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sfmt-erlang: SIMD-oriented Fast Mersenne Twister (SFMT) for Erlang
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sfmt-erlang: SIMD-oriented Fast Mersenne Twister (SFMT) for Erlang

  • Version 0.8.2_RELEASE 28-MAY-2012
  • Edited and written by Kenji Rikitake (Kyoto University)
  • Email contact:

Copyright (c) 2010-2012 Kenji Rikitake and Kyoto University. All rights reserved.

Copyright (c) 2006,2007 Mutsuo Saito, Makoto Matsumoto and Hiroshima University. All rights reserved.

See LICENSE.txt for the license (new/simplified BSD license). (Note: license of rebar is Apache 2.0 License.)

This software is based on SFMT ver. 1.3.3 (SIMD oriented Fast Mersenne Twister(SFMT)) by Mutsuo Saito (Hiroshima University) and Makoto Matsumoto (Hiroshima University)

Details of SFMT algorithm


  • new module sfmt607 and sfmt216091 added (from 0.5.1_RELEASE)
  • new module sfmt4253 added (from 0.5.3_RELEASE)
  • new module sfmt86243 added (from 0.6.1_BETA)
  • Pure SFMT module now added as working code by request (from 0.8.0_RELEASE)

Seeding algorithm changed for seed(integer()) functions

  • The old seed/1 function called init_gen_rand/1 (up to 0.8.0_RELEASE)
  • The internal state generated by init_gen_rand/1 is predictable, especially when the value of the 1st element of the state list is very close to the given seed value. (Michael Gebetsroither discovered this behavior)
  • The new seed/1 function calls init_by_list32/1 (from 0.8.1_RELEASE) and the seed is given as [integer()], to reduce predictability of the 1st element of the state list.

Supported SFMT PRNG periods

  • sfmt607: (2^607 - 1)
  • sfmt4253: (2^4253 - 1)
  • sfmt: (2^19937 - 1) (also on sfmt_pure)
  • sfmt86243: (2^86243 - 1)
  • sfmt216091: (2^216091 - 1)

C NIFs based on SFMT 1.3.3 added (from 0.3.0_RELEASE)

Wichmann-Hill 2006 algorithm code also included (from 0.6.0_RELEASE)

  • See src/random_wh06.erl for the details
  • Reference for the algorithm:

    B. A. Wichmann and I. D. Hill, "Generating good pseudo-random numbers", Computational Statistics & Data Analysis 51 (2006) 1614-1622.

  • See src/random_wh06_int.erl for a bigint version (by Michael Truog)

    Note: this bigint version is not tested yet (no eunit test case)

Simple test of 512x512 pixmap included (from 0.6.2_RELEASE)

  • see the files under reference_texts/pbm_512_512/ for the details

Notable bugfixes

  • gen_rand_all/1 is now properly applied in sfmt_pure module when gen_rand32/1 was first invoked (from 0.8.2_RELEASE)
  • Catched up with the latest rebar configuration file (from 0.7.0_RELEASE)
  • Dynamically building ebin/ (from 0.7.0_RELEASE)
  • PDIC_SEED now named differently for each period (bugfix, from 0.5.2_RELEASE)

Tested platforms

  • FreeBSD/amd64 9.0-STABLE with Erlang/OTP R15B01
  • FreeBSD/i386 8.3-RELEASE with Erlang/OTP R15B01
  • RedHat Enterprise Linux 6 of x86_64 with Erlang/OTP R15B01 (Subsystem B of the Kyoto University ACCMS Supercomputer System)


  • Use GNU/BSD make and then

    make compile

The build script is Basho's rebar at, which will be automatically fetched under the directory support/.


  • For the HTML documentation files of the Erlang source

    make doc

    The documentation will be accessible at doc/index.html.

  • For the HTML documentation files of the C NIF source (Note: Doxygen required)

    make c_doc

    The documentation will be accessible at c_doc/index.html.


  • For unit testing with EUnit, do

    make eunit

  • For testing the speed of 100 times of invoking 100000 gen_rand32/1 function, do

    make speed

    (Previously this was 1000 times x 100000 invocations, but that was practically too slow.)

API compatible with the random module

seed0, seed/0, seed/3, uniform/0, uniform/1, uniform_s/1, uniform_s/3 


  • No more new feature; more load testing needed
  • More documentation
  • Code upgrading/reloading behavior check

Code authors:

  • Kenji Rikitake
  • Mutsuo Saito
  • Makoto Matsumoto
  • Dan Gudmundsson
  • Michael Truog


  • Dave "dizzyd" Smith
  • Tuncer Ayaz
  • Tim Bates (random_mt.erl implementator of Mersenne Twister)
  • Dan Gudmundsson
  • Richard O'Keefe
  • Yurii Rashkovskii
  • Kostis Sagonas
  • Michael Gebetsroither


During the compatibility test of this software, Kenji Rikitake used the supercomputer service provided by Academic Center for Computing and Media Studies (ACCMS), Kyoto University.

Erlang Solutions kindly gave Kenji Rikitake an opportunity to give a presentation about this software at Erlang Factory SF Bay 2011.

Notes on refactoring

  • Speedup by NIF: ~40 times faster than the pure Erlang code (when fully inline-optimized (see rebar.config))
  • For the pure-Erlang code: writing ++ (append) operators by ring buffer loops (as a pair of lists consuming the head elements, and the corresponding accumulators) made the code ~50% faster; the pure Erlang code available under reference_texts/
  • gen_rand32/1, gen_rand32_max/2, and gen_rand_float/1 use Erlang lists (Dan Gudmudsson showed the list version is faster)
  • SSE2 code and options in sfmt-extstate were removed due to causing crash of Erlang BEAM (and even if the SSE2 code was enabled the performance increase would be minimal)
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