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.
Bibtex:
@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