Exact and Approximated Error of the FMA

Author

Boldo, Sylvie ; Muller, Jean-Michel

Author_Institution

INRIA Saclay-Ile-de-France, Orsay, France

Volume

60

Issue

2

fYear

2011

Firstpage

157

Lastpage

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.

Keywords

error compensation; floating point arithmetic; formal verification; instruction sets; FMA; IEEE 754-2008 standard; approximated error; error compensation; floating point arithmetic; formal proof; fused multiply accumulate add instruction; Algorithm design and analysis; Approximation algorithms; Approximation error; Computer errors; Digital arithmetic; Error compensation; Floating-point arithmetic; Helium; Polynomials; Standards organizations; FMA; Floating-point arithmetic; computer arithmetic; error compensation; error of an FMA.; error-free transforms; fused multiply-add;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/TC.2010.139

Filename

5487502