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Re: Random number generators in gfortran
- From: Tobias Schlüter <Tobias dot Schlueter at physik dot uni-muenchen dot de>
- To: Mark dot Miller at usu dot edu
- Cc: fortran at gcc dot gnu dot org
- Date: Tue, 24 Jul 2007 16:51:54 +0200
- Subject: Re: Random number generators in gfortran
- References: <46A60ED8.8020408@cc.usu.edu>
Mark.Miller wrote:
What algorithms are used in gfortran for generating random numbers? Is
it the Mersenne Twister? Or is it something with a much shorter period?
There are two random number generators in gfortran, one is a simple
modulo generator that is there for compatibility with g77, this is what
you get when you call RAND().
The other is the RNG that implements the Fortran 90 RANDOM_NUMBER
intrinsic. From its implementation libgfortran/intrinsics/random.c:
=========================================================================
/* libgfortran previously had a Mersenne Twister, taken from the paper:
Mersenne Twister: 623-dimensionally equidistributed
uniform pseudorandom generator.
by Makoto Matsumoto & Takuji Nishimura
which appeared in the: ACM Transactions on Modelling and Computer
Simulations: Special Issue on Uniform Random Number
Generation. ( Early in 1998 ).
The Mersenne Twister code was replaced due to
(1) Simple user specified seeds lead to really bad sequences for
nearly 100000 random numbers.
(2) open(), read(), and close() were not properly declared via header
files.
(3) The global index i was abused and caused unexpected behavior with
GET and PUT.
(4) See PR 15619.
libgfortran currently uses George Marsaglia's KISS (Keep It Simple
Stupid)
random number generator. This PRNG combines:
(1) The congruential generator x(n)=69069*x(n-1)+1327217885 with a
period
of 2^32,
(2) A 3-shift shift-register generator with a period of 2^32-1,
(3) Two 16-bit multiply-with-carry generators with a period of
597273182964842497 > 2^59.
The overall period exceeds 2^123.
http://www.ciphersbyritter.com/NEWS4/RANDC.HTM#369F6FCA.74C7C041@stat.fsu.edu
The above web site has an archive of a newsgroup posting from George
Marsaglia with the statement:
Subject: Random numbers for C: Improvements.
Date: Fri, 15 Jan 1999 11:41:47 -0500
From: George Marsaglia <geo@stat.fsu.edu>
Message-ID: <369F6FCA.74C7C041@stat.fsu.edu>
References: <369B5E30.65A55FD1@stat.fsu.edu>
Newsgroups: sci.stat.math,sci.math,sci.math.numer-analysis
Lines: 93
As I hoped, several suggestions have led to
improvements in the code for RNG's I proposed for
use in C. (See the thread "Random numbers for C: Some
suggestions" in previous postings.) The improved code
is listed below.
A question of copyright has also been raised. Unlike
DIEHARD, there is no copyright on the code below. You
are free to use it in any way you want, but you may
wish to acknowledge the source, as a courtesy.
"There is no copyright on the code below." included the original
KISS algorithm. */
/* We use three KISS random number generators, with different
seeds.
As a matter of Quality of Implementation, the random numbers
we generate for different REAL kinds, starting from the same
seed, are always the same up to the precision of these types.
We do this by using three generators with different seeds, the
first one always for the most significant bits, the second one
for bits 33..64 (if present in the REAL kind), and the third one
(called twice) for REAL(16).
*/
=================================================================
This should answers any questions you had :-)
Cheers,
- Tobi