Efficient and portable multiple recursive generators of large order

ACM Transactions on Modeling and Computer Simulation

Volumn 15, Issue 1, 2005, Pages 1-13

  Deng, Lih Yuan ^a,b  

^a UNIVERSITY OF MEMPHIS   (United States)

^b University of Memphis   (United States)

Author keywords

DX k generator; GMP; Irreducible polynomial; Linear congruential generator; MRG; Primitive polynomial

Indexed keywords

DX-K GENERATOR; GMP; IRREDUCIBLE POLYNOMIALS; LINEAR CONRUENTIAL GENERATORS (LCG); MULTIPLE RECURSIVE GENERATORS (MRG); PRIMITIVE POLYNOMIALS;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; DESIGN; PARAMETER ESTIMATION; PERFORMANCE; POLYNOMIALS; PROBLEM SOLVING;

RANDOM NUMBER GENERATION;

EID: 17644416411     PISSN: 10493301     EISSN: None     Source Type: Journal    
DOI: 10.1145/1044322.1044323     Document Type: Article

References (20)

1. ALANEN, J. D. AND KNUTH, D. E. 1964. Tables of finite fields. Sankhya, Series A 26, 305-328.
2. CRANDALL, R. AND POMERANCE, C. 2000. Prime Numbers - A Computational Perspective. Springer-Verlag, New York, NY.
3. DENG, L. Y. 2004. Generalized Mersenne prime number and its application to random number generation. In Monte Carlo and Quasi-Monte Carlo Methods 2002, H. Niederreiter, Ed. Springer-Verlag, 167-180.
4. DENG, L. Y., AND LIN, D. K. J. 2000. Random number generation for the new century. Amer. Statist. 54, 145-150.
5. DENG, L. Y. AND XU, H. 2003. A system of high-dimensional, efficient, long-cycle and portable uniform random number generators, ACM Trans. Model. Comput. Simul. 13, 4, 299-309.
6. GRUBE, A. 1973. Mehrfach rekursiv-erzeugte Pseudo-Zufallszahlen. Zeitschrift für angewandte Mathematik und Mechanik 53, 223-225.
7. KNUTH, D. E. 1998. The Art of Computer Programming, Vol 2: Seminumerical Algorithms. 3rd Ed. Addison-Wesley, Reading, MA.
8. L'ECUYER, P. 1988. Efficient and portable combined random number generators. Commun. ACM 31, 742-748, 774.
9. L'ECUYEB, P. 1997. Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J. Comput. 9, 57-60.
10. L'ECUYER, P. 1999. Good parameter sets for combined multiple recursive random number generators. Operat. Resear. 47, 159-164.
11. L'ECUYER, P. AND BLOUIN, F. 1988. Linear congruential generators of order k > 1. 1988 Winter Simulation Conference Proceedings, 432-439.
12. L'ECUYER, P., BLOUIN, F., AND COUTURE , R. 1993. A search for good multiple recursive linear random number generators. ACM Trans. Model. Comput. Simul. 3, 87-98.
13. L'ECUYER, P. AND COUTURE, R. 1997. An implementation of the lattice and spectral tests for multiple recursive linear random number generators, INFORMS J. Comput. 9, 2, 206-217.
14. r. ACM Trans. Math. Softw. 25, 367-374.
15. L'ECUYER, P. AND TOUZIN, R. 2004. On the Deng-Lin random number generators and related methods. Statist. Comput. 14, 5-9.
16. LEHMER, D. H. 1951. Mathematical methods in large-scale computing units. Proceedings of the 2nd Symposium on Large Scale Digital Computing Machinery. Harvard University Press, Cambridge, MA, 141-146.
17. LIDL, R. AND NIEDERREITER, H. 1994. Introduction to Finite Fields and Their Applications. Revised Ed. Cambridge University Press, Cambridge, MA.
18. MARSAGLIA, G. 1996. The Marsaglia random number CDROM including the DIEHARD battery of tests of randomness. See http://stat.fsu.edu/pub/diehard.
19. PAYNE, W. H., RABUNG, J. R., AND BOGYO, T. 1969. Coding the Lehmer pseudo number generator. Comm. ACM 12, 85-86.
20. P - 1. ACM Trans. Math. Softw. 23, 255-265.