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
2 ARIC - Arithmetic and Computing

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

Domains: Computer Science [cs]; Other [cs.OH]

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, 2015, 70 (3), pp.653-667. ⟨10.1007/s11075-015-9967-8⟩. ⟨ensl-00945033v2⟩