# On the maximum relative error when computing $x^n$ in floating-point arithmetic

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 : In this paper, 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.
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Reports
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00945033
Contributor : Jean-Michel Muller <>
Submitted on : Tuesday, February 11, 2014 - 3:47:05 PM
Last modification on : Friday, September 10, 2021 - 2:34:05 PM
Long-term archiving on: : Monday, May 12, 2014 - 2:05:38 PM

### Files

x-puissance-n.pdf
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### Identifiers

• HAL Id : ensl-00945033, version 1
• ARXIV : 1402.2991

### Citation

Stef Graillat, Vincent Lefèvre, Jean-Michel Muller. On the maximum relative error when computing $x^n$ in floating-point arithmetic. [Research Report] Université Pierre et Marie Curie Paris 6; CNRS; Inria. 2014, pp.16. ⟨ensl-00945033v1⟩

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