From: (Nick Maclaren)
Newsgroups: comp.arch.arithmetic

Subject: Re: Psuedo Random Numbers
Date: 14 Oct 1995 21:15:23 GMT
Organization: University of Cambridge, England
Lines: 26
Message-ID: <45p99b$>
References: <44vm6r$> 
+           <4593t4$> 

In article ,
Arthur Chance  wrote:
>In article <4593t4$> (Herman Rub
in) writes:
>> The period is essentially unimprtant.  A Tausworthe generator like
>> x[n] = x[n-460] + x[n-607] has period 2^(s-1)*(2^607 -1), where s
>> is the word length; this is in integer arithmetic.  This class of
>> procedures are now known to have drawbacks.
>Could you explain that last sentence? I tend to use that style of RNG
>as a convenient and easily programmed workhorse, so if there are
>problems with it, I'd like to be aware of them.

See M. Luescher, Computer Physics Communications, 79 (1994) p. 100.

The problems have been known for many years (see Knuth), but previously
to Luescher nobody had succeeded in describing them coherently.  I had
a heuristic argument about their failings back in the 1980s, but could
never tighten it enough to publish in any worthwhile journal.  It was
VERY heuristic!

Nick Maclaren,
University of Cambridge Computer Laboratory,
New Museums Site, Pembroke Street, Cambridge CB2 3QG, England.
Tel.:  +44 1223 334761    Fax:  +44 1223 334679