Relative error in floating-point multiplication
type: Item
instance of: scholarly article
title: Relative error in floating-point multiplication
zbMATH Open document ID: 0564.65030
DOI: 10.1007/BF02260500
author: R. H. Goodman
author: Alan Feldstein
author: J. Bustoz
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of computer design parameters. These parameters include the base, the type of rounding rule, the number of guard digits, and whether the post- arithmetic normalization shift (if needed) is done before or after rounding. Under the assumption of logarithmic distribution for the fraction (mantissa), the major stochastic conclusions are: 1. The average relative error in multiplication increases as the base increases. 2. This error is minimized by selecting the machine based to be binary (better yet, binary with a hidden bit) and is rather large for machines with base 16. 3. The classical relative error bounds are pessimistic. The average overestimation by those bounds increases as the base increases.
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 3900053
zbMATH Keywords: relative error
zbMATH Keywords: computer arithmetic
zbMATH Keywords: floating point multiplication
zbMATH Keywords: normalization options
zbMATH Keywords: guard digits
zbMATH Keywords: floating point numbers
zbMATH Keywords: floating point precision and significance
zbMATH Keywords: round-off error
zbMATH Keywords: fraction error
zbMATH Keywords: mean and standard deviation of errors
zbMATH Keywords: logarithmically distributed numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3900053