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 wellknown conditions, these discretetime dynamical systems have the highly desirable Kmixing 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 pseudorandom 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 multidimensional generalization of the famous catmap. 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:  pseudorandom number generator; Kolmogorov Ksystem; 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 Csystems MIXMAX random number generator. Zbl 1372.37060 Savvidy, Konstantin; Savvidy, George 
2016

The MIXMAX random number generator. Zbl 1360.65031 Savvidy, Konstantin G. 
2015

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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 (65XX) 
2  Dynamical systems and ergodic theory (37XX) 
1  Number theory (11XX) 
1  Geometry (51XX) 