"Phoenex" <rib### [at] sapopt> wrote:
> Jay Fox
>
> Thank you for your work.
>
> This is what I need.
>
> I did some accounts, with Microsoft Calculator and with the Excel2003 and the
> results were very different.
>
> However you are right. With s = 123.4567 and with x = 0.4 the test failed to
> Diehard
>
> BIRTHDAY SPACINGS TEST
> THE overlapping 20-tuples Bitstream TEST
>
> I had the perception that.
> The seed has to be special. Why? I do not know.
> If you see my page is not by chance that I do
> s = seed + 12345.67890123456 0 <= seed <= 99999
>
> I have the feeling that the whole part of "s" should have 4 to 5 digits.
> Again thank you for your cooperation in such analysis.
>
> Can you will continue to do more analysis?
I'm having fun with it so far.

As far as s goes, the more entropy it contains, the better the randomness of the
output. Also, the larger the value of s is, the better the randomness. However,
larger values of s seem to reduce the period. The default seed of
12345.67890123456 has a period of 31,752,133. Changing s to 12345.6789
increases the period to about 79,639,459.

On the other hand, 1234.56789 has a period of 116,032,317, and 123.456789 has a
period of 1,078,493,612. Finally, a value of s of 12.3456789 has a period in
excess of a hundred billion (i.e., my program is still running, having already
produced over 110 billion iterates).

I assume that this is because the larger values of s cause greater truncation of
the lower bits of s*x, which causes information loss. The lost information was
vital to achieving a longer period.

Based on these heuristics, my guess is that good values of s will be in the low
three-digit range. This should provide reasonable randomness (as good or better
than a 32-bit LCG) with a reasonable period (longer than 2^32). That might be
better than a 32-bit LCG, but it will be inferior to a 64-bit LCG or a 32-bit
lag-1 MWC generator.

> Question: Are you a mathematician?
In my spare time, I suppose. My degree is in computer science, with the
equivalent of a minor in mathematics and physics. I hope to pursue a masters in
statistics in the near future.

>
> BTW see http://en.wikipedia.org/wiki/Multiply-with-carry
>
> This have a very big period.
The MWC (and CMWC, complementary MWC) generators are currently my favorite. They
are by far the simplest to understand of all the long-period generators, and
with careful planning, they can be just as effective as anything else out
there, at least for non-cryptographic purposes. I hope that at least one
long-period MWC or CMWC gets considered in POV-Ray.

Post a reply to this message