"Phoenex" <rib### [at] sapopt> wrote:
> cllpka
>
> I mean * p-values of * 0 *  zero and * 1 * one.
>
>
> Many people, say to get a good PRNG algorithm, several conditions are necessary:
>
> Must have a very large, which according to some, the more better.
> Must pass in a large number of mathematical/statistical tests.
> Should be easily portable and implementation.
>
> In my humble opinion, a * good * algorithm should have a period on the needs.

Yes, but your needs might not match the needs of other users. If all you need is
a trillion random numbers, where you are going to do the SAME EXACT operation on
each of those trillion numbers, then all you need is a period on the order of
trillions (e.g., a trillion squared). If you only need a thousand, then a
period of a million will probably suffice.

On the other hand, if you need ordered n-tuples (the simplest example relevant
to POV-Ray would be ordered triples as position or direction vectors), then
you'll need something on the order of a trillion to the n-th power, e.g., a
trillion to the 2*n power. Scientific applications routinely involve large n,
where even the best RNG's available are theoretically deficient, but we use
what we have because that's all we have. For POV-Ray, an example n might be 81,
where we're talking about sampling 81 pixels for anti-aliasing in a 9x9 grid.
Another example would be focal blur. Currently the jitter algorithm is pretty
weak, so visual artifacts can be trivially generated on purpose (above what we
would expect from a random sampling), and unfortunately, occasionally by
accident.

If you only need a thousand n-tuples (a very low number), you might think that a
period of a million is sufficient. But if n is 3, a million is already quite
insufficient.

So be careful when you say that a period is based on the needs: you might
convince yourself that a "really long" period is long enough, when in fact
it's very insufficient. Longer periods, if they can be attained at very little
additional cost (e.g., just a few extra bytes of storage, but no extra
computational time), should always be favored.

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