MIXMAX

MIXMAX is the matrix-recursive random number generator introduced by my parents in:

On the Monte Carlo Simulation of Physical Systems
J.Comput.Phys. 97, 566 (1991), (DOI link)

Some of the algorithms used in this implementation, plus the theory behind the period is in my paper:

The MIXMAX random number generator
Comp. Phys. Commun. 196 (2015) 161 (DOI link) (Arxiv link)

Underlying MIXMAX is the theory of dynamical systems, more precisely of Kolmogorov's K-systems. Therefore, the floating point numbers generated by MIXMAX carry strong theoretical guarantees. This, and the fact that it passes all non-contrived tests of randomness, makes MIXMAX suitable for large scale Monte-Carlo simulations.


The generator is now mature and has proven itself over the years. The more recent versions include the code for skipping, which we strongly suggest for seeding and parallelization of Monte-Carlo. It is guaranteed that even if the user seeds from sequential seeds, e.g. 1,2,3... the initial vectors are independent and are located on the MIXMAX trajectory at least 10^100 steps apart. This is vastly superior to the usual practice of choosing random or non-ramdom seeds and hoping that the generator would not produce a collision in the streams produced from different seeds. There is a rather detailed Manual available.