Editing Mersenne Twister (section)

== Applications ==

The Mersenne Twister is used as default PRNG by the following software:

* Programming languages: Dyalog [[APL (programming language)|APL]],<ref>{{cite web|title=Random link|url=http://help.dyalog.com/latest/#Language/System%20Functions/rl.htm|access-date=2020-06-04|work=Dyalog Language Reference Guide}}</ref> [[IDL (programming language)|IDL]],<ref>{{cite web|title=RANDOMU (IDL Reference)|url=http://www.exelisvis.com/docs/RANDOMU.html|access-date=2013-08-23|work=Exelis VIS Docs Center}}</ref> [[R (programming language)|R]],<ref>{{cite web|title=Random Number Generators|url=https://cran.r-project.org/web/views/Distributions.html|access-date=2012-05-29|work=CRAN Task View: Probability Distributions}}</ref> [[Ruby (programming language)|Ruby]],<ref>{{cite web|title="Random" class documentation|url=https://docs.ruby-lang.org/en/master/Random.html}}</ref> [[Free Pascal]],<ref>{{cite web|title=random|url=http://www.freepascal.org/docs-html/rtl/system/random.html|access-date=2013-11-28|work=free pascal documentation}}</ref> [[PHP (programming language)|PHP]],<ref>{{cite web|title=mt_rand — Generate a better random value|url=http://php.net/manual/en/function.mt-rand.php|access-date=2016-03-02|work=PHP Manual}}</ref> [[Python (programming language)|Python]] (also available in [[NumPy]], however the default was changed to [[Permuted congruential generator|PCG64]] instead as of version 1.17<ref>{{Cite web|title=NumPy 1.17.0 Release Notes — NumPy v1.21 Manual|url=https://numpy.org/doc/stable/release/1.17.0-notes.html?highlight=random|access-date=2021-06-29|website=numpy.org}}</ref>),<ref>{{cite web|title=9.6 random — Generate pseudo-random numbers|url=https://docs.python.org/release/2.6.8/library/random.html|access-date=2012-05-29|work=Python v2.6.8 documentation}}</ref><ref>{{cite web|title=8.6 random — Generate pseudo-random numbers|url=https://docs.python.org/release/3.2/library/random.html|access-date=2012-05-29|work=Python v3.2 documentation}}</ref><ref>{{cite web|title=random — Generate pseudo-random numbers — Python 3.8.3 documentation|url=https://docs.python.org/3/library/random.html|access-date=2020-06-23|work=Python 3.8.3 documentation}}</ref> [[CMU Common Lisp]],<ref>{{cite web|title=Design choices and extensions|url=http://common-lisp.net/project/cmucl/doc/cmu-user/extensions.html|access-date=2014-02-03|work=CMUCL User's Manual}}</ref> [[Embeddable Common Lisp]],<ref>{{cite web|title=Random states|url=https://common-lisp.net/project/ecl/manual/ch12s02.html|access-date=2015-09-20|work=The ECL manual}}</ref> [[Steel Bank Common Lisp]],<ref>{{cite web|title=Random Number Generation|url=http://www.sbcl.org/manual/#Random-Number-Generation|work=SBCL User's Manual}}</ref> [[Julia (programming language)|Julia]] (up to Julia 1.6 LTS, still available in later, but a better/faster RNG used by default as of 1.7)<ref>{{Cite web |title=Random Numbers · The Julia Language |url=https://docs.julialang.org/en/v1/stdlib/Random/ |access-date=2022-06-21 |website=docs.julialang.org}}</ref>
* [[Unix-like]]s libraries and software: [[GLib]],<ref>{{cite web|title=Random Numbers: GLib Reference Manual|url=https://developer.gnome.org/glib/stable/glib-Random-Numbers.html}}</ref> [[GNU Multiple Precision Arithmetic Library]],<ref>{{cite web|title=Random Number Algorithms|url=http://gmplib.org/manual/Random-Number-Algorithms.html|access-date=2013-11-21|work=GNU MP}}</ref> [[GNU Octave]],<ref>{{cite web|title=16.3 Special Utility Matrices|url=https://www.gnu.org/software/octave/doc/interpreter/Special-Utility-Matrices.html|work=GNU Octave|quote=Built-in Function: rand}}</ref> [[GNU Scientific Library]]<ref>{{cite web|title=Random number environment variables|url=https://www.gnu.org/software/gsl/manual/html_node/Random-number-environment-variables.html|access-date=2013-11-24|work=GNU Scientific Library}}</ref>
* Other: [[Microsoft Excel]],<ref>{{citation|last=Mélard|first=G.|title=On the accuracy of statistical procedures in Microsoft Excel 2010|journal=[[Computational Statistics (journal)|Computational Statistics]]|volume=29|issue=5|pages=1095–1128|year=2014|citeseerx=10.1.1.455.5508|doi=10.1007/s00180-014-0482-5|s2cid=54032450}}.</ref> [[GAUSS (software)|GAUSS]],<ref>{{cite web|title=GAUSS 14 Language Reference|url=http://www.aptech.com/wp-content/uploads/2014/01/GAUSS14_LR.pdf}}</ref> [[gretl]],<ref>"[http://gretl.sourceforge.net/gretl-help/funcref.html#uniform uniform]". ''Gretl Function Reference''.</ref> [[Stata]],<ref>{{cite web|title=New random-number generator—64-bit Mersenne Twister|url=https://www.stata.com/new-in-stata/random-number-generators/}}</ref> [[SageMath]],<ref>{{cite web|title=Probability Distributions — Sage Reference Manual v7.2: Probablity|url=http://doc.sagemath.org/html/en/reference/probability/sage/gsl/probability_distribution.html}}</ref> [[Scilab]],<ref>{{cite web|title=grand - Random numbers|url=https://help.scilab.org/docs/5.5.2/en_US/grand.html|work=Scilab Help}}</ref> [[Maple (software)|Maple]],<ref>{{cite web|title=random number generator|url=http://www.maplesoft.com/support/help/Maple/view.aspx?path=rand|access-date=2013-11-21|work=Maple Online Help}}</ref> [[MATLAB]]<ref>{{cite web|title=Random number generator algorithms|url=http://www.mathworks.co.uk/help/matlab/ref/randstream.list.html|work=Documentation Center, [[MathWorks]]}}</ref>

It is also available in [[Apache Commons]],<ref>{{cite web|title=Data Generation|url=http://commons.apache.org/proper/commons-math/userguide/random.html|work=Apache Commons Math User Guide}}</ref> in the standard [[C++]] library (since [[C++11]]),<ref>{{cite web|title=Random Number Generation in C++11|url=https://isocpp.org/files/papers/n3551.pdf|work=Standard C++ Foundation}}</ref><ref>{{cite web|title=std::mersenne_twister_engine|url=http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine|access-date=2012-09-25|work=Pseudo Random Number Generation}}</ref> and in [[Mathematica]].<ref>[http://reference.wolfram.com/language/tutorial/RandomNumberGeneration.html#569959585] Mathematica Documentation</ref> Add-on implementations are provided in many program libraries, including the [[Boost (C++ libraries)|Boost C++ Libraries]],<ref>{{cite web|title=boost/random/mersenne_twister.hpp|url=http://www.boost.org/doc/libs/1_49_0/boost/random/mersenne_twister.hpp|access-date=2012-05-29|work=Boost C++ Libraries}}</ref> the [[CUDA|CUDA Library]],<ref>{{cite web|title=Host API Overview|url=http://docs.nvidia.com/cuda/curand/host-api-overview.html#generator-types|access-date=2016-08-02|work=CUDA Toolkit Documentation}}</ref> and the [[NAG Numerical Library]].<ref>{{cite web|title=G05 – Random Number Generators|url=http://www.nag.co.uk/numeric/fl/nagdoc_fl23/xhtml/G05/g05intro.xml|access-date=2012-05-29|work=NAG Library Chapter Introduction}}</ref>

The Mersenne Twister is one of two PRNGs in [[SPSS]]: the other generator is kept only for compatibility with older programs, and the Mersenne Twister is stated to be "more reliable".<ref>{{cite web|title=Random Number Generators|url=http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fidh_seed.htm|access-date=2013-11-21|work=IBM SPSS Statistics}}</ref> The Mersenne Twister is similarly one of the PRNGs in [[SAS (software)|SAS]]: the other generators are older and deprecated.<ref>{{cite web|title=Using Random-Number Functions|url=http://support.sas.com/documentation/cdl/en/lrdict/64316/HTML/default/viewer.htm#a001281561.htm|access-date=2013-11-21|work=SAS Language Reference}}</ref> The Mersenne Twister is the default PRNG in [[Stata]], the other one is [[KISS (algorithm)|KISS]], for compatibility with older versions of Stata.<ref>Stata help: [https://www.stata.com/help.cgi?set%20rng set rng -- Set which random-number generator (RNG) to use]</ref>