Class Random

public Random()

public Random(long seed)

Creates a new random number generator using a single long seed. The seed is the initial value of the internal state of the pseudorandom number generator which is maintained by method next(int).

The invocation new Random(seed) is equivalent to:

Random rnd = new Random();
 rnd.setSeed(seed);

public void setSeed(long seed)

Sets the seed of this random number generator using a single long seed. The general contract of 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 seed as a seed. The method setSeed is implemented by class Random by atomically updating the seed to

(seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)

and clearing the haveNextNextGaussian flag used by nextGaussian().

The implementation of setSeed by class Random happens to use only 48 bits of the given seed. In general, however, an overriding method may use all 64 bits of the long argument as a seed value.

protected int next(int bits)

Generates the next pseudorandom number. Subclasses should override this, as this is used by all other methods.

The general contract of next is that it returns an int value and if the argument bits is between 1 and 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 0 or 1. The method next is implemented by class Random by atomically updating the seed to

(seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)

and returning

(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 2: Seminumerical Algorithms, section 3.2.1.

public void nextBytes(byte[] bytes)

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 nextBytes is implemented by class Random as if by:

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;
 }

public int nextInt()

Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence. The general contract of nextInt is that one int value is pseudorandomly generated and returned. All 2³² possible int values are produced with (approximately) equal probability.

The method nextInt is implemented by class Random as if by:

public int nextInt() {
   return next(32);
 }

public int nextInt(int bound)

Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence. The general contract of nextInt is that one int value in the specified range is pseudorandomly generated and returned. All bound possible int values are produced with (approximately) equal probability. The method nextInt(int bound) is implemented by class Random as if by:

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;
 }

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 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.

public long nextLong()

Returns the next pseudorandom, uniformly distributed long value from this random number generator's sequence. The general contract of nextLong is that one long value is pseudorandomly generated and returned.

The method nextLong is implemented by class Random as if by:

public long nextLong() {
   return ((long)next(32) << 32) + next(32);
 }

Because class Random uses a seed with only 48 bits, this algorithm will not return all possible long values.

public boolean nextBoolean()

Returns the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence. The general contract of nextBoolean is that one boolean value is pseudorandomly generated and returned. The values true and false are produced with (approximately) equal probability.

The method nextBoolean is implemented by class Random as if by:

public boolean nextBoolean() {
   return next(1) != 0;
 }

public float nextFloat()

Returns the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence.

The general contract of nextFloat is that one float value, chosen (approximately) uniformly from the range 0.0f (inclusive) to 1.0f (exclusive), is pseudorandomly generated and returned. All 2²⁴ possible 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 nextFloat is implemented by class Random as if by:

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 float values from the stated range with perfect uniformity.

[In early versions of Java, the result was incorrectly calculated as:

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.]

public double nextDouble()

Returns the next pseudorandom, uniformly distributed double value between 0.0 and 1.0 from this random number generator's sequence.

The general contract of nextDouble is that one double value, chosen (approximately) uniformly from the range 0.0d (inclusive) to 1.0d (exclusive), is pseudorandomly generated and returned.

The method nextDouble is implemented by class Random as if by:

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 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 double values from the stated range with perfect uniformity.

[In early versions of Java, the result was incorrectly calculated as:

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.]

public double nextGaussian()

Returns the next pseudorandom, Gaussian ("normally") distributed double value with mean 0.0 and standard deviation 1.0 from this random number generator's sequence.

The general contract of nextGaussian is that one double value, chosen from (approximately) the usual normal distribution with mean 0.0 and standard deviation 1.0, is pseudorandomly generated and returned.

The method nextGaussian is implemented by class Random as if by a threadsafe version of the following:

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 2: 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 StrictMath.log and one call to StrictMath.sqrt.

public IntStream ints(long streamSize)

Returns a stream producing the given streamSize number of pseudorandom int values.

A pseudorandom int value is generated as if it's the result of calling the method nextInt().

public IntStream ints()

Returns an effectively unlimited stream of pseudorandom int values.

A pseudorandom int value is generated as if it's the result of calling the method nextInt().

public IntStream ints(long streamSize,
                      int randomNumberOrigin,
                      int randomNumberBound)

Returns a stream producing the given streamSize number of pseudorandom int values, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom int value is generated as if it's the result of calling the following method with the origin and bound:

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;
   }
 }

public IntStream ints(int randomNumberOrigin,
                      int randomNumberBound)

Returns an effectively unlimited stream of pseudorandom int values, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom int value is generated as if it's the result of calling the following method with the origin and bound:

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;
   }
 }

public LongStream longs(long streamSize)

Returns a stream producing the given streamSize number of pseudorandom long values.

A pseudorandom long value is generated as if it's the result of calling the method nextLong().

public LongStream longs()

Returns an effectively unlimited stream of pseudorandom long values.

A pseudorandom long value is generated as if it's the result of calling the method nextLong().

public LongStream longs(long streamSize,
                        long randomNumberOrigin,
                        long randomNumberBound)

Returns a stream producing the given streamSize number of pseudorandom long, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom long value is generated as if it's the result of calling the following method with the origin and bound:

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;
 }

public LongStream longs(long randomNumberOrigin,
                        long randomNumberBound)

Returns an effectively unlimited stream of pseudorandom long values, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom long value is generated as if it's the result of calling the following method with the origin and bound:

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;
 }

public DoubleStream doubles(long streamSize)

Returns a stream producing the given streamSize number of pseudorandom double values, each between zero (inclusive) and one (exclusive).

A pseudorandom double value is generated as if it's the result of calling the method nextDouble().

public DoubleStream doubles()

Returns an effectively unlimited stream of pseudorandom double values, each between zero (inclusive) and one (exclusive).

A pseudorandom double value is generated as if it's the result of calling the method nextDouble().

public DoubleStream doubles(long streamSize,
                            double randomNumberOrigin,
                            double randomNumberBound)

Returns a stream producing the given streamSize number of pseudorandom double values, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom double value is generated as if it's the result of calling the following method with the origin and bound:

double nextDouble(double origin, double bound) {
   double r = nextDouble();
   r = r * (bound - origin) + origin;
   if (r >= bound) // correct for rounding
     r = Math.nextDown(bound);
   return r;
 }

public DoubleStream doubles(double randomNumberOrigin,
                            double randomNumberBound)

Returns an effectively unlimited stream of pseudorandom double values, each conforming to the given origin (inclusive) and bound (exclusive).

A pseudorandom double value is generated as if it's the result of calling the following method with the origin and bound:

double nextDouble(double origin, double bound) {
   double r = nextDouble();
   r = r * (bound - origin) + origin;
   if (r >= bound) // correct for rounding
     r = Math.nextDown(bound);
   return r;
 }