Random.java

/*
 * Copyright (c) 1995, 2022, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.util;

import java.io.*;
import java.util.concurrent.atomic.AtomicLong;
import java.util.random.RandomGenerator;
import java.util.stream.DoubleStream;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

import jdk.internal.util.random.RandomSupport.*;

import static jdk.internal.util.random.RandomSupport.*;

import jdk.internal.misc.Unsafe;

/**
 * An instance of this class is used to generate a stream of
 * pseudorandom numbers; its period is only 2<sup>48</sup>.
 * The class uses a 48-bit seed, which is
 * modified using a linear congruential formula. (See Donald E. Knuth,
 * <cite>The Art of Computer Programming, Volume 2, Third
 * edition: Seminumerical Algorithms</cite>, Section 3.2.1.)
 * <p>
 * If two instances of {@code Random} are created with the same
 * seed, and the same sequence of method calls is made for each, they
 * will generate and return identical sequences of numbers. In order to
 * guarantee this property, particular algorithms are specified for the
 * class {@code Random}. Java implementations must use all the algorithms
 * shown here for the class {@code Random}, for the sake of absolute
 * portability of Java code. However, subclasses of class {@code Random}
 * are permitted to use other algorithms, so long as they adhere to the
 * general contracts for all the methods.
 * <p>
 * The algorithms implemented by class {@code Random} use a
 * {@code protected} utility method that on each invocation can supply
 * up to 32 pseudorandomly generated bits.
 * <p>
 * Many applications will find the method {@link Math#random} simpler to use.
 *
 * <p>Instances of {@code java.util.Random} are threadsafe.
 * However, the concurrent use of the same {@code java.util.Random}
 * instance across threads may encounter contention and consequent
 * poor performance. Consider instead using
 * {@link java.util.concurrent.ThreadLocalRandom} in multithreaded
 * designs.
 *
 * <p>Instances of {@code java.util.Random} are not cryptographically
 * secure.  Consider instead using {@link java.security.SecureRandom} to
 * get a cryptographically secure pseudo-random number generator for use
 * by security-sensitive applications.
 *
 * @author  Frank Yellin
 * @since   1.0
 */
@RandomGeneratorProperties(
        name = "Random",
        i = 48, j = 0, k = 0,
        equidistribution = 0
)
public class Random implements RandomGenerator, java.io.Serializable {

    /**
     * Class used to wrap a {@link java.util.random.RandomGenerator} to
     * {@link java.util.Random}.
     */

    @SuppressWarnings("serial")
    private static final class RandomWrapper extends Random implements RandomGenerator {
        private final RandomGenerator generator;
        //randomToWrap must never be null
        private RandomWrapper(RandomGenerator randomToWrap) {
            super(null);
            this.generator = randomToWrap;
        }

        /**
         * Throws {@code NotSerializableException}.
         *
         * @param s the object input stream
         * @throws NotSerializableException always
         */
        @Serial
        private void readObject(ObjectInputStream s) throws NotSerializableException {
            throw new NotSerializableException("not serializable");
        }

        /**
         * Throws {@code NotSerializableException}.
         *
         * @param s the object output stream
         * @throws NotSerializableException always
         */
        @Serial
        private void writeObject(ObjectOutputStream s) throws NotSerializableException {
            throw new NotSerializableException("not serializable");
        }

        /**
         * setSeed does not exist in {@link java.util.random.RandomGenerator} so can't
         * use it.
         */
        @Override
        public void setSeed(long seed) {
            throw new UnsupportedOperationException();
        }

        @Override
        public boolean isDeprecated() {
            return generator.isDeprecated();
        }

        @Override
        public void nextBytes(byte[] bytes) {
            this.generator.nextBytes(bytes);
        }

        @Override
        public int nextInt() {
            return this.generator.nextInt();
        }

        @Override
        public int nextInt(int bound) {
            return this.generator.nextInt(bound);
        }

        @Override
        public int nextInt(int origin, int bound) {
            return generator.nextInt(origin, bound);
        }

        @Override
        public long nextLong() {
            return this.generator.nextLong();
        }

        @Override
        public long nextLong(long bound) {
            return generator.nextLong(bound);
        }

        @Override
        public long nextLong(long origin, long bound) {
            return generator.nextLong(origin, bound);
        }

        @Override
        public boolean nextBoolean() {
            return this.generator.nextBoolean();
        }

        @Override
        public float nextFloat() {
            return this.generator.nextFloat();
        }

        @Override
        public float nextFloat(float bound) {
            return generator.nextFloat(bound);
        }

        @Override
        public float nextFloat(float origin, float bound) {
            return generator.nextFloat(origin, bound);
        }

        @Override
        public double nextDouble() {
            return this.generator.nextDouble();
        }

        @Override
        public double nextDouble(double bound) {
            return generator.nextDouble(bound);
        }

        @Override
        public double nextDouble(double origin, double bound) {
            return generator.nextDouble(origin, bound);
        }

        @Override
        public double nextExponential() {
            return generator.nextExponential();
        }

        @Override
        public double nextGaussian() {
            return this.generator.nextGaussian();
        }

        @Override
        public double nextGaussian(double mean, double stddev) {
            return generator.nextGaussian(mean, stddev);
        }

        @Override
        public IntStream ints(long streamSize) {
            return this.generator.ints(streamSize);
        }

        @Override
        public IntStream ints() {
            return this.generator.ints();
        }

        @Override
        public IntStream ints(long streamSize, int randomNumberOrigin, int randomNumberBound) {
            return this.generator.ints(streamSize, randomNumberOrigin, randomNumberBound);
        }

        @Override
        public IntStream ints(int randomNumberOrigin, int randomNumberBound) {
            return this.generator.ints(randomNumberOrigin, randomNumberBound);
        }

        @Override
        public LongStream longs(long streamSize) {
            return this.generator.longs(streamSize);
        }

        @Override
        public LongStream longs() {
            return this.generator.longs();
        }

        @Override
        public LongStream longs(long streamSize, long randomNumberOrigin, long randomNumberBound) {
            return this.generator.longs(streamSize, randomNumberOrigin, randomNumberBound);
        }

        @Override
        public LongStream longs(long randomNumberOrigin, long randomNumberBound) {
            return this.generator.longs(randomNumberOrigin, randomNumberBound);
        }

        @Override
        public DoubleStream doubles(long streamSize) {
            return this.generator.doubles(streamSize);
        }

        @Override
        public DoubleStream doubles() {
            return this.generator.doubles();
        }

        @Override
        public DoubleStream doubles(long streamSize, double randomNumberOrigin, double randomNumberBound) {
            return this.generator.doubles(streamSize, randomNumberOrigin, randomNumberBound);
        }

        @Override
        public DoubleStream doubles(double randomNumberOrigin, double randomNumberBound) {
            return this.generator.doubles(randomNumberOrigin, randomNumberBound);
        }

        //This method should never be reached unless done by reflection so we should throw when tried
        @Override
        protected int next(int bits) {
            throw new UnsupportedOperationException();
        }

        @Override
        public String toString() {
            return "RandomWrapper[" + generator + "]";
        }
    }

    /** use serialVersionUID from JDK 1.1 for interoperability */
    @java.io.Serial
    static final long serialVersionUID = 3905348978240129619L;

    /**
     * The internal state associated with this pseudorandom number generator.
     * (The specs for the methods in this class describe the ongoing
     * computation of this value.)
     */
    private final AtomicLong seed;

    private static final long multiplier = 0x5DEECE66DL;
    private static final long addend = 0xBL;
    private static final long mask = (1L << 48) - 1;

    private static final double DOUBLE_UNIT = 0x1.0p-53; // 1.0 / (1L << Double.PRECISION)
    private static final float FLOAT_UNIT = 0x1.0p-24f; // 1.0f / (1 << Float.PRECISION)

    /**
     * Creates a new random number generator. This constructor sets
     * the seed of the random number generator to a value very likely
     * to be distinct from any other invocation of this constructor.
     */
    public Random() {
        this(seedUniquifier() ^ System.nanoTime());
    }

    private Random(Void unused) {
        this.seed = null;
    }

    private static long seedUniquifier() {
        // L'Ecuyer, "Tables of Linear Congruential Generators of
        // Different Sizes and Good Lattice Structure", 1999
        for (;;) {
            long current = seedUniquifier.get();
            long next = current * 1181783497276652981L;
            if (seedUniquifier.compareAndSet(current, next))
                return next;
        }
    }

    private static final AtomicLong seedUniquifier
            = new AtomicLong(8682522807148012L);

    /**
     * Creates a new random number generator using a single {@code long} seed.
     * The seed is the initial value of the internal state of the pseudorandom
     * number generator which is maintained by method {@link #next}.
     *
     * @implSpec The invocation {@code new Random(seed)} is equivalent to:
     * <pre>{@code
     * Random rnd = new Random();
     * rnd.setSeed(seed);
     * }</pre>
     *
     * @param seed the initial seed
     * @see   #setSeed(long)
     */
    public Random(long seed) {
        if (getClass() == Random.class)
            this.seed = new AtomicLong(initialScramble(seed));
        else {
            // subclass might have overridden setSeed
            this.seed = new AtomicLong();
            setSeed(seed);
        }
    }

    private static long initialScramble(long seed) {
        return (seed ^ multiplier) & mask;
    }

    /**
     * Returns an instance of {@code Random} that delegates method calls to the {@link RandomGenerator}
     * argument. If the generator is an instance of {@code Random}, it is returned. Otherwise, this method
     * returns an instance of {@code Random} that delegates all methods except {@code setSeed} to the generator.
     * The returned instance's {@code setSeed} method always throws {@link UnsupportedOperationException}.
     * The returned instance is not serializable.
     *
     * @param generator the {@code RandomGenerator} calls are delegated to
     * @return the delegating {@code Random} instance
     * @throws NullPointerException if generator is null
     * @since 19
     */
    public static Random from(RandomGenerator generator) {
        Objects.requireNonNull(generator);
        if (generator instanceof Random rand)
            return rand;

        return new RandomWrapper(generator);
    }

    /**
     * Sets or updates the seed of this random number generator using the
     * provided {@code long} seed value (optional operation).
     *
     * @implSpec
     * The implementation in this class alters the state of this random number
     * generator so that it is in the same state as if it had just been created with
     * {@link #Random(long) new Random(seed)}. It atomically updates the seed to
     *  <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre>
     * and clears the {@code haveNextNextGaussian} flag used by {@link #nextGaussian}.
     * Note that this uses only 48 bits of the given seed value.
     *
     * @param seed the seed value
     * @throws UnsupportedOperationException if the {@code setSeed}
     *         operation is not supported by this random number generator
     */
    public synchronized void setSeed(long seed) {
        this.seed.set(initialScramble(seed));
        haveNextNextGaussian = false;
    }

    /**
     * Generates the next pseudorandom number. This method returns an
     * {@code int} value such that, if the argument {@code bits} is between
     * {@code 1} and {@code 32} (inclusive), then that many low-order
     * bits of the returned value will be (approximately) independently
     * chosen bit values, each of which is (approximately) equally
     * likely to be {@code 0} or {@code 1}.
     *
     * @apiNote
     * The other random-producing methods in this class are implemented
     * in terms of this method, so subclasses can override just this
     * method to provide a different source of pseudorandom numbers for
     * the entire class.
     *
     * @implSpec
     * The implementation in this class atomically updates the seed to
     *  <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre>
     * and returns
     *  <pre>{@code (int)(seed >>> (48 - bits))}.</pre>
     *
     * <p>This is a linear congruential pseudorandom number generator, as
     * defined by D. H. Lehmer and described by Donald E. Knuth in
     * <cite>The Art of Computer Programming, Volume 2, Third edition:
     * Seminumerical Algorithms</cite>, section 3.2.1.
     *
     * @param  bits random bits
     * @return the next pseudorandom value from this random number
     *         generator's sequence
     * @since  1.1
     */
    protected int next(int bits) {
        long oldseed, nextseed;
        AtomicLong seed = this.seed;
        do {
            oldseed = seed.get();
            nextseed = (oldseed * multiplier + addend) & mask;
        } while (!seed.compareAndSet(oldseed, nextseed));
        return (int)(nextseed >>> (48 - bits));
    }

    /**
     * Generates random bytes and places them into a user-supplied
     * byte array.  The number of random bytes produced is equal to
     * the length of the byte array.
     *
     * @implSpec The method {@code nextBytes} is
     * implemented by class {@code Random} as if by:
     * <pre>{@code
     * public void nextBytes(byte[] bytes) {
     *   for (int i = 0; i < bytes.length; )
     *     for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4);
     *          n-- > 0; rnd >>= 8)
     *       bytes[i++] = (byte)rnd;
     * }}</pre>
     *
     * @param  bytes the byte array to fill with random bytes
     * @throws NullPointerException if the byte array is null
     * @since  1.1
     */
    @Override
    public void nextBytes(byte[] bytes) {
        for (int i = 0, len = bytes.length; i < len; )
            for (int rnd = nextInt(),
                 n = Math.min(len - i, Integer.SIZE/Byte.SIZE);
                 n-- > 0; rnd >>= Byte.SIZE)
                bytes[i++] = (byte)rnd;
    }

    /**
     * Returns the next pseudorandom, uniformly distributed {@code int}
     * value from this random number generator's sequence. The general
     * contract of {@code nextInt} is that one {@code int} value is
     * pseudorandomly generated and returned. All 2<sup>32</sup> possible
     * {@code int} values are produced with (approximately) equal probability.
     *
     * @implSpec The method {@code nextInt} is
     * implemented by class {@code Random} as if by:
     * <pre>{@code
     * public int nextInt() {
     *   return next(32);
     * }}</pre>
     *
     * @return the next pseudorandom, uniformly distributed {@code int}
     *         value from this random number generator's sequence
     */
    @Override
    public int nextInt() {
        return next(32);
    }

    /**
     * Returns a pseudorandom, uniformly distributed {@code int} value
     * between 0 (inclusive) and the specified value (exclusive), drawn from
     * this random number generator's sequence.  The general contract of
     * {@code nextInt} is that one {@code int} value in the specified range
     * is pseudorandomly generated and returned.  All {@code bound} possible
     * {@code int} values are produced with (approximately) equal
     * probability.
     *
     * @implSpec The method {@code nextInt(int bound)} is implemented by
     * class {@code Random} as if by:
     * <pre>{@code
     * public int nextInt(int bound) {
     *   if (bound <= 0)
     *     throw new IllegalArgumentException("bound must be positive");
     *
     *   if ((bound & -bound) == bound)  // i.e., bound is a power of 2
     *     return (int)((bound * (long)next(31)) >> 31);
     *
     *   int bits, val;
     *   do {
     *       bits = next(31);
     *       val = bits % bound;
     *   } while (bits - val + (bound-1) < 0);
     *   return val;
     * }}</pre>
     *
     * <p>The hedge "approximately" is used in the foregoing description only
     * because the next method is only approximately an unbiased source of
     * independently chosen bits.  If it were a perfect source of randomly
     * chosen bits, then the algorithm shown would choose {@code int}
     * values from the stated range with perfect uniformity.
     * <p>
     * The algorithm is slightly tricky.  It rejects values that would result
     * in an uneven distribution (due to the fact that 2^31 is not divisible
     * by n). The probability of a value being rejected depends on n.  The
     * worst case is n=2^30+1, for which the probability of a reject is 1/2,
     * and the expected number of iterations before the loop terminates is 2.
     * <p>
     * The algorithm treats the case where n is a power of two specially: it
     * returns the correct number of high-order bits from the underlying
     * pseudo-random number generator.  In the absence of special treatment,
     * the correct number of <i>low-order</i> bits would be returned.  Linear
     * congruential pseudo-random number generators such as the one
     * implemented by this class are known to have short periods in the
     * sequence of values of their low-order bits.  Thus, this special case
     * greatly increases the length of the sequence of values returned by
     * successive calls to this method if n is a small power of two.
     *
     * @param bound the upper bound (exclusive).  Must be positive.
     * @return the next pseudorandom, uniformly distributed {@code int}
     *         value between zero (inclusive) and {@code bound} (exclusive)
     *         from this random number generator's sequence
     * @throws IllegalArgumentException if bound is not positive
     * @since 1.2
     */
    @Override
    public int nextInt(int bound) {
        if (bound <= 0)
            throw new IllegalArgumentException(BAD_BOUND);
        int r = next(31);
        int m = bound - 1;
        if ((bound & m) == 0)  // i.e., bound is a power of 2
            r = (int)((bound * (long)r) >> 31);
        else { // reject over-represented candidates
            for (int u = r;
                 u - (r = u % bound) + m < 0;
                 u = next(31))
                ;
        }
        return r;
    }
    /**
     * Returns the next pseudorandom, uniformly distributed {@code long}
     * value from this random number generator's sequence. The general
     * contract of {@code nextLong} is that one {@code long} value is
     * pseudorandomly generated and returned.
     *
     * @implSpec The method {@code nextLong} is implemented by class {@code Random}
     * as if by:
     * <pre>{@code
     * public long nextLong() {
     *   return ((long)next(32) << 32) + next(32);
     * }}</pre>
     *
     * Because class {@code Random} uses a seed with only 48 bits,
     * this algorithm will not return all possible {@code long} values.
     *
     * @return the next pseudorandom, uniformly distributed {@code long}
     *         value from this random number generator's sequence
     */
    @Override
    public long nextLong() {
        // it's okay that the bottom word remains signed.
        return ((long)(next(32)) << 32) + next(32);
    }

    /**
     * Returns the next pseudorandom, uniformly distributed
     * {@code boolean} value from this random number generator's
     * sequence. The general contract of {@code nextBoolean} is that one
     * {@code boolean} value is pseudorandomly generated and returned.  The
     * values {@code true} and {@code false} are produced with
     * (approximately) equal probability.
     *
     * @implSpec The method {@code nextBoolean} is implemented by class
     * {@code Random} as if by:
     * <pre>{@code
     * public boolean nextBoolean() {
     *   return next(1) != 0;
     * }}</pre>
     *
     * @return the next pseudorandom, uniformly distributed
     *         {@code boolean} value from this random number generator's
     *         sequence
     * @since 1.2
     */
    @Override
    public boolean nextBoolean() {
        return next(1) != 0;
    }

    /**
     * Returns the next pseudorandom, uniformly distributed {@code float}
     * value between {@code 0.0} and {@code 1.0} from this random
     * number generator's sequence.
     *
     * <p>The general contract of {@code nextFloat} is that one
     * {@code float} value, chosen (approximately) uniformly from the
     * range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is
     * pseudorandomly generated and returned. All 2<sup>24</sup> possible
     * {@code float} values of the form <i>m&nbsp;x&nbsp;</i>2<sup>-24</sup>,
     * where <i>m</i> is a positive integer less than 2<sup>24</sup>, are
     * produced with (approximately) equal probability.
     *
     * @implSpec The method {@code nextFloat} is implemented by class
     * {@code Random} as if by:
     * <pre>{@code
     * public float nextFloat() {
     *   return next(24) / ((float)(1 << 24));
     * }}</pre>
     * <p>The hedge "approximately" is used in the foregoing description only
     * because the next method is only approximately an unbiased source of
     * independently chosen bits. If it were a perfect source of randomly
     * chosen bits, then the algorithm shown would choose {@code float}
     * values from the stated range with perfect uniformity.<p>
     * [In early versions of Java, the result was incorrectly calculated as:
     *  <pre> {@code return next(30) / ((float)(1 << 30));}</pre>
     * This might seem to be equivalent, if not better, but in fact it
     * introduced a slight nonuniformity because of the bias in the rounding
     * of floating-point numbers: it was slightly more likely that the
     * low-order bit of the significand would be 0 than that it would be 1.]
     *
     * @return the next pseudorandom, uniformly distributed {@code float}
     *         value between {@code 0.0f} and {@code 1.0f} from this
     *         random number generator's sequence
     */
    @Override
    public float nextFloat() {
        return next(Float.PRECISION) * FLOAT_UNIT;
    }

    /**
     * Returns the next pseudorandom, uniformly distributed
     * {@code double} value between {@code 0.0} and
     * {@code 1.0} from this random number generator's sequence.
     *
     * <p>The general contract of {@code nextDouble} is that one
     * {@code double} value, chosen (approximately) uniformly from the
     * range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is
     * pseudorandomly generated and returned.
     *
     * @implSpec The method {@code nextDouble} is implemented by class
     * {@code Random} as if by:
     * <pre>{@code
     * public double nextDouble() {
     *   return (((long)next(26) << 27) + next(27))
     *     / (double)(1L << 53);
     * }}</pre>
     * <p>The hedge "approximately" is used in the foregoing description only
     * because the {@code next} method is only approximately an unbiased source
     * of independently chosen bits. If it were a perfect source of randomly
     * chosen bits, then the algorithm shown would choose {@code double} values
     * from the stated range with perfect uniformity.
     * <p>[In early versions of Java, the result was incorrectly calculated as:
     * <pre> {@code return (((long)next(27) << 27) + next(27)) / (double)(1L << 54);}</pre>
     * This might seem to be equivalent, if not better, but in fact it
     * introduced a large nonuniformity because of the bias in the rounding of
     * floating-point numbers: it was three times as likely that the low-order
     * bit of the significand would be 0 than that it would be 1! This
     * nonuniformity probably doesn't matter much in practice, but we strive
     * for perfection.]
     *
     * @return the next pseudorandom, uniformly distributed {@code double}
     *         value between {@code 0.0} and {@code 1.0} from this
     *         random number generator's sequence
     * @see Math#random
     */
    @Override
    public double nextDouble() {
        return (((long)(next(Double.PRECISION - 27)) << 27) + next(27)) * DOUBLE_UNIT;
    }

    private double nextNextGaussian;
    private boolean haveNextNextGaussian = false;

    /**
     * Returns the next pseudorandom, Gaussian ("normally") distributed
     * {@code double} value with mean {@code 0.0} and standard
     * deviation {@code 1.0} from this random number generator's sequence.
     * <p>
     * The general contract of {@code nextGaussian} is that one
     * {@code double} value, chosen from (approximately) the usual
     * normal distribution with mean {@code 0.0} and standard deviation
     * {@code 1.0}, is pseudorandomly generated and returned.
     *
     * @implSpec The method {@code nextGaussian} is implemented by class
     * {@code Random} as if by a threadsafe version of the following:
     * <pre>{@code
     * private double nextNextGaussian;
     * private boolean haveNextNextGaussian = false;
     *
     * public double nextGaussian() {
     *   if (haveNextNextGaussian) {
     *     haveNextNextGaussian = false;
     *     return nextNextGaussian;
     *   } else {
     *     double v1, v2, s;
     *     do {
     *       v1 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
     *       v2 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
     *       s = v1 * v1 + v2 * v2;
     *     } while (s >= 1 || s == 0);
     *     double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
     *     nextNextGaussian = v2 * multiplier;
     *     haveNextNextGaussian = true;
     *     return v1 * multiplier;
     *   }
     * }}</pre>
     *
     * This uses the <i>polar method</i> of G. E. P. Box, M. E. Muller, and
     * G. Marsaglia, as described by Donald E. Knuth in <cite>The Art of
     * Computer Programming, Volume 2, third edition: Seminumerical Algorithms</cite>,
     * section 3.4.1, subsection C, algorithm P. Note that it generates two
     * independent values at the cost of only one call to {@code StrictMath.log}
     * and one call to {@code StrictMath.sqrt}.
     *
     * @return the next pseudorandom, Gaussian ("normally") distributed
     *         {@code double} value with mean {@code 0.0} and
     *         standard deviation {@code 1.0} from this random number
     *         generator's sequence
     */
    @Override
    public synchronized double nextGaussian() {
        // See Knuth, TAOCP, Vol. 2, 3rd edition, Section 3.4.1 Algorithm C.
        if (haveNextNextGaussian) {
            haveNextNextGaussian = false;
            return nextNextGaussian;
        } else {
            double v1, v2, s;
            do {
                v1 = 2 * nextDouble() - 1; // between -1 and 1
                v2 = 2 * nextDouble() - 1; // between -1 and 1
                s = v1 * v1 + v2 * v2;
            } while (s >= 1 || s == 0);
            double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
            nextNextGaussian = v2 * multiplier;
            haveNextNextGaussian = true;
            return v1 * multiplier;
        }
    }

    /**
     * Serializable fields for Random.
     *
     * @serialField    seed long
     *              seed for random computations
     * @serialField    nextNextGaussian double
     *              next Gaussian to be returned
     * @serialField      haveNextNextGaussian boolean
     *              nextNextGaussian is valid
     */
    @java.io.Serial
    private static final ObjectStreamField[] serialPersistentFields = {
            new ObjectStreamField("seed", Long.TYPE),
            new ObjectStreamField("nextNextGaussian", Double.TYPE),
            new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE)
    };

    /**
     * Reconstitute the {@code Random} instance from a stream (that is,
     * deserialize it).
     *
     * @param  s the {@code ObjectInputStream} from which data is read
     *
     * @throws IOException if an I/O error occurs
     * @throws ClassNotFoundException if a serialized class cannot be loaded
     */
    @java.io.Serial
    private void readObject(java.io.ObjectInputStream s)
            throws java.io.IOException, ClassNotFoundException {

        ObjectInputStream.GetField fields = s.readFields();

        // The seed is read in as {@code long} for
        // historical reasons, but it is converted to an AtomicLong.
        long seedVal = fields.get("seed", -1L);
        if (seedVal < 0)
            throw new java.io.StreamCorruptedException(
                    "Random: invalid seed");
        resetSeed(seedVal);
        nextNextGaussian = fields.get("nextNextGaussian", 0.0);
        haveNextNextGaussian = fields.get("haveNextNextGaussian", false);
    }

    /**
     * Save the {@code Random} instance to a stream.
     *
     * @param  s the {@code ObjectOutputStream} to which data is written
     *
     * @throws IOException if an I/O error occurs
     */
    @java.io.Serial
    private synchronized void writeObject(ObjectOutputStream s)
            throws IOException {

        // set the values of the Serializable fields
        ObjectOutputStream.PutField fields = s.putFields();

        // The seed is serialized as a long for historical reasons.
        fields.put("seed", seed.get());
        fields.put("nextNextGaussian", nextNextGaussian);
        fields.put("haveNextNextGaussian", haveNextNextGaussian);

        // save them
        s.writeFields();
    }

    // Support for resetting seed while deserializing
    private static final Unsafe unsafe = Unsafe.getUnsafe();
    private static final long seedOffset;
    static {
        try {
            seedOffset = unsafe.objectFieldOffset
                    (Random.class.getDeclaredField("seed"));
        } catch (Exception ex) { throw new Error(ex); }
    }
    private void resetSeed(long seedVal) {
        unsafe.putReferenceVolatile(this, seedOffset, new AtomicLong(seedVal));
    }

    /**
     * Returns a stream producing the given {@code streamSize} number of
     * pseudorandom {@code int} values.
     *
     * <p>A pseudorandom {@code int} value is generated as if it's the result of
     * calling the method {@link #nextInt()}.
     *
     * @param streamSize the number of values to generate
     * @return a stream of pseudorandom {@code int} values
     * @throws IllegalArgumentException if {@code streamSize} is
     *         less than zero
     * @since 1.8
     */
    @Override
    public IntStream ints(long streamSize) {
        return AbstractSpliteratorGenerator.ints(this, streamSize);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code int}
     * values.
     *
     * <p>A pseudorandom {@code int} value is generated as if it's the result of
     * calling the method {@link #nextInt()}.
     *
     * @implNote This method is implemented to be equivalent to {@code
     * ints(Long.MAX_VALUE)}.
     *
     * @return a stream of pseudorandom {@code int} values
     * @since 1.8
     */
    @Override
    public IntStream ints() {
        return AbstractSpliteratorGenerator.ints(this);
    }

    /**
     * Returns a stream producing the given {@code streamSize} number
     * of pseudorandom {@code int} values, each conforming to the given
     * origin (inclusive) and bound (exclusive).
     *
     * <p>A pseudorandom {@code int} value is generated as if it's the result of
     * calling the following method with the origin and bound:
     * <pre> {@code
     * int nextInt(int origin, int bound) {
     *   int n = bound - origin;
     *   if (n > 0) {
     *     return nextInt(n) + origin;
     *   }
     *   else {  // range not representable as int
     *     int r;
     *     do {
     *       r = nextInt();
     *     } while (r < origin || r >= bound);
     *     return r;
     *   }
     * }}</pre>
     *
     * @param streamSize the number of values to generate
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code int} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException if {@code streamSize} is
     *         less than zero, or {@code randomNumberOrigin}
     *         is greater than or equal to {@code randomNumberBound}
     * @since 1.8
     */
    @Override
    public IntStream ints(long streamSize, int randomNumberOrigin, int randomNumberBound) {
        return AbstractSpliteratorGenerator.ints(this, streamSize, randomNumberOrigin, randomNumberBound);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code
     * int} values, each conforming to the given origin (inclusive) and bound
     * (exclusive).
     *
     * <p>A pseudorandom {@code int} value is generated as if it's the result of
     * calling the following method with the origin and bound:
     * <pre> {@code
     * int nextInt(int origin, int bound) {
     *   int n = bound - origin;
     *   if (n > 0) {
     *     return nextInt(n) + origin;
     *   }
     *   else {  // range not representable as int
     *     int r;
     *     do {
     *       r = nextInt();
     *     } while (r < origin || r >= bound);
     *     return r;
     *   }
     * }}</pre>
     *
     * @implNote This method is implemented to be equivalent to {@code
     * ints(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)}.
     *
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code int} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException if {@code randomNumberOrigin}
     *         is greater than or equal to {@code randomNumberBound}
     * @since 1.8
     */
    @Override
    public IntStream ints(int randomNumberOrigin, int randomNumberBound) {
        return AbstractSpliteratorGenerator.ints(this, randomNumberOrigin, randomNumberBound);
    }

    /**
     * Returns a stream producing the given {@code streamSize} number of
     * pseudorandom {@code long} values.
     *
     * <p>A pseudorandom {@code long} value is generated as if it's the result
     * of calling the method {@link #nextLong()}.
     *
     * @param streamSize the number of values to generate
     * @return a stream of pseudorandom {@code long} values
     * @throws IllegalArgumentException if {@code streamSize} is
     *         less than zero
     * @since 1.8
     */
    @Override
    public LongStream longs(long streamSize) {
        return AbstractSpliteratorGenerator.longs(this, streamSize);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code long}
     * values.
     *
     * <p>A pseudorandom {@code long} value is generated as if it's the result
     * of calling the method {@link #nextLong()}.
     *
     * @implNote This method is implemented to be equivalent to {@code
     * longs(Long.MAX_VALUE)}.
     *
     * @return a stream of pseudorandom {@code long} values
     * @since 1.8
     */
    @Override
    public LongStream longs() {
        return AbstractSpliteratorGenerator.longs(this);
    }

    /**
     * Returns a stream producing the given {@code streamSize} number of
     * pseudorandom {@code long}, each conforming to the given origin
     * (inclusive) and bound (exclusive).
     *
     * <p>A pseudorandom {@code long} value is generated as if it's the result
     * of calling the following method with the origin and bound:
     * <pre> {@code
     * long nextLong(long origin, long bound) {
     *   long r = nextLong();
     *   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 = nextLong() >>> 1) // retry
     *         ;
     *     r += origin;
     *   }
     *   else {              // range not representable as long
     *     while (r < origin || r >= bound)
     *       r = nextLong();
     *   }
     *   return r;
     * }}</pre>
     *
     * @param streamSize the number of values to generate
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code long} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException if {@code streamSize} is
     *         less than zero, or {@code randomNumberOrigin}
     *         is greater than or equal to {@code randomNumberBound}
     * @since 1.8
     */
    @Override
    public LongStream longs(long streamSize, long randomNumberOrigin, long randomNumberBound) {
        return AbstractSpliteratorGenerator.longs(this, streamSize, randomNumberOrigin, randomNumberBound);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code
     * long} values, each conforming to the given origin (inclusive) and bound
     * (exclusive).
     *
     * <p>A pseudorandom {@code long} value is generated as if it's the result
     * of calling the following method with the origin and bound:
     * <pre> {@code
     * long nextLong(long origin, long bound) {
     *   long r = nextLong();
     *   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 = nextLong() >>> 1) // retry
     *         ;
     *     r += origin;
     *   }
     *   else {              // range not representable as long
     *     while (r < origin || r >= bound)
     *       r = nextLong();
     *   }
     *   return r;
     * }}</pre>
     *
     * @implNote This method is implemented to be equivalent to {@code
     * longs(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)}.
     *
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code long} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException if {@code randomNumberOrigin}
     *         is greater than or equal to {@code randomNumberBound}
     * @since 1.8
     */
    @Override
    public LongStream longs(long randomNumberOrigin, long randomNumberBound) {
        return AbstractSpliteratorGenerator.longs(this, randomNumberOrigin, randomNumberBound);
    }

    /**
     * Returns a stream producing the given {@code streamSize} number of
     * pseudorandom {@code double} values, each between zero
     * (inclusive) and one (exclusive).
     *
     * <p>A pseudorandom {@code double} value is generated as if it's the result
     * of calling the method {@link #nextDouble()}.
     *
     * @param streamSize the number of values to generate
     * @return a stream of {@code double} values
     * @throws IllegalArgumentException if {@code streamSize} is
     *         less than zero
     * @since 1.8
     */
    @Override
    public DoubleStream doubles(long streamSize) {
        return AbstractSpliteratorGenerator.doubles(this, streamSize);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code
     * double} values, each between zero (inclusive) and one
     * (exclusive).
     *
     * <p>A pseudorandom {@code double} value is generated as if it's the result
     * of calling the method {@link #nextDouble()}.
     *
     * @implNote This method is implemented to be equivalent to {@code
     * doubles(Long.MAX_VALUE)}.
     *
     * @return a stream of pseudorandom {@code double} values
     * @since 1.8
     */
    @Override
    public DoubleStream doubles() {
        return AbstractSpliteratorGenerator.doubles(this);
    }

    /**
     * Returns a stream producing the given {@code streamSize} number of
     * pseudorandom {@code double} values, each conforming to the given origin
     * (inclusive) and bound (exclusive).
     *
     * @param streamSize the number of values to generate
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code double} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException {@inheritDoc}
     * @since 1.8
     */
    @Override
    public DoubleStream doubles(long streamSize, double randomNumberOrigin, double randomNumberBound) {
        return AbstractSpliteratorGenerator.doubles(this, streamSize, randomNumberOrigin, randomNumberBound);
    }

    /**
     * Returns an effectively unlimited stream of pseudorandom {@code
     * double} values, each conforming to the given origin (inclusive) and bound
     * (exclusive).

     * @implNote This method is implemented to be equivalent to {@code
     * doubles(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)}.
     *
     * @param randomNumberOrigin the origin (inclusive) of each random value
     * @param randomNumberBound the bound (exclusive) of each random value
     * @return a stream of pseudorandom {@code double} values,
     *         each with the given origin (inclusive) and bound (exclusive)
     * @throws IllegalArgumentException {@inheritDoc}
     * @since 1.8
     */
    @Override
    public DoubleStream doubles(double randomNumberOrigin, double randomNumberBound) {
        return AbstractSpliteratorGenerator.doubles(this, randomNumberOrigin, randomNumberBound);
    }
}