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]

A fast implementation in C/C++ of the generator was developed by Konstantin Savvidy.[2] The period of the generator is and the Kolmogorov entropy is for the matrix size [3].

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, and there exists a ROOT interface [4] as well the CLHEP interface for use in Geant4.[5] It has been recently tested extensively on very wide variety of platforms, as part of the release of ROOT.

A detailed analysis by L’Ecuyer, Wambergue and Bourceret[6] revealed that MINMAX generators, similarly to linear congruential generators, have a lattice structure and that produced random numbers, when considered as coordinate in a n-dimentional space, lie on a relativelly small number of parallel hyperplanes.

References

  1. ↑ Savvidy, G.K; Ter-Arutyunyan-Savvidy, N.G (1991). "On the Monte Carlo simulation of physical systems". Journal of Computational Physics. 97 (2): 566. Bibcode:1991JCoPh..97..566S. doi:10.1016/0021-9991(91)90015-D.
  2. ↑ K. Savvidy (2015). "The MIXMAX Random Number Generator". Computer Physics Communications. 196: 161–165. arXiv:1403.5355. Bibcode:2015CoPhC.196..161S. doi:10.1016/j.cpc.2015.06.003.
  3. ↑ K. Savvidy and G.Savvidy (2015). "Spectrum and Entropy of C-systems MIXMAX Random Number Generator". Chaos, Solitons and Fractals. 91: 33–38. arXiv:1510.06274. Bibcode:2016CSF....91...33S. doi:10.1016/j.chaos.2016.05.003.
  4. ↑ "ROOT: ROOT::Math::MixMaxEngine Class Reference". root.cern.ch. Retrieved 2016-04-09.
  5. ↑ "CLHEP - A Class Library for High Energy Physics". proj-clhep.web.cern.ch. Retrieved 2016-04-09.
  6. ↑ Pierre L’Ecuyer, Paul Wambergue, and Erwan Bourceret (September 22, 2017). "Spectral Analysis of the MIXMAX Random Number Generators" (PDF).
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