Good news for PPC Random-Number Generator

[Albert Chan]

(05-19-2021 10:04 PM)Thomas Okken Wrote:  With the HP-42S (and RPL, Free42, 71B) RNG, just looking for a repeated number is not sufficient, since they use a 15-digit seed internally, and then truncate it to 12 digits before returning it to the user code environment.

Last 3 digits are hidden, but is easily deduced.
Example, I just tried Free42 RAN, and get 0.248998059347, 0.866775882678

>>> a, m = 2851130928467, 10**15
>>> x1, x2 = 248998059347, 866775882678
>>> t = x1 * 1000
>>> [t+b for b in range(1000) if (t+b)*a % m // 1000 == x2]
[248998059347131L]
>>> _[0] * a % m
866775882678177L
>>> _ * a % m
34252568964659L

It predicted next RAN is 0.0342525689646, which is indeed the case.

Quote: The least significant of those 15 digits is always a 1, 3, 7, or 9, so the theoretical maximum cycle is 4e14 long, but I don't know if the actual cycles exhibited by that RNG are that long or whether there are multiple disjoint cycles.

Period is 5E13, from Joe Horn's post