×

On the CRAY-system random number generator. (English) Zbl 1036.68633

Simulation 72, No. 3, 163-169 (1999).
Summary: We present a theoretical and empirical analysis of the quality of the CRAY-system random number generator RANF in parallel settings. Subsequences of this generator are used to obtain parallel streams of random numbers for each processor. We use the spectral rest to analyze the equality of lagged subsequences of RANF with stepsizes \(2^l\), \(l\geq 1\), appropriate for CRAY systems. Our results demonstrate that with increasing \(l\), the quality of lagged subsequence is strongly reduced in comparison to the original sequence. The results are supported by a numerical Monte Carlo integration study. We also use the spectral test to exhibit the well known long-range correlations between consecutive blocks of random numbers obtained from RANF.

MSC:

68U20 Simulation (MSC2010)
Full Text: DOI

References:

[1] Anderson, S.L., SIAM Rev. 32 pp 221– (1990) · Zbl 0708.65004
[2] Coddington, P., International Journal of Modern Physics 5 pp 547– (1994)
[3] Coddington, P., Random Number Generators for Parallel Computers (1996)
[4] DeMatteis, A., Numer. Math. 53 pp 595– (1988) · Zbl 0633.65006
[5] DeMatteis, A., Parallel Computing 13 pp 193– (1990) · Zbl 0703.65009
[6] DeMatteis, A., International Journal of Computer Mathematics 43 pp 189– (1992) · Zbl 0758.65003
[7] Durst, M.J., Proceedings of the 1989 Winter Simulation Conference
[8] Fishman, G.S., Monte Carlo: Concepts, Algorithms, and Applications (1996)
[9] Hellekalek, P., Lecture Notes in Statistics, in: On the Assessment of Random and Quasi-Random Point Sets (1998) · Zbl 0937.65004
[10] Percus, O.E., Journal of Parallel and Distributed Computing 6 pp 477– (1989)
[11] Ripley, B.D., Proceedings of the Royal Society of London 389 pp 197– (1983) · Zbl 0516.65003
[12] Vattulainen, I., Comp. Phys. Comm. 86 pp 209– (1995) · Zbl 0873.65004
[13] Knuth, D.E., The Art of Computer Programming, Volume 2: Seminumerical Algorithms (1981) · Zbl 0477.65002
[14] Dieter, U., Mathematics of Computation 29 (131) pp 827– (1975)
[15] L’Ecuyer, P., Mathematics of Computation 68 (225) pp 249– (1999) · Zbl 0917.65002
[16] L’Ecuyer, P., Annals of Operations Research 53 pp 77– (1994) · Zbl 0843.65004
[17] Entacher, K., ACM Transactions on Modeling and Computer Simulation 7 (1) pp 61– (1998) · Zbl 0917.65006
[18] Entacher, K., ACM Transactions on Modeling and Computer Simulation (1999)
[19] L’Ecuyer, P., INFORMS journal on Computing 9 (2) pp 206– (1997) · Zbl 0889.65004
[20] Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods (1992) · Zbl 0761.65002
[21] DeMatteis, A., Journal of Comp. Appl. Math. 39 pp 49– (1992) · Zbl 0745.65005
[22] Eichenauer-Herrmann, J., Numerical Mathematics 56 pp 609– (1989) · Zbl 0662.65003
[23] Entacher, K., Monte Carlo Methods and Applications 4 (1) pp 1– (1998) · Zbl 0907.65005
[24] Hellekalek, P., Twelfth Workshop on Parallel and Distributed Simultation, PADS’98
[25] Entacher, K., A Collection of Selected Pseudorandom Number Generators with Linear Structures–Updated Version (1998) · Zbl 0917.65006
[26] L’Ecuyer, P., INFORMS Journal on Computing 9 pp 57– (1997) · Zbl 0894.65004
[27] Ceperley, D., SPRNG: Scalable Parallel Random Number Generators (1997)
[28] L’Ecuyer, P., Mathematics and Computers in Simulation 44 pp 99– (1997) · Zbl 1017.65501
[29] Eichenauer-Herrmann, J., Math. Comp. 60 pp 375– (1993)
[30] Niederreiter, H., Lecture Notes in Statistics, in: New Developments in Uniform Pseudorandom Number and Vector Generation (1995) · Zbl 0893.11030
[31] Mascagni, M., Parallel Computing 24 (5) pp 923– (1998) · Zbl 0909.68006
[32] Hellekalek, P., The PLAB www-server (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.