Mixed Congruential Random Number Generators for Binary Machines

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Mixed Congruential Random Number Generators for Binary Machines

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Journal of the ACM (JACM) archive
Volume 11 , Issue 1 (January 1964) table of contents

Pages: 31 - 40

Year of Publication: 1964

ISSN:0004-5411

Authors

T. E. Hull	University of Toronto, Toronto, Ont., Canada and University of British Columbia, Vancouver, B.C., Canada
A. R. Dobell	University of British Columbia, Vancouver, B.C., Canada

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 27, Citation Count: 12

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abstract references cited by index terms collaborative colleagues

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ABSTRACT

Random number generators of the mixed congruential type have recently been proposed. They appear to have some advantages over those of the multiplicative type, except that their statistical behavior is unsatisfactory in some cases. It is shown theoretically that a certain class of these mixed generators should be expected to fail statistical tests for randomness. Extensive testing confirms this hypothesis and makes possible a more precise definition of the unsatisfactory class. It is concluded that the advantages of mixed generators can be realized only in special circumstances. On machines with relatively short multiplication times the multiplicative generators are to be preferred.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	J. L. Allard , A. R. Dobell , T. E. Hull, Mixed Congruential Random Number Generators for Decimal Machines, Journal of the ACM (JACM), v.10 n.2, p.131-141, April 1963 [doi>10.1145/321160.321163]
	2	R. R. Coveyou, Serial Correlation in the Generation of Pseudo-Random Numbers, Journal of the ACM (JACM), v.7 n.1, p.72-74, Jan. 1960 [doi>10.1145/321008.321018]
	3	GOOD, 1. J. The serial test for sampling numbers and other tests for randomness. Proc. Camb. Phil. Soc. 49 (1953), 276-284.
	4	GOOD, I .J . On the serial test for random sequences. Ann. Math. Stat. 28 (1957), 262-264.
	5	Martin Greenberger, Notes on a New Pseudo-Random Number Generator, Journal of the ACM (JACM), v.8 n.2, p.163-167, April 1961 [doi>10.1145/321062.321065]
	6	GREENBEIGER, MARTIN. An a priori determination of serial correlation in computer generated random numbers. Math. Comp. 15 (1961), 383-389. See also: corrigenda, Math. Comp. 16 (1962), 126 and 406.
	7	HULL, W. E., AND DO,ELL, A.R. Random number generators. SIAM Rev. 4 (1962), 230-254.
	8	Heidi G. Kuehn, A 48-bit pseudo-random generator, Communications of the ACM, v.4 n.8, p.350-352, Aug. 1961 [doi>10.1145/366678.366690]
	9	PEACH, PAUL. Bias in pseudo-random numbers. J. Am. Stat. Assoc. 56 (1961), 610-618.
	10	A. Rotenberg, A New Pseudo-Random Number Generator, Journal of the ACM (JACM), v.7 n.1, p.75-77, Jan. 1960 [doi>10.1145/321008.321019]
	11	THOMSON, W. E. A modified congruence method of generating pseudo-random numbers. Comput. J. 1 (1958), 83 and 86.

CITED BY 12

	P. A. D. de Maine, The self-judgment method of curve fitting, Communications of the ACM, v.8 n.8, p.518-526, Aug. 1965
	Samuel Gorenstein, Testing a random number generator, Communications of the ACM, v.10 n.2, p.111-118, Feb. 1967
	John M. Gleason, Screening tests of pseudorandom number generators on IBM PC's and compatibles, Proceedings of the 17th conference on Winter simulation, p.505-507, December 11-13, 1985, San Francisco, California, United States
	John RB Whittlesey, A comparison of the correlational behavior of random number generators for the IBM 360, Communications of the ACM, v.11 n.9, p.641-644, Sept. 1968
	George C. Canavos, A comparative analysis of two concepts in the generation of uniform pseudo-random numbers, Proceedings of the 1967 22nd national conference, p.485-501, January 1967, Washington, D.C., United States
	J. E. L. Peck , M. R. Williams, Algorithm 286: Examination scheduling, Communications of the ACM, v.9 n.6, p.433-434, June 1966
	M. Donald MacLaren , George Marsaglia, Uniform Random Number Generators, Journal of the ACM (JACM), v.12 n.1, p.83-89, Jan. 1965
	Harry Felder, The GPSS/360 random number generator, Proceedings of the second conference on Applications of simulations, p.21-28, December 02-04, 1968, New York, New York, United States
	A. Van Gelder, Some New Results in Pseudo-Random Number Generation, Journal of the ACM (JACM), v.14 n.4, p.785-792, Oct. 1967
	C. L. Overstreet, The relationship between the multiplicative and mixed generators modulo 2^b, ACM SIGSIM Simulation Digest, v.7 n.3, p.43-45, April 1976
	David W. Hutchinson, A new uniform pseudorandom number generator, Communications of the ACM, v.9 n.6, p.432-433, June 1966
	J. M. Carroll , P. M. McLelland, Fast "infinite-key" privacy transformation for resource-sharing systems, Proceedings of the November 17-19, 1970, fall joint computer conference, November 17-19, 1970, Houston, Texas