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Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs

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  • L’Ecuyer, Pierre
  • Munger, David
  • Oreshkin, Boris
  • Simard, Richard

Abstract

We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environments. In this context, for the great majority of applications, independent streams of random numbers are required, each being computed on a single processing element at a time. Sometimes, thousands or even millions of such streams are needed. We explain how they can be produced and managed. We devote particular attention to multiple streams for GPU devices.

Suggested Citation

  • L’Ecuyer, Pierre & Munger, David & Oreshkin, Boris & Simard, Richard, 2017. "Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 3-17.
    • Handle: RePEc:eee:matcom:v:135:y:2017:i:c:p:3-17
    DOI: 10.1016/j.matcom.2016.05.005
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    References listed on IDEAS

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    1. Lih-Yuan Deng & Jyh-Jen Horng Shiau & Henry Horng-Shing Lu, 2012. "Large-Order Multiple Recursive Generators with Modulus 2 31 - 1," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 636-647, November.
    2. L'Ecuyer, Pierre & Andres, Terry H., 1997. "A random number generator based on the combination of four LCGs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(1), pages 99-107.
    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. Hellekalek, P., 1998. "Good random number generators are (not so) easy to find," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(5), pages 485-505.
    5. 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.
    6. Andrew Karl & Randy Eubank & Jelena Milovanovic & Mark Reiser & Dennis Young, 2014. "Using RngStreams for parallel random number generation in C++ and R," Computational Statistics, Springer, vol. 29(5), pages 1301-1320, October.
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    Cited by:

    1. Kolonko, Michael & Gu, Feng & Wu, Zijun, 2019. "Improving the statistical quality of random number generators by applying a simple ratio transformation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 130-142.
    2. 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.
    3. 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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