java.lang.Objectjava.util.Random
public class Random
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
2
, Section 3.2.1.)
If two instances of 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
Random.
Random
.
Java implementations must use all the algorithms shown here for the class
Random,
Random
,
for the sake of absolute portability of Java code. However, subclasses of class
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 Random use a protected utility method that on each invocation can supply up to 32 pseudorandomly generated bits.
Many applications will find the
random
method
Math.random()
in class Math
simpler to use.
Constructor Summary | |
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Random
() Creates a new random number generator. |
|
Random
(long seed) Creates a new random number generator using a single long ![]() ![]() |
Method Summary | |
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protected int |
next
(int bits) Generates the next pseudorandom number. |
boolean |
nextBoolean
() Returns the next pseudorandom, uniformly distributed boolean 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 |
nextDouble
() Returns the next pseudorandom, uniformly distributed double value between 0.0 and 1.0 from this random number generator's sequence. |
float |
nextFloat
() Returns the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence. |
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. |
int |
nextInt
() Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence. |
int |
nextInt
(int n) Returns a pseudorandom, uniformly distributed int 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 long value from this random number generator's sequence. |
void |
setSeed
(long seed) Sets the seed of this random number generator using a single long 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 new Random(seed) is equivalent to:
Creates a new random number generator using a single long seed:
Random rnd = new Random(); rnd.setSeed(seed);
public Random(long seed) { setSeed(seed); }
Method Detail |
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public void setSeed(long seed)
(seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)
and clearing the haveNextNextGaussian flag used by
nextGaussian()
.
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synchronized public void setSeed(long seed) { this.seed = (seed ^ 0x5DEECE66DL) & ((1L< < 48) - 1); haveNextNextGaussian = false; }
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)
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.
1
.
The method
next
is implemented by class
Random
by atomically updating the seed to
as follows:
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(seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)
synchronized protected int next(int bits) { seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L<< 48) - 1); return (int)(seed >>> (48 - bits)); }and returning
(int)(seed >>> (48 - bits)).
public void nextBytes(byte[] bytes)
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()
The method
nextInt
is implemented by class
Random
as
if by:
follows:
public int nextInt() { return next(32); }
public int nextInt(int n)
public int nextInt(int n) { if (n< 0); return val; }<= 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)) >> <=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
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.
public long nextLong()
All 2
64
possible
long
values are produced with (approximately) equal probability.
The method
nextLong
is implemented by class
Random
as
if by:
follows:
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.
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public long nextLong() { return ((long)next(32)< < 32) + next(32); }
public boolean nextBoolean()
The method
nextBoolean
is implemented by class
Random
as
if by:
follows:
public boolean nextBoolean(){ return
{returnnext(1) !=0; }
0;}
public float nextFloat()
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 2 24 possible float values of the form m x  2 -24 , where m is a positive integer less than 2 24 , are produced with (approximately) equal probability.
The method
nextFloat
is implemented by class
Random
as
if by:
follows:
public float nextFloat() { return next(24) / ((float)(1 << 24)); }
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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:
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 next(30) / ((float)(1< < 30));<< 30));
public double nextDouble()
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.
All 2
53
possible
float
values of the form
m x
2
-53
, where
m
is a positive integer less than 2
53
, are produced with (approximately) equal probability.
The method
nextDouble
is implemented by class
Random
as
if by:
follows:
public double nextDouble() { return (((long)next(26) << 27) + next(27)) / (double)(1L << 53); }
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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
or
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:
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 (((long)next(27)< < 27) + next(27)) / (double)(1L < < 54);<< 27) + next(27)) / (double)(1L << 54);
public double nextGaussian()
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,
1.0
,
is pseudorandomly generated and returned.
The method
nextGaussian
is implemented by class
Random
as if by
a threadsafe version of
the following:
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 , Volumeprivate double nextNextGaussian; private boolean haveNextNextGaussian = false;
synchronizedpublic 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; } }