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Fourier Analysis of Uniform Random Number Generators

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Published:01 January 1967Publication History
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Abstract

A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to understand and predict relevant statistical properties of such generators and compare and evaluate such methods. Many such analyses and comparisons have been carried out. The performance of these methods as implemented on differing computers is also studied. The main practical conclusions of the study are: (a) Such a priori analysis and prediction of statistical behavior of uniform random number generators is feasible. (b) The commonly used multiplicative congruence method of generation is satisfactory with careful choice of the multiplier for computers with an adequate (≥ ∼ 35-bit) word length. (c) Further work may be necessary on generators to be used on machines of shorter word length.

References

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  1. Fourier Analysis of Uniform Random Number Generators

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    • Published in

      cover image Journal of the ACM
      Journal of the ACM  Volume 14, Issue 1
      Jan. 1967
      202 pages
      ISSN:0004-5411
      EISSN:1557-735X
      DOI:10.1145/321371
      Issue’s Table of Contents

      Copyright © 1967 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 January 1967
      Published in jacm Volume 14, Issue 1

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