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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 L128X256MixRandom} 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 L128X256MixRandom} 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 L128X256MixRandom} 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 L128X256MixRandom} does use a mixing function).

 *

 * <p>The LCG subgenerator for {@code L128X256MixRandom} has an update step of the

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

 * 128-bit integers; {@code s} is the mutable state, the multiplier {@code m}

 * is fixed (the same for all instances of {@code L128X256MixRandom}}) 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>128</sup>); therefore there are 2<sup>127</sup> distinct choices

 * of parameter.

 *

 * <p>The Xorshift subgenerator for {@code L128X256MixRandom} is the {@code xoshiro256} algorithm,

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

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

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

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

 * 

 * <p> The mixing function for {@code L128X256MixRandom} is the 64-bit MurmurHash3 finalizer.

 *

 * <p> Because the periods 2<sup>128</sup> and 2<sup>256</sup>-1 of the two subgenerators

 * are relatively prime, the <em>period</em> of any single {@code L128X256MixRandom} 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>128</sup>(2<sup>256</sup>-1),

 * which is just slightly smaller than 2<sup>384</sup>.  Moreover, if two distinct

 * {@code L128X256MixRandom} 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 L128X256MixRandom}, over the course of its cycle each

 * of the 2<sup>64</sup> possible {@code long} values will be produced 2<sup>256</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 exactly

 * 2-equidistributed.  For any specific instance of {@code L128X256MixRandom}, 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>128</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,

 * which consists of 2 64-bit values, can have one of 2<sup>128</sup> values, and each

 * such value occurs  2<sup>256</sup>-1 times.  The values produced by the {@code nextInt()},

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

 *

 * <p>Moreover, the 64-bit values produced by the {@code nextLong()} method are 4-equidistributed.

 * To be precise: for any specific instance of {@code L128X256MixRandom}, consider

 * the (overlapping) length-4 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 <sup>128</sup>(2<sup>256</sup>-1) such subsequences, and each subsequence,

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

 * 2<sup>256</sup> subsequence values, nearly all of them (2<sup>256</sup>-2<sup>128</sup>)

 * occur 2<sup>128</sup> times over the course of the entire cycle, and the other

 * 2<sup>128</sup> subsequence values occur only 2<sup>128</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>-128</sup>.

 * (Note that the set of 2<sup>128</sup> less-common subsequence values will differ from

 * one instance of {@code L128X256MixRandom} 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 4-equidistributed.

 *

 * <p>Method {@link #split} constructs and returns a new {@code L128X256MixRandom}

 * 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 L128X256MixRandom} object.

 * This is because, with high probability, distinct {@code L128X256MixRandom} 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 L128X256MixRandom} 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(someL128X256MixRandom.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 L128X256MixRandom} 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 L128X256MixRandom extends AbstractSplittableRng {

    /*

     * Implementation Overview.

     *

     * The 128-bit parameter `a` is represented as two long fields `ah` and `al`.

     * The 128-bit state variable `s` is represented as two long fields `sh` and `sl`.

     *

     * The split operation uses the current generator to choose eight

     * new 64-bit long values that are then used to initialize the

     * parameters `ah` and `al` and the state variables `sh`, `sl`,

     * `x0`, `x1`, `x2`, and `x3` 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 L128X256MixRandom}

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

     *

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

     * "defaultGen" to generate eight 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**256 - 1) * 2**128.

     */

    private static final BigInteger thePeriod =

	BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(128);

    /*

     * The multiplier used in the LCG portion of the algorithm is 2**64 + m;

     * where m is 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>).

     *

     * This is almost certainly not the best possible 128-bit multiplier

     * for an LCG, but it is sufficient for our purposes here; because

     * is is larger than 2**64, the 64-bit values produced by nextLong()

     * are exactly 2-equidistributed, and the fact that it is of the

     * form (2**64 + m) simplifies the code, given that we have only

     * 64-bit arithmetic to work with.

     */

    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 ah, al;

    /**

     * The per-instance state: sh and sl for the LCG; x0, x1, x2, and x3 for the xorshift.

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

     */

    private long sh, sl, x0, x1, x2, x3;

    /* ---------------- 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.

     *

     * @param ah high half of the additive parameter for the LCG

     * @param al low half of the additive parameter for the LCG

     * @param sh high half of the initial state for the LCG

     * @param sl low half of the initial state for the LCG

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

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

     * @param x2 third word of the initial state for the xorshift generator

     * @param x3 fourth word of the initial state for the xorshift generator

     */

    public L128X256MixRandom(long ah, long al, long sh, long sl, long x0, long x1, long x2, long x3) {

	// Force a to be odd.

        this.ah = ah;

        this.al = al | 1;

        this.sh = sh;

        this.sl = sl;

        this.x0 = x0;

        this.x1 = x1;

        this.x2 = x2;

        this.x3 = x3;

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

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

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

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

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

	    this.x2 = RngSupport.mixStafford13(sh += RngSupport.GOLDEN_RATIO_64);

	    this.x3 = RngSupport.mixStafford13(sh + RngSupport.GOLDEN_RATIO_64);

	}

    }

    /**

     * Creates a new instance of {@code L128X256MixRandom} using the

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

     * {@code L128X256MixRandom} created with the same seed in the same

     * program generate identical sequences of values.

     *

     * @param seed the initial seed

     */

    public L128X256MixRandom(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.

	// The other x values are 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),

	     RngSupport.mixMurmur64(seed += RngSupport.GOLDEN_RATIO_64),

	     0,

	     1,

	     RngSupport.mixStafford13(seed),

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

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

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

    }

    /**

     * Creates a new instance of {@code L128X256MixRandom} 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 L128X256MixRandom() {

	// 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 L128X256MixRandom} using the specified array of

     * initial seed bytes. Instances of {@code L128X256MixRandom} created with the same

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

     *

     * @param seed the initial seed

     */

    public L128X256MixRandom(byte[] seed) {

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

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

	long ah = data[0], al = data[1], sh = data[2], sl = data[3], x0 = data[4], x1 = data[5], x2 = data[6], x3 = data[7];

	// Force a to be odd.

        this.ah = ah;

        this.al = al | 1;

        this.sh = sh;

        this.sl = sl;

        this.x0 = x0;

        this.x1 = x1;

        this.x2 = x2;

        this.x3 = x3;

    }

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

    /**

     * Constructs and returns a new instance of {@code L128X256MixRandom}

     * 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 L128X256MixRandom} 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 L128X256MixRandom}

     */

    public L128X256MixRandom split(SplittableRng source) {

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

        return new L128X256MixRandom(source.nextLong(), source.nextLong(), 

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

				     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 = sh + x0;

	// The LCG: in effect, s = ((1LL << 64) + m) * s + a, if only we had 128-bit arithmetic.

	final long u = m * sl;

	sh = (m * sh) + Math.multiplyHigh(m, sl) + sl + ah;

	sl = u + al;

	if (Long.compareUnsigned(sl, u) < 0) ++sh;  // Handle the carry propagation from low half to high half.

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

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

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

	return RngSupport.mixLea64(z);  // mixing function

    }

    public BigInteger period() { return thePeriod; }

}