RAIRO-Theor. Inf. Appl.
Volume 41, Number 1, January-March 2007Real Numbers
|Page(s)||57 - 69|
|Published online||24 April 2007|
Formally certified floating-point filters for homogeneous geometric predicates
Laboratoire de l'informatique du parallélisme,
UMR 5668 CNRS, ENS Lyon, INRIA, UCBL,
46 allée d'Italie, 69364 Lyon Cedex 07, France;
2 INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France; Sylvain.Pion@sophia.inria.fr
Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification of this algorithm avoided many pitfalls. The presented method is not limited to this particular predicate, it can easily be used to produce correct semi-static floating-point filters for other geometric predicates.
Mathematics Subject Classification: 65D18 / 65G50 / 68Q60
Key words: Geometric predicates / semi-static filters / formal proofs / floating-point
© EDP Sciences, 2007
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