Information on calculator Random Number Generators from PPC Journal articles

[Paul Dale]

(11-13-2016 07:27 AM)Namir Wrote:  Regarding the maximum absolute auto-correlation values, Algorithm 2 was 0.0287, while Algorithms 1 and 3 where 0.036316 and 0.0375916, respectively. Thus Algorithm 1 seem to yield less correlated numbers.

Wouldn't this favour Algorithm 2? It's autocorrelation is the lowest of the three.

Earlier this year I created a "random" number generator that passes the NIST SP 800-90B tests for randomness:

\[ { x_0 = frac ( \pi ) } \] \[ { x_{n+1} = frac ( e^{2 x_n + 1} ) } \] \[ R_n = frac( 2^{20} x_n ) \]

These \( R_n \) are completely deterministic and are produced from a rather well behaved function. There are also no problems with floating point rounding errors where the exponential is evaluated.

The point is that it is impossible to demonstrate randomness. It is only possible to demonstrate non-randomness.


Pauli

[ As an aside, the TestU01 suite did pick this function as non-random.]