Journal of Information Processing and Cybernetics EIK 24(9), 443-455.
ISSN/ISBN: 0863-0593 DOI: Not available at this time.
Abstract: A survey is given of the stochastic behaviour of floating-point mantissas. The mantissas of products and of sums, respectively, are considered in case the number of operands tendding to infinity. Under weak assumptions the mantissas are logarithmically distributed in the limit. This entails a logarithmic mantissa distribution in extensive computing and explains Benford's law. Benford's law states a logarithmic first digit distribution in physical, chemical and statistical tables. It can also be founded by metric theorems concerning the uniform distribution of sequences. Applications are met above all in the probabilistic analysis of roundoff errors.
Bibtex:
@article {MR984516,
AUTHOR = {Schatte, Peter},
TITLE = {On mantissa distributions in computing and {B}enford's law},
JOURNAL = {J. Inform. Process. Cybernet.},
FJOURNAL = {Journal of Information Processing and Cybernetics},
VOLUME = {24},
YEAR = {1988},
NUMBER = {9},
PAGES = {443--455},
ISSN = {0863-0593},
MRCLASS = {60E05 (11K06 11K31 65G99)},
MRNUMBER = {984516 (90g:60016)},
MRREVIEWER = {F. Schweiger},
}
Reference Type: Journal Article
Subject Area(s): Computer Science