New PRNG for calculators

[ttw]

The function as written Frac(exp(exp(exp(x))) is uniformly distributed mod 1. So the OP's pRNG should work, except for rounding and discretization errors (All pRNGs have this problem.).

Frac(Exp(x)) is also uniformly distributed, Frac(Ln(x)) isn't. I found a paper proving this result and giving criteria for the uniform distribution of some types of functions.

https://dwc.knaw.nl/DL/publications/PU00018885.pdf

Daniel Shanks: "ln( ln( ln ( x ) ) ) approaches infinity with great dignity."

(It's a comment about the inverse function. I've only seen ln(ln(ln(ln(x)))) in practice.)