
Java™ Platform Standard Ed. 6 

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java.lang.Object java.util.Random
public class Random
An instance of this class is used to generate a stream of pseudorandom numbers. The class uses a 48bit 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 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
. Java implementations must use all the algorithms
shown here for the class 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 method Math.random()
simpler to use.
Constructor Summary  

Random()
Creates a new random number generator. 

Random(long seed)
Creates a new random number generator using a single long seed. 
Method Summary  

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 usersupplied 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 

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 

public Random()
public Random(long seed)
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);
seed
 the initial seedsetSeed(long)
Method Detail 

public void setSeed(long seed)
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.
seed
 the initial seedprotected 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 loworder
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 3:
Seminumerical Algorithms, section 3.2.1.
bits
 random 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;
}
bytes
 the byte array to fill with random bytes
NullPointerException
 if the byte array is nullpublic int nextInt()
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 2^{32
} 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);
}
int
value from this random number generator's sequencepublic int nextInt(int n)
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 n
possible
int
values are produced with (approximately) equal
probability. The method nextInt(int n)
is implemented by
class Random
as if by:
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 + (n1) < 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 highorder bits from the underlying pseudorandom number generator. In the absence of special treatment, the correct number of loworder bits would be returned. Linear congruential pseudorandom number generators such as the one implemented by this class are known to have short periods in the sequence of values of their loworder 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.
int
value between 0
(inclusive) and n
(exclusive)
from this random number generator's sequence
IllegalArgumentException
 if n is not positivepublic long nextLong()
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.
long
value from this random number generator's sequencepublic boolean nextBoolean()
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;
}
boolean
value from this random number generator's
sequencepublic float nextFloat()
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 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:
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 floatingpoint numbers: it was slightly more likely that the
loworder bit of the significand would be 0 than that it would be 1.]
float
value between 0.0
and 1.0
from this
random number generator's sequencepublic double nextDouble()
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 floatingpoint numbers: it was three times as likely that the
loworder 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.]
double
value between 0.0
and 1.0
from this
random number generator's sequenceMath.random()
public double nextGaussian()
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 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 StrictMath.log
and one call to StrictMath.sqrt
.
double
value with mean 0.0
and
standard deviation 1.0
from this random number
generator's sequence

Java™ Platform Standard Ed. 6 

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