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Feldstein, A and Goodman, R (1976)

Convergence Estimates for Distribution of Trailing Digits

Journal of the Association for Computing Machinery, 23(2), 287-297.

ISSN/ISBN: 0004-5411 DOI: Not available at this time.



Abstract: 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:
Not available at this time.


Reference Type: Journal Article

Subject Area(s): Numerical Analysis