Linear recurrences with carry as uniform random number generators

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Linear recurrences with carry as uniform random number generators

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Winter Simulation Conference archive
Proceedings of the 27th conference on Winter simulation table of contents

Arlington, Virginia, United States

Pages: 263 - 267

Year of Publication: 1995

ISBN:0-7803-3018-8

Authors

Raymond Couture	Département d'IRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Pierre L'Ecuyer	Département d'IRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada

Sponsors

IIE : Institute of Industrial Engineers
SCS : Society for Computer Simulation
ASA : American Statistical Association
NIST : National Institue of Standards & Technology
IEEE-CS : Computer Society
IEEE-SMCS : Systems, Man & Cybernetics Society
ACM: Association for Computing Machinery
INFORMS/CS : Computer Science TC
SIGSIM: ACM Special Interest Group on Simulation and Modeling

Publisher

IEEE Computer Society Washington, DC, USA

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Downloads (6 Weeks): 0, Downloads (12 Months): 11, Citation Count: 2

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ABSTRACT

We study the multiply-with-carry family of generators proposed by G. Marsaglia (1994) as a generalisation of the previous add-with-carry and subtract-with-borrow families of G. Marsaglia and A. Zaman (1991). We define for them a general (infinite) state space and focus our attention on the (finite) subset of recurrent states. This subset will, in turn, split into possibly several subgenerators. We discuss the uniformity of the d-dimensional distribution of the output of these subgenerators over their full period. In order to improve this uniformity for higher dimensions, we propose a method for finding good parameters in terms of the spectral test.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Raymond Couture , Pierre L'Ecuyer, On the lattice structure of certain linear congruential sequences related to AWC/SWB generators, Mathematics of Computation, v.62 n.206, p.799-808, April 1994 [doi>10.2307/2153540]
	2	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	3	L'Ecuyer, P. 1994. Uniform random number generation. Annals of Operations Research, 53:77-120.
	4	Marsaglia, G. 1994. Yet another rng. Posted to the electronic billboard sci. star .ma, August 1.
	5	Marsaglia, G., and A. Zaman. 1991. A new class of random number generators. The Annals of Applied Probability, 1:462-480.
	6	Harald Niederreiter, Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
	7	Shu Tezuka , Pierre L'Ecuyer , Raymond Couture, On the lattice structure of the add-with-carry and subtract-with-borrow random number generators, ACM Transactions on Modeling and Computer Simulation (TOMACS), v.3 n.4, p.315-331, Oct. 1993 [doi>10.1145/159737.159749]

CITED BY 2

	Pierre L'Ecuyer, Uniform random number generators, Proceedings of the 30th conference on Winter simulation, p.97-104, December 13-16, 1998, Washington, D.C., United States
	Pierre L'Ecuyer, Uniform random number generators: a review, Proceedings of the 29th conference on Winter simulation, p.127-134, December 07-10, 1997, Atlanta, Georgia, United States