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Reports (Research Report) Year : 2010

On the Computation of Correctly-Rounded Sums

Vincent Lefèvre
Nicolas Louvet
Jean-Michel Muller

Abstract

This paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. In particular, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2Sum algorithm introduced by Knuth is minimal, both in terms of number of operations and depth of the dependency graph. We investigate the possible use of another algorithm, Dekker's Fast2Sum algorithm, in radix-10 arithmetic. We give methods for computing, in radix 10, the floating-point number nearest the average value of two floating-point numbers. Under reasonable conditions, we also prove that no algorithms performing only round-to-nearest additions/subtractions exist to compute the round-to-nearest sum of at least three floating-point numbers. Starting from an algorithm due to Boldo and Melquiond, we also present new results about the computation of the correctly-rounded sum of three floating-point numbers.
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Dates and versions

inria-00475279 , version 1 (21-04-2010)

Identifiers

  • HAL Id : inria-00475279 , version 1

Cite

Peter Kornerup, Vincent Lefèvre, Nicolas Louvet, Jean-Michel Muller. On the Computation of Correctly-Rounded Sums. [Research Report] RR-7262, INRIA. 2010, pp.24. ⟨inria-00475279⟩
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