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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

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package java.util;

import java.util.concurrent.atomic.AtomicLong;

import java.util.function.DoubleConsumer;

import java.util.function.IntConsumer;

import java.util.function.LongConsumer;

import java.util.stream.DoubleStream;

import java.util.stream.IntStream;

import java.util.stream.LongStream;

import java.util.stream.StreamSupport;

/**

 * A generator of uniform pseudorandom values applicable for use in

 * (among other contexts) isolated parallel computations that may

 * generate subtasks. Class {@code SplittableRandom} supports methods for

 * producing pseudorandom numbers of type {@code int}, {@code long},

 * and {@code double} with similar usages as for class

 * {@link java.util.Random} but differs in the following ways:

 *

 * <ul>

 *

 * <li>Series of generated values pass the DieHarder suite testing

 * independence and uniformity properties of random number generators.

 * (Most recently validated with <a

 * href="http://www.phy.duke.edu/~rgb/General/dieharder.php"> version

 * 3.31.1</a>.) 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. The <em>period</em>

 * (length of any series of generated values before it repeats) is at

 * least 2<sup>64</sup>.

 *

 * <li>Method {@link #split} constructs and returns a new

 * SplittableRandom 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

 * SplittableRandom} object.

 *

 * <li>Instances of SplittableRandom 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(aSplittableRandom.split()).fork()}.

 *

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

 * streams, that employ the above techniques when used in {@code

 * stream.parallel()} mode.

 *

 * </ul>

 *

 * <p>Instances of {@code SplittableRandom} 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

 * @author  Doug Lea

 * @since   1.8

 */

public final class SplittableRandom {

    /*

     * Implementation Overview.

     *

     * This algorithm was inspired by the "DotMix" algorithm by

     * Leiserson, Schardl, and Sukha "Deterministic Parallel

     * Random-Number Generation for Dynamic-Multithreading Platforms",

     * PPoPP 2012, as well as those in "Parallel random numbers: as

     * easy as 1, 2, 3" by Salmon, Morae, Dror, and Shaw, SC 2011.  It

     * differs mainly in simplifying and cheapening operations.

     *

     * The primary update step (method nextSeed()) is to add a

     * constant ("gamma") to the current (64 bit) seed, forming a

     * simple sequence.  The seed and the gamma values for any two

     * SplittableRandom instances are highly likely to be different.

     *

     * Methods nextLong, nextInt, and derivatives do not return the

     * sequence (seed) values, but instead a hash-like bit-mix of

     * their bits, producing more independently distributed sequences.

     * For nextLong, the mix64 function is based on David Stafford's

     * (http://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html)

     * "Mix13" variant of the "64-bit finalizer" function in Austin

     * Appleby's MurmurHash3 algorithm (see

     * http://code.google.com/p/smhasher/wiki/MurmurHash3). The mix32

     * function is based on Stafford's Mix04 mix function, but returns

     * the upper 32 bits cast as int.

     *

     * The split operation uses the current generator to form the seed

     * and gamma for another SplittableRandom.  To conservatively

     * avoid potential correlations between seed and value generation,

     * gamma selection (method mixGamma) uses different

     * (Murmurhash3's) mix constants.  To avoid potential weaknesses

     * in bit-mixing transformations, we restrict gammas to odd values

     * with at least 24 0-1 or 1-0 bit transitions.  Rather than

     * rejecting candidates with too few or too many bits set, method

     * mixGamma flips some bits (which has the effect of mapping at

     * most 4 to any given gamma value).  This reduces the effective

     * set of 64bit odd gamma values by about 2%, and serves as an

     * automated screening for sequence constant selection that is

     * left as an empirical decision in some other hashing and crypto

     * algorithms.

     *

     * The resulting generator thus transforms a sequence in which

     * (typically) many bits change on each step, with an inexpensive

     * mixer with good (but less than cryptographically secure)

     * avalanching.

     *

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

     * split() for a common "defaultGen" SplittableRandom.  Unlike

     * other cases, this split must be performed in a thread-safe

     * manner, so we use an AtomicLong to represent the seed rather

     * than use an explicit SplittableRandom. 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.

     *

     * It is a relatively simple matter to apply the basic design here

     * to use 128 bit seeds. However, emulating 128bit arithmetic and

     * carrying around twice the state add more overhead than appears

     * warranted for current usages.

     *

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

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

     * some custom spliterator classes needed for stream methods.

     */

    /**

     * The golden ratio scaled to 64bits, used as the initial gamma

     * value for (unsplit) SplittableRandoms.

     */

    private static final long GOLDEN_GAMMA = 0x9e3779b97f4a7c15L;

    /**

     * The least non-zero value returned by nextDouble(). This value

     * is scaled by a random value of 53 bits to produce a result.

     */

    private static final double DOUBLE_UNIT = 0x1.0p-53; // 1.0 / (1L << 53);

    /**

     * The seed. Updated only via method nextSeed.

     */

    private long seed;

    /**

     * The step value.

     */

    private final long gamma;

    /**

     * Internal constructor used by all others except default constructor.

     */

    private SplittableRandom(long seed, long gamma) {

        this.seed = seed;

        this.gamma = gamma;

    }

    /**

     * Computes Stafford variant 13 of 64bit mix function.

     */

    private static long mix64(long z) {

        z = (z ^ (z >>> 30)) * 0xbf58476d1ce4e5b9L;

        z = (z ^ (z >>> 27)) * 0x94d049bb133111ebL;

        return z ^ (z >>> 31);

    }

    /**

     * Returns the 32 high bits of Stafford variant 4 mix64 function as int.

     */

    private static int mix32(long z) {

        z = (z ^ (z >>> 33)) * 0x62a9d9ed799705f5L;

        return (int)(((z ^ (z >>> 28)) * 0xcb24d0a5c88c35b3L) >>> 32);

    }

    /**

     * Returns the gamma value to use for a new split instance.

     */

    private static long mixGamma(long z) {

        z = (z ^ (z >>> 33)) * 0xff51afd7ed558ccdL; // MurmurHash3 mix constants

        z = (z ^ (z >>> 33)) * 0xc4ceb9fe1a85ec53L;

        z = (z ^ (z >>> 33)) | 1L;                  // force to be odd

        int n = Long.bitCount(z ^ (z >>> 1));       // ensure enough transitions

        return (n < 24) ? z ^ 0xaaaaaaaaaaaaaaaaL : z;

    }

    /**

     * Adds gamma to seed.

     */

    private long nextSeed() {

        return seed += gamma;

    }

    // IllegalArgumentException messages

    static final String BAD_BOUND = "bound must be positive";

    static final String BAD_RANGE = "bound must be greater than origin";

    static final String BAD_SIZE  = "size must be non-negative";

    /**

     * The seed generator for default constructors.

     */

    private static final AtomicLong defaultGen

        = new AtomicLong(mix64(System.currentTimeMillis()) ^

                         mix64(System.nanoTime()));

    // at end of <clinit> to survive static initialization circularity

    static {

        if (java.security.AccessController.doPrivileged(

            new java.security.PrivilegedAction<Boolean>() {

                public Boolean run() {

                    return Boolean.getBoolean("java.util.secureRandomSeed");

                }})) {

            byte[] seedBytes = java.security.SecureRandom.getSeed(8);

            long s = (long)seedBytes[0] & 0xffL;

            for (int i = 1; i < 8; ++i)

                s = (s << 8) | ((long)seedBytes[i] & 0xffL);

            defaultGen.set(s);

        }

    }

    /*

     * Internal versions of nextX methods used by streams, as well as

     * the public nextX(origin, bound) methods.  These exist mainly to

     * avoid the need for multiple versions of stream spliterators

     * across the different exported forms of streams.

     */

    /**

     * The form of nextLong used by LongStream Spliterators.  If

     * origin is greater than bound, acts as unbounded form of

     * nextLong, else as bounded form.

     *

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

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

     * @return a pseudorandom value

     */

    final long internalNextLong(long origin, long bound) {

        /*

         * Four Cases:

         *

         * 1. If the arguments indicate unbounded form, act as

         * nextLong().

         *

         * 2. If the range is an exact power of two, apply the

         * associated bit mask.

         *

         * 3. If the range is positive, loop to avoid potential bias

         * when the implicit nextLong() bound (2<sup>64</sup>) is not

         * evenly divisible by the range. The loop rejects candidates

         * computed from otherwise over-represented values.  The

         * expected number of iterations under an ideal generator

         * varies from 1 to 2, depending on the bound. The loop itself

         * takes an unlovable form. Because the first candidate is

         * already available, we need a break-in-the-middle

         * construction, which is concisely but cryptically performed

         * within the while-condition of a body-less for loop.

         *

         * 4. Otherwise, the range cannot be represented as a positive

         * long.  The loop repeatedly generates unbounded longs until

         * obtaining a candidate meeting constraints (with an expected

         * number of iterations of less than two).

         */

        long r = mix64(nextSeed());

        if (origin < bound) {

            long n = bound - origin, m = n - 1;

            if ((n & m) == 0L)  // power of two

                r = (r & m) + origin;

            else if (n > 0L) {  // reject over-represented candidates

                for (long u = r >>> 1;            // ensure nonnegative

                     u + m - (r = u % n) < 0L;    // rejection check

                     u = mix64(nextSeed()) >>> 1) // retry

                    ;

                r += origin;

            }

            else {              // range not representable as long

                while (r < origin || r >= bound)

                    r = mix64(nextSeed());

            }

        }

        return r;

    }

    /**

     * The form of nextInt used by IntStream Spliterators.

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

     *

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

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

     * @return a pseudorandom value

     */

    final int internalNextInt(int origin, int bound) {

        int r = mix32(nextSeed());

        if (origin < bound) {

            int n = bound - origin, m = n - 1;

            if ((n & m) == 0)

                r = (r & m) + origin;

            else if (n > 0) {

                for (int u = r >>> 1;

                     u + m - (r = u % n) < 0;

                     u = mix32(nextSeed()) >>> 1)

                    ;

                r += origin;

            }

            else {

                while (r < origin || r >= bound)

                    r = mix32(nextSeed());

            }

        }

        return r;

    }

    /**

     * The form of nextDouble used by DoubleStream Spliterators.

     *

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

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

     * @return a pseudorandom value

     */

    final double internalNextDouble(double origin, double bound) {

        double r = (nextLong() >>> 11) * DOUBLE_UNIT;

        if (origin < bound) {

            r = r * (bound - origin) + origin;

            if (r >= bound) // correct for rounding

                r = Double.longBitsToDouble(Double.doubleToLongBits(bound) - 1);

        }

        return r;

    }

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

    /**

     * Creates a new SplittableRandom instance using the specified

     * initial seed. SplittableRandom instances created with the same

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

     *

     * @param seed the initial seed

     */

    public SplittableRandom(long seed) {

        this(seed, GOLDEN_GAMMA);

    }

    /**

     * Creates a new SplittableRandom instance that is likely to

     * generate sequences of values that are statistically independent

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

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

     */

    public SplittableRandom() { // emulate defaultGen.split()

        long s = defaultGen.getAndAdd(2 * GOLDEN_GAMMA);

        this.seed = mix64(s);

        this.gamma = mixGamma(s + GOLDEN_GAMMA);

    }

    /**

     * Constructs and returns a new SplittableRandom instance 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 the

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

     * a single SplittableRandom 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.

     *

     * @return the new SplittableRandom instance

     */

    public SplittableRandom split() {

        return new SplittableRandom(nextLong(), mixGamma(nextSeed()));

    }

    /**

     * Returns a pseudorandom {@code int} value.

     *

     * @return a pseudorandom {@code int} value

     */

    public int nextInt() {

        return mix32(nextSeed());

    }

    /**

     * Returns a pseudorandom {@code int} value between zero (inclusive)

     * and the specified bound (exclusive).

     *

     * @param bound the upper bound (exclusive).  Must be positive.

     * @return a pseudorandom {@code int} value between zero

     *         (inclusive) and the bound (exclusive)

     * @throws IllegalArgumentException if {@code bound} is not positive

     */

    public int nextInt(int bound) {

        if (bound <= 0)

            throw new IllegalArgumentException(BAD_BOUND);

        // Specialize internalNextInt for origin 0

        int r = mix32(nextSeed());

        int m = bound - 1;

        if ((bound & m) == 0) // power of two

            r &= m;

        else { // reject over-represented candidates

            for (int u = r >>> 1;

                 u + m - (r = u % bound) < 0;

                 u = mix32(nextSeed()) >>> 1)

                ;

        }

        return r;

    }

    /**

     * Returns a pseudorandom {@code int} value between the specified

     * origin (inclusive) and the specified bound (exclusive).

     *

     * @param origin the least value returned

     * @param bound the upper bound (exclusive)

     * @return a pseudorandom {@code int} value between the origin

     *         (inclusive) and the bound (exclusive)

     * @throws IllegalArgumentException if {@code origin} is greater than

     *         or equal to {@code bound}

     */

    public int nextInt(int origin, int bound) {

        if (origin >= bound)

            throw new IllegalArgumentException(BAD_RANGE);

        return internalNextInt(origin, bound);

    }

    /**

     * Returns a pseudorandom {@code long} value.

     *

     * @return a pseudorandom {@code long} value

     */

    public long nextLong() {

        return mix64(nextSeed());

    }

    /**

     * Returns a pseudorandom {@code long} value between zero (inclusive)

     * and the specified bound (exclusive).

     *

     * @param bound the upper bound (exclusive).  Must be positive.

     * @return a pseudorandom {@code long} value between zero

     *         (inclusive) and the bound (exclusive)

     * @throws IllegalArgumentException if {@code bound} is not positive

     */

    public long nextLong(long bound) {

        if (bound <= 0)

            throw new IllegalArgumentException(BAD_BOUND);

        // Specialize internalNextLong for origin 0

        long r = mix64(nextSeed());

        long m = bound - 1;

        if ((bound & m) == 0L) // power of two

            r &= m;

        else { // reject over-represented candidates

            for (long u = r >>> 1;

                 u + m - (r = u % bound) < 0L;

                 u = mix64(nextSeed()) >>> 1)

                ;

        }

        return r;

    }

    /**

     * Returns a pseudorandom {@code long} value between the specified

     * origin (inclusive) and the specified bound (exclusive).

     *

     * @param origin the least value returned

     * @param bound the upper bound (exclusive)

     * @return a pseudorandom {@code long} value between the origin

     *         (inclusive) and the bound (exclusive)

     * @throws IllegalArgumentException if {@code origin} is greater than

     *         or equal to {@code bound}

     */

    public long nextLong(long origin, long bound) {

        if (origin >= bound)

            throw new IllegalArgumentException(BAD_RANGE);

        return internalNextLong(origin, bound);

    }

    /**

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

     * (inclusive) and one (exclusive).

     *

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

     *         (inclusive) and one (exclusive)

     */

    public double nextDouble() {

        return (mix64(nextSeed()) >>> 11) * DOUBLE_UNIT;

    }

    /**

     * Returns a pseudorandom {@code double} value between 0.0

     * (inclusive) and the specified bound (exclusive).

     *