Multiplicative congruential random number generators with modulus2ß: An exhaustive analysis for ß=32 and a partial analysis for ß=48

Mathematics of Computation

Volumn 54, Issue 189, 1990, Pages 331-344

  Fishman, George S ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Congruential generator; Discrepancy; Random number generation; Spectral test

Indexed keywords

EID: 84966232835     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1990-0993929-9     Document Type: Article

References (18)

1. J. H. Ahrens and U. Dieter, Uniform random numbers, Technical University of Graz, 1977.
2. W. Beyer, Private communication, 1988.
3. I. Borosh and H. Niederreiter, Optimal multipliers for pseudo-random number generation by the linear congruential method, BIT 23 (1983), 65-74.
4. J. W. S. Cassels, An introduction to the geometry of numbers. Springer-Verlag, New York, 1959.
5. R. R. Coveyou and R. D. MacPherson, Fourier analysis of uniform random number generators, J. Assoc. Comput. Mach. 14 (1967), 100-119.
6. U. Dieter, Pseudo-random numbers: the exact distribution of pairs, Math. Comp. 25 (1971), 855-883.
7. U. Dieter, How to calculate shortest vectors in a lattice, Math. Comp. 29 (1975), 827-833.
8. M. Durst, Private communication, 1989.
9. G. S. Fishman and L. R. Moore, An exhaustive analysis of multiplicative congruential random number generators with modulus 2 - 1, SIAM J. Sei. Statist. Comput. 7 (1986), 24-45.
10. D. E. Knuth, The art of computer programming: Semi-numerical algorithms, 2nd ed., Addison- Wesley, 1981.
11. G. Marsaglia, Random numbers fall mainly in the plane, Proc. Nat. Acad. Sei. USA. 61 (1968), 25-28.
12. G. Marsaglia, The structure of linear congruential sequences, in Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), Academic Press, New York, 1972, pp. 249-285.
13. H. Niederreiter, Statistical independence of linear congruential pseudo-random numbers, Bull. Amer. Math. Soc. 82 (1976), 927-929.
14. H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. Math. 26 (1977), 99-181.
15. H. Niederreiter, The serial test for linear congruential pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 273-274.
16. H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041.
17. H. Niederreiter, The serial test for pseudo-random numbers generated by the linear congruential method, Numer. Math. 46 (1985), 51-68.
18. C. S. Smith, Multiplicative pseudo-random number generators with prime modulus, J. Assoc. Comput. Mach. 18 (1971), 586-593