These classes and interfaces support the definition and use of "random generators", a term covering what have traditionally been called "random number generators" as well as generators of other sorts of randomly chosen values (eg. booleans). These classes and interfaces cover not only deterministic (pseudorandom) algorithms but also generators of values that use some "truly random" physical source (stochastic algorithms perhaps making use of thermal noise, for example, or quantum-mechanical effects).
The principal interface is
RandomGenerator, which provides
methods for requesting individual values of type
boolean chosen pseudorandomly
from a uniform distribution; methods for requesting values of type
double chosen pseudorandomly from a normal distribution or from an
exponential distribution; and methods for creating streams of values of type
double chosen pseudorandomly from a
uniform distribution (such streams are spliterator-based, allowing for
parallel processing of their elements). There are also static factory methods
for creating an instance of a specific random number generator algorithm
given its name.
The principal supporting class is
can be used to generate multiple random number generators for a specific
RandomGeneratorFactory also provides methods for
selecting random number generator algorithms. RandomGeneratorFactory
registers implementations of
RandomGenerator interface using the
service provider API.
An important subsidiary interface is
RandomGenerator.StreamableGenerator, which provides methods for
creating spliterator-based streams of
allowing for parallel processing of these objects using multiple threads.
Random, most implementations of
RandomGenerator are not thread-safe. The intent is that
instances should not be shared among threads; rather, each thread should have
its own random generator(s) to use. The various pseudorandom algorithms
provided by this package are designed so that multiple instances will (with
very high probability) behave as if statistically independent.
For many purposes, these are the only two interfaces that a consumer of
pseudorandom values will need. There are also some more specialized
interfaces that describe more specialized categories of random number
that have specific strategies for creating statistically independent instances.
Using the Random Number Generator InterfacesTo get started, an application should first create one instance of a generator class. Assume that the contents of the package
java.util.randomhas been imported:
Then one can choose a specific implementation by giving the name of a generator algorithm to the static method
RandomGenerator.of(java.lang.String), in which case the no-arguments constructor for that implementation is used:
For a single-threaded application, this is all that is needed. One can then invoke methods of
RandomGenerator g = RandomGenerator.of("L64X128MixRandom");
nextBoolean()to generate individual randomly chosen values. One can also use the methods
doubles()to create streams of randomly chosen values. The methods
nextExponential()draw floating-point values from nonuniform distributions.
For a multi-threaded application, one can repeat the preceding steps
to create additional RandomGenerators, but
often it is preferable to use methods of the one single initially
created generator to create others like it. (One reason is that some
generator algorithms, if asked to create a new set of generators all at
once, can make a special effort to ensure that the new generators are
statistically independent.) If the initial generator implements the
RandomGenerator.StreamableGenerator, then the method
rngs() can be used to
create a stream of generators. If this is a parallel stream, then it is
easy to get parallel execution by using the
map() method on the stream.
For a multi-threaded application that forks new threads dynamically,
another approach is to use an initial generator that implements the interface
RandomGenerator.SplittableGenerator, which is then considered to
"belong" to the initial thread for its exclusive use; then whenever any
thread needs to fork a new thread, it first uses the
split() method of its own
generator to create a new generator, which is then passed to the newly
created thread for exclusive use by that new thread.
Choosing a Random Number Generator Algorithm
There are three groups of random number generator algorithm provided in Java: the Legacy group, the LXM group, and the Xoroshiro/Xoshiro group.
The legacy group includes random number generators that existed
before JDK 17: Random, ThreadLocalRandom, SplittableRandom, and
SecureRandom. Random (LCG) is the weakest of the available algorithms, and it
is recommended that users migrate to newer algorithms. If an application
requires a random number generator algorithm that is cryptographically
secure, then it should continue to use an instance of the class
The algorithms in the LXM group are similar to each other. The parameters of each algorithm can be found in the algorithm name. The number after "L" indicates the number of state bits for the LCG subgenerator, and the number after "X" indicates the number of state bits for the XBG subgenerator. "Mix" indicates that the algorithm uses an 8-operation bit-mixing function; "StarStar" indicates use of a 3-operation bit-scrambler.
The algorithms in the Xoroshiro/Xoshiro group are more traditional algorithms (see David Blackman and Sebastiano Vigna, "Scrambled Linear Pseudorandom Number Generators," ACM Transactions on Mathematical Software, 2021); the number in the name indicates the number of state bits.
For applications (such as physical simulation, machine learning, and
games) that do not require a cryptographically secure algorithm, this package
provides multiple implementations of interface
provide trade-offs among speed, space, period, accidental correlation, and
For applications with no special requirements,
L64X128MixRandom has a good balance among speed, space,
and period, and is suitable for both single-threaded and multi-threaded
applications when used properly (a separate instance for each thread).
If the application uses only a single thread, then
Xoroshiro128PlusPlus is even smaller and faster, and
certainly has a sufficiently long period.
For an application running in a 32-bit hardware environment and using
only one thread or a small number of threads,
L32X64MixRandom may be a good
For an application that uses many threads that are allocated in one batch
at the start of the computation, either a "jumpable" generator such as
Xoshiro256PlusPlus may be used, or a "splittable"
generator such as
L64X256MixRandom may be used.
For an application that creates many threads dynamically, perhaps through
the use of spliterators, a "splittable" generator such as
recommended. If the number of generators created dynamically may
be very large (millions or more), then using generators such as
which use a 128-bit parameter rather than a 64-bit parameter for their LCG
subgenerator, will make it much less likely that two instances use the same
For an application that uses tuples of consecutively generated values, it
may be desirable to use a generator that is k-equidistributed such
that k is at least as large as the length of the tuples being
generated. The generator
L64X256MixRandom is provably
L64X1024MixRandom is provably
For applications that generate large permutations, it may be best to use
a generator whose period is much larger than the total number of possible
permutations; otherwise it will be impossible to generate some of the
intended permutations. For example, if the goal is to shuffle a deck of 52
cards, the number of possible permutations is 52! (52 factorial), which is
larger than 2225 (but smaller than 2226), so it may be
best to use a generator whose period at least 2256, such as
L128X1024MixRandom. (It is of course also necessary to
provide sufficiently many seed bits when the generator is initialized, or
else it will still be impossible to generate some of the intended
In addition, as another life-cycle phase, an algorithm may be deprecated. A deprecated algorithm is not recommended for use. If a required algorithm is deprecated, it may be removed in a future release. Due to advances in random number generator algorithm development and analysis, an algorithm may be deprecated during the lifetime of a particular Java SE release. Changing the deprecation status of an algorithm is not a specification change.
* ThreadLocalRandom can only be accessed via
Categories of Random Number Generator AlgorithmsHistorically, most pseudorandom generator algorithms have been based on some sort of finite-state machine with a single, large cycle of states; when it is necessary to have multiple threads use the same algorithm simultaneously, the usual technique is to arrange for each thread to traverse a different region of the state cycle. These regions may be doled out to threads by starting with a single initial state and then using a "jump function" that travels a long distance around the cycle (perhaps 264 steps or more); the jump function is applied repeatedly and sequentially, to identify widely spaced states that are then doled out, one to each thread, to serve as the initial state for the generator to be used by that thread. This strategy is supported by the interface
RandomGenerator.JumpableGenerator. Sometimes it is desirable to support two levels of jumping (by long distances and by really long distances); this strategy is supported by the interface
RandomGenerator.LeapableGenerator. In this package, implementations of this interface include "Xoroshiro128PlusPlus" and "Xoshiro256PlusPlus". There is also an interface
RandomGenerator.ArbitrarilyJumpableGeneratorfor algorithms that allow jumping along the state cycle by any user-specified distance; there are currently no implementations of this interface in this package.
A more recent category of "splittable" pseudorandom generator algorithms
uses a large family of state cycles and makes some attempt to ensure that
distinct instances use different state cycles; but even if two instances
"accidentally" use the same state cycle, they are highly likely to traverse
different regions parts of that shared state cycle. This strategy is
supported by the interface
In this package, implementations of this interface include
"L128X1024MixRandom"; note that the class
SplittableRandom also implements this interface.
The LXM Family of Random Number Generator AlgorithmsThe structure of the central nextLong (or nextInt) method of an LXM algorithm follows a suggestion in December 2017 by Sebastiano Vigna that using one Linear Congruential Generator (LCG) as a first subgenerator and one Xor-Based Generator (XBG) as a second subgenerator (rather than using two LCG subgenerators) would provide a longer period, superior equidistribution, scalability, and better quality. Each of the specific implementations here combines one of the best currently known XBG algorithms (xoroshiro128 or xoshiro256, described by Blackman and Vigna in "Scrambled Linear Pseudorandom Number Generators", ACM Transactions on Mathematical Software, 2021) with an LCG that uses one of the best currently known multipliers (found by a search for better multipliers in 2019 by Steele and Vigna, described in "Computationally Easy, Spectrally Good Multipliers for Congruential Pseudorandom Number Generators", Software: Practice and Experience (2021), doi:10.1002/spe.3030), and then applies either a mixing function identified by Doug Lea or or a simple scrambler proposed by Blackman and Vigna. Testing has confirmed that the LXM algorithm is far superior in quality to the SplitMix algorithm (2014) used by
SplittableRandom(see Steele and Vigna, "LXM: Better Splittable Pseudorandom Number Generators (and Almost as Fast)", Proc. 2021 ACM OOPSLA Conference). Each class with a name of the form
SomethingRandomuses some specific member of the LXM family of random number algorithms; "LXM" is short for "LCG, XBG, Mixer". Every LXM generator has two subgenerators; one is an LCG (Linear Congruential Generator) and the other is an XBG (Xor-Based Generator). Each output of an LXM generator is the result of combining state from the LCG with state from the XBG using a Mixing function (and then the state of the LCG and the state of the XBG are advanced).
The LCG subgenerator has an update step of the form
s = m*s + a,
a are all binary integers of the same
size, each having p bits;
s is the mutable state, the
m is fixed (the same for all instances of a class) and the
a is a parameter (a final field of the instance). The
a is required to be odd (this allows the LCG to have the
maximal period, namely 2p); therefore there are
2p−1 distinct choices of parameter. (When the size of
s is 128 bits, then we use the name "
sh" below to refer to
the high half of
s, that is, the high-order 64 bits of
The XBG subgenerator can in principle be any one of a wide variety
of XBG algorithms; in this package it is always either
xoroshiro1024, in each
case without any final scrambler (such as "+" or "**") because LXM uses
a separate Mixer later in the process. The XBG state consists of
some fixed number of
long fields, generally named
x1, and so on, which can take on any values provided that
they are not all zero. The collective total size of these fields is q
bits; therefore the period of this subgenerator is
Because the periods 2p and 2q−1
of the two subgenerators are relatively prime, the period of any
single instance of an LXM algorithm (the length of the series of generated
values before it repeats) is the product of the periods of the subgenerators,
that is, 2p(2q−1), which is just
slightly smaller than 2(p+q). Moreover, if two
distinct instances of the same LXM algorithm have different
parameters, then their cycles of produced values will be different.
Generally speaking, among the "
generators, the memory required for an instance is 2p+q bits.
(If q is 1024 or larger, the XBG state is represented as an
array, so additional bits are needed for the array object header, and another
32 bits are used for an array index.)
Larger values of p imply a lower probability that two distinct
instances will traverse the same state cycle, and larger values of q
imply that the generator is equidistributed in a larger number of dimensions
(this is provably true when p is 64, and conjectured to be
approximately true when p is 128). A class with "
Mix" in its
name uses a fairly strong mixing function with excellent avalanche
characteristics; a class with "
StarStar" in its name uses a weaker
but faster mixing function.
The specific LXM algorithms used in this package are all chosen so that
the 64-bit values produced by the
method are exactly equidistributed (for example, for any specific instance of
"L64X128MixRandom", over the course of its cycle each of the
long values will be produced
2128−1 times). The values produced by the
nextDouble() methods are likewise exactly
equidistributed. Some algorithms provide a further guarantee of
k-equidistribution for some k greater than 1, meaning that successive
non-overlapping k-tuples of 64-bit values produced by the
nextLong() method are exactly
equidistributed (equally likely to occur).
The following table gives the period, state size (in bits), parameter size (in bits, including the low-order bit that is required always to be a 1-bit), and equidistribution property for each of the specific LXM algorithms used in this package.
|Implementation||Period||State size||Parameter size|
|"L32X64MixRandom"||232(264−1)||96 bits||32 bits|
|"L64X128StarStarRandom"||264(2128−1)||192 bits||64 bits||2-equidistributed and exactly equidistributed|
|"L64X128MixRandom"||264(2128−1)||192 bits||64 bits||2-equidistributed and exactly equidistributed|
|"L64X256MixRandom"||264(2256−1)||320 bits||64 bits||4-equidistributed and exactly equidistributed|
|"L64X1024MixRandom"||264(21024−1)||1088 bits||64 bits||16-equidistributed and exactly equidistributed|
|"L128X128MixRandom"||2128(2128−1)||256 bits||128 bits||exactly equidistributed|
|"L128X256MixRandom"||2128(2256−1)||384 bits||128 bits||exactly equidistributed|
|"L128X1024MixRandom"||2128(21024−1)||1152 bits||128 bits||exactly equidistributed|
L32, the 32-bit values produced by the
nextInt()method are exactly equidistributed, but the 64-bit values produced by the
nextLong()method are not exactly equidistributed.
For the algorithms listed above whose names begin with
L128, the 64-bit values produced by the
nextLong() method are exactly
equidistributed: every instance, over the course of its cycle, will
produce each of the 264 possible
long values exactly the
same number of times. For example, any specific instance of
"L64X256MixRandom", over the course of its cycle each of the
long values will be produced
2256−1 times. The values produced by the
nextDouble() methods are likewise exactly
In addition, for the algorithms listed above whose names begin with
L64, the 64-bit values produced by the
nextLong() method are
k-equidistributed (but not exactly k-equidistributed). To be
precise, and taking "L64X256MixRandom" as an example: for
any specific instance of "L64X256MixRandom", consider the
(overlapping) length-4 subsequences of the cycle of 64-bit values produced by
nextLong() (assuming no other methods are
called that would affect the state). There are
264(2256−1) such subsequences, and each
subsequence, which consists of 4 64-bit values, can have one of
2256 values. Of those 2256 subsequence values, nearly
all of them (2256−264) occur 264 times
over the course of the entire cycle, and the other 264 subsequence
values occur only 264−1 times. So the ratio of the
probability of getting any specific one of the less common subsequence values
and the probability of getting any specific one of the more common
subsequence values is 1−2-64. (Note that the set of
264 less-common subsequence values will differ from one instance
of "L64X256MixRandom" to another, as a function of the
additive parameter of the LCG.) The values produced by the
nextDouble() methods are likewise
4-equidistributed (but not exactly 4-equidistributed).
The next table gives the LCG multiplier value, the name of the specific
XBG algorithm used, the specific numeric parameters for that XBG
algorithm, and the mixing function for each of the specific LXM algorithms
used in this package. (Note that the multiplier used for the 128-bit LCG
cases is 65 bits wide, so the constant
0x1d605bbb58c8abbfdL shown in
the table cannot actually be used in code; instead, only the 64 low-order
0xd605bbb58c8abbfdL are represented in the source code, and the
missing 1-bit is handled through special coding of the multiply-add algorithm
used in the LCG.)
||XBG algorithm||XBG parameters||Mixing function|
RandomGeneratorinterface is designed to provide a common protocol for objects that generate random or (more typically) pseudorandom sequences of numbers (or Boolean values).This interface is designed to provide a common protocol for objects that generate sequences of pseudorandom values and can easily jump forward, by an arbitrary amount, to a distant point in the state cycle.This interface is designed to provide a common protocol for objects that generate pseudorandom values and can easily jump forward, by a moderate amount (ex. 264) to a distant point in the state cycle.This interface is designed to provide a common protocol for objects that generate sequences of pseudorandom values and can easily not only jump but also leap forward, by a large amount (ex. 2128), to a very distant point in the state cycle.This interface is designed to provide a common protocol for objects that generate sequences of pseudorandom values and can be split into two objects (the original one and a new one) each of which obey that same protocol (and therefore can be recursively split indefinitely).This is a factory class for generating multiple random number generators of a specific algorithm.