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F2-Linear Random Number Generators

Part of the International Series in Operations Research & Management Science book series (ISOR,volume 133)

Abstract

Random number generators based on linear recurrences modulo 2 are among the fastest long-period generators currently available. The uniformity and independence of the points they produce, by taking vectors of successive output values from all possible initial states, can be measured by theoretical figures of merit that can be computed quickly, and the generators having good values for these figures of merit are statistically reliable in general. Some of these generators can also provide disjoint streams and substreams efficiently. In this paper, we review the most interesting construction methods for these generators, examine their theoretical and empirical properties, describe the relevant computational tools and algorithms, and make comparisons.

Keywords

  • Random Number Generator
  • Characteristic Polynomial
  • Combine Generator
  • Minimal Polynomial
  • Linear Feedback Shift Register

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

This work has been supported by NSERC-Canada grant No. ODGP0110050 and a Canada Research Chair to the first author. This paper was written while the first author was a visiting scientist at the University of Salzburg, Austria, in 2005, and at IRISA, Rennes, in 2006. A short draft of it appeared in the Proceedings of the 2005 Winter Simulation Conference. Richard Simard helped doing the speed tests.

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Correspondence to Pierre L’Ecuyer .

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L’Ecuyer, P., Panneton, F. (2009). F2-Linear Random Number Generators. In: Alexopoulos, C., Goldsman, D., Wilson, J. (eds) Advancing the Frontiers of Simulation. International Series in Operations Research & Management Science, vol 133. Springer, Boston, MA. https://doi.org/10.1007/b110059_9

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