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{{Task}} The task is to: : State the type of random number generator algorithm used in a language's builtin random number generator. If the language or its immediate libraries don't provide a random number generator, skip this task. : If possible, give a link to a wider [[wp:List of random number generatorsexplanation]] of the algorithm used.
Note: the task is ''not'' to create an RNG, but to report on the languages inbuilt RNG that would be the most likely RNG used.
The main types of pseudorandom number generator ([[wp:PRNGPRNG]]) that are in use are the [[linear congruential generatorLinear Congruential Generator]] ([[wp:Linear congruential generatorLCG]]), and the Generalized Feedback Shift Register ([[wp:Generalised_feedback_shift_register#Nonbinary_Galois_LFSRGFSR]]), (of which the [[wp:Mersenne twisterMersenne twister]] generator is a subclass). The last main type is where the output of one of the previous ones (typically a Mersenne twister) is fed through a [[cryptographic hash function]] to maximize unpredictability of individual bits.
Note that neither LCGs nor GFSRs should be used for the most demanding applications (cryptography) without additional steps.
8th
The default random number generator in 8th is a cryptographically strong one using [https://en.wikipedia.org/wiki/Fortuna_%28PRNG%29 Fortuna], which is seeded from the system's entropy provider. An additional random generator (which is considerably faster) is a [http://www.pcgrandom.org/ PCG], though it is not cryptographically strong.
ActionScript
In both Actionscript 2 and 3, the type of pseudorandom number generator is implementationdefined. This number generator is accessed through the Math.random() function, which returns a double greater than or equal to 0 and less than 1.[http://livedocs.adobe.com/flash/9.0/ActionScriptLangRefV3/Math.html#random%28%29][http://flashreference.icod.de/Math.html#random%28%29] In Actionscript 2, the global random() function returns an integer greater than or equal to 0 and less than the given argument, but it is deprecated and not recommended.[http://flashreference.icod.de/global_functions.html#random()]
Ada
The Ada standard defines Random Number Generation in Annex A.5.2. There are two kinds of RNGs, Ada.Numerics.Float_Random for floating point values from 0.0 to 1.0, and Ada.Numerics.Discrete_Random for pseudorandom values of enumeration types (including integer types). It provides facilities to initialize the generator and to save it's state.
The standard requires the implementation to uniformly distribute over the range of the result type.
The used algorithm is implementation defined. The standard says: "To enable the user to determine the suitability of the random number generators for the intended application, the implementation shall describe the algorithm used and shall give its period, if known exactly, or a lower bound on the period, if the exact period is unknown."
 [http://www.adahome.com/rm95/rm9xA0502.html Ada 95 RM  A.5.2 Random Number Generation]
 [http://www.adaic.com/standards/05rm/html/RMA52.html Ada 2005 RM  A.5.2 Random Number Generation]
 [http://www.adaic.org/resources/add_content/standards/12rm/html/RMA52.html Ada 2005 RM  A.5.2 Random Number Generation]
ALGOL 68
Details of the random number generator are in the Revised Reports sections: 10.2.1. and 10.5.1.
 [http://vestein.arbphys.unidortmund.de/~wb/RR/rrA2.html 10.2. The standard prelude  10.2.1. Environment enquiries]
 [http://vestein.arbphys.unidortmund.de/~wb/RR/rrA5.html 10.5. The particular preludes and postlude  10.5.1. The particular preludes]
PROC ℒ next random = (REF ℒ INT a)ℒ REAL: ( a :=
¢ the next pseudorandom ℒ integral value after 'a' from a
uniformly distributed sequence on the interval [ℒ 0,ℒ maxint] ¢;
¢ the real value corresponding to 'a' according to some mapping of
integral values [ℒ 0, ℒ max int] into real values [ℒ 0, ℒ 1)
i.e. such that 0 <= x < 1 such that the sequence of real
values so produced preserves the properties of pseudorandomness
and uniform distribution of the sequence of integral values ¢);
INT ℒ last random := # some initial random number #;
PROC ℒ random = ℒ REAL: ℒ next random(ℒ last random);
Note the suitable "next random number" is suggested to be: ( a := ¢ the next pseudorandom ℒ integral value after 'a' from a uniformly distributed sequence on the interval [ℒ 0,ℒ maxint] ¢; ¢ the real value corresponding to 'a' according to some mapping of integral values [ℒ 0, ℒ max int] into real values [ℒ 0, ℒ 1) i.e., such that 0 <= x < 1 such that the sequence of real values so produced preserves the properties of pseudorandomness and uniform distribution of the sequence of integral values ¢);
Algol68 supports random number generation for all precisions available for the specific implementation. The prefix '''ℒ real''' indicates all the available precisions. eg '''short short real''', '''short real''', '''real''', '''long real''', '''long long real''' etc
For an ASCII implementation and for '''long real''' precision these routines would appears as:
PROC long next random = (REF LONG INT a)LONG REAL: # some suitable next random number #;
INT long last random := # some initial random number #;
PROC long random = LONG REAL: long next random(long last random);
AutoHotkey
The builtin command [http://www.autohotkey.com/docs/commands/Random.htm Random] generates a pseudorandom number using Mersenne Twister "MT19937" (see documentation).
AWK
The builtin command "rand" generates a pseudorandom uniform distributed random variable. More information is available from the documentation of [http://www.gnu.org/software/gawk/manual/html_node/NumericFunctions.html gawk].
It is important that the RNG is seeded with the funtions "srand", otherwise, the same random number is produced.
Example usage: see [http://rosettacode.org/wiki/Random_number_generator_(included)#UNIX_Shell #UNIX_Shell]
BASIC
The RND function generates a pseudo random number greater than or equal to zero, but less than one. The implementation is machine specific based on contents of the ROM and there is no fixed algorithm.
Batch File
Windows batch files can use the %RANDOM%
pseudovariable which returns a pseudorandom number between 0 and 32767. Behind the scenes this is just a call to the C runtime's rand()
function which uses an LCG in this case:
:$X\_\{n+1\}=X\_n\backslash cdot\; 214013\; +\; 2531011\; \backslash pmod\; \{2^\{15\}\}$
BBC BASIC
The RND function uses a 33bit maximallength Linear Feedback Shift Register (LFSR), with 32bits being used to provide the result. Hence the sequence length is 2^331, during which the value zero is returned once and all nonzero 32bit values are each returned twice.
Befunge
The ? instruction usually uses the random number generator in the interpreter's language. The original interpreter is written in C and uses rand().
C
Standard C has rand(). Some implementations of C have other sources of random numbers, along with rand().
===C rand()=== The C standard specifies the interface to the rand() and srand() functions in <stdlib.h>.
void srand(unsigned int seed)
begins a new sequence of pseudorandom integers.int rand(void)
returns a pseudorandom integer in the range from 0 to RAND_MAX. ** RAND_MAX must be at least 32767.
The same seed to srand() reproduces the same sequence. The default seed is 1, when a program calls rand() without calling srand(); so srand(1) reproduces the default sequence. ([http://www.openstd.org/jtc1/sc22/wg14/www/docs/n1124.pdf n1124.pdf])
There are no requirements as to the algorithm to be used for generating the random numbers. All versions of rand() return integers that are uniformly distributed in the interval from 0 to RAND_MAX, but some algorithms have problems in their randomness. For example, the cycle might be too short, or the probabilities might not be independent.
Many popular C libraries implement rand() with a [[linear congruential generator]]. The specific multiplier and constant varies by implementation, as does which subset of bits within the result is returned as the random number. These rand() functions should not be used where a good quality random number generator is required.
====BSD rand()==== Among current systems, [[BSD]] might have the worst algorithm for rand(). BSD rand() sets RAND_MAX to $2^\{31\}\; \; 1$ and uses this linear congruential formula:
 $state\_\{n\; +\; 1\}\; =\; 1103515245\; \backslash times\; state\_n\; +\; 12345\; \backslash pmod\{2^\{31\}\}$
 $rand\_n\; =\; state\_n$
[[FreeBSD]] switched to a different formula, but [[NetBSD]] and [[OpenBSD]] stayed with this formula. ([http://cvsweb.netbsd.org/bsdweb.cgi/src/lib/libc/stdlib/rand.c?only_with_tag=MAIN NetBSD rand.c], [http://www.openbsd.org/cgibin/cvsweb/src/lib/libc/stdlib/rand.c OpenBSD rand.c])
BSD rand() produces a cycling sequence of only $2^\{31\}$ possible states; this is already too short to produce good random numbers. The big problem with BSD rand() is that the low $n$ bits' cycle sequence length is only $2^n$. (This problem happens because the modulus $2^\{31\}$ is a power of two.) The worst case, when $n\; =\; 1$, becomes obvious if one uses the low bit to flip a coin.
#include <stdio.h> #include <stdlib.h> /* Flip a coin, 10 times. */ int main() { int i; srand(time(NULL)); for (i = 0; i < 10; i++) puts((rand() % 2) ? "heads" : "tails"); return 0; }
If the C compiler uses BSD rand(), then this program has only two possible outputs.
 At even seconds: heads, tails, heads, tails, heads, tails, heads, tails, heads, tails.
 At odd seconds: tails, heads, tails, heads, tails, heads, tails, heads, tails, heads.
The low bit manages a uniform distribution between heads and tails, but it has a period length of only 2: it can only flip a coin 2 times before it must repeat itself. Therefore it must alternate heads and tails. This is not a real coin, and these are not truly random flips.
In general, the low bits from BSD rand() are much less random than the high bits. This defect of BSD rand() is so famous that some programs ignore the low bits from rand().
====Microsoft rand()==== Microsoft sets RAND_MAX to 32767 and uses this linear congruential formula:
 $state\_\{n\; +\; 1\}\; =\; 214013\; \backslash times\; state\_n\; +\; 2531011\; \backslash pmod\{2^\{31\}\}$
 $rand\_n\; =\; seed\_n\; \backslash div\; 2^\{16\}$
===POSIX drand48()=== POSIX adds the drand48() family to <stdlib.h>.
void srand48(long seed)
begins a new sequence.double drand48(void)
returns a random double in [0.0, 1.0).long lrand48(void)
returns a random long in [0, 2**31).long mrand48(void)
returns a random long in [231, 231).
This family uses a 48bit linear congruential generator with this formula:
 $r\_\{n\; +\; 1\}\; =\; 25214903917\; \backslash times\; r\_n\; +\; 11\; \backslash pmod\; \{2^\{48\}\}$
C++
As part of the C++11 specification the language now includes various forms of random number generation.
While the default engine is implementation specific (ex, unspecified), the following Pseudorandom generators are available in the standard:
 Linear congruential (minstd_rand0, minstd_rand)
 Mersenne twister (mt19937, mt19937_64)
 Subtract with carry (ranlux24_base, ranlux48_base)
 Discard block (ranlux24, ranlux48)
 Shuffle order (knuth_b)
Additionally, the following distributions are supported:
 Uniform distributions: uniform_int_distribution, uniform_real_distribution
 Bernoulli distributions: bernoulli_distribution, geometric_distribution, binomial_distribution, negative_binomial_distribution
 Poisson distributions: poisson_distribution, gamma_distribution, exponential_distribution, weibull_distribution, extreme_value_distribution
 Normal distributions: normal_distribution, fisher_f_distribution, cauchy_distribution, lognormal_distribution, chi_squared_distribution, student_t_distribution
 Sampling distributions: discrete_distribution, piecewise_linear_distribution, piecewise_constant_distribution
Example of use: {{works withC++11}}
#include <iostream> #include <string> #include <random> int main() { std::random_device rd; std::uniform_int_distribution<int> dist(1, 10); std::mt19937 mt(rd()); std::cout << "Random Number (hardware): " << dist(rd) << std::endl; std::cout << "Mersenne twister (hardware seeded): " << dist(mt) << std::endl; }
C#
The .NET Random class says that it uses Knuth's subtractive random number generator algorithm.[http://msdn.microsoft.com/enus/library/system.random.aspx#remarksToggle]
Clojure
See Java.
CMake
CMake has a random ''string'' generator.
# Show random integer from 0 to 9999. string(RANDOM LENGTH 4 ALPHABET 0123456789 number) math(EXPR number "${number} + 0") # Remove extra leading 0s. message(STATUS ${number})
The current implementation (in [http://cmake.org/gitweb?p=cmake.git;a=blob;f=Source/cmStringCommand.cxx;hb=HEAD cmStringCommand.cxx] and [http://cmake.org/gitweb?p=cmake.git;a=blob;f=Source/cmSystemTools.cxx;hb=HEAD cmSystemTools.cxx]) calls [[{{PAGENAME}}#Crand() and srand() from C]]. It picks random letters from the alphabet. The probability of each letter is near ''1 ÷ length'', but the implementation uses floatingpoint arithmetic to map ''RAND_MAX + 1'' values onto ''length'' letters, so there is a small modulo bias when ''RAND_MAX + 1'' is not a multiple of ''length''.
CMake 2.6.x has [http://public.kitware.com/Bug/view.php?id=9851 bug #9851]; two random strings might be equal because they use the same seed. CMake 2.8.0 fixes this bug by seeding the random generator only once, during the first call to string(RANDOM ...)
.
CMake 2.8.5 tries a [[random number generator (device)secure seed]] (CryptGenRandom or /dev/urandom) or falls back to highresolution [[system time]]. Older versions seed the random generator with time(NULL)
, the current time in seconds.
Common Lisp
The easiest way to generate random numbers in Common Lisp is to use the builtin rand function after seeding the random number generator. For example, the first line seeds the random number generator and the second line generates a number from 0 to 9
(setf *randomstate* (makerandomstate t)) (rand 10)
[https://www.cs.cmu.edu/Groups/AI/html/cltl/clm/node133.html Common Lisp: The Language, 2nd Ed.] does not specify a specific random number generator algorithm.
D
From std.random:
The generators feature a number of wellknown and welldocumented methods of generating random numbers. An overall fast and reliable means to generate random numbers is the Mt19937 generator, which derives its name from "[http://en.wikipedia.org/wiki/Mersenne_twister Mersenne Twister] with a period of 2 to the power of 19937". In memoryconstrained situations, [http://en.wikipedia.org/wiki/Linear_congruential_generator linear congruential] generators such as MinstdRand0 and MinstdRand might be useful. The standard library provides an alias Random for whichever generator it considers the most fit for the target environment.
=={{headerDéjà Vu}}==
The standard implementation, [[vu]]
, uses a Mersenne twister.
!print randomint # prints a 32bit random integer
Delphi
According to [[wp:Linear_congruential_generator#Parameters_in_common_useWikipedia]], Delphi uses a Linear Congruential Generator.
Random functions: function Random : Extended; function Random ( LimitPlusOne : Integer ) : Integer; procedure Randomize;
Based on the values given in the wikipedia entry here is a Delphi compatible implementation for use in other pascal dialects.
{$ifdef fpc}{$mode objfpc}{$endif} interface function LCGRandom: extended; overload;inline; function LCGRandom(const range:longint):longint;overload;inline; implementation function IM:cardinal;inline; begin RandSeed := RandSeed * 134775813 + 1; Result := RandSeed; end; function LCGRandom: extended; overload;inline; begin Result := IM * 2.32830643653870e10; end; function LCGRandom(const range:longint):longint;overload;inline; begin Result := IM * range shr 32; end; end.
DWScript
DWScript currently uses a 64bit [[wp:XorshiftXorShift]] PRNG, which is a fast and light form of GFSR.
EchoLisp
EchoLisp uses an ARC4 (or RCA4) implementation by David Bau, which replaces the JavaScript Math.random(). Thanks to him. [https://github.com/davidbau/seedrandom]. Some examples :
(randomseed "albert") (random) → 0.9672510261922906 ; random float in [0 ... 1[ (random 1000) → 726 ; random integer in [0 ... 1000 [ (random 1000) → 936 ; random integer in ]1000 1000[ (lib 'bigint) (random 1e200) → 48635656441292641677...3917639734865662239925...9490799697903133046309616766848265781368
Elena
ELENA 4.x :
import extensions;
public program()
{
console.printLine(randomGenerator.nextReal());
console.printLine(randomGenerator.eval(0,100))
}
{{out}}
0.706398
46
Elixir
Elixir does not come with its own module for random number generation. But you can use the appropriate Erlang functions instead. Some examples:
# Seed the RNG :random.seed(:erlang.now()) # Integer in the range 1..10 :random.uniform(10) # Float between 0.0 and 1.0 :random.uniform()
For further information, read the Erlang section.
Erlang
Random number generator. The method is attributed to B.A. Wichmann and I.D.Hill, in 'An efficient and portable pseudorandom number generator', Journal of Applied Statistics. AS183. 1982. Also Byte March 1987.
The current algorithm is a modification of the version attributed to Richard A O'Keefe in the standard Prolog library.
Every time a random number is requested, a state is used to calculate it, and a new state produced. The state can either be implicit (kept in the process dictionary) or be an explicit argument and return value. In this implementation, the state (the type ran()) consists of a tuple of three integers.
It should be noted that this random number generator is not cryptographically strong. If a strong cryptographic random number generator is needed for example crypto:rand_bytes/1 could be used instead.
Seed with a fixed known value triplet A1, A2, A3:
random:seed(A1, A2, A3)
Example with the running time:
... {A1,A2,A3} = erlang:now(), random:seed(A1, A2, A3), ...sequence of randoms used random:seed(A1, A2, A3), ...same sequence of randoms used
Get a random float value between 0.0 and 1.0:
Rfloat = random:uniform(),
Get a random integer value between 1 and N (N is an integer >= 1):
Rint = random:uniform(N),
Euler Math Toolbox
Bays and Durham as describend in Knuth's book.
Factor
The default RNG used when the random
vocabulary is used, is the [[wp:Mersenne twisterMersenne twister]] algorithm [http://docs.factorcode.org/content/articlerandom.html]. But there are other RNGs available, including [[wp:SFMTSFMT]], the system RNG ([[wp:/dev/random/dev/random]] on Unix) and [[wp:Blum Blum ShubBlum Blum Shub]]. It's also very easy to implement your own RNG and integrate it into the system. [http://docs.factorcode.org/content/articlerandomprotocol.html]
Fortran
Fortran has intrinsic random_seed() and random_number() subroutines. Used algorithm of the pseudorandom number generator is compiler dependent (not specified in ISO Fortran Standard, see ISO/IEC 15391:2010 (E), 13.7.135 RANDOM NUMBER). For algorithm in GNU gfortran see https://gcc.gnu.org/onlinedocs/gfortran/RANDOM_005fNUMBER.html Note that with the GNU gfortran compiler program needs to call random_seed with a random PUT= argument to get a pseudorandom number otherwise the sequence always starts with the same number. Intel compiler ifort reinitializes the seed randomly without PUT argument to random value using the system date and time. Here we are seeding random_seed() with some number obtained from the Linux urandom device.
program rosetta_random
implicit none
integer, parameter :: rdp = kind(1.d0)
real(rdp) :: num
integer, allocatable :: seed(:)
integer :: un,n, istat
call random_seed(size = n)
allocate(seed(n))
! Seed with the OS random number generator
open(newunit=un, file="/dev/urandom", access="stream", &
form="unformatted", action="read", status="old", iostat=istat)
if (istat == 0) then
read(un) seed
close(un)
end if
call random_seed (put=seed)
call random_number(num)
write(*,'(E24.16)') num
end program rosetta_random
FreeBASIC
FreeBASIC has a Rnd() function which produces a pseudorandom double precision floating point number in the halfclosed interval [0, 1) which can then be easily used to generate pseudorandom numbers (integral or decimal) within any range.
The sequence of pseudorandom numbers can either by seeded by a parameter to the Rnd function itself or to the Randomize statement and, if omitted, uses a seed based on the system timer.
However, a second parameter to the Randomize statement determines which of 5 different algorithms is used to generate the pseudorandom numbers:

Uses the C runtime library's rand() function (based on LCG) which differs depending on the platform but produces a low degree of randomness.

Uses a fast, platform independent, algorithm with 32 bit granularity and a reasonable degree of randomness. The basis of this algorithm is not specified in the language documentation.

Uses the Mersenne Twister algorithm (based on GFSR) which is platform independent, with 32 bit granularity and a high degree of randomness. This is good enough for most noncryptographic purposes.

Uses a QBASIC compatible algorithm which is platform independent, with 24 bit granularity and a low degree of randomness.

Uses system features (Win32 Crypto API or /dev/urandom device on Linux) to generate pseudorandom numbers, with 32 bit granularity and a very high degree of randomness (cryptographic strength).
A parameter of 0 can also be used (and is the default if omitted) which uses algorithm 3 in the lang fb dialect, 4 in the lang qb dialect and 1 in the lang fblite dialect.
Free Pascal
FreePascal's function random uses the MersenneTwister (for further details, see the file rtl/inc/system.inc). The random is conform MT19937 and is therefor compatible with e.g. the C++11 MT19937 implementation.
program RandomNumbers; // Program to demonstrate the Random and Randomize functions. var RandomInteger: integer; RandomFloat: double; begin Randomize; // generate a new sequence every time the program is run RandomFloat := Random(); // 0 <= RandomFloat < 1 Writeln('Random float between 0 and 1: ', RandomFloat: 5: 3); RandomFloat := Random() * 10; // 0 <= RandomFloat < 10 Writeln('Random float between 0 and 10: ', RandomFloat: 5: 3); RandomInteger := Random(10); // 0 <= RandomInteger < 10 Writeln('Random integer between 0 and 9: ', RandomInteger); // Wait for <enter> Readln; end.
FutureBasic
Syntax:
randomInteger = rnd(expr)
This function returns a pseudorandom long integer uniformly distributed in the range 1 through expr. The expr parameter should be greater than 1, and must not exceed 65536. If the value returned is to be assigned to a 16bit integer (randomInteger), expr should not exceed 32767. The actual sequence of numbers returned by rnd depends on the random number generator's "seed" value. (Note that rnd(1) always returns the value 1.)
Syntax:
random (or randomize) [expr]
This statement "seeds" the random number generator: this affects the sequence of values which are subsequently returned by the rnd function and the maybe function. The numbers returned by rnd and maybe are not truly random, but follow a "pseudorandom" sequence which is uniquely determined by the seed number (expr). If you use the same seed number on two different occasions, you'll get the same sequence of "random" numbers both times. When you execute random without any expr parameter, the system's current time is used to seed the random number generator.
Example 1:
random 375 // using seed number
Example 2:
random // current system time used as seed
Example: To get a random integer between two arbitrary limits min and max, use the following statement. (Note: max  min must be less than or equal to 65536.):
randomInteger = rnd(max  min + 1) + min  1
To get a random fraction, greater than or equal to zero and less than 1, use this statement:
frac! = (rnd(65536)1)/65536.0
To get a random long integer in the range 1 through 2,147,483,647, use this statement:
randomInteger& = ((rnd(65536)  1)<<15) + rnd(32767)
GAP
GAP may use two algorithms : MersenneTwister, or algorithm A in section 3.2.2 of TAOCP (which is the default). One may create several ''random sources'' in parallel, or a global one (based on the TAOCP algorithm).
# Creating a random source
rs := RandomSource(IsMersenneTwister);
# Generate a random number between 1 and 10
Random(rs, 1, 10);
# Same with default random source
Random(1, 10);
One can get random elements from many objects, including lists
Random([1, 10, 100]);
# Random permutation of 1..200
Random(SymmetricGroup(200));
# Random element of Z/23Z :
Random(Integers mod 23);
Go
Go has two random number packages in the standard library and another package in the "subrepository."
[https://golang.org/pkg/math/rand/ math/rand] in the standard library provides general purpose random number support, implementing some sort of feedback shift register. (It uses a large array commented "feeback register" and has variables named "tap" and "feed.") Comments in the code attribute the algorithm to DP Mitchell and JA Reeds. A little more insight is in [https://github.com/golang/go/issues/21835 this issue] in the Go issue tracker.
[https://golang.org/pkg/crypto/rand/ crypto/rand], also in the standard library, says it "implements a cryptographically secure pseudorandom number generator." I think though it should say that it ''accesses'' a cryptographically secure pseudorandom number generator. It uses /dev/urandom on Unixlike systems and the CryptGenRandom API on Windows.
[https://godoc.org/golang.org/x/exp/rand x/exp/rand] implements the Permuted Congruential Generator which is also described in the issue linked above.
Golfscript
Golfscript uses Ruby's Mersenne Twister algorithm
~rand
produces a random integer between 0 and n1, where n is a positive integer piped into the program
Groovy
Same as Java.
Haskell
The [http://www.haskell.org/onlinereport/random.html Haskell 98 report] specifies an interface for pseudorandom number generation and requires that implementations be minimally statistically robust. It is silent, however, on the choice of algorithm.
=={{headerIcon}} and {{headerUnicon}} == Icon and Unicon both use the same linear congruential random number generator x := (x * 1103515245 + 453816694) mod 2^31. Icon uses an initial seed value of 0 and Unicon randomizes the initial seed.
This LCRNG has a number of well documented quirks (see [http://www.cs.arizona.edu/icon/analyst/ia.htm The Icon Analyst issues #26, 28, 38]) relating to the choices of an even additive and a power of two modulus. This LCRNG produces two independent sequences of length 2^30 one of even numbers the other odd.
Additionally, the {{libheaderIcon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/random.icn random] provides related procedures including a parametrized LCRNG that defaults to the builtin values.
Io
Io's [http://iolanguage.org/scm/io/docs/reference/index.html#/Math/Random/Random Random object] uses the Mersenne Twister algorithm.
Inform 7
Inform's random functions are built on the random number generator exposed at runtime by the virtual machine, which is implementationdefined.
J
By default J's ?
primitive (Roll/Deal) uses the Mersenne twister algorithm, but can be set to use a number of other algorithms as detailed on the [http://www.jsoftware.com/help/dictionary/d640.htm J Dictionary page for Roll/Deal].
Java
Java's Random
class uses a [[wp:Linear congruential generatorLinear congruential formula]], as described in [http://java.sun.com/javase/6/docs/api/java/util/Random.html its documentation]. The commonly used Math.random()
uses a Random
object under the hood.
JavaScript
The only builtin random number generation facility is Math.random()
, which returns a floatingpoint number greater than or equal to 0 and less than 1, with approximately uniform distribution. The standard (ECMA262) does not specify what algorithm is to be used.
Julia
Julia's [http://docs.julialang.org/en/latest/stdlib/base/#randomnumbers builtin randomnumber generation functions], rand()
etcetera, use the Mersenne Twister algorithm.
Kotlin
As mentioned in the Java entry, the java.util.Random class uses a linear congruential formula and is not therefore cryptographically secure. However, there is also a derived class, java.security.SecureRandom, which can be used for cryptographic purposes
Lua
Lua's math.random()
is an interface to the C rand()
function provided by the OS libc; its implementation varies by platform.
Mathematica
Mathematica 7, by default, uses an Extended Cellular Automaton method ("ExtendedCA") to generate random numbers. The main PRNG functions are RandomReal[]
and RandomInteger[]
You can specify alternative generation methods including the Mersenne Twister and a Linear Congruential Generator (the default earlier versions). Information about random number generation is provided at [http://reference.wolfram.com/mathematica/tutorial/RandomNumberGeneration.html#185956823 Mathematica].
MATLAB
MATLAB uses the Mersenne Twister as its default random number generator. Information about how the "rand()" function is utilized is given at [http://www.mathworks.com/help/techdoc/ref/rand.html MathWorks].
Maxima
Maxima uses a Lisp implementation of the Mersenne Twister. See ? random
for help, or file share/maxima/5.28.02/src/randmt19937.lisp
for the source code.
There are also random generators for several [[wp:Probability distributiondistributions]] in package distrib
:
[[wp:Bernoulli distributionrandom_bernoulli]]
[[wp:Beta distributionrandom_beta]]
[[wp:Binomial distributionrandom_binomial]]
[[wp:Cauchy distributionrandom_cauchy]]
[[wp:Chisquared distributionrandom_chi2]]
[[wp:Uniform distribution (continuous)random_continuous_uniform]]
[[wp:Uniform distribution (discrete)random_discrete_uniform]]
[[wp:Exponential distributionrandom_exp]]
[[wp:Fdistributionrandom_f]]
[[wp:Gamma distributionrandom_gamma]]
[[wp:Categorical distributionrandom_general_finite_discrete]]
[[wp:Geometric distributionrandom_geometric]]
[[wp:Gumbel distributionrandom_gumbel]]
[[wp:Hypergeometric distributionrandom_hypergeometric]]
[[wp:Laplace distributionrandom_laplace]]
[[wp:Logistic distributionrandom_logistic]]
[[wp:Lognormal distributionrandom_lognormal]]
[[wp:Negative binomial distributionrandom_negative_binomial]]
[[wp:Noncentral chisquared distributionrandom_noncentral_chi2]]
[[wp:Noncentral tdistributionrandom_noncentral_student_t]]
[[wp:Normal distributionrandom_normal]]
[[wp:Pareto distributionrandom_pareto]]
[[wp:Poisson distributionrandom_poisson]]
[[wp:Rayleigh distributionrandom_rayleigh]]
[[wp:Student's tdistributionrandom_student_t]]
[[wp:Weibull distributionrandom_weibull]]
Note: the package distrib
also has functions starting with pdf
, cdf
, quantile
, mean
, var
, std
, skewness
or kurtosis
instead of random
, except the Cauchy distribution, which does not have [[wp:Moment (mathematics)moments]].
=={{headerModula3}}== The Random interface in Modula3 states that it uses "an additive generator based on Knuth's Algorithm 3.2.2A".
Nemerle
Uses .Net Random class; so, as mentioned under C#, above, implements Knuth's subtractive random number generator algorithm. Random class documentation at [http://msdn.microsoft.com/enus/library/system.random.aspx#remarksToggle MSDN].
NetRexx
As NetRexx runs in the JVM it simply leverages the Java library. See [[#JavaJava]] for details of the algorithms used.
Nim
There are two PRNGs provided in the standard library:
 '''random''' : Based on xoroshiro128+ (xor/rotate/shift/rotate), see [http://xoroshiro.di.unimi.it/ here].
 '''mersenne''' : The Mersenne Twister.
OCaml
OCaml provides a module called [http://caml.inria.fr/pub/docs/manualocaml/libref/Random.html Random] in its standard library. It used to be a "Linear feedback shift register" pseudorandom number generator (References: Robert Sedgewick, "Algorithms", AddisonWesley). It is now (as of version 3.12.0) a "laggedFibonacci F(55, 24, +) with a modified addition function to enhance the mixing of bits." It passes the Diehard test suite.
Octave
As explained [https://www.gnu.org/software/octave/doc/interpreter/SpecialUtilityMatrices.html#SpecialUtilityMatrices here] (see '''rand''' function), Octave uses the "Mersenne Twister with a period of 2^199371".
Oz
Oz provides a binding to the C [http://www.opengroup.org/onlinepubs/000095399/functions/rand.html rand]
function as [http://www.mozartoz.org/home/doc/system/node56.html#label719 OS.rand]
.
PARI/GP
random
uses Richard Brent's [http://wwwmaths.anu.edu.au/~brent/random.html xorgens]. It's a member of the xorshift class of PRNGs and provides good, fast pseudorandomness (passing the BigCrush test, unlike the Mersenne twister), but it is not cryptographically strong. As implemented in PARI, its period is "at least $2^\{4096\}1$".
setrand(3)
random(6)+1
\\ chosen by fair dice roll.
\\ guaranteed to the random.
Pascal
See [[#Delphi]] and [[#Free Pascal]].
Random functions: function Random(l: LongInt) : LongInt; function Random : Real; procedure Randomize;
Perl
Previous to Perl 5.20.0 (May 2014), Perl's [http://perldoc.perl.org/functions/rand.html rand]
function will try and call [http://www.opengroup.org/onlinepubs/007908775/xsh/drand48.html drand48]
, [http://www.opengroup.org/onlinepubs/000095399/functions/random.html random]
or [http://www.opengroup.org/onlinepubs/000095399/functions/rand.html rand]
from the C library [http://www.opengroup.org/onlinepubs/000095399/basedefs/stdlib.h.html stdlib.h]
in that order.
Beginning with Perl 5.20.0, a drand48() implementation is built into Perl and used on all platforms. The implementation is from FreeBSD and uses a 48bit linear congruential generator with this formula:
 $r\_\{n\; +\; 1\}\; =\; 25214903917\; \backslash times\; r\_n\; +\; 11\; \backslash pmod\; \{2^\{48\}\}$ Seeds for drand48 are 32bit and the initial seed uses 4 bytes of data read from /dev/urandom if possible; a 32bit mix of various system values otherwise.
Additionally, there are many PRNG's available as modules. Two good Mersenne Twister modules are [https://metacpan.org/pod/Math::Random::MTwist Math::Random::MTwist] and [https://metacpan.org/pod/Math::Random::MT::Auto Math::Random::MT::Auto]. Modules supporting other distributions can be found in [https://metacpan.org/pod/Math::Random Math::Random] and [https://metacpan.org/pod/Math::GSL::Randist Math::GSL::Randist] among others. CSPRNGs include [https://metacpan.org/pod/Bytes::Random::Secure Bytes::Random::Secure], [https://metacpan.org/pod/Math::Random::Secure Math::Random::Secure], [https://metacpan.org/pod/Math::Random::ISAAC Math::Random::ISAAC], and many more.
Perl 6
The implementation underlying the rand function is platform and VM dependent. The JVM backend uses that platform's SecureRandom class.
Phix
The rand(n) routine returns an integer in the range 1 to n, and rnd() returns a floating point number between 0.0 and 1.0.
In both cases the underlying algorithm is just about as trivial as it can be, certainly not suitable for serious cryptographic work.
There are at least a couple of Mersenne twister components in the archive.
PHP
PHP has two random number generators: [http://us3.php.net/manual/en/function.rand.php rand]
, which uses the underlying C library's rand
function; and [http://us3.php.net/manual/en/function.mtrand.php mt_rand]
, which uses the [[wp:Mersenne twisterMersenne twister]] algorithm.
PicoLisp
PicoLisp uses a linear congruential generator in the builtin (rand) function, with a multiplier suggested in Knuth's "Seminumerical Algorithms". See the [http://softwarelab.de/doc/refR.html#rand documentation].
PL/I
Values produced by IBM Visualage PL/I compiler builtin random number generator are uniformly distributed between 0 and 1 [0 <= random < 1]
It uses a multiplicative congruential method:
seed(x) = mod(950706376 * seed(x1), 2147483647)
random(x) = seed(x) / 2147483647
PL/SQL
Oracle Database has two packages that can be used for random numbers generation.
===DBMS_RANDOM=== The DBMS_RANDOM package provides a builtin random number generator. This package is not intended for cryptography. It will automatically initialize with the date, user ID, and process ID if no explicit initialization is performed. If this package is seeded twice with the same seed, then accessed in the same way, it will produce the same results in both cases.
DBMS_RANDOM.RANDOM produces integers in [2^^31, 2^^31).
DBMS_RANDOM.VALUE produces numbers in [0,1) with 38 digits of precision.
DBMS_RANDOM.NORMAL produces normal distributed numbers with a mean of 0 and a variance of 1
===DBMS_CRYPTO=== The DBMS_CRYPTO package contains basic cryptographic functions and procedures. The DBMS_CRYPTO.RANDOMBYTES function returns a RAW value containing a cryptographically secure pseudorandom sequence of bytes, which can be used to generate random material for encryption keys. This function is based on the RSA X9.31 PRNG (PseudoRandom Number Generator).
DBMS_CRYPTO.RANDOMBYTES returns RAW value
DBMS_CRYPTO.RANDOMINTEGER produces integers in the BINARY_INTEGER datatype
DBMS_CRYPTO.RANDOMNUMBER produces integer in the NUMBER datatype in the range of [0..2**1281]
PowerShell
The [http://technet.microsoft.com/enus/library/dd315402.aspx GetRandom
] cmdlet (part of PowerShell 2) uses the .NETsupplied pseudorandom number generator which uses Knuth's subtractive method; see [[#C#C#]].
PureBasic
PureBasic has two random number generators, Random() and CryptRandom(). Random() uses a RANROT type W generator [http://www.agner.org/random/theory/chaosran.pdf]. CryptRandom() uses a very strong PRNG that makes use of a cryptographic safe random number generator for its 'seed', and refreshes the seed if such data is available. The exact method used for CryptRandom() is uncertain.
Python
Python uses the [[wp:Mersenne twisterMersenne twister]] algorithm accessed via the builtin [http://docs.python.org/library/random.html random module].
R
For uniform random numbers, R may use WichmannHill, Marsagliamulticarry, SuperDuper, MersenneTwister, or KnuthTAOCP (both 1997 and 2002 versions), or a userdefined method. The default is Mersenne Twister.
R is able to generate random numbers from a variety of distributions, e.g.
Beta
Binomial
Cauchy
ChiSquared
Exponential
F
Gamma
Geometric
Hypergeometric
Logistic
Log Normal
Multinomial
Negative Binomial
Normal
Poisson
Student t
Uniform
Weibull
See R help on [http://pbil.univlyon1.fr/library/base/html/Random.html Random number generation], or in the R system type
?RNG help.search("Distribution", package="stats")
Racket
Racket's random number generator uses a 54bit version of L’Ecuyer’s MRG32k3a algorithm [L'Ecuyer02], as specified in the [http://docs.racketlang.org/reference/genericnumbers.html#%28def.%28%28quote.~23~25kernel%29.random%29%29 docs]. In addition, the "math" library has a bunch of additional [http://docs.racketlang.org/math/base.html#%28part..Random_.Number_.Generation%29 random functions].
Rascal
Rascal does not have its own arbitrary number generator, but uses the [[Random_number_generator_(included)#Java  Java]] generator. Nonetheless, you can redefine the arbitrary number generator if needed. Rascal has the following functions connected to the random number generator:
import util::Math;
arbInt(int limit); // generates an arbitrary integer below limit
arbRat(int limit, int limit); // generates an arbitrary rational number between the limits
arbReal(); // generates an arbitrary real value in the interval [0.0, 1.0]
arbSeed(int seed);
The last function can be used to redefine the arbitrary number generator. This function is also used in the getOneFrom() functions.
import List;
ok
rascal>getOneFrom(["zebra", "elephant", "snake", "owl"]);
str: "owl"
REXX
The RANDOM BIF function is a pseudorandom number (nonnegative integer) generator, with a range (spread) limited to 100,000 (but some REXX interpreters support a larger range).
The random numbers generated are not consistent between different REXX interpreters or
even the same REXX interpreters executing on different hardware.
/*(below) returns a random integer between 100 & 200, inclusive.*/
y = random(100, 200)
The random numbers may be repeatable by specifiying a ''seed'' for the '''random''' BIF:
call random ,,44 /*the seed in this case is "44". */
.
.
.
y = random(100, 200)
Comparison of '''random''' BIF output for different REXX implementations using a deterministic ''seed''.
/* REXX ***************************************************************
* 08.09.2013 Walter Pachl
* Please add the output from other REXXes
* 10.09.2013 Walter Pachl added REXX/TSO
* 01.08.2014 Walter Pachl show what ooRexx supports
**********************************************************************/
Parse Version v
Call random ,,44
ol=v':'
Do i=1 To 10
ol=ol random(1,10)
End
If left(v,11)='REXXooRexx' Then
ol=ol random(999999999,0) /* ooRexx supports negative limits */
Say ol
'''outputs''' from various REXX interpreters:
REXXooRexx_4.1.3(MT) 6.03 4 Jul 2013: 3 10 6 8 6 9 9 1 1 6
REXXooRexx_4.2.0(MT)_32bit 6.04 22 Feb 2014: 3 10 6 8 6 9 9 1 1 6 403019526
REXX/Personal 4.00 21 Mar 1992: 7 7 6 7 8 8 5 9 4 7
REXXr4 4.00 17 Aug 2013: 8 10 7 5 4 2 10 5 2 4
REXXroo 4.00 28 Jan 2007: 8 10 7 5 4 2 10 5 2 4
REXXRegina_3.7(MT) 5.00 14 Oct 2012: 10 2 7 10 1 1 8 2 4 1
are the following necessary??
REXXRegina_3.4p1 (temp bug fix sf.org 1898218)(MT) 5.00 21 Feb 2008: 10 2 7 10 1 1 8 2 4 1
REXXRegina_3.2(MT) 5.00 25 Apr 2003: 10 2 7 10 1 1 8 2 4 1
REXXRegina_3.3(MT) 5.00 25 Apr 2004: 10 2 7 10 1 1 8 2 4 1
REXXRegina_3.4(MT) 5.00 30 Dec 2007: 10 2 7 10 1 1 8 2 4 1
REXXRegina_3.5(MT) 5.00 31 Dec 2009: 10 2 7 10 1 1 8 2 4 1
REXXRegina_3.6(MT) 5.00 31 Dec 2011: 10 2 7 10 1 1 8 2 4 1
REXX370 3.48 01 May 1992: 8 7 3 1 6 5 5 8 3 2
Conclusion: It's not safe to transport a program that uses 'reproducable' use of randombif (i.e. with a seed) from one environment/implementation to another :(
Ring
nr = 10
for i = 1 to nr
see random(i) + nl
next
Ruby
Ruby's rand
function currently uses the [[wp:Mersenne twisterMersenne twister]] algorithm, as described in [http://www.rubydoc.org/core/classes/Kernel.html#M005974 its documentation].
Run BASIC
rmd(0)
 Return a pseudorandom value between 0 and 1
Rust
Rust's [https://crates.io/crates/rand rand]
crate offers several PRNGs. (It is also available via #![feature(rustc_private)]
). The offering includes some cryptographically secure PRNGs: [https://docs.rs/rand/0.4/rand/isaac/index.html ISAAC] (both 32 and 64bit variants) and [https://docs.rs/rand/0.4/rand/chacha/struct.ChaChaRng.html ChaCha20]. StdRng
is a wrapper of one of those efficient on the current platform. The crate also provides a weak PRNG: [https://docs.rs/rand/0.4/rand/struct.XorShiftRng.html Xorshift128]. It passes diehard but fails TestU01, replacement is being [https://github.com/dhardy/rand/issues/60 considered]. [https://docs.rs/rand/0.4/rand/fn.thread_rng.html thread_rng]
returns a thread local StdRng
initialized from the OS. Other PRNGs can be created from the OS or with thread_rng
.
For any other PRNGs not provided, they merely have to implement the [https://docs.rs/rand/0.4/rand/trait.Rng.html Rng]
trait.
Scala
Scala's scala.util.Random
class uses a [[wp:Linear congruential generatorLinear congruential formula]] of the JVM runtime libary, as described in [http://java.sun.com/javase/6/docs/api/java/util/Random.html its documentation].
An example can be found here:
import scala.util.Random /** * Histogram of 200 throws with two dices. */ object Throws extends App { Stream.continually(Random.nextInt(6) + Random.nextInt(6) + 2) .take(200).groupBy(identity).toList.sortBy(_._1) .foreach { case (a, b) => println(f"$a%2d:" + "X" * b.size) } }
{{out}}
2:XXX
3:XXXXXXXXX
4:XXXXXXXXXXXXX
5:XXXXXXXXXXXXXXXXXXXXXXXXXX
6:XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
7:XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
8:XXXXXXXXXXXXXXXXXXXXXXXXXXXX
9:XXXXXXXXXXXXXXXXXXXXXXXXXXXX
10:XXXXXXXXXXXXXXXXX
11:XXXXXXXXXXXXXX
12:XX
Seed7
Seed7 uses a linear congruential generator to compute pseudorandom numbers. Usually random number generators deliver a random value in a fixed range, The Seed7 function [http://seed7.sourceforge.net/libraries/integer.htm#rand%28in_integer,in_integer%29 rand(low, high)] delivers a random number in the requested range [low, high]. Seed7 overloads the ''rand'' functions for the types char, boolean, [http://seed7.sourceforge.net/libraries/bigint.htm#rand%28in_bigInteger,in_bigInteger%29 bigInteger], [http://seed7.sourceforge.net/libraries/float.htm#rand%28ref_float,ref_float%29 float] and others.
Sidef
Latest versions of Sidef use the Mersenne Twister algorithm to compute pseudorandom numbers, with different initial seeds (and implementations) for floatingpoints and integers.
say 1.rand # random float in the interval [0,1) say 100.irand # random integer in the interval [0,100)
Sparkling
Sparkling uses the builtin PRNG of whichever C library implementation the interpreter is compiled against. The Sparkling library functions random() and seed() map directly to the C standard library functions rand() and srand() with only one small difference: the return value of rand() is divided by RAND_MAX so that the generated number is between 0 and 1.
Stata
See '''[http://www.stata.com/help.cgi?set%20rng set rng]''' in Stata help. Stata uses the '''[https://en.wikipedia.org/wiki/Mersenne_Twister Mersenne Twister]''' RNG by default, and may use the 32bit '''[https://en.wikipedia.org/wiki/KISS_(algorithm) KISS]''' RNG for compatibility with versions earlier than Stata 14.
Tcl
Tcl uses a [[wp:Linear congruential generatorlinear congruential generator]] in it's builtin rand()
function. This is seeded by default from the system time, and kept perinterpreter so different security contexts and different threads can't affect each other's generators (avoiding key deployment issues with the rand function from [[C]]'s math library).
Citations (from Tcl source code):
 S.K. Park & K.W. Miller, “''Random number generators: good ones are hard to find'',” Comm ACM 31(10):11921201, Oct 1988
 W.H. Press & S.A. Teukolsky, “''Portable random number generators'',” Computers in Physics 6(5):522524, Sep/Oct 1992.
=={{headerTI83 BASIC}}== TI83 uses L'Ecuyer's algorithm to generate random numbers. See [https://www.gnu.org/software/gsl/manual/html_node/Randomnumbergeneratoralgorithms.html L'Ecuyer's algorithm]. More explainations can be found in this [http://www.iro.umontreal.ca/~lecuyer/myftp/papers/handstat.pdf paper].
Random function:
## TXR
TXR 50 has a PRNG API, and uses a reimplementation of WELL 512 (avoiding contagion by the "contact authors for commercial uses" virus present in the reference implementation, which attacks BSD licenses). Mersenne Twister was a runner up. There is an object of type randomstate, and a global variable *randomstate* which holds the default random state. Programs can create random states which are snapshots of existing ones, or which are seeded using an integer value (which can be a bignum). The random function produces a random number modulo some integer value, which can have arbitrary precision. The randomfixnum function produces a nonheapallocated positive integer with random bits.
## UNIX Shell
All '''Bourne Shell''' clones have a very quick pseudo random number generator.
```bash
echo $RANDOM
Rach time $RANDOM is referenced it changes it's value (with it's maximum value 32767).
Ursa
Standard Ursa defines the ursa.util.random
type for random number generators and gives objects of this type a standard interface, but leaves the choice of algorithm up to the implementor.
Cygnus/X Ursa is written in Java and makes calls to java.util.Random, which uses a [[wp:Linear congruential generatorLinear congruential formula]].
Ursala
Ursala uses the [[wp:Mersenne twisterMersenne twister]] algorithm as implemented by the [http://www.basis.uklinux.net/avram Avram] run time system for most purposes, except for arbitrary precision floating point random numbers, which are generated by the urandomb
function from the
[http://www.mpfr.org mpfr] library.
XPL0
A 31bit linear congruential generator is used based on an algorithm by Donald Knuth in his book "Art of Computer Programming" Vol 2, 3rd ed. p. 185. It passes all tests in the Diehard suite. The seed is initialized with the system timer count (at 046C) whenever a program starts. The seed can also be set within a program to give a repeatable sequence of (pseudo) random numbers. Calls to the random number intrinsic return values modulo the argument.
include c:\cxpl\codes; \intrinsic 'code' declarations
int I;
[RanSeed(12345); \set random number generator seed to 12345
for I:= 1 to 5 do
[IntOut(0, Ran(1_000_000)); CrLf(0)];
]
Output:
905495
181227
755989
244883
213142
zkl
zkl uses the Xorshift (http://en.wikipedia.org/wiki/Xorshift) random number generator. It will also, on occasion, read from /dev/urandom.
ZX Spectrum Basic
The ZX Spectrum uses a ParkMiller (also called a Lehmer) number generator that produces a number between 0 and nearly 1 from a sequence; the RANDOMIZE command can leap to a new entry in the sequence. Multiply the output of RND by 65536 to see the sequence more clearly. The random numbers produced will repeat after 65536 iterations.
{{omit frombcNo RNG.}} {{omit fromdcNo RNG.}} {{omit fromGUISS}} {{omit fromsedThis language has no numbers!}} {{omit fromUnlambda}}
[[Category:Randomness]]