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  * 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

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  * 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)

     };

     /**

      * Reconstitute the {@code Random} instance from a stream (that is,

      * deserialize it).

      */

     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.

      */

     synchronized private 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.putObjectVolatile(this, seedOffset, new AtomicLong(seedVal));

     }

 }