Re: When random isn't random

From: Sven Pran (no.direct_at_mail.please)
Date: 12/12/03 

Date: Fri, 12 Dec 2003 11:26:51 +0100

"Jens Gruschel" wrote
> I understand your argumenation now, but still have some questions...
>
> > As will be understood I made an error when stating this condition as
> > N <= (M div a), I should have written N <= SQRT(M).
>
> RandSeed has 32 bit (M = 2^32). Why are we allowed to call Random(N) with
a
> N with more than 16 bit (the old TurboPascal limitation)?
>
> > But this is really not important, for all known generators a is already
> > chosen
> > less than the square root of M
>
> In Delphi a = $08088405 > Sqrt(M = $100000000). Why?

My answer to both your questions is simply that I have no idea.
(I believe you have typed a "greater than" sign where it should have
been a "less than" sign?)

One explanation can be that the theory behind random generators is
fairly young, even Donald E Knuth who wrote his important textbooks:
"The Art of Computer Programming" second edition as late as in 1980
does not touch the above limitations in his otherwise very comprehensive
analysis of Pseudo Random Generators.

Regards Sven