
Foundation 1.1.2  
PREV CLASS NEXT CLASS  FRAMES NO FRAMES  
SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 
java.lang.Object java.util.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 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. 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 random
method in
class Math
simpler to use.
Math.random()
,
Serialized FormConstructor 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()
Two Random objects created within the same millisecond will have the same sequence of random numbers.public Random() { this(System.currentTimeMillis()); }
System.currentTimeMillis()
public Random(long seed)
long
seed:
Used by method next to hold the state of the pseudorandom number generator.public Random(long seed) { setSeed(seed); }
seed
 the initial seed.setSeed(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 as follows:
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. Note: Although the seed value is an AtomicLong, this method must still be synchronized to ensure correct semantics of haveNextNextGaussian.synchronized public void setSeed(long seed) { this.seed = (seed ^ 0x5DEECE66DL) & ((1L << 48)  1); haveNextNextGaussian = false; }
seed
 the initial seed.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 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 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 2: Seminumerical Algorithms, section 3.2.1.synchronized protected int next(int bits) { seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48)  1); return (int)(seed >>> (48  bits)); }
bits
 random bits
public void nextBytes(byte[] bytes)
bytes
 the nonnull byte array in which to put the
random bytes.public 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 follows:
public int nextInt() { return next(32); }
int
value from this random number generator's sequence.public int nextInt(int n)
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.
IllegalArgumentException
 n is not positive.public 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. All 2^{64}
possible long values are produced with (approximately) equal
probability. The method nextLong is implemented by class
Random as follows:
public long nextLong() { return ((long)next(32) << 32) + next(32); }
long
value from this random number generator's sequence.public 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 follows:
public boolean nextBoolean() {return next(1) != 0;}
boolean
value from this random number generator's
sequence.public 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 follows:
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 or randomly chosen bits, then the algorithm shown would choose float values from the stated range with perfect uniformity.public float nextFloat() { return next(24) / ((float)(1 << 24)); }
[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 floatingpoint numbers: it was slightly more likely that the loworder bit of the significand would be 0 than that it would be 1.]return next(30) / ((float)(1 << 30));
float
value between 0.0
and 1.0
from this
random number generator's sequence.public 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. 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 follows:
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 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 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.]return (((long)next(27) << 27) + next(27)) / (double)(1L << 54);
double
value between 0.0
and
1.0
from this random number generator's sequence.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 follows:
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 Math.log and one call to Math.sqrt.synchronized 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 = Math.sqrt(2 * Math.log(s)/s); nextNextGaussian = v2 * multiplier; haveNextNextGaussian = true; return v1 * multiplier; } }
double
value with mean 0.0
and
standard deviation 1.0
from this random number
generator's sequence.

Foundation 1.1.2  
PREV CLASS NEXT CLASS  FRAMES NO FRAMES  
SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 