Newsgroups: comp.parallel
From: Steve Tether <tether@cdfmt1.fnal.gov>
Subject: Re: Random Numbers
Organization: Massachusetts Institute of Technology
Date: Thu, 12 Jan 1995 18:39:44 GMT
Message-ID: <3f3kmj$8u1@fnnews.fnal.gov>

In article <3f174p$lcc@stc06.CTD.ORNL.GOV>
hdc@ORNL.GOV (Hank Cochran) writes:

> The ticklish task of generating (pseudo)random numbers for computations is made 
> substantially more complicated on a massively parallel computer (correlation of 
> random number chains on different processors). Can anyone recommend a thoughtful 
> overview of this subject for a non-specialist--how-to for the scientific user?

The October 1990 issue of _Communications of the ACM_ has an article by Pierre
L'Ecuyer that covers pseudo-random number generation pretty thoroughly, and
which provides more than 100 references. Here's an outline of the article:

Random Numbers for Simulation (title)
  Intro
  Views of Randomness
    Classical definitions
    A Framework for PRNGs
    PT-perfect generators
  Matrix Linear Congruential Recurrences
    Prime Modulus
    Composite Modulus
    Jumping Ahead, Splitting, and Vectorization (*)
    Implementations
    Multiple Recursive Generators
    Lattice Structure and Spectral Test
    Tausworthe, GFSR, Lagged-Fibonacci
    Other Variants
  Non-linear Generators
    A Class of Generators by Inversion
    Combined Generators
  Transforming into U(0,1) Variates
  Statistical Testing
  Discrepancy
  Conclusion

I've marked with (*) the section dealing with PRNGs and parallel machines. The
article as a whole is a mixture of abstract mathematical analysis and
practical advice.

- Steve Tether
  Research Scientist, MIT Lab. for Nuclear Science
  tether@cdfmt1.fnal.gov



