Augmented Precision Square Roots and 2-D Norms, and Discussion on Correctly Rounding sqrt(x^2+y^2)

Peter Kornerup, Nicolas Brisebarre, Mioara Joldes, Erik Martin-Dorel, Jean-Michel Muller

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Abstrakt

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 √x 2 +y 2 . Then we give tight lower bounds on the minimum distance (in ulps) between √x 2 +y 2 and a midpoint when √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.
OriginalsprogEngelsk
TitelProceedings of 20th IEEE Symposium on Computer Arithmetic
Antal sider8
Udgivelses stedPiscataway, NJ, USA
ForlagIEEE Computer Society Press
Publikationsdato25. jun. 2011
Sider23-30
ISBN (Trykt)978-0-7695-4318-5
StatusUdgivet - 25. jun. 2011

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Citationsformater

Kornerup, P., Brisebarre, N., Joldes, M., Martin-Dorel, E., & Muller, J-M. (2011). Augmented Precision Square Roots and 2-D Norms, and Discussion on Correctly Rounding sqrt(x^2+y^2). I Proceedings of 20th IEEE Symposium on Computer Arithmetic (s. 23-30). IEEE Computer Society Press.