Augmented precision square roots, 2-D norms, and discussion on correctly rounding {x^2+y^2} - Archive ouverte HAL Access content directly
Conference Papers Year : 2011

Augmented precision square roots, 2-D norms, and discussion on correctly rounding {x^2+y^2}

(1) , (1) , (2) , (1) , (1)
1
2
Nicolas Brisebarre
Mioara Maria Joldes
Érik Martin-Dorel
Jean-Michel Muller

Abstract

Define an "augmented precision" algorithm as an algorithm that returns, in precision-p floating-point arithmetic, its result as the unevaluated sum of two floating-point numbers, with a relative error of the order of 2^(−2p). Assuming an FMA instruction is available, we perform a tight error analysis of an augmented precision algorithm for the square root, and introduce two slightly different augmented precision algorithms for the 2D-norm sqrt(x^2 + y^2). Then we give tight lower bounds on the minimum distance (in ulps) between sqrt(x^2 + y^2) and a midpoint when sqrt(x^2 + y^2) is not itself a midpoint. This allows us to determine cases when our algorithms make it possible to return correctly-rounded 2D-norms.
Fichier principal
Vignette du fichier
PID1818753.pdf (207.29 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

ensl-00545591 , version 1 (10-12-2010)
ensl-00545591 , version 2 (14-11-2011)

Identifiers

Cite

Nicolas Brisebarre, Mioara Maria Joldes, Peter Kornerup, Érik Martin-Dorel, Jean-Michel Muller. Augmented precision square roots, 2-D norms, and discussion on correctly rounding {x^2+y^2}. 20th IEEE Symposium on Computer Arithmetic (ARITH-20), Jul 2011, Tübingen, Germany. pp.23-30, ⟨10.1109/ARITH.2011.13⟩. ⟨ensl-00545591v2⟩
348 View
383 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More