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 * 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

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package java.util;

import java.io.*;

import java.util.concurrent.atomic.AtomicLong;

import sun.misc.Unsafe;

/**

 * An instance of this class is used to generate a stream of

 * pseudorandom numbers. The class uses a 48-bit seed, which is

 * modified using a linear congruential formula. (See Donald Knuth,

 * <i>The Art of Computer Programming, Volume 2</i>, 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

 */

public

class Random implements java.io.Serializable {

    /** use serialVersionUID from JDK 1.1 for interoperability */

    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;

    /**

     * 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 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 * 181783497276652981L;

            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}.

     *

     * <p>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) {

        this.seed = new AtomicLong(initialScramble(seed));

    }

    private static long initialScramble(long seed) {

        return (seed ^ multiplier) & mask;

    }

    /**

     * Sets the seed of this random number generator using a single

     * {@code long} seed. The general contract of {@code setSeed} is

     * that it alters the state of this random number generator object

     * so as to be in exactly the same state as if it had just been

     * created with the argument {@code seed} as a seed. The method

     * {@code setSeed} is implemented by class {@code Random} by

     * atomically updating the seed to

     *  <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre>

     * and clearing the {@code haveNextNextGaussian} flag used by {@link

     * #nextGaussian}.

     *

     * <p>The implementation of {@code setSeed} by class {@code Random}

     * happens to use only 48 bits of the given seed. In general, however,

     * an overriding method may use all 64 bits of the {@code long}

     * argument as a seed value.

     *

     * @param seed the initial seed

     */

    synchronized public void setSeed(long seed) {

        this.seed.set(initialScramble(seed));

        haveNextNextGaussian = false;

    }

    /**

     * Generates the next pseudorandom number. Subclasses should

     * override this, as this is used by all other methods.

     *

     * <p>The general contract of {@code next} is that it returns an

     * {@code int} value and 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}. The method {@code next} is

     * implemented by class {@code Random} by atomically updating the seed to

     *  <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre>

     * and returning

     *  <pre>{@code (int)(seed >>> (48 - bits))}.</pre>

     *

     * This is a linear congruential pseudorandom number generator, as

     * defined by D. H. Lehmer and described by Donald E. Knuth in

     * <i>The Art of Computer Programming,</i> Volume 3:

     * <i>Seminumerical Algorithms</i>, 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.

     *

     * <p>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

     */

    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<font size="-1"><sup>32

     * </sup></font> possible {@code int} values are produced with

     * (approximately) equal probability.

     *

     * <p>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

     */

    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 n} possible

     * {@code int} values are produced with (approximately) equal

     * probability.  The method {@code nextInt(int n)} is implemented by

     * class {@code Random} as if by:

     *  <pre> {@code

     * public int nextInt(int n) {

     *   if (n <= 0)

     *     throw new IllegalArgumentException("n must be positive");

     *

     *   if ((n & -n) == n)  // i.e., n is a power of 2

     *     return (int)((n * (long)next(31)) >> 31);

     *

     *   int bits, val;

     *   do {

     *       bits = next(31);

     *       val = bits % n;

     *   } while (bits - val + (n-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 n the bound on the random number to be returned.  Must be

     *        positive.

     * @return the next pseudorandom, uniformly distributed {@code int}

     *         value between {@code 0} (inclusive) and {@code n} (exclusive)

     *         from this random number generator's sequence

     * @throws IllegalArgumentException if n is not positive

     * @since 1.2

     */

    public int nextInt(int n) {

        if (n <= 0)

            throw new IllegalArgumentException("n must be positive");

        if ((n & -n) == n)  // i.e., n is a power of 2

            return (int)((n * (long)next(31)) >> 31);

        int bits, val;

        do {

            bits = next(31);

            val = bits % n;

        } while (bits - val + (n-1) < 0);

        return val;

    }

    /**

     * 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.

     *

     * <p>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

     */

    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.

     *

     * <p>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

     */

    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<font

     * size="-1"><sup>24</sup></font> possible {@code float} values

     * of the form <i>m&nbsp;x&nbsp</i>2<font

     * size="-1"><sup>-24</sup></font>, where <i>m</i> is a positive

     * integer less than 2<font size="-1"><sup>24</sup> </font>, are

     * produced with (approximately) equal probability.

     *

     * <p>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 0.0} and {@code 1.0} from this

     *         random number generator's sequence

     */

    public float nextFloat() {

        return next(24) / ((float)(1 << 24));

    }

    /**

     * 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.

     *

     * <p>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

     */

    public double nextDouble() {

        return (((long)(next(26)) << 27) + next(27))

            / (double)(1L << 53);

    }

    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.

     *

     * <p>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 <i>The Art of

     * Computer Programming</i>, Volume 3: <i>Seminumerical Algorithms</i>,

     * 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

     */

    synchronized public double nextGaussian() {

        // See Knuth, ACP, 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

     */

    private static final ObjectStreamField[] serialPersistentFields = {

        new ObjectStreamField("seed", Long.TYPE),

        new ObjectStreamField("nextNextGaussian", Double.TYPE),

        new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE)

    };