A Pseudo-Random Number Generator Based on Normal Numbers

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In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which ... continued below

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Bailey, David H. December 31, 2004.

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In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.

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  • Report No.: LBNL--57489
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/860344 | External Link
  • Office of Scientific & Technical Information Report Number: 860344
  • Archival Resource Key: ark:/67531/metadc786093

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  • December 31, 2004

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  • Dec. 3, 2015, 9:30 a.m.

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  • Sept. 22, 2017, 3:04 p.m.

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Bailey, David H. A Pseudo-Random Number Generator Based on Normal Numbers, report, December 31, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc786093/: accessed November 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.