IMPLEMENTATION OF FORTRAN RANDOM NUMBER GENERATORS ON COMPUTERS WITH ONE'S COMPLEMENT ARITHMETIC

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THE MIXED METHOD OF RANDOM NUMBER GENERATION: A TUTORIAL

Several motivations are recognized for user-defined random number generators in preference to built-in generators. The mixed method of random number generation is discussed) and the conditions for achieving full period with a modulus of 2^b are explained. Implementation of mixed random number generators is affected both by the computer and language used. Guidelines are presented for realizing acceptable mixed generators on several machines using the FORTRAN, PL/l and SNOBOL4 languages

THE RELATIONSHIP BETWEEN THE MULTIPLICATIVE AND MIXED GENERATORS MODULO 2^b

MacLaren and Marsaglia [4] comment that their test results suggest that the multiplicative generator performs better than the mixed generator. We attempt to answer the above question by showing that for any sequence of real values in (0,1) produced by the multiplicative generator modulo 2^b a corresponding mixed generator exists which, for practical purposes, produces the same sequence of real values

SOME EXPERIMENTAL OBSERVATIONS ON THE BEHAVIOR OF COMPOSITE RANDOM NUMBER GENERATORS

A series of experiments with composite random number generators utilizing shuffling tables is described. The factors investigated are: (1) the magnitude of the modulus (equivalently, the word-size of the machine), (2) the effect of the modulus value for the indexing generator, and (3) the table size used for shuffling. Experimental results indicate that: (1) on large word-length machines (permitting large modulus values), shuffling accomplishes little in comparison with selected simple generators, (2) on small word-length machines, shuffling can produce sequences having an increased period and demonstrating acceptable statistical behavior, and (3) a table size of 2 produces results comparable to those obtained with larger tables