The invocation new Random(seed) is equivalent to:

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

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)

(int)(seed >>> (48 - bits)).

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

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

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;}

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);

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));

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;
   }
 }}

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

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

 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 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.

n	the bound on the random number to be returned. Must be positive.
return	the next pseudorandom, uniformly distributed int value between 0 (inclusive) and n (exclusive) from this random number generator's sequence
Throws	IllegalArgumentException: if n is not positive
since	1.2

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

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

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

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.

seed	the initial seed