Some issues related to double roundings

Érik Martin-Dorel 1 Guillaume Melquiond 2, 3 Jean-Michel Muller 4
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
3 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
LRI - Laboratoire de Recherche en Informatique, Inria Saclay - Ile de France
4 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Double rounding is a phenomenon that may occur when different floating- point precisions are available on the same system. Although double rounding is, in general, innocuous, it may change the behavior of some useful small floating-point algorithms. We analyze the potential influence of double rounding on the Fast2Sum and 2Sum algorithms, on some summation algorithms, and Veltkamp's splitting.
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Submitted on : Monday, July 8, 2013 - 9:58:38 AM
Last modification on : Friday, October 4, 2019 - 1:53:35 AM
Long-term archiving on : Wednesday, April 5, 2017 - 8:09:23 AM

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Érik Martin-Dorel, Guillaume Melquiond, Jean-Michel Muller. Some issues related to double roundings. BIT Numerical Mathematics, Springer Verlag, 2013, 53 (4), pp.897-924. ⟨10.1007/s10543-013-0436-2⟩. ⟨ensl-00644408v3⟩

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