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Conversion of Mersenne Twister to double-precision floating-point numbers

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  • Harase, Shin

Abstract

The 32-bit Mersenne Twister generator MT19937 is a widely used random number generator. To generate numbers with more than 32 bits in bit length, and particularly when converting into 53-bit double-precision floating-point numbers in [0,1) in the IEEE 754 format, the typical implementation concatenates two successive 32-bit integers and divides them by a power of 2. In this case, the 32-bit MT19937 is optimized in terms of its equidistribution properties (the so-called dimension of equidistribution with v-bit accuracy) under the assumption that one will mainly be using 32-bit output values, and hence the concatenation sometimes degrades the dimension of equidistribution compared with the simple use of 32-bit outputs. In this paper, we analyze such phenomena by investigating hidden F2-linear relations among the bits of high-dimensional outputs. Accordingly, we report that MT19937 with a specific lag set fails several statistical tests, such as the overlapping collision test, matrix rank test, and Hamming independence test.

Suggested Citation

  • Harase, Shin, 2019. "Conversion of Mersenne Twister to double-precision floating-point numbers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 76-83.
    • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:76-83
    DOI: 10.1016/j.matcom.2018.08.006
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    References listed on IDEAS

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    1. L’Ecuyer, Pierre & Simard, Richard, 2001. "On the performance of birthday spacings tests with certain families of random number generators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 131-137.
    2. Pierre L'Écuyer & Jean-François Cordeau & Richard Simard, 2000. "Close-Point Spatial Tests and Their Application to Random Number Generators," Operations Research, INFORMS, vol. 48(2), pages 308-317, April.
    3. Pierre L’Ecuyer & François Panneton, 2009. "F2-Linear Random Number Generators," International Series in Operations Research & Management Science, in: Christos Alexopoulos & David Goldsman & James R. Wilson (ed.), Advancing the Frontiers of Simulation, pages 169-193, Springer.
    4. Pierre L'Ecuyer & Richard Simard, 2014. "On the Lattice Structure of a Special Class of Multiple Recursive Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 449-460, August.
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    Cited by:

    1. Akahori, Jirô & Kinuya, Masahiro & Sawai, Takashi & Yuasa, Tomooki, 2021. "An efficient weak Euler–Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 540-565.

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