MIXMAX generator

The MIXMAX generator is a family of pseudorandom number generators (PRNG) and is based on Anosov C-systems (Anosov diffeomorphism) and Kolmogorov K-systems (Kolmogorov automorphism). It was introduced in a 1986 preprint by G. Savvidy and N. Ter-Arutyunyan-Savvidy and published in 1991.[1]

MIXMAX generator

A pseudorandom number generator.
Class	pseudorandom number generator
Data structure	Array
Worst-case performance	O(n)
Best-case performance	O(n)
Average performance	O(n)
Worst-case space complexity	O(n)

A fast implementation in C/C++ of the generator was developed by Konstantin Savvidy.[2] The period of the generator is ${\displaystyle 10^{4389}}$ and the Kolmogorov entropy is ${\displaystyle 8679.2}$ for the matrix size ${\displaystyle N=240}$.[3] That generator occupies less than 2 kb, and if a smaller generator state is required, a N = 17 version with less than 200 bytes memory requirement also exists.

The generator works on most 64-bit systems, including 64-bit Linux flavors and Intel Mac. It has also been tested on PPC and ARM architectures. The latest version also runs on 32-bit systems and on Windows. The generator is equally usable with C++ programs, has been chosen as the default generator in CLHEP[4] for use in Geant4[5] and there exists a ROOT interface.[6] It has been recently tested extensively on very wide variety of platforms, as part of the CLHEP/Geant4 release.

An analysis by L’Ecuyer, Wambergue and Bourceret,[7] see also,[8] showed that MIXMAX generators, just as all other Multiple Recursive Generators and linear congruential generators, has a lattice structure and that the produced random numbers, when considered as coordinate in a n > N - dimensional space, lie on a set of parallel hyperplanes and determined the maximum distance between the covering hyperplanes.