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From: hrubin@b.stat.purdue.edu (Herman Rubin)
Newsgroups: comp.arch.arithmetic

Subject: Re: Psuedo Random Numbers
Date: 9 Oct 1995 12:30:37 -0500
Organization: Purdue University Statistics Department
Lines: 25
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References: <44vm6r\$1q5@bug.rahul.net>
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In article ,
Arthur Chance  wrote:
>In article <4593t4\$2nm0@b.stat.purdue.edu> hrubin@b.stat.purdue.edu (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.

I have not seen the original sources, but the bad example was such a
generator with a largest lag of 1279.  In an Ising model for which the
results were known, simulation gave wrong answers.  Further analysis
showed that this type of generator is, appropriately looked at, a
LCG, and as so few bits are non-zero, has the random numbers falling
mainly in the planes.

I have seen suggestions that four of these with different largest lags
be XOR'ed.  Another possibility would be to XOR one of these with the
output of a physical generator, which may have to be recycled.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu   Phone: (317)494-6054   FAX: (317)494-0558
```