| Article Id: |
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ensl-00409366, version 3 |
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| Domaine: |
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Computer Science/Other
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| Titre: |
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Midpoints and exact points of some algebraic functions in floating-point arithmetic |
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| Auteur(s): |
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Claude-Pierre Jeannerod1, 2, Nicolas Louvet1, 2, Jean-Michel Muller1, 2, Adrien Panhaleux1, 2 |
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| Laboratoire: |
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| 1: |
Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme - ARENAIRE |
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| 2: |
LIP - Laboratoire de l'Informatique du Parallélisme |
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| Équipe de recherche: |
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[ARENAIRE - Arithmétique des ordinateurs] |
| Résumé: |
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When implementing a function f in floating-point arithmetic, if we wish correct rounding and good performance, it is important to know if there are input floating-point values x such that f(x) is either the middle of two consecutive floating-point numbers (assuming rounded-to-nearest arithmetic), or a floating-point number (assuming rounded towards infinity or towards 0 arithmetic). In the first case, we say that f(x) is a midpoint, and in the second case, we say that f(x) is an exact point. For some usual algebraic functions, and various floating-point formats, we prove whether or not there exist midpoints or exact points. When there exist midpoints or exact points, we characterize them or list all of them (if there are not too many). The results and the techniques presented in this paper can be used in particular to deal with both the binary and the decimal formats defined in the IEEE 754-2008 standard for floating-point arithmetic. |
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Langue du texte
intégral: |
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English |
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| Mots-clés: |
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Computer arithmetic – Floating-point arithmetic – Function implementation – Midpoints – Algebraic functions |
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| Commentaire: |
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Recherche en partie supportée par le "Pole de competitivite mondial" Minalogic et le projet ANR EVA-Flo. |
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| Classification: |
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ACM B.2.4; G.1.0 |
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