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Mathematics of Computation

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Generating pseudo-random numbers by shuffling a Fibonacci sequence

Author: Friedrich Gebhardt
Journal: Math. Comp. 21 (1967), 708-709
MSC: Primary 65.15
MathSciNet review: 0223064
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Abstract: M. D. MacLaren and G. Marsaglia [2] have proposed to mix two pseudo-random number generators in the following way: The first generator is used at the beginning to fill an array with pseudo-random numbers; whenever a random number is needed, the second generator determines which element of the array is to be used and replaced by a new number from the first generator. In this study, only one generator is utilized for both purposes; moreover, the generator chosen (a Fibonacci sequence) is by itself a rather poor one. Nevertheless, the final sequence of pseudo-random numbers passed all statistical tests applied to it, including $ {\chi ^2} - $ tests of the maximum and minimum of two to ten succeeding numbers and tests applied to sequences immediately following a small number or two almost equal ones.

References [Enhancements On Off] (What's this?)

  • [1] M. Greenberger, "Method in randomness," Comm. ACM, v. 8, 1965, pp. 177-179.
  • [2] M. D. MacLaren & G. Marsaglia, "Uniform random number generators," J. Assoc. Comput. Mach., v. 12, 1965, pp. 83-89. MR 30 #687. MR 0170449 (30:687)
  • [3] D. D. Wall, "Fibonacci series modulo m," Amer. Math. Monthly, v. 67, 1960, pp. 525-532. MR 22 #10945. MR 0120188 (22:10945)

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Article copyright: © Copyright 1967 American Mathematical Society

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