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When double rounding is odd

Sylvie Boldo 1, Guillaume Melquiond 1

(2004)

Double rounding consists in a first rounding in an intermediate extended precision and then a second rounding in the working precision. The natural question is then of the precision and correctness of the final result. Unfortunately, the used double rounding algorithms do not obtain a correct rounding of the initial value. We prove an efficient algorithm for the double rounding to give the correct rounding to the nearest value assuming the first rounding is to odd. As this rounding is unusual and this property is surprising, we formally proved this property using the Coq automatic proof checker.

1 :	ARENAIRE (Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme)
	INRIA – CNRS : UMR5668 – Université Claude Bernard - Lyon I – École Normale Supérieure - Lyon

Domaine

:

Informatique/Autre

Mots-clés : Floating-point – double rounding – formal proof – Coq

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Soumis le : Vendredi 19 Mai 2006, 20:59:07

Dernière modification le : Mercredi 8 Octobre 2008, 11:56:52