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On the error of Computing ab + cd using Cornea, Harrison and Tang's method

Jean-Michel Muller 1, 2
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : In their book Scientific Computing on The Itanium, Cornea, Harrison and Tang introduce an accurate algorithm for evaluating expressions of the form ab + cd in binary floating-point arithmetic, assuming an FMA instruction is available. They show that if p is the precision of the floating-point (FP) format and if u = 2^(−p), the relative error of the result is of order u. We improve their proof to show that the relative error is bounded by 2u+7u^2 +6u^3. Furthermore, by building an example for which the relative error is asymptotically (as p → ∞ or, equivalently, as u → 0) equivalent to 2u, we show that our error bound is asymptotically optimal.
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Preprints, Working Papers, ...
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00862910
Contributor : Jean-Michel Muller Connect in order to contact the contributor
Submitted on : Tuesday, September 17, 2013 - 5:39:59 PM
Last modification on : Friday, September 10, 2021 - 2:34:05 PM
Long-term archiving on: : Friday, December 20, 2013 - 2:31:03 PM

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AnalysisCornea.pdf
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  • HAL Id : ensl-00862910, version 1

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Jean-Michel Muller. On the error of Computing ab + cd using Cornea, Harrison and Tang's method. 2013. ⟨ensl-00862910v1⟩

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