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

Stef Graillat (1) , Vincent Lefèvre (2) , Jean-Michel Muller (2)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
2 ARIC - Arithmetic and Computing

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.

Mots clés: floating-point arithmetic; rounding error; accurate error bound; exponentiation

Domaines: Autre [cs.OH]

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⟩