HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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 et al. [2002] 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 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00862910
Contributor : Jean-Michel Muller Connect in order to contact the contributor
Submitted on : Tuesday, September 24, 2013 - 11:51:32 AM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM
Long-term archiving on: : Friday, April 7, 2017 - 1:55:02 AM

File

AnalysisCornea.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-00862910, version 2

Collections

Citation

Jean-Michel Muller. On the error of Computing ab + cd using Cornea, Harrison and Tang's method. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2015, 41 (2), pp.8. ⟨ensl-00862910v2⟩

Share

Metrics

Record views

270

Files downloads

344