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Formal certification of arithmetic filters for geometric predicates

Abstract : 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.
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Submitted on : Friday, December 5, 2008 - 3:11:31 AM
Last modification on : Friday, February 4, 2022 - 3:24:52 AM
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  • HAL Id : inria-00344518, version 1



Guillaume Melquiond, Sylvain Pion. Formal certification of arithmetic filters for geometric predicates. 17th IMACS World Congress, 2005, Paris, France. ⟨inria-00344518⟩



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