On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic

Stef Graillat 1 Vincent Lefèvre 2 Jean-Michel Muller 2
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is simpler. We also discuss the more general problem of computing the product of n terms.
Document type :
Journal articles
Complete list of metadatas

Cited literature [7 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00945033
Contributor : Jean-Michel Muller <>
Submitted on : Friday, October 17, 2014 - 3:34:19 PM
Last modification on : Thursday, March 21, 2019 - 2:36:47 PM
Long-term archiving on : Sunday, January 18, 2015 - 10:35:11 AM

File

x-puissance-n-revision.pdf
Files produced by the author(s)

Identifiers

Citation

Stef Graillat, Vincent Lefèvre, Jean-Michel Muller. On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic. Numerical Algorithms, Springer Verlag, 2015, 70 (3), pp.653-667. ⟨10.1007/s11075-015-9967-8⟩. ⟨ensl-00945033v2⟩

Share

Metrics

Record views

561

Files downloads

391