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Some issues related to double roundings

Érik Martin-Dorel 1 Guillaume Melquiond 2, 3 Jean-Michel Muller 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : Double rounding is a phenomenon that may occur when different floating-point precisions are available on a same system, or when performing scaled operations whose final result is subnormal. 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 roundings on the Fast2Sum and 2Sum algorithms, on some summation algorithms, and Veltkamp's splitting. We also show how to handle possible double roundings when performing scaled Newton-Raphson division iterations (to avoid possible underflow problems).
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Contributor : Jean-Michel Muller <>
Submitted on : Friday, December 2, 2011 - 3:56:15 PM
Last modification on : Friday, September 10, 2021 - 2:34:02 PM
Long-term archiving on: : Monday, December 5, 2016 - 9:56:16 AM


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  • HAL Id : ensl-00644408, version 2


Érik Martin-Dorel, Guillaume Melquiond, Jean-Michel Muller. Some issues related to double roundings. 2011, pp.42. ⟨ensl-00644408v2⟩



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