Tables of linear congruential generators
of different sizes and good lattice structure
Author:
Pierre L'Ecuyer
Journal:
Math. Comp. 68 (1999), 249-260
MSC (1991):
Primary 65C10
DOI:
https://doi.org/10.1090/S0025-5718-99-00996-5
MathSciNet review:
1489972
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Abstract | References | Similar Articles | Additional Information
Abstract: We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For , we take as a modulus
the largest prime smaller than
, and provide a list of multipliers
such that the MLCG with modulus
and multiplier
has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli
, for multiplicative and non-multiplicative LCGs.
- 1. J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1988. With contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 920369
- 2. George S. Fishman, Multiplicative congruential random number generators with modulus 2^{𝛽}: an exhaustive analysis for 𝛽=32 and a partial analysis for 𝛽=48, Math. Comp. 54 (1990), no. 189, 331–344. MR 993929, https://doi.org/10.1090/S0025-5718-1990-0993929-9
- 3. George S. Fishman, Monte Carlo, Springer Series in Operations Research, Springer-Verlag, New York, 1996. Concepts, algorithms, and applications. MR 1392474
- 4.
G. S. Fishman and L. S. Moore III, An exhaustive analysis of multiplicative congruential random number generators with modulus
, SIAM Journal on Scientific and Statistical Computing 7 (1986), no. 1, 24-45, 1058. MR 87g:65010
- 5. Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878
- 6. Pierre L’Ecuyer, Efficient and portable combined random number generators, Comm. ACM 31 (1988), no. 6, 742–749, 774. MR 945034, https://doi.org/10.1145/62959.62969
- 7. -, Random number generation, Handbook on Simulation (Jerry Banks, ed.), Wiley, 1998, To appear.
- 8. P. L'Ecuyer, F. Blouin, and R. Couture, A search for good multiple recursive random number generators, ACM Transactions on Modeling and Computer Simulation 3 (1993), no. 2, 87-98.
- 9. P. L'Ecuyer and R. Couture, An implementation of the lattice and spectral tests for multiple recursive linear random number generators, INFORMS Journal on Computing 9 (1997), no. 2, 206-217. CMP 98:03
- 10. F. Delaurens and F.-J. Mustieles, A deterministic particle method for solving kinetic transport equations: the semiconductor Boltzmann equation case, SIAM J. Appl. Math. 52 (1992), no. 4, 973–988. MR 1174041, https://doi.org/10.1137/0152056
- 11. M. Sakamoto and S. Morito, Combination of multiplicative congruential random number generators with safe prime modulus, Proceedings of the 1995 Winter Simulation Conference, IEEE Press, 1995, pp. 309-315.
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Additional Information
Pierre L'Ecuyer
Affiliation:
Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email:
lecuyer@iro.umontreal.ca
DOI:
https://doi.org/10.1090/S0025-5718-99-00996-5
Keywords:
Random number generation,
linear congruential,
lattice structure,
spectral test
Received by editor(s):
May 9, 1997
Additional Notes:
This work has been supported by NSERC-Canada grants ODGP0110050 and SMF0169893, and FCAR-Québec grant 93ER1654. Thanks to Raymond Couture, Peter Hellekalek, and Harald Niederreiter for useful suggestions, to Ajmal Chaumun who helped in computing the tables, and to Karl Entacher who pointed out an error in an earlier version.
Article copyright:
© Copyright 1999
American Mathematical Society