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Generation of nonrecursive 𝑛-bit pseudorandom numbers based on 𝛽-transformation on [1, 2) (𝑛 = 64, 128, 192, …, 8192)

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  • Yaguchi Hirotake

    (Ajina 4-32-7, Hatsukaichi City, Hiroshima Prefecture, 738-0054, Japan)

Abstract

We show that we can generate nonrecursive 𝑛-bit pseudorandom numbers using a simple algorithm whose essential computation is five times repetition of (𝑛-bit) × \times (𝑛-bit) multiplication and taking out an 𝑛-bit integer from the result of multiplication. The algorithm can be described by 𝛽-transformation T β ⁢ ( X ) = β ⁢ X − ⌊ β ⁢ X ⌋ + 1 , X ∈ [ 1 , 2 ) , β > 1 . T_{\beta}(X)=\beta X-\lfloor\beta X\rfloor+1,\quad X\in[1,2),\,\beta>1. We consider the condition that repetition of 𝛽-transformation generates random numbers, and see why our simple algorithm works well for various values of 𝑛

Suggested Citation

  • Yaguchi Hirotake, 2025. "Generation of nonrecursive 𝑛-bit pseudorandom numbers based on 𝛽-transformation on [1, 2) (𝑛 = 64, 128, 192, …, 8192)," Monte Carlo Methods and Applications, De Gruyter, vol. 31(3), pages 257-263.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:3:p:257-263:n:1006
    DOI: 10.1515/mcma-2025-2015
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