HAL - INRIA :: [inria-00429617, version 1] Exact and Approximated error of the FMA

inria-00429617, version 1

Exact and Approximated error of the FMA

Sylvie Boldo () ^1, 2, Jean-Michel Muller () ^3, 4

IEEE Transactions on Computers 60, 2 (2011) 157-164

Abstract: The fused multiply accumulate-add (FMA) instruction, specified by the IEEE 754-2008 Standard for Floating-Point Arithmetic, eases some calculations, and is already available on some current processors such as the Power PC or the Itanium. We first extend an earlier work on the computation of the exact error of an FMA (by giving more general conditions and providing a formal proof). Then, we present a new algorithm that computes an approximation to the error of an FMA, and provide error bounds and a formal proof for that algorithm.

1: PROVAL (INRIA Saclay - Ile de France)
INRIA – Université Paris XI - Paris Sud – CNRS : UMR
2: Laboratoire de Recherche en Informatique (LRI)
CNRS : UMR8623 – Université Paris XI - Paris Sud
3: Laboratoire de l'Informatique du Parallélisme (LIP)
Université de Lyon – CNRS : UMR5668 – INRIA – École Normale Supérieure - Lyon – Université Claude Bernard - Lyon I
4: ARENAIRE (Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme)
INRIA – CNRS : UMR5668 – Université Claude Bernard - Lyon I – École Normale Supérieure - Lyon

inria-00429617, version 1
http://hal.inria.fr/inria-00429617
oai:hal.inria.fr:inria-00429617
From: Sylvie Boldo <>
Submitted on: Tuesday, 3 November 2009 16:45:02
Updated on: Monday, 12 December 2011 11:17:54

See detailed view

Associated documents

PDF :

DOI: 10.1109/TC.2010.139

Export

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Articles in peer-reviewed journal</head>
<biblStruct type="article" xml:id="inria-00429617"><analytic>
<author><persName><forename>Sylvie</forename><surname>Boldo</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Saclay - Ile de France</orgName>
<orgName type="team">PROVAL</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
<orgName type="institution">CNRS : UMR</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">LRI</orgName>
<orgName type="team">Laboratoire de Recherche en Informatique</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
</author>
<author><persName><forename>Jean-Michel</forename><surname>Muller</surname></persName>
<affiliation>
<orgName type="laboratory">LIP</orgName>
<orgName type="team">Laboratoire de l'Informatique du Parallélisme</orgName>
<country>FR</country>
<orgName type="institution">Université de Lyon</orgName>
<orgName type="institution">CNRS : UMR5668</orgName>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">École Normale Supérieure - Lyon</orgName>
<orgName type="institution">Université Claude Bernard - Lyon I</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme</orgName>
<orgName type="team">ARENAIRE</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR5668</orgName>
<orgName type="institution">Université Claude Bernard - Lyon I</orgName>
<orgName type="institution">École Normale Supérieure - Lyon</orgName>
</affiliation>
</author>
<title type="main" level="a">Exact and Approximated error of the FMA</title></analytic><monogr><title level="j" type="main">IEEE Transactions on Computers</title><imprint><publisher>IEEE</publisher><biblScope type="publicationDate">2011-02-01</biblScope><biblScope type="vol">60</biblScope><biblScope type="issue">2</biblScope><biblScope type="pp">157-164</biblScope></imprint></monogr><idno type="doi">10.1109/TC.2010.139</idno><idno type="HALid">http://hal.inria.fr/inria-00429617</idno><idno type="HALFile">http://hal.inria.fr/inria-00429617/PDF/fma_err.pdf</idno></biblStruct>
</listBibl>
</listBibl>