"Phoenex" <rib### [at] sapopt> wrote:
> To Jay Fox
>
> With a speed of 5 seconds to generate random 1000000000 numbers is needed more
> than 1 year and six months to sweep sequentially (0.0000000000000001 to
> 0.9999999999999999) a period of 2^53 or about 10^16 with a computer to work
> without stopping.
>
> How?
>
> 5 sec * (1E16) / 1E9 / 3600 / 24 / 365 = 1.585489599 years
>
> It is a long time working.
>
> Another example:
>
> If each number occupying one micrometer then the whole period is 10^16
> micrometers or 10000000 km, a long distance.
>
> However, as the generation of numbers is not sequential, it is natural
> that after a generation over a year never runs some numbers and other will be
> repeated.
> Precisely what happens in the real world random.
>
> So I still say that the importance of the size of the period is a question of
> need in each case.
>
> If this is the case with POVRay, then I fully agree with you, because I do not
> know the POVRay and do not know which their needs.
>
> If the POVRay works with integers, then it is better in fact a good random
> number generator with integers.
> The numbers generated by PRNGAlvo need to be converted in integers, and as such
> it takes time to be consumed at work.
>
> The algorithm PRNGAlvo was put in this discussion, always with an attitude of
> helping, and to receive critics about it.

Perhaps you missed my point. As I said, if all you need is one million random
numbers, with which you will perform the same set of operations, then a period
of a trillion is fine, or even a billion. So 2^52 is certainly overkill
(doesn't hurt, but doesn't necessarily help).

However, let's take sets of ordered triples, for example. Using only
single-precision accuracy (23 bits, assuming an equal-spaced lattice), there
are 2^(23*3) or 2^69 ordered triples in the unit cube. With a period of 2^52,
your generator cannot possibly produce every possible ordered triple in
single-precision, let alone produce every possible ordered triple at double
precision with approximately equal probability. For that, you would need a
period of at least 2^156, and more realistically, probably greater than 2^180.
And what if you need two ordered triples? For example, two random points in
space, or a random point and a random direction? Then we might demand a period
of at least 2^312.

Keep in mind, I understand that we'll never exhaust the total period of the RNG
by actually drawing that many values. That's not the point. The point is
whether, given a totally random seed value, an RNG can produce a particular
ordered triple. If a particular ordered triple can never be produced, no matter
how the RNG is seeded, then the RNG has a serious flaw. Maybe not for you, maybe
not for most people. But apparently enough people are concerned about the flaws
in LCG's that we're having this discussion. People care.

POV-Ray is all about ordered triples: positions or direction vectors in 3-D
space, color vectors (ignorning alpha), etc. POV-Ray's default RNG should have
a period of AT LEAST 2^156, if not 2^312. But why aim for the bare minimum? If
a period of 2^1000 or 2^10000 can be had for little or no additional
computational power, and a pittance in terms of storage space (system memory is
typically measured in GB, so why are we so concerned about a few KB?), then why
settle for something far, far, less?

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