A system of high-dimensional, efficient, long-cycle and portable uniform random number generators

ACM Transactions on Modeling and Computer Simulation

Volumn 13, Issue 4, 2003, Pages 299-309

  Deng, Lih Yuan ^a,c   Xu, Hongquan ^b  

^a UNIVERSITY OF MEMPHIS   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c University of Memphis   (United States)

Author keywords

DX k generator; FMRG k generator; Linear congruential generator; MT19937; Multiple recursive generator; Portable and efficient generator; Primitive polynomial

Indexed keywords

COMPUTATION IN FINITE FIELDS; CONGRUENTIAL GENERATORS; NUMERICAL ALGORITHMS; PRIMITIVE POLYNOMIALS;

ALGORITHMS; DECISION TABLES; LINEAR SYSTEMS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POLYNOMIALS; RANDOM NUMBER GENERATION;

NUMBER THEORY;

EID: 4243066342     PISSN: 10493301     EISSN: None     Source Type: Journal    
DOI: 10.1145/945511.945513     Document Type: Article

References (22)

1. ALANEN, J. D. AND KNUTH, D. E. 1964. Tables of finite fields. Sankhyā, Ser. A 26, 305-328.
2. CRANDALL, R. AND POMERANCE, C. 2000. Prime Numbers - A Computational Perspective. Springer-Verlag, New York, N.Y.
3. DENG, L. Y. AND GEORGE, E. O. 1990. Generation of uniform variates from several nearly uniformly distributed variables. Commun. Stat. B 19, 145-154.
4. DENG, L. Y. AND LIN, D. K. J. 2000. Random number generation for the new century. Amer. Statistician 54, 145-150.
5. DENG, L. Y., LIN, D. K. J., WANG, J., AND YUAN, Y. 1997. Statistical justification of combination generators. Stat. Sin. 7, 993-1003.
6. DENG, L. Y. AND ROUSSEAU, C. 1991. Recent development in random number generation. In Proceedings of the 29th ACM Annual Southeast Regional Conference (Apr.). ACM New York, 89-94.
7. GOLOMB, S. W. 1967. Shift Register Sequence. Holden-Day, San Francisco, Calif.
8. GRUBE, A. 1973. Mehrfach rekursiv-erzeugte Pseudo-Zufallszahlen. Z. für angewandte Math. und Mechanik 53, 223-225.
9. KNUTH, D. E. 1998. The Art of Computer Programming, Vol 2: Seminumerical Algorithms. 3rd ed. Addison-Wesley, Reading, Mass.
10. L'ECUYER, P. 1988. Efficient and portable combined random number generators. Commun. ACM 31, 742-748, 774.
11. L'ECUYER, P. 1990. Random numbers for simulation. Commun. ACM 33, 85-97.
12. L'ECUYER, P. 1997. Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J. Comput. 9, 57-60.
13. L'ECUYER, P. 1999. Good parameter sets for combined multiple recursive random number generators. Oper. Res. 47, 159-164.
14. L'ECUYER, P. AND BLOUIN, F. 1988. Linear congruential generators of order k > 1. In 1988 Winter Simulation Conference Proceedings, 432-439.
15. L'ECUYER, P., BLOUIN, F., AND COUTURE, R. 1993. A search for good multiple recursive linear random number generators. ACM Trans. Math. Softw. 3, 87-98.
16. r. ACM Trans. Math. Softw. 25, 367-374.
17. LEHMER, D. H. 1951. Mathematical methods in large-scale computing units. In Proceedings of the Second Symposium on Large Scale Digital Computing Machinery, Harvard University Press, Cambridge, Mass, 141-146.
18. LIDL, R. AND NIEDERREITEH, H. 1986. Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge, UK.
19. MATSUMOTO, M. AND NISHIMURA, T. 1998. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8, 3-20.
20. PAYNE, W. H., RABUNG, J. R., AND BOGYO, T. 1969. Coding the Lehmer pseudo number generator. Commun. ACM 12, 85-86.
21. p - 1. ACM Trans. Math. Softw. 23, 255-265.
22. ZIERLER, N. 1959. Linear recurring sequences. J. SIAM 7, 31-48.