RAN function?

[Intel_C_Intel]

Can anyone detail precisely what algorithm for the
random number generator RAN was used in
Fortran Powerstation 4.0 and subsequently in DVF and
successors? I need to know for a course I will be teaching
next month....

BBB

[Steven_L_Intel1]

I can't say what PowerStation used, but for RAN, Visual Fortran uses "Prime Modulus M Multiplicative Linear Congruential Generator," a modified version of the random number generator by Park and Miller in "Random Number Generators: Good Ones Are Hard to Find," CACM, October 1988, Vol. 31, No. 10.)

We recommend instead the Fortran 90 standard intrinsic RANDOM_NUMBER, for which we use the one by Pierre L'ecuyer as published in "Efficient and Portable Combined Random Number Generators", Communications of the ACM vol 31 num 6 June 1988

Steve

[Intel_C_Intel]

Steve:

I forwarded you message to Pierre L'Ecuyer. Here is what he told me.
You may wish to get your programming team to incorporate this info in future
releases of Fortran.

Sender: lecuyer@IRO.UMontreal.CA
Date: Wed, 16 May 2001 15:38:33 -0400
From: "Pierre L'Ecuyer"
Organization: Universite de Montreal
X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.2.19pre10 i686)
X-Accept-Language: en
To: "Dr. Bernard B. Beard" ,
"Pierre L'Ecuyer"
Subject: Re: Fwd: re: RAN function?
....[echoed text deleted for clarity]
The RNG recommended in the Park-Miller paper is often wrongly attributed to
Park and Miller. It was in fact taken from the paper:

AUTHOR="P. A. W. Lewis and A. S. Goodman and J. M. Miller",
TITLE="A Pseudo-random Number Generator for the System/360",
JOURNAL={{IBM} System's Journal},
VOLUME={8},
YEAR={1969},
PAGES={136--143} }

It is an LCG with multiplier a=16807.
See the paper birth.ps in my publication's list for good reason why to
never use it. This paper is:

AUTHOR="P. L'Ecuyer and R. Simard",
TITLE="On the Performance of Birthday Spacings Tests
for Certain Families of Random Number Generators",
JOURNAL={Mathematics and Computers in Simulation},
VOLUME={55},
number ={1--3},
PAGES={131--137},
YEAR={2001}

> >
> > We recommend instead the Fortran 90 standard intrinsic RANDOM_NUMBER, for which we use
> > the one by Pierre L'ecuyer as published in "Efficient and Portable Combined Random
> > Number Generators", Communications of the ACM vol 31 num 6 June 1988

This is the first RNG I designed, 15 years ago.
Nowadays, there are better alternatives. See, e.g.,

AUTHOR="P. L'Ecuyer",
TITLE="Tables of Maximally Equidistributed Combined {LFSR} Generators",
JOURNAL={Mathematics of Computation},
VOLUME={68},
NUMBER={225},
PAGES={261--269},
YEAR={1999}
}

AUTHOR="P. L'Ecuyer",
TITLE="Good Parameters and Implementations for
Combined Multiple Recursive Random Number Generators",
JOURNAL={Operations Research},
VOLUME={47},
NUMBER={1},
PAGES={159--164},
YEAR={1999}

AUTHOR="P. L'Ecuyer and T. H. Andres",
TITLE="A Random Number Generator Based on the Combination of
Four {LCG}s",
JOURNAL={Mathematics and Computers in Simulation},
VOLUME={44},
PAGES={99--107},
YEAR={1997},

--
Pierre L'Ecuyer
Departement d'informatique et de recherche operationnelle (I.R.O.)
Universite de Montreal, C.P. 6128, succ. Centre-Ville, Montreal, H3C 3J7
Tel. Bureau: (514) 343-2143 FAX: (514) 343-5834
e-mail: lecuyer@iro.umontreal.ca
web : http://www.iro.umontreal.ca/~lecuyer

[Steven_L_Intel1]

Yes, we know there have been advancements since then. But it would be a never-ending task to keep up with all the new generators. The one we're using is very good, overall - much better than the one we had before, which was rather simple.

I find that most programmers who care a lot about random numbers get their own source code rather than relying on whatever the vendor has implemented. I don't see any real advantage in continuously changing the algorithm - and then explaining to customers why they're seeing different results!

Steve