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Hamming, R (1970)

On the distribution of numbers

Bell Syst. Tech. J. 49(8), pp. 1609-1625.

ISSN/ISBN: 0005-8580 DOI: 10.1002/j.1538-7305.1970.tb04281.x

Abstract: This paper examines the distribution of the mantissas of floating point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution r(x) = 1/(x ln b), 1/b≤x≤1, where b is the base of the number system. The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is included.

@article {MR0267809, AUTHOR = {Hamming, R. W.}, TITLE = {On the distribution of numbers}, JOURNAL = {Bell System Tech. J.}, FJOURNAL = {The Bell System Technical Journal}, VOLUME = {49}, YEAR = {1970}, PAGES = {1609--1625}, ISSN = {0005-8580}, MRCLASS = {68.00}, MRNUMBER = {0267809 (42 \#2711)}, MRREVIEWER = {A. D. Booth}, }

Reference Type: Journal Article

Subject Area(s): Applied Mathematics