On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations (1992)
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@TECHREPORT{Priest92onproperties,
author = {Douglas M. Priest},
title = {On Properties of Floating Point Arithmetics: Numerical Stability and the Cost of Accurate Computations},
institution = {},
year = {1992}
}
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Abstract
Floating point arithmetics generally possess many regularity properties in addition to those that are typically used in roundoff error analyses; these properties can be exploited to produce computations that are more accurate and cost effective than many programmers might think possible. Furthermore, many of these properties are quite simple to state and to comprehend, but few programmers seem to be aware of them (or at least willing to rely on them). This dissertation presents some of these properties and explores their consequences for computability, accuracy, cost, and portability. For example, we consider several algorithms for summing a sequence of numbers and show that under very general hypotheses, we can compute a sum to full working precision at only somewhat greater cost than a simple accumulation, which can often produce a sum with no significant figures at all. This example, as well as others we present, can be generalized further by substituting still more complex algorith...
