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

Stef Graillat; Vincent Lefèvre; Jean-Michel Muller

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.

Keywords : accurate error bound floating-point arithmetic rounding error exponentiation

Document type :

Journal articles

Domain :

Computer Science [cs] / Other [cs.OH]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00945033
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On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic

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