Journal of the Association for Computing Machinery 23(2), pp. 287-297.
ISSN/ISBN: 0004-5411 DOI: 10.1145/321941.321948
Abstract: This paper analyzes the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $\beta$ and randomly chosen from a logarithmic distribution. The analysis shows that the nth digit for $n\ge 2$ is actually approximately uniformly distributed. The approximation depends upon both n and the base $\beta$. It becomes better as n increases, and it is exact in the limit as $n\to \infty$. A table of this distribution is presented for various $\beta$ and n, along with a table of the maximum digit by digit deviation $\Delta$ of the logarithmic distribution from the uniform distribution. Various asymptotic results for $\Delta$ are included. These results have application in resolving open questions of Henrici, of Kaneko and Liu, and of Tsao.
Bibtex:
@article{,
author = {Feldstein, Alan and Goodman, Richard},
title = {Convergence Estimates for the Distribution of Trailing Digits},
journal = {J. ACM},
issue_date = {April 1976},
volume = {23},
number = {2},
month = {apr},
year = {1976},
issn = {0004-5411},
pages = {287--297},
url = {https://dl.acm.org/citation.cfm?doid=321941.321948},
doi = {10.1145/321941.321948},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Numerical Analysis