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A fast uniform astronomical random number generator

A fast uniform astronomical random number generator The present method generates machine-independent uniform random sequences of real numbers in the interval (0.,1.) excluding 1. It uses a set of up to 1024 independent multiplicative congruential generators working with:• modulii which are chosen prime numbers whose values have been fixed according to the positive 31-bit positive integer arithmetic available and in the form of 2.P'+1, where P's are also primes.• multipliers which are selected from one of their corresponding primitive elements as multipliers to achieve each full cycle independently. The "astronomical" maximum periodicity can be considered as infinite: O (10 6021 ) ; it can be adjusted if required by the user in the sequential version RAN01 or statistically reaching the maximum in the improved "stagger" version DAN01. An "acceptable" composite period is estimated to be O (10 189 ) for a set of only 32 of such independent generators: this fact could find a nice application in the realization of efficient hash-functions in smart cards.An implementation in structured FORTRAN 77 shows very good results in terms of statistical proprieties, velocity and periodicity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGSAC Review Association for Computing Machinery

A fast uniform astronomical random number generator

ACM SIGSAC Review , Volume 7 (1) – Feb 1, 1989

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1989 by ACM Inc.
ISSN
0277-920X
DOI
10.1145/70951.70952
Publisher site
See Article on Publisher Site

Abstract

The present method generates machine-independent uniform random sequences of real numbers in the interval (0.,1.) excluding 1. It uses a set of up to 1024 independent multiplicative congruential generators working with:• modulii which are chosen prime numbers whose values have been fixed according to the positive 31-bit positive integer arithmetic available and in the form of 2.P'+1, where P's are also primes.• multipliers which are selected from one of their corresponding primitive elements as multipliers to achieve each full cycle independently. The "astronomical" maximum periodicity can be considered as infinite: O (10 6021 ) ; it can be adjusted if required by the user in the sequential version RAN01 or statistically reaching the maximum in the improved "stagger" version DAN01. An "acceptable" composite period is estimated to be O (10 189 ) for a set of only 32 of such independent generators: this fact could find a nice application in the realization of efficient hash-functions in smart cards.An implementation in structured FORTRAN 77 shows very good results in terms of statistical proprieties, velocity and periodicity.

Journal

ACM SIGSAC ReviewAssociation for Computing Machinery

Published: Feb 1, 1989

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