Fast random number generators based on linear recurrences modulo 2: Overview and comparison

Proceedings - Winter Simulation Conference

Volumn 2005, Issue , 2005, Pages 110-119

  L'Ecuyer, Pierre ^a   Panneton, François ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; LINEAR EQUATIONS; STATISTICAL METHODS;

LINEAR RECURRENCES; LONG-PERIOD GENERATORS;

RANDOM NUMBER GENERATION;

EID: 33846673959     PISSN: 08917736     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/WSC.2005.1574244     Document Type: Conference Paper

References (41)

1. Compagner, A. 1991. The hierarchy of correlations in random binary sequences. Journal of Statistical Physics 63:883-896.
2. Couture, R., and P. L'Ecuyer. 2000. Lattice computations for random numbers. Mathematics of Computation 69 (230): 757-765.
3. Erdmann, E. D. 1992. Empirical tests of binary keystreams. Master's thesis, Department of Mathematics, Royal Holloway and Bedford New College, University of London.
4. Fushimi, M. 1983. Increasing the orders of equidistribution of the leading bits of the Tausworthe sequence. Information Processing Letters 16:189-192.
5. Hellekalek, P., and G. Larcher. (Eds.) 1998. Random and quasi-random point sets, Volume 138 of Lecture Notes in Statistics. New York: Springer.
6. Knuth, D. E. 1998. The art of computer programming, volume 2: Seminumerical algorithms. Third ed. Reading, Mass.: Addison-Wesley.
7. Law, A. M., and W. D. Kelton. 2000. Simulation modeling and analysis. Third ed. New York: McGraw-Hill.
8. L'Ecuyer, P. 1994. Uniform random number generation. Annals of Operations Research 53:77-120.
9. L'Ecuyer, P. 1996. Maximally equidistributed combined Tausworthe generators. Mathematics of Computation 65 (213): 203-213.
10. L'Ecuyer, P. 1999a. Good parameters and implementations for combined multiple recursive random number generators. Operations Research 47 (1): 159-164.
11. L'Ecuyer, P. 1999b. Tables of maximally equidistributed combined LFSR generators. Mathematics of Computation 68 (225): 261-269.
12. L'Ecuyer, P. 2004a. Polynomial integration lattices. In Monte Carlo and Quasi-Monte Carlo Methods 2002, ed. H. Niederreiter, 73-98. Berlin: Springer-Verlag.
13. L'Ecuyer, P. circa 2004b. Uniform random number generation. In Stochastic Simulation, ed. S. G. Henderson and B. L. Nelson, Handbooks of Operations Research and Management Science. Elsevier Science, chapter 3, to appear.
14. L'Ecuyer, P., and E. Buist. 2005. Simulation in Java with SSJ. In Proceedings of the 2005 Winter Simulation Conference.
15. L'Ecuyer, P., and J. Granger-Piché. 2003. Combined generators with components from different families. Mathematics and Computers in Simulation 62:395-404.
16. L'Ecuyer, P., and C. Lemieux. 2002. Recent advances in randomized quasi-Monte Carlo methods. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, ed. M. Dror, P. L'Ecuyer, and F. Szidarovszky, 419-474. Boston: Kluwer Academic Publishers.
17. L'Ecuyer, P., and F. Panneton. 2002. Construction of equidistributed generators based on linear recurrences modulo 2. In Monte Carlo and Quasi-Monte Carlo Methods 2000, ed. K.-T. Fang, F. J. Hickernell, and H. Niederreiter, 318-330. Berlin: Springer-Verlag.
18. L'Ecuyer, P., and R. Simard. 2002. TestU01: A software library in ANSI C for empirical testing of random number generators. Software user's guide. Available at 〈www.iro.umontreal.ca/~lecuyer〉.
19. L'Ecuyer, P., R. Simard, E. J. Chen, and W. D. Kelton. 2002. An object-oriented random-number package with many long streams and substreams. Operations Research 50 (6): 1073-1075.
20. r. In Proceedings of the 2000 Winter Simulation Conference, ed. J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, 683-689. Pistacaway, NJ: IEEE Press.
21. Lemieux, C., and P. L'Ecuyer. 2003. Randomized polynomial lattice rules for multivariate integration and simulation. SIAM Journal on Scientific Computing 24 (5): 1768-1789.
22. Lewis, T. G., and W. H. Payne. 1973. Generalized feedback shift register pseudorandom number algorithm. Journal of the ACM 20 (3): 456-468.
23. Lindholm, J. H. 1968. An analysis of the pseudo-randomness properties of subsequences of long m-sequences. IEEE Transactions on Information Theory IT-14 (4): 569-576.
24. Marsaglia, G. 1985. A current view of random number generators. In Computer Science and Statistics, Sixteenth Symposium on the Interface, 3-10. North-Holland, Amsterdam: Elsevier Science Publishers.
25. Marsaglia, G. 2003. Xorshift RNGs. Journal of Statistical Software 8 (14): 1-6. See 〈www.jstatsoft.org/v08/i14/xorshift.pdf〉.
26. Matsumoto, M., and Y. Kurita. 1992. Twisted GFSR generators. ACM Transactions on Modeling and Computer Simulation 2 (3): 179-194.
27. Matsumoto, M., and Y. Kurita. 1994. Twisted GFSR generators II. ACM Transactions on Modeling and Computer Simulation 4 (3): 254-266.
28. Matsumoto, M., and Y. Kurita. 1996. Strong deviations from randomness in m-sequences based on trinomials. ACM Transactions on Modeling and Computer Simulation 6 (2): 99-106.
29. Matsumoto, M., and T. Nishimura. 1998. Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modeling and Computer Simulation 8(1): 3-30.
30. Niederreiter, H. 1992. Random number generation and quasi-Monte Carlo methods, Volume 63 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: SIAM.
31. Nishimura, T. 2000. Tables of 64-bit Mersenne twisters. ACM Transactions on Modeling and Computer Simulation 10 (4): 348-357.
32. Panneton, F. 2004, August. Construction d'ensembles de points basée sur des récurrences linéaires dans un corps fini de caractéristique 2 pour la simulation Monte Carlo et l'intégration quasi-Monte Carlo. Ph. D. thesis, Département d'informatique et de recherche opérationnelle, Université de Montréal, Canada.
33. Panneton, F., and P. L'Ecuyer. 2004a. On the xorshift random number generators. ACM TOMACS, to appear.
34. 2w. In Monte Carlo and Quasi-Monte Carlo Methods 2002, ed. H. Niederreiter, 367-378. Berlin: Springer-Verlag.
35. 2w. In Monte Carlo and Quasi-Monte Carlo Methods 2004, ed. H. Niederreiter and D. Talay. To appear.
36. Panneton, F., P. L'Ecuyer, and M. Matsumoto. 2005. Improved long-period generators based on linear recurrences modulo 2. ACM Transactions on Mathematical Software, to appear.
37. Tausworthe, R. C. 1965. Random numbers generated by linear recurrence modulo two. Mathematics of Computation 19:201-209.
38. Tezuka, S. 1995. Uniform random numbers: Theory and practice. Norwell, Mass.: Kluwer Academic Publishers.
39. Tezuka, S., and P. L'Ecuyer. 1991. Efficient and portable combined Tausworthe random number generators. ACM Transactions on Modeling and Computer Simulation 1 (2): 99-112.
40. Tootill, J. P. R., W. D. Robinson, and D. J. Eagle. 1973. An asymptotically random Tausworthe sequence. Journal of the ACM 20:469-481.
41. Wang, D., and A. Compagner. 1993. On the use of reducible polynomials as random number generators. Mathematics of Computation 60:363-374.