🚀 go-pugleaf

In article <dmurdoch.393.726873235@mast.queensu.ca> dmurdoch@mast.queensu.ca (Duncan Murdoch) writes:
>In article <1993Jan12.140114.620@hnrc.tufts.edu> jerry@hnrc.tufts.edu (Jerry Dallal) writes:
>>For those who do not have the Times, the article says, " . . . the scientists
>>showed that five of the most popular computer programs for generating streams
>>of random numbers produced errors when they were used in a simple mathematical
>>model of the behavior of atoms in a magnetic crystal."  
>
>>Unfortunately (and understandably) the article does not identify the 5 
>>algorithms.  However, the article cites the original report from Ferrenberg et
>>al. in the Dec. 7 issue of Physical Review Letters.  I would be grateful if
>>someone with access to PRL would post the five generators.
>
>The paper is Ferrenberg, A. M., Landau, D.P., and Wong, Y.J. (1992), Monte 
>Carlo simulations:  hidden errors from "good" random number generators,
>Physical Review Letters 69 no. 23, 3382-3384.
>
>The generators tested were:
>
>CONG:  A linear congruential generator
>         X_n = (16807 X_{n-1}) mod (2^{31} - 1)
>
>R250:  A shift register algorithm:
>         X_n = X_{n-103} XOR X_{n-250}
>
>R1279: Another shift register algorithm:
>         X_n = X_{n-1063} XOR X_{n-1279}
>
>In R250 and R1279, "XOR" is a bitwise exclusive OR; it doesn't say how 
>many bits were used, but I'd assume 32 from the context.
>
>SWC:   A subtract with carry generator (Marsaglia et al, Comput Phys Commun
>60, p 345, 1990):
>
>         X_n = X_{n-22} - X_{n-43} - C
>         if X_n >= 0, C=0,
>         if X_n < 0, X_n = X_n + (2^32-5), C=1
>
>SWCW:   A combined subtract with carry Weyl generator (ibid):
>
>         Z_n = X_{n-22} - Z_{n-43} - C
>	 if Z_n >= 0, C=0
>         if Z_n < 0, Z_n = Z_n+(2^32-5), C=1
>	 Y_n = (Y_{n-1} - 362436069) mod 2^32
>	 X_n = (Z_n - Y_n) mod 2^32

Trouble is, none of these are "good" generators.  For safety, one should
XOR two "independent" generators as Marsaglia et al. do with the "super-duper"
and "ultra" generators.

Have any problems ever been reported with either of these?

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu