How to Compute the Area of a Triangle: a Formal Revisit with a Tighter Error Bound

Sylvie Boldo 1, 2
2 TOCCATA - Certified Programs, Certified Tools, Certified Floating-Point Computations
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : Mathematical values are usually computed using well-known mathematical formulas without thinking about their accuracy, which may turn awful with particular instances. This is the case for the computation of the area of a triangle. When the triangle is needle-like, the common formula has a very poor accuracy. Kahan proposed in 1986 an algorithm he claimed correct within a few ulps. Goldberg took over this algorithm in 1991 and gave a precise error bound. This article presents a formal proof of this algorithm, investigations in case of underflow and a new improvement of its error bound.
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Pré-publication, Document de travail
2013
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Contributeur : Sylvie Boldo <>
Soumis le : mardi 17 septembre 2013 - 11:17:26
Dernière modification le : jeudi 5 avril 2018 - 12:30:22
Document(s) archivé(s) le : vendredi 20 décembre 2013 - 14:20:32

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Sylvie Boldo. How to Compute the Area of a Triangle: a Formal Revisit with a Tighter Error Bound. 2013. 〈hal-00862653〉

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