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Fonctions élémentaires : algorithmes et implémentations efficaces pour l'arrondi correct en double précision

David Defour 1, 2 
2 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The representation formats and behaviors of floating point arithmetics available in computers are defined by the IEEE-754 standard. This standard imposes the system to return as a result of one of the four basic operations (+, *, /, sqrt), the rounding of the exact result. This property is called <>,this warranties the quality of the result. It enables construction of proof that this particular algorithms can be manipulated independently of the machine. However, due to the <>, elementary functions (sine, cosine, exponential...) are
absent in the IEEE-754 standard. Contrary to basic operations, it is difficult to discover the necessary accuracy required to guarantee correct rounding for elementary functions. However if the
representation format is set, it is possible that an exhaustive
search will help determine this bound: it was Lefevre's work for the double precision.

The objectives of this thesis is to exploit these bounds for each
functions and rounding modes, to certify correct rounding in double
precision. Thanks to this bound we have defined an evaluation within 2 steps: a quick phase which is based on the property of the IEEE standard that often proves satisfactory and an accurate step based on multiprecision operations which is precise all the time. For the second step we have designed a multiprecision library which was optimized in order to acquire precision corresponding to the bound, and the caracteristics of processors in 2003.
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Contributor : David DEFOUR Connect in order to contact the contributor
Submitted on : Friday, May 7, 2004 - 2:40:01 PM
Last modification on : Tuesday, October 25, 2022 - 4:24:57 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 3:45:10 PM


  • HAL Id : tel-00006022, version 1


David Defour. Fonctions élémentaires : algorithmes et implémentations efficaces pour l'arrondi correct en double précision. Modélisation et simulation. Ecole normale supérieure de lyon - ENS LYON, 2003. Français. ⟨NNT : ⟩. ⟨tel-00006022⟩



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