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 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 method Math.random()
simpler to use.
Instances of java.util.Random
are threadsafe. However, the concurrent use of the same java.util.Random
instance across threads may encounter contention and consequent poor performance. Consider instead using ThreadLocalRandom
in multithreaded designs.
Instances of java.util.Random
are not cryptographically secure. Consider instead using SecureRandom
to get a cryptographically secure pseudo-random number generator for use by security-sensitive applications.
public Random()
Creates a new random number generator. This constructor sets the seed of the random number generator to a value very likely to be distinct from any other invocation of this constructor.
public Random(long seed)
Creates a new random number generator using a single 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)
public void setSeed(long seed)
Sets the seed of this random number generator using a single 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)
Generates the next pseudorandom number. Subclasses should override this, as this is used by all other methods.
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)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 bitspublic void nextBytes(byte[] bytes)
Generates random bytes and places them into a user-supplied byte array. The number of random bytes produced is equal to the length of the byte array.
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 bytesNullPointerException
- if the byte array is nullpublic int nextInt()
Returns the next pseudorandom, uniformly distributed 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 232 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 bound)
Returns a pseudorandom, uniformly distributed 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 bound
possible int
values are produced with (approximately) equal probability. The method nextInt(int bound)
is implemented by class Random
as if by:
public int nextInt(int bound) { if (bound <= 0) throw new IllegalArgumentException("bound must be positive"); if ((bound & -bound) == bound) // i.e., bound is a power of 2 return (int)((bound * (long)next(31)) >> 31); int bits, val; do { bits = next(31); val = bits % bound; } while (bits - val + (bound-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.
bound
- the upper bound (exclusive). Must be positive.int
value between zero (inclusive) and bound
(exclusive) from this random number generator's sequenceIllegalArgumentException
- if bound is not positivepublic long nextLong()
Returns the next pseudorandom, uniformly distributed 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()
Returns the next pseudorandom, uniformly distributed 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()
Returns the next pseudorandom, uniformly distributed 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 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));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.]
float
value between 0.0
and 1.0
from this random number generator's sequencepublic double nextDouble()
Returns the next pseudorandom, uniformly distributed 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 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.]
double
value between 0.0
and 1.0
from this random number generator's sequenceMath.random()
public 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.
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 sequencepublic IntStream ints(long streamSize)
Returns a stream producing the given streamSize
number of pseudorandom int
values.
A pseudorandom int
value is generated as if it's the result of calling the method nextInt()
.
streamSize
- the number of values to generateint
valuesIllegalArgumentException
- if streamSize
is less than zeropublic IntStream ints()
Returns an effectively unlimited stream of pseudorandom int
values.
A pseudorandom int
value is generated as if it's the result of calling the method nextInt()
.
ints(Long.MAX_VALUE)
.int
valuespublic IntStream ints(long streamSize, int randomNumberOrigin, int randomNumberBound)
Returns a stream producing the given streamSize
number of pseudorandom int
values, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom int
value is generated as if it's the result of calling the following method with the origin and bound:
int nextInt(int origin, int bound) { int n = bound - origin; if (n > 0) { return nextInt(n) + origin; } else { // range not representable as int int r; do { r = nextInt(); } while (r < origin || r >= bound); return r; } }
streamSize
- the number of values to generaterandomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valueint
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if streamSize
is less than zero, or randomNumberOrigin
is greater than or equal to randomNumberBound
public IntStream ints(int randomNumberOrigin, int randomNumberBound)
Returns an effectively unlimited stream of pseudorandom int
values, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom int
value is generated as if it's the result of calling the following method with the origin and bound:
int nextInt(int origin, int bound) { int n = bound - origin; if (n > 0) { return nextInt(n) + origin; } else { // range not representable as int int r; do { r = nextInt(); } while (r < origin || r >= bound); return r; } }
ints(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)
.randomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valueint
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if randomNumberOrigin
is greater than or equal to randomNumberBound
public LongStream longs(long streamSize)
Returns a stream producing the given streamSize
number of pseudorandom long
values.
A pseudorandom long
value is generated as if it's the result of calling the method nextLong()
.
streamSize
- the number of values to generatelong
valuesIllegalArgumentException
- if streamSize
is less than zeropublic LongStream longs()
Returns an effectively unlimited stream of pseudorandom long
values.
A pseudorandom long
value is generated as if it's the result of calling the method nextLong()
.
longs(Long.MAX_VALUE)
.long
valuespublic LongStream longs(long streamSize, long randomNumberOrigin, long randomNumberBound)
Returns a stream producing the given streamSize
number of pseudorandom long
, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom long
value is generated as if it's the result of calling the following method with the origin and bound:
long nextLong(long origin, long bound) { long r = nextLong(); long n = bound - origin, m = n - 1; if ((n & m) == 0L) // power of two r = (r & m) + origin; else if (n > 0L) { // reject over-represented candidates for (long u = r >>> 1; // ensure nonnegative u + m - (r = u % n) < 0L; // rejection check u = nextLong() >>> 1) // retry ; r += origin; } else { // range not representable as long while (r < origin || r >= bound) r = nextLong(); } return r; }
streamSize
- the number of values to generaterandomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valuelong
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if streamSize
is less than zero, or randomNumberOrigin
is greater than or equal to randomNumberBound
public LongStream longs(long randomNumberOrigin, long randomNumberBound)
Returns an effectively unlimited stream of pseudorandom long
values, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom long
value is generated as if it's the result of calling the following method with the origin and bound:
long nextLong(long origin, long bound) { long r = nextLong(); long n = bound - origin, m = n - 1; if ((n & m) == 0L) // power of two r = (r & m) + origin; else if (n > 0L) { // reject over-represented candidates for (long u = r >>> 1; // ensure nonnegative u + m - (r = u % n) < 0L; // rejection check u = nextLong() >>> 1) // retry ; r += origin; } else { // range not representable as long while (r < origin || r >= bound) r = nextLong(); } return r; }
longs(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)
.randomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valuelong
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if randomNumberOrigin
is greater than or equal to randomNumberBound
public DoubleStream doubles(long streamSize)
Returns a stream producing the given streamSize
number of pseudorandom double
values, each between zero (inclusive) and one (exclusive).
A pseudorandom double
value is generated as if it's the result of calling the method nextDouble()
.
streamSize
- the number of values to generatedouble
valuesIllegalArgumentException
- if streamSize
is less than zeropublic DoubleStream doubles()
Returns an effectively unlimited stream of pseudorandom double
values, each between zero (inclusive) and one (exclusive).
A pseudorandom double
value is generated as if it's the result of calling the method nextDouble()
.
doubles(Long.MAX_VALUE)
.double
valuespublic DoubleStream doubles(long streamSize, double randomNumberOrigin, double randomNumberBound)
Returns a stream producing the given streamSize
number of pseudorandom double
values, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom double
value is generated as if it's the result of calling the following method with the origin and bound:
double nextDouble(double origin, double bound) { double r = nextDouble(); r = r * (bound - origin) + origin; if (r >= bound) // correct for rounding r = Math.nextDown(bound); return r; }
streamSize
- the number of values to generaterandomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valuedouble
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if streamSize
is less than zeroIllegalArgumentException
- if randomNumberOrigin
is greater than or equal to randomNumberBound
public DoubleStream doubles(double randomNumberOrigin, double randomNumberBound)
Returns an effectively unlimited stream of pseudorandom double
values, each conforming to the given origin (inclusive) and bound (exclusive).
A pseudorandom double
value is generated as if it's the result of calling the following method with the origin and bound:
double nextDouble(double origin, double bound) { double r = nextDouble(); r = r * (bound - origin) + origin; if (r >= bound) // correct for rounding r = Math.nextDown(bound); return r; }
doubles(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound)
.randomNumberOrigin
- the origin (inclusive) of each random valuerandomNumberBound
- the bound (exclusive) of each random valuedouble
values, each with the given origin (inclusive) and bound (exclusive)IllegalArgumentException
- if randomNumberOrigin
is greater than or equal to randomNumberBound
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