Exact and Approximated Error of the FMA

被引：9

作者：

Boldo, Sylvie ^{[1
]}

Muller, Jean-Michel ^{[2
]}

机构：

[1] Parc Orsay Univ, INRIA Saclay Ile de France, ZAC Vignes, F-91893 Orsay, France

[2] Univ Lyon 1, Ecole Normale Super Lyon, CNRS, INRIA, F-69364 Lyon 07, France

来源：

IEEE TRANSACTIONS ON COMPUTERS | 2011年 / 60卷 / 02期

关键词：

Floating-point arithmetic; FMA; fused multiply-add; computer arithmetic; error-free transforms; error compensation; error of an FMA; FLOATING-POINT;

D O I：

10.1109/TC.2010.139

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：157 / 164

页数：8

共 25 条

[1] Series approximation methods for divide and square root in the Power3™ processor [J].

Agarwal, RC ;

Gustavson, FG ;

Schmookler, MS .

14TH IEEE SYMPOSIUM ON COMPUTER ARITHMETIC, PROCEEDINGS, 1999, :116-123

[2]

[Anonymous], COMPUTER VALIDATED P

[3]

[Anonymous], 1974, Floating-Point Computation

[4]

[Anonymous], 1965, BIT, DOI DOI 10.1007/BF01975722

[5]

[Anonymous], 2009, Handbook of Floating-Point Arithmetic

[6]

Bertot Y., 2004, TEXT THEORET COMP S

[7] Representable correcting terms for possibly underflowing floating point operations [J].

Boldo, S ;

Daumas, M .

16TH IEEE SYMPOSIUM ON COMPUTER ARITHMETIC, PROCEEDINGS, 2003, :79-86

[8]

BOLDO S, 2006, P 3 INT JOINT C AUT, P52

[9]

Cornea M, 2002, Scientific Computing on Itanium-Based Systems

[10] FLOATING-POINT TECHNIQUE FOR EXTENDING AVAILABLE PRECISION [J].

DEKKER, TJ .

NUMERISCHE MATHEMATIK, 1971, 18 (03) :224-+

← 1 2 3 →