JF IEEE Transactions on Computers

YR 2010

VO 60

IS

SP 157

TI Exact and Approximated Error of the FMA

A1 Jean-Michel Muller,

A1 Sylvie Boldo,

K1 Floating-point arithmetic

K1 FMA

K1 fused multiply-add

K1 computer arithmetic

K1 error-free transforms

K1 error compensation

K1 error of an FMA.

AB 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.

PB IEEE Computer Society, [URL:http://www.computer.org]

SN 0018-9340

LA English

DO 10.1109/TC.2010.139

LK http://doi.ieeecomputersociety.org/10.1109/TC.2010.139