MIXMAX swMATH ID: 29765 Software Authors: Savvidy, Konstantin G. Description: The MIXMAX random number generator. In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with (O(N)) operations. Second, to recursively compute its characteristic polynomial with (O(N^2)) operations, and third, to apply skips of large number of steps (S) to the sequence in (O(N^2 log(S))) operations. Homepage: https://mixmax.hepforge.org/ Keywords: pseudo-random number generator; Kolmogorov K-system; deterministic chaos Related Software: TestU01; RANLUX; MRG32k3a; MersenneTwister; K2; GitHub; PARI/GP Cited in: 6 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Spectrum and entropy of C-systems MIXMAX random number generator. Zbl 1372.37060Savvidy, Konstantin; Savvidy, George 2016 The MIXMAX random number generator. Zbl 1360.65031Savvidy, Konstantin G. 2015 all top 5 Cited by 8 Authors 4 Savvidy, George K. 4 Savvidy, Konstantin G. 1 Babujian, Hratchya M. 1 Bourceret, Erwan 1 L’Ecuyer, Pierre 1 Martirosyan, Narek 1 Poghosyan, H. R. 1 Wambergue, Paul Cited in 4 Serials 3 Chaos, Solitons and Fractals 1 Computer Physics Communications 1 Theoretical and Mathematical Physics 1 INFORMS Journal on Computing Cited in 4 Fields 5 Numerical analysis (65-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Number theory (11-XX) 1 Geometry (51-XX) Citations by Year