On roundoff error distributions in floating point and logarithmic arithmetic
type: Item
instance of: scholarly article
title: On roundoff error distributions in floating point and logarithmic arithmetic
zbMATH Open document ID: 0556.65036
DOI: 10.1007/BF02251833
author: E. H. Bareiss
author: Jesse L. Barlow
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: Probabilistic models of floating point and logarithmic arithmetic are constructed using assumptions with both theoretical and empirical justification. The justification of these assumptions resolves open questions of \textit{R. W. Hamming} [Bell Syst. Tech. J. 49, 1609-1625 (1970; Zbl 0211.467)] and \textit{J. Bustoz}, \textit{A. Feldstein}, \textit{R. Goodman} and \textit{S. Linnainmaa} [J. Assoc. Comput. Mach. 26, 716-730 (1979; Zbl 0429.65038)]. These models are applied to errors from sums and inner products. A comparison is made between the error analysis properties of floating point and logarithmic computers. We conclude that the logarithmic computer has smaller error confidence intervals for roundoff errors than a floating point computer with the same computer word size and approximately the same number range.
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 3886994
zbMATH Keywords: floating point arithmetic
zbMATH Keywords: Probabilistic models
zbMATH Keywords: logarithmic arithmetic
zbMATH Keywords: sums
zbMATH Keywords: inner products
zbMATH Keywords: comparison
zbMATH Keywords: error confidence intervals
zbMATH Keywords: roundoff errors
MaRDI profile type: Publication
cites work: Q3323143
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full work available at URL: https://doi.org/10.1007/bf02251833
OpenAlex ID: W90649232
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description: scientific article; zbMATH DE number 3886994