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package java.util.random;

import java.math.BigInteger;

import java.util.concurrent.atomic.AtomicLong;

import java.util.random.RandomGenerator.SplittableGenerator;

/**

 * A generator of uniform pseudorandom values applicable for use in

 * (among other contexts) isolated parallel computations that may

 * generate subtasks.  Class {@link L64X256MixRandom} implements

 * interfaces {@link RandomGenerator} and {@link SplittableGenerator},

 * 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 {@link L64X256MixRandom} 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>

 * {@link L64X256MixRandom} 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

 * <p>

 * The LCG subgenerator for {@link L64X256MixRandom} 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 {@link L64X256MixRandom}) 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 {@link L64X256MixRandom} 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>

 * <p>

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

 * are relatively prime, the <em>period</em> of any single {@link L64X256MixRandom} 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>256</sup>-1),

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

 * {@link L64X256MixRandom} 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 {@link L64X256MixRandom}, 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 4-equidistributed.

 * To be precise: for any specific instance of {@link L64X256MixRandom}, 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 2<sup>64</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>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

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

 * one instance of {@link L64X256MixRandom} 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 {@link L64X256MixRandom}

 * 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 {@link L64X256MixRandom} object.

 * This is because, with high probability, distinct {@link L64X256MixRandom} 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

 * {@link L64X256MixRandom} 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(someL64X256MixRandom.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 {@link L64X256MixRandom} 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}.

 *

 * @since 14

 */

    /*

     * Implementation Overview.

     *

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

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

     * state variables `s`, `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 {@link L64X256MixRandom}

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

     *

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

     * "defaultGen" to generate six 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(RandomSupport.initialSeed());

    /*

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

     */

    private static final BigInteger PERIOD =

        BigInteger.ONE.shiftLeft(256).subtract(BigInteger.ONE).shiftLeft(64);

    /*

     */

    /* ---------------- 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, x1, x2, and x3 for the xorshift.

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

     */

    private long s, 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 a additive parameter for the LCG

     * @param s 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 L64X256MixRandom(long a, long s, long x0, long x1, long x2, long x3) {

        // Force a to be odd.

        this.a = a | 1;

        this.s = s;

        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.

        }

    }

    /**

     * Creates a new instance of {@link L64X256MixRandom} using the

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

     * {@link L64X256MixRandom} created with the same seed in the same

     * program generate identical sequences of values.

     *

     * @param seed the initial seed

     */

    public L64X256MixRandom(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

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

             1,

             RandomSupport.mixStafford13(seed),

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

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

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

    }

    /**

     * Creates a new instance of {@link L64X256MixRandom} 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 L64X256MixRandom() {

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

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

    }

    /**

     * Creates a new instance of {@link L64X256MixRandom} using the specified array of

     * initial seed bytes. Instances of {@link L64X256MixRandom} created with the same

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

     *

     * @param seed the initial seed

     */

    public L64X256MixRandom(byte[] seed) {

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

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

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

        // Force a to be odd.

        this.a = a | 1;

        this.s = s;

        this.x0 = x0;

        this.x1 = x1;

        this.x2 = x2;

        this.x3 = x3;

    }

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

    /**

     * 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

     * 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.

     *

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

     *               initialize the state of the new ones.

     */

    }

    /**

     * Returns a pseudorandom {@code long} value.

     *

     * @return a pseudorandom {@code long} value

     */

    public long nextLong() {

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

        {   // xoshiro256 1.0

            long t = q1 << 17;

            q2 ^= q0;

            q3 ^= q1;

            q1 ^= q2;

            q0 ^= q3;

            q2 ^= t;

            q3 = Long.rotateLeft(q3, 45);

        }

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

    }

    public BigInteger period() {

        return PERIOD;

    }

}