Journal of the Association for Computing Machinery 26(4), pp. 716-730.
ISSN/ISBN: 0004-5411 DOI: 10.1145/322154.322162
Abstract: New results are given on the distribution of trailing digits for logarithmically distributed numbers and on error in floating-point multiplication. Some of the results have application to computer design. In particular, there are certain values of the base (indeed, β = 2, 4, 6, and sometimes 8, but NOT 16) which, when carefully balanced with other design parameters, minimize the mean multiplicative error. For these special minimizing situations, it suffices to have only one guard bit provided that postnormalizatlon occurs after symmetric rounding.
Bibtex:
article{,
author = {Bustoz, Joaqu\'{\i}n and Feldstein, Alan and Goodman, Richard and Linnainmaa, Seppo},
title = {Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic},
journal = {J. ACM},
issue_date = {Oct. 1979},
volume = {26},
number = {4},
month = oct,
year = {1979},
issn = {0004-5411},
pages = {716--730},
numpages = {15},
url = {http://doi.acm.org/10.1145/322154.322162},
doi = {10.1145/322154.322162},
acmid = {322162},
publisher = {ACM},
address = {New York, NY, USA},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Computer Science, Numerical Analysis