Parallel linear congruential generators with Sophie-Germain moduli

Parallel Computing

Volumn 30, Issue 11, 2004, Pages 1217-1231

  Mascagni, Michael ^a   Chi, Hongmei ^a  

^a Florida State University   (United States)

Author keywords

Mersenne prime; Parallel random number generation; Prime modulus linear congruential generators; Sophie Germain prime

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MONTE CARLO METHODS; RANDOM NUMBER GENERATION; SOCIETIES AND INSTITUTIONS;

MERSENNE PRIME; PARALLEL RANDOM NUMBER GENERATION; PRIME MODULUS LINEAR CONGRUENTIAL GENERATORS; SOPHIE-GERMAIN PRIME;

PARALLEL PROCESSING SYSTEMS;

EID: 10644261506     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2004.08.002     Document Type: Article

References (22)

1. S.L. Anderson, Random number generators on vector supercomputers and other advanced architectures, SIAM Rev. 32 (1990) 221-251.
2. P.D. Coddington, Random number generators for parallel computers, http://www.npac.syr. edu/users/paulc/papers/NHSEreviewl.1/PRNGreview.ps, 1997.
3. A. DeMatteis, S. Pagnutti, Parallelization of random number generators and long-range correlations, Numerische Math. 53 (1988) 595-608.
4. A. DeMatteis, S. Pagnutti, Parallelization of random number generators and long-range correlations, Parallel Comput. 15 (1990) 155-164.
5. A. DeMatteis, S. Pagnutti, Controlling correlations in parallel Monte Carlo, Parallel Comput. 21 (1995) 73-84.
6. GIMPS. Great Internet Mersenne Prime Search, http://www.mersenne.org, 2004.
7. D. Gordon, Discrete logarithms in GF(p) using the number field sieve, SIAM J. Discrete Math. 6 (1) (1993) 124-138.
8. D.E. Knuth, The Art of Computer Programming Seminumerical Algorithms, vol. 2, 2nd ed., Addison-Wesley, Reading, Massachusetts, 1997.
9. L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences, John Wiley and Sons, New York, 1974.
10. P. L'Ecuyer, T.H. Andres, A random number generator based on the combination of four legs, Math. Comput. Simul. 44 (1997) 99-107.
11. H. Leeb, Asymptotic properties of the spectral test, diaphony, and related quantities, Math. Comput. 71 (237) (2002) 297-309.
12. M. Marsaglia, The diehard battery of tests of randomness. http://stat.fsu.edu/pub/ diehard, 1987.
13. M. Mascagni, Some methods of parallel pseudorandom number generation, In: Proceedings of the IMA Workshop on Algorithms for Parallel Processing, 1997.
14. M. Mascagni, Parallel linear congruential generators with prime moduli, Parallel Comput. 24 (1998) 923-936.
15. M. Mascagni, S.A. Cuccaro, D.V. Pryor, M.L. Robinson, A fast, high quality, and reproducible parallel lagged Fibonacci pseudorandom number generator, J. Comput. Phys. 119 (1995) 211-219.
16. M. Mascagni, A. Srinivasan, Algorithm 806: SPRNG: a scalable library for pseudorandom number generation, ACM Trans. Math. Software 26 (2000) 436-461.
17. H. Niederreiter, Random Number Generations and Quasi-Monte Carlo Methods, SIAM, Philadephia, 1992.
18. O.E. Percus, M.H. Kalo, Random number generators for mimd parallel processors, J. Parallel Distr. Comput. 6 (1989) 477-497.
19. P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, New York, 1996.
20. W.M. Schmidt, Equations over Finite Field: An Elementary Approach, Berlin, Springer, Lecture Notes in Mathematics, vol. 536, 1976.
21. SPRNG. Scalable parallel random number generators, http://sprng.fsu.edu.
22. A. Srinivasan, M. Mascagni, D. Ceperley, Testing parallel random number generators, Parallel Comput. 29 (2003) 69-94.