New PRNG for calculators

[ttw]

(06-07-2024 02:05 AM)Namir Wrote:  I guess MATLAB uses more significant figures than typical calculators. How many random numbers did you generate?

Namir

None. I just looked at small intervals. The image of sufficiently small intervals with the same length transforms to another image that doesn't exceed 1.0 in length, but it does differ with the position of the interval. Knowing the interval allows one to guess the output of the next number (at least its range) with pretty good probability. For those that wrap around quite a bit, (near 1.0), one knows little about the next number; .90001's successor is .555669 (to HP50g precision)' .90002's successor is .276095. These results come from the pre-reduction interval 120626.555669 and 120661.27695. Neither of these results helps in figuring out .900015's successor (which is .914477). The successor of .10001 is 20.4866596716 and of .10002 is 20.487343122; the successor of .10015 is 20.487001537. This lies between the successors of .10001 and .10002 both before and after the MOD 1 mapping.

Exp(x) expands differently for each x. For this reason, mappings within finite fields (like shift registers) or rings (like linear congruential generators) are often used. Points within a small interval, no matter where in the range of the generator, will get spread out approximately uniformly over the whole space.

Without doing any analysis, I think you could make the exp(exp(exp(x))) work by mapping the output to binary ,then XORing with the output of a linear congruential generator.