New PRNG for calculators

[Namir]

(06-07-2024 01:35 AM)ttw Wrote:  Does the loss of significance (Exp(Exp(Exp(1))) is 3814279.1...) give any trouble? On an HP50g, the smallest result before the MOD 1 reduction is 15.1542622415 and the largest is 3814279.10484. The next inputs would differ in the last 4 digits. This may have no significance as the output wraps around the unit interval 15 or more times.

Interval transformations are not preserved.
Transformation of (.10001,.10002) yields: (.486654,.48734).
Transformation of (.20001, .20002) yields: (.72485, .72609).
Transformation of (.65001, .65002) yields ( .57199, .68771).
Transformation of (.69001, .69002) yields (.20483, .43117).
Transformation of(.69003, .69004) yields (.65744, .88376).

The successors of numbers falling to a small interval on the 0 side of the unit interval have a very different distribution from those falling to a small interval on the 1 side.

I guess MATLAB uses more significant figures than typical calculators. How many random numbers did you generate?

Namir