From: nmm1 on 24 Nov 2009 03:40
In article <7n0t1kF3jle00U2(a)mid.individual.net>,
frank <frank(a)example.invalid> wrote:
>> A Limit on the Usable Length of a Pseudorandom Number Sequence (Journal
>> of Statistical Computation and Simulation (1992), vol.\ 42, pp.\ 47-54).
>> Regrettably, I have only offprints, and I managed to bury them in a
>> previous office move. SOMEWHERE I will have the source of the paper! I
>> will take a look tonight.
I haven't had time - university politics :-(
>I hope it turns up. It sounds pretty interesting. I haven't had good
>library access since Twin Cities, where you can be Joe Anybody and they
>let you export liberally from the local university libraries. They
>shipped in an anthology of Gauss's works from the University of
>Wisconsin. No charge, but I always paid my late fees and created them as
>a matter of civic pride.
I can summarise the results very simply.
For cryptographic use, never use more numbers than the square root
of the period, because the (realistic) birthday test starts to fail.
For statistical use, the excess uniformity will show in the (again
realistic) chi-squared test at period^(2/3).
You need to stay well below the inverse of the precision, because
the (again realistic) spacings test starts to fail. That means
no more than about a million numbers for IEEE 32-bit, or 10^14 for
IEEE 64-bit. But it ALSO means no more than about a hundred
million for 32-bit integers converted to IEEE 64-bit results.
Because those rules are based on statistical analyses of the number
representation, and NOTHING else, they are true for all classes
of generator, past, present and future.
I didn't publish the iterated spacing test results, but they are
the ones that reject most of Marsaglia's generators in the forms
they are published. Many are fixable. I didn't invent even that
test, incidentally, and it dates from 1948.
From: Gib Bogle on 27 Nov 2009 18:56
Ron Shepard wrote:
> In article <heeddb$h6f$1(a)soup.linux.pwf.cam.ac.uk>, nmm1(a)cam.ac.uk
>> A Limit on the Usable Length of a Pseudorandom Number Sequence (Journal of
>> Statistical Computation and Simulation (1992), vol.\ 42, pp.\ 47-54).
> I have no doubt that the original statement in this discussion, that
> less than a million numbers should be sampled from a 32-bit PRNG, is
> true for many statistical simulations. However, there are indeed
> many applications that are just fine with relatively short cycles.
> For example, is the simulation depends not only on the current state
> but on the history, then this can effectively increases the cycle
This is the case with virtually all the uses I make of RNGs. nmm1's
statement is nonsense for my applications.