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public class Random extends Object implements Serializable
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, The Art of Computer Programming, Volume 3, Section 3.2.1.)
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.
Constructor Summary | |
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Random() Creates a new random number generator. |
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Random(long seed) Creates a new random number generator using a single seed. |
Method Summary | |
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protected int |
next(int bits) Generates the next pseudorandom number. |
boolean |
Returns the next pseudorandom, uniformly distributed value from this random number generator's sequence. |
void |
nextBytes(byte[] bytes) Generates random bytes and places them into a user-supplied byte array. |
double |
Returns the next pseudorandom, uniformly distributed value between and from this random number generator's sequence. |
float |
Returns the next pseudorandom, uniformly distributed value between and from this random number generator's sequence. |
double |
Returns the next pseudorandom, Gaussian ("normally") distributed value with mean and standard deviation from this random number generator's sequence. |
int |
nextInt() Returns the next pseudorandom, uniformly distributed value from this random number generator's sequence. |
int |
nextInt(int n) Returns a pseudorandom, uniformly distributed value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence. |
long |
nextLong() Returns the next pseudorandom, uniformly distributed value from this random number generator's sequence. |
void |
setSeed(long seed) Sets the seed of this random number generator using a single seed. |
Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public Random()
public Random(long seed)
The invocation {@code new Random(seed)} is equivalent to:
{@code Random rnd = new Random(); rnd.setSeed(seed);}
seed
- the initial seedMethod Detail |
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protected int next(int bits)
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.
bits
- random bitspublic boolean nextBoolean()
The method {@code nextBoolean} is implemented by class {@code Random} as if by:
{@code public boolean nextBoolean() { return next(1) != 0; }}
public void nextBytes(byte[] bytes)
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; }}
bytes
- the byte array to fill with random bytespublic double nextDouble()
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.]
public float nextFloat()
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.]
public synchronized double nextGaussian()
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}.
public int nextInt()
The method {@code nextInt} is implemented by class {@code Random} as if by:
{@code public int nextInt() { return next(32); }}
public int nextInt(int n)
{@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.
n
- the bound on the random number to be returned. Must be
positive.public long nextLong()
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.
public synchronized void setSeed(long seed)
{@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.
seed
- the initial seed
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