Random number generators in gfortran

[Tobias Schlüter]

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