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From: Tim Rentsch
Newsgroups: comp.lang.c
Subject: Re: Article of Melissa O'Nail
Date: Thu, 08 Jan 2026 09:40:21 -0800
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antispam@fricas.org (Waldek Hebisch) writes:
> Michael S wrote:
>
>> I experimented a bit more (in fact, more like a lot more) with
>> test batteries of L?Ecuyer. It led me to conclusion that occasional
>> failure in the either middle or big battery means nothing.
>> Sometimes even cripto-quality PRNG does not pass one or another test.
>> Then you try to reproduce it and see that with any other seed that you
>> try a failure does not happen.
>> All in all, it makes me more suspect of PRNGs that consistently pass
>> both batteries with various seed. I start to see it as a sign of
>> PRNG being rigged to pass tests.
>
> Well, that depends on the tests and threshhold in the tests.
> Some tests when fed with trurly random source will produce produce
> very small variation of the results. With generous threshhold
> such test will essentially never fail for trurly random source.
> OTOH when expected variation of the results is larger and
> threshhold is tight, then trurly random source will fail the
> test from time to time. And if you test long enough you should
> be able to estimate probability of failure and possibly compare
> is with theoretical result if available.
It's inherent in the nature of statistical testing that every
so often a statistical test will "fail" even for a truly random
input. An input source that never fails can also be indicative
of a low quality source (and perhaps one that was tuned to the
particular set of tests being done). It took me a while to
learn that the results of a PRNG test suite should not be seen
as purely binary.