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Spectral test of the MIXMAX random number generators

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  • Martirosyan, Narek
  • Savvidy, Konstantin
  • Savvidy, George

Abstract

An important statistical test on the pseudo-random number generators is called the spectral test. The test is aimed at answering the question of distribution of the generated pseudo-random vectors in dimensions d that are larger than the genuine dimension of a generator N. In particular, the default MIXMAX generators have various dimensions: N=8,17,240 and higher. Therefore the spectral test is important to perform in dimensions d > 8 for N=8 generator, d > 17 for N=17 and d > 240 for N=240 generator. These tests have been performed by L’Ecuyer and collaborators. When d > N the vectors of the generated numbers fall into the parallel hyperplanes and the distances between them can be larger than the genuine “resolution” of the MIXMAX generators, which is l=2−61. The aim of this article is to further study the spectral properties of the MIXMAX generators, to investigate the dependence of the spectral properties of the MIXMAX generators as a function of their internal parameters and in particular their dependence on the parameter m. We found that the best spectral properties are realized when m is between 224 and 236, a range which is inclusive of the value of the N=17 generator. We also provide the alternative parameters for the generators, N=8 and N=240 with m in this optimized range.

Suggested Citation

  • Martirosyan, Narek & Savvidy, Konstantin & Savvidy, George, 2019. "Spectral test of the MIXMAX random number generators," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 242-248.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:242-248
    DOI: 10.1016/j.chaos.2018.11.024
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    References listed on IDEAS

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    1. Savvidy, George & Savvidy, Konstantin, 2018. "Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 244-250.
    2. Savvidy, Konstantin & Savvidy, George, 2016. "Spectrum and entropy of C-systems MIXMAX random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 33-38.
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    1. Savvidy, George & Savvidy, Konstantin, 2018. "Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 244-250.
    2. Pierre L’Ecuyer & Paul Wambergue & Erwan Bourceret, 2020. "Spectral Analysis of the MIXMAX Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 135-144, January.

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