Editing Mersenne Twister (section)

== Variants ==

[[CryptMT]] is a [[stream cipher]] and [[cryptographically secure pseudorandom number generator]] which uses Mersenne Twister internally.<ref name="eSTREAM">{{cite web|title=CryptMt and Fubuki|url=http://www.ecrypt.eu.org/stream/cryptmtfubuki.html|access-date=2017-11-12|publisher=[[eCRYPT]]|archive-date=2012-07-01|archive-url=https://web.archive.org/web/20120701135329/http://www.ecrypt.eu.org/stream/cryptmtfubuki.html|url-status=dead}}</ref><ref>{{Cite web|last1=Matsumoto|first1=Makoto|last2=Nishimura|first2=Takuji|last3=Hagita|first3=Mariko|last4=Saito|first4=Mutsuo|year=2005|title=Cryptographic Mersenne Twister and Fubuki Stream/Block Cipher|url=http://eprint.iacr.org/2005/165.pdf}}</ref> It was developed by Matsumoto and Nishimura alongside Mariko Hagita and Mutsuo Saito. It has been submitted to the [[eSTREAM]] project of the [[eCRYPT]] network.<ref name="eSTREAM" /> Unlike Mersenne Twister or its other derivatives, CryptMT is [[Software patent|patented]].

MTGP is a variant of Mersenne Twister optimised for [[Graphics processing unit|graphics processing units]] published by Mutsuo Saito and Makoto Matsumoto.<ref>{{cite arXiv|eprint=1005.4973v3|class=cs.MS|author1=Mutsuo Saito|author2=Makoto Matsumoto|title=Variants of Mersenne Twister Suitable for Graphic Processors|year=2010}}</ref> The basic linear recurrence operations are extended from MT and parameters are chosen to allow many threads to compute the recursion in parallel, while sharing their state space to reduce memory load.  The paper claims improved [[equidistribution]] over MT and performance on an old (2008-era) GPU ([[Nvidia]] GTX260 with 192 cores) of 4.7&nbsp;ms for 5×10<sup>7</sup> random 32-bit integers.

The SFMT ([[Single instruction, multiple data|SIMD]]-oriented Fast Mersenne Twister) is a variant of Mersenne Twister, introduced in 2006,<ref>{{cite web|title=SIMD-oriented Fast Mersenne Twister (SFMT)|url=http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/index.html|access-date=4 October 2015|work=hiroshima-u.ac.jp}}</ref> designed to be fast when it runs on 128-bit SIMD.

* It is roughly twice as fast as Mersenne Twister.<ref>{{cite web|title=SFMT:Comparison of speed|url=http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/speed.html|access-date=4 October 2015|work=hiroshima-u.ac.jp}}</ref>
* It has a better [[equidistribution]] property of v-bit accuracy than MT but worse than [[Well Equidistributed Long-period Linear|WELL ("Well Equidistributed Long-period Linear")]].
* It has quicker recovery from zero-excess initial state than MT, but slower than WELL.
* It supports various periods from 2<sup>607</sup>&nbsp;−&nbsp;1 to 2<sup>216091</sup>&nbsp;−&nbsp;1.

Intel [[SSE2]] and [[PowerPC]] AltiVec are supported by SFMT. It is also used for games with the [[Cell (microprocessor)|Cell BE]] in the [[PlayStation 3]].<ref>{{cite web|title=PlayStation3 License|url=http://www.scei.co.jp/ps3-license/index.html|access-date=4 October 2015|work=scei.co.jp}}</ref>

TinyMT is a variant of Mersenne Twister, proposed by Saito and Matsumoto in 2011.<ref>{{cite web|title=Tiny Mersenne Twister (TinyMT)|url=http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/TINYMT/index.html|access-date=4 October 2015|work=hiroshima-u.ac.jp}}</ref> TinyMT uses just 127 bits of state space, a significant decrease compared to the original's 2.5 KiB of state. However, it has a period of <math>2^{127}-1</math>, far shorter than the original, so it is only recommended by the authors in cases where memory is at a premium.