BIT Numerical Mathematics

, Volume 53, Issue 4, pp 897–924 | Cite as

Some issues related to double rounding

  • Érik Martin-Dorel
  • Guillaume Melquiond
  • Jean-Michel Muller
Article
First Online:
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Accepted:

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.

Keywords

Floating-point arithmetic Double rounding Correct rounding 2Sum Fast2Sum Summation algorithms 

Mathematics Subject Classification (2010)

65G99 65Y04 68M15 
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Notes

Acknowledgements

We are extremely grateful to the anonymous referees, whose suggestions have been very helpful for revising this paper. Especially, one of them suggested a drastic simplification of the proof of Theorem 4.1.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Érik Martin-Dorel
    • 1
  • Guillaume Melquiond
    • 2
  • Jean-Michel Muller
    • 3
  1. 1.Inria Sophia Antipolis - MéditerranéeMarelle teamSophia Antipolis CedexFrance
  2. 2.Inria Saclay–Île-de-France, Toccata team, LRI Lab.CNRSOrsay CedexFrance
  3. 3.CNRS, lab. LIP, Inria Aric teamUniversité de LyonLyon Cedex 07France

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