Mersenne Twister for Graphic Processors (MTGP)

Mersenne Twister for Graphic Processors (MTGP):
a new variant of Mersenne Twister^*1.

News

MTGP ver1.1.2 is released. (2012/10/24)
MTGP ver1.1.1 seems to have some bugs.(2012/10/18)
MTGP ver1.1.1 is released. (2012/10/16)
A slide in MCQMC 2012 is added. (2012/2/22)
TinyMT is released. (2011/6/20)
MTGP ver1.1 is released. (2011/6/6)
MTGPDC ver0.3.1 is released. (2011/3/9)
MTGPDC ver0.3 is released. (2011/3/4)
MTGPDC ver0.2 is released. (2010/6/8)

What is MTGP?

MTGP is a new variant of Mersenne Twister (MT) introduced by Mutsuo Saito and Makoto Matsumoto in 2009. MTGP is designed with some features of Graphic Processors, such as parallel execution and hi-speed constant reference. It supports 32-bit and 64-bit integers, as well as single and double precision floating point as output.

The periods of generated sequence are ¹¹²¹³-1,2²³²⁰⁹-1 and 2⁴⁴⁴⁹⁷-1 for 32-bit version, and 2²³²⁰⁹-1, 2⁴⁴⁴⁹⁷-1, 2¹¹⁰⁵⁰³-1 for 64-bit version. It support 128 parameter sets for each period, in other words, it can generate 128 independent pseudorandom number sequences for each period. We have developed Dynamic Creator for MTGP, which generates more parameter sets.

Preprint in arXiv.
A paper of MTGP (under review, coauthored with Makoto Matsumoto).

A PDF slide 'A deviation of XORWOW of CURAND' in MCQMC 2012.

There are sample implementations on CUDA in an archive source. There are no samples on OpenCL or on ATI Stream in it. But we think MTGP is also fast on RADEONs.

Download MTGP

This code is released on November 17th in 2009, so it may contain some bugs. Any feedback is welcome (send an email to Mutsuo Saito, saito "at sign" math.sci.hiroshima-u.ac.jp and m-mat "at sign" math.sci.hiroshima-u.ac.jp)

version	archive	changes
new! 1.1.2	MTGP-src-1.1.2.zip MTGP-src-1.1.2.tar.gz	CUDA samples are fixed to run on CUDA 5.0. (2012/10/24)
1.1.1	MTGP-src-1.1.1.zip MTGP-src-1.1.1.tar.gz	add jump function. add OpenCL sample with jump. Does not run correctly on CUDA 5.0.(2012/10/18)
1.1	MTGP-src-1.1.zip MTGP-src-1.1.tar.gz	Parameter files of mtgp32 are changed for better dimension of equidistributions. This change cause changes of outputs, but this not cause effect on floating point outputs. The changes affect only on 9 LSB bits of unsigned integers and the 9 LSB bits are discarded when converting to floating points. You can also use old paramter files instead of new ones. This change reflects the improvement of MTGPDC ver. 0.3. Sample files for cuda now can be compiled in CUDA 4.0 environment. (2011/6/6)
1.0.2	MTGP-src-1.0.2.zip MTGP-src-1.0.2.tar.gz	change MEXPs of CUDA-sample from 23209 and 44497 to 11213. This is because CUDA occupancy of the latter is larger than those of the formers. (2010/3/26)
1.0.1	MTGP-src-1.0.1.zip MTGP-src-1.0.1.tar.gz	64-bit initialization bug fixed. (2010/1/5)
1.0	MTGP-src-1.0.zip MTGP-src-1.0.tar.gz	First version. (2009/11/17)

If you have some trouble to download, try this page.

MTGP Dynamic Creator (MTGPDC)

MTGPDC creates parameter sets for MTGP. MTGP has 128 parameter sets for each period. If you need more parameter sets, use MTGPDC to create them. MTGPDC can create 2³² parameter sets for each period.

MTGPDC can create parameter sets of MTGPs which have period of 2³²¹⁷,2⁴⁴²³,2¹¹²¹³, 2²³²⁰⁹ or 2⁴⁴⁴⁹⁷.

MTGPDC requires some libraries.

Victor Shoup's NTL: A Library for doing Number Theory.
C++ TR1 Libraries. (g++ ver. 4.0 or later)
Boost C++ Libraries.
OpenSSL.

And MTGP requires UNIX like Operating System with GNU C++ compiler(g++).

Download MTGP

This code is released on March 26th in 2010, so it may contain some bugs. Any feedback is welcome (send an email to Mutsuo Saito, saito "at sign" math.sci.hiroshima-u.ac.jp and m-mat "at sign" math.sci.hiroshima-u.ac.jp)

version	archive	changes
new! 0.3.1	MTGPDC-src-0.3.1.zip MTGPDC-src-0.3.1.tar.gz	Fix the bug in mtgp64dc mentioned below. (2011/3/9)
0.3	MTGPDC-src-0.3.zip MTGPDC-src-0.3.tar.gz	A small bug in search_temper.hpp is fixed. The bug effects only on the least significant 5 bits, but it makes the dimension of equidistribution of the LSBs smaller than they should be. In addition, we modified the algorithm of searching tempering parameters, so that the algorithm tempers the dimensions of equidistribution of LSBs too, in addition to those of MSBs. This is to address a report on some statistical tests of these LSBs due to Jonathan Passerat-Palmbach, David R.C. Hill and Claude Mazel. We thank them. (2011/3/4) The 64 bit version, mtgp64dc in this version has a serious bug, and should not be used. BUG:All tempering parameters searched by mtgp64dc are zeros. This bug exists only in this version 0.3. It does not exist in the earlier versions, and it is fixed in the version 0.3.1 above. (2011/3/9)
0.2	MTGPDC-src-0.2.zip MTGPDC-src-0.2.tar.gz	some bug fixes. (2010/6/8)
0.1	MTGPDC-src-0.1.zip MTGPDC-src-0.1.tar.gz	First version. (2010/3/26)

If you have some trouble to download, try this page.

License

MTGP, as well as MT, can be used freely for any purpose, including commercial use. See LICENSE.txt for detail.

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*1 This work is supported in part by JSPS Core-to-Core Program No. 18005: "New Developments of Arithmetic Geometry, Motive, Galois Theory, and Their Practical Applications."
This work is also partially supported by JSPS Grant-in-Aid for Scientific Research No. 19204002, No. 18654021 and No. 21654004.