00 = Math.floorMod(z2_00, (long)m2);

   406 		m2_01 = Math.floorMod(z2_01, (long)m2);

   407 		m2_02 = Math.floorMod(z2_02, (long)m2);

   408 		m2_10 = Math.floorMod(z2_10, (long)m2);

   409 		m2_11 = Math.floorMod(z2_11, (long)m2);

   410 		m2_12 = Math.floorMod(z2_12, (long)m2);

   411 		m2_20 = Math.floorMod(z2_20, (long)m2);

   412 		m2_21 = Math.floorMod(z2_21, (long)m2);

   413 		m2_22 = Math.floorMod(z2_22, (long)m2);

   414 	    }

   415 	    // Divide distance by 2.

   416 	    distance = dhalf;

   417 	}

   418 	final long w10 = m1_00 * (long)s10 + m1_01 * (long)s11 + m1_02 * (long)s12;

   419 	final long w11 = m1_10 * (long)s10 + m1_11 * (long)s11 + m1_12 * (long)s12;

   420 	final long w12 = m1_20 * (long)s10 + m1_21 * (long)s11 + m1_22 * (long)s12;

   421 	s10 = Math.floorMod(w10, (long)m1);

   422 	s11 = Math.floorMod(w11, (long)m1);

   423 	s12 = Math.floorMod(w12, (long)m1);

   424 	final long w20 = m2_00 * (long)s20 + m2_01 * (long)s21 + m2_02 * (long)s22;

   425 	final long w21 = m2_10 * (long)s20 + m2_11 * (long)s21 + m2_12 * (long)s22;

   426 	final long w22 = m2_20 * (long)s20 + m2_21 * (long)s21 + m2_22 * (long)s22;

   427 	s20 = Math.floorMod(w20, (long)m2);

   428 	s21 = Math.floorMod(w21, (long)m2);

   429 	s22 = Math.floorMod(w22, (long)m2);

   430     }

   431         

   432     /**

   433      * Alter the state of this pseudorandom number generator so as to

   434      * jump forward a distance equal to 2<sup>{@code logDistance}</sup>

   435      * within its state cycle.

   436      *

   437      * @param logDistance the base-2 logarithm of the distance to jump

   438      *        forward within the state cycle.  Must be non-negative and

   439      *        not greater than 192.

   440      * @throws IllegalArgumentException if {@code logDistance} is

   441      *         less than zero or 2<sup>{@code logDistance}</sup> is

   442      *         greater than the period of this generator

   443      */

   444     public void jumpPowerOfTwo(int logDistance) {

   445         if (logDistance < 0 || logDistance > 192)

   446             throw new IllegalArgumentException(BadLogDistance);

   447 	jump(Math.scalb(1.0, logDistance));

   448     }

   449 

   450 }