+ * 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. + *
+ * 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. + *
+ * Many applications will find the method {@link Math#random} simpler to use. + * + *
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. + * + *
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 long 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 synchronized long seedUniquifier() { + // L'Ecuyer, "Tables of Linear Congruential Generators of + // Different Sizes and Good Lattice Structure", 1999 + long current = seedUniquifier; + long next = current * 181783497276652981L; + seedUniquifier = next; + return next; + } + + private static long seedUniquifier = 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}. + * + *
The invocation {@code new Random(seed)} is equivalent to: + *
{@code
+ * Random rnd = new Random();
+ * rnd.setSeed(seed);}
+ *
+ * @param seed the initial seed
+ * @see #setSeed(long)
+ */
+ public Random(long seed) {
+ this.seed = 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
+ * {@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}
+ * and clearing the {@code haveNextNextGaussian} flag used by {@link
+ * #nextGaussian}.
+ *
+ * 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 = initialScramble(seed); + haveNextNextGaussian = false; + } + + /** + * Generates the next pseudorandom number. Subclasses should + * override this, as this is used by all other methods. + * + *
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 + *
{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}
+ * and returning
+ * {@code (int)(seed >>> (48 - bits))}.
+ *
+ * This is a linear congruential pseudorandom number generator, as
+ * defined by D. H. Lehmer and described by Donald E. Knuth in
+ * The Art of Computer Programming, Volume 3:
+ * Seminumerical Algorithms, section 3.2.1.
+ *
+ * @param bits random bits
+ * @return the next pseudorandom value from this random number
+ * generator's sequence
+ * @since 1.1
+ */
+ protected synchronized int next(int bits) {
+ long oldseed, nextseed;
+ long seed = this.seed;
+ oldseed = seed;
+ nextseed = (oldseed * multiplier + addend) & mask;
+ this.seed = 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.
+ *
+ * The method {@code nextBytes} is implemented by class {@code Random} + * as if by: + *
{@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;
+ * }}
+ *
+ * @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 232
+ * possible {@code int} values are produced with
+ * (approximately) equal probability.
+ *
+ * The method {@code nextInt} is implemented by class {@code Random} + * as if by: + *
{@code
+ * public int nextInt() {
+ * return next(32);
+ * }}
+ *
+ * @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:
+ * {@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;
+ * }}
+ *
+ * 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. + *
+ * 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. + *
+ * 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 low-order 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. + * + *
The method {@code nextLong} is implemented by class {@code Random} + * as if by: + *
{@code
+ * public long nextLong() {
+ * return ((long)next(32) << 32) + next(32);
+ * }}
+ *
+ * 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.
+ *
+ * The method {@code nextBoolean} is implemented by class {@code Random} + * as if by: + *
{@code
+ * public boolean nextBoolean() {
+ * return next(1) != 0;
+ * }}
+ *
+ * @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.
+ *
+ * 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 224 possible {@code float} values + * of the form m x 2-24, where m is a positive + * integer less than 224 , are + * produced with (approximately) equal probability. + * + *
The method {@code nextFloat} is implemented by class {@code Random} + * as if by: + *
{@code
+ * public float nextFloat() {
+ * return next(24) / ((float)(1 << 24));
+ * }}
+ *
+ * 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.
+ * [In early versions of Java, the result was incorrectly calculated as: + *
{@code
+ * return next(30) / ((float)(1 << 30));}
+ * 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.
+ *
+ * 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. + * + *
The method {@code nextDouble} is implemented by class {@code Random} + * as if by: + *
{@code
+ * public double nextDouble() {
+ * return (((long)next(26) << 27) + next(27))
+ * / (double)(1L << 53);
+ * }}
+ *
+ * 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. + *
[In early versions of Java, the result was incorrectly calculated as: + *
{@code
+ * return (((long)next(27) << 27) + next(27))
+ * / (double)(1L << 54);}
+ * 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.
+ * + * 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. + * + *
The method {@code nextGaussian} is implemented by class + * {@code Random} as if by a threadsafe version of the following: + *
{@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;
+ * }
+ * }}
+ * This uses the polar method of G. E. P. Box, M. E. Muller, and
+ * G. Marsaglia, as described by Donald E. Knuth in The Art of
+ * Computer Programming, Volume 3: Seminumerical Algorithms,
+ * 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 = Math.sqrt(-2 * Math.log(s)/s);
+ nextNextGaussian = v2 * multiplier;
+ haveNextNextGaussian = true;
+ return v1 * multiplier;
+ }
+ }
+}