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

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// package java.util;

import java.math.BigInteger;

import java.util.concurrent.atomic.AtomicLong;

/**

 * A generator of uniform pseudorandom values applicable for use in

 * (among other contexts) isolated parallel computations that may

 * generate subtasks.  Class {@code L64X128MixRandom} implements

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

 * and therefore supports methods for producing pseudorandomly chosen

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

 * as well as creating new split-off {@code L64X128MixRandom} objects,

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

 *

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

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

 * (Most recently validated with

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

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

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

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

 * These tests validate only the methods for certain

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

 * least approximately, for others as well.

 *

 * <p>{@code L64X128MixRandom} is a specific member of the LXM family of algorithms

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

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

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

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

 * (and {@code L64X128MixRandom} does use a mixing function).

 *

 * <p>The LCG subgenerator for {@code L64X128MixRandom} has an update step of the

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

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

 * is fixed (the same for all instances of {@code L64X128MixRandom}}) and the addend

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

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

 * period, namely 2<sup>64</sup>); therefore there are 2<sup>63</sup> distinct choices

 * of parameter.

 *

 * <p>The Xorshift subgenerator for {@code L64X128MixRandom} is the {@code xoroshiro128} algorithm,

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

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

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

 * The period of this subgenerator is 2<sup>128</sup>-1.

 * 

 * <p> The mixing function for {@code L64X128MixRandom} is the 64-bit "starstar(5,7,9)" function.

 *

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

 * are relatively prime, the <em>period</em> of any single {@code L64X128MixRandom} object 

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

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

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

 * {@code L64X128MixRandom} objects have different {@code a} parameters, then their

 * cycles of produced values will be different.

 *

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

 * For any specific instance of {@code L64X128MixRandom}, over the course of its cycle each

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

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

 * methods are likewise exactly equidistributed.

 *

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

 * To be precise: for any specific instance of {@code L64X128MixRandom}, consider

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

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

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

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

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

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

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

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

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

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

 * one instance of {@code L64X128MixRandom} to another, as a function of the additive

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

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

 *

 * <p>Method {@link #split} constructs and returns a new {@code L64X128MixRandom}

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

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

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

 * generated by a single thread using a single {@code L64X128MixRandom} object.

 * This is because, with high probability, distinct {@code L64X128MixRandom} objects

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

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

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

 * cycle.

 *

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

 * {@code L64X128MixRandom} are <em>not</em> thread-safe.

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

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

 * computation using random numbers might include a construction

 * of the form {@code new Subtask(someL64X128MixRandom.split()).fork()}.

 *

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

 * streams, that employ the above techniques when used in

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

 *

 * <p>Instances of {@code L64X128MixRandom} are not cryptographically

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

 * in security-sensitive applications. Additionally,

 * default-constructed instances do not use a cryptographically random

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

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

 *

 * @author  Guy Steele

 * @since   1.9

 */

public final class L64X128MixRandom extends AbstractSplittableRng {

    /*

     * Implementation Overview.

     *

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

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

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

     *

     * With extremely high probability, no two generators so chosen

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

     * that the values generated by two instances of {@code L64X128MixRandom}

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

     *

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

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

     * purpose.  Multiple generators created in this way will certainly

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

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

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

     * seed based on current time unless the

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

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

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

     *

     * File organization: First static fields, then instance

     * fields, then constructors, then instance methods.

     */

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

    /**

     * The seed generator for default constructors.

     */

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

    /*

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

     */

    private static final BigInteger thePeriod =

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

    /*

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

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

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

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

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

     */

    private static final long m = 2862933555777941757L;

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

    /**

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

     * Must be odd.

     */

    private final long a;

    /**

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

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

     */

    private long s, x0, x1;

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

    /**

     * Basic constructor that initializes all fields from parameters.

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

     * all constraints on the values of fields are met.

     */

    public L64X128MixRandom(long a, long s, long x0, long x1) {

	// Force a to be odd.

        this.a = a | 1;

        this.s = s;

	this.x0 = x0;

        this.x1 = x1;

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

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

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

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

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

	}

    }

    /**

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

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

     * {@code L64X128MixRandom} created with the same seed in the same

     * program generate identical sequences of values.

     *

     * @param seed the initial seed

     */

    public L64X128MixRandom(long seed) {

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

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

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

	//

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

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

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

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

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

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

	     1,

	     RngSupport.mixStafford13(seed),

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

    }

    /**

     * Creates a new instance of {@code L64X128MixRandom} that is likely to

     * generate sequences of values that are statistically independent

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

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

     */

    public L64X128MixRandom() {

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

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

    }

    /**

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

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

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

     *

     * @param seed the initial seed

     */

    public L64X128MixRandom(byte[] seed) {

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

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

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

	// Force a to be odd.

        this.a = a | 1;

        this.s = s;

        this.x0 = x0;

        this.x1 = x1;

    }

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

    /**

     * Constructs and returns a new instance of {@code L64X128MixRandom}

     * that shares no mutable state with this instance.

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

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

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

     * a single {@code L64X128MixRandom} object.  Either or both of the two

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

     * and the same expected statistical properties apply to the

     * entire set of generators constructed by such recursive splitting.

     *

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

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

     *               initialize the state of the new ones.

     * @return a new instance of {@code L64X128MixRandom}

     */

    public L64X128MixRandom split(SplittableRng source) {

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

        return new L64X128MixRandom(source.nextLong(), source.nextLong(),

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

    }

    /**

     * Returns a pseudorandom {@code long} value.

     *

     * @return a pseudorandom {@code long} value

     */

    public long nextLong() {

	final long z = s + x0;

	s = m * s + a;  // LCG

	long q0 = x0, q1 = x1;

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

	x0 = q0; x1 = q1;

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

    }

    public BigInteger period() { return thePeriod; }

}