On the maximum relative error when computing xⁿ in floating-point arithmetic

2014/02/11 by Stef Graillat, Graillat, Stef, Vincent Lefèvre +3
Computer Science · #Cryptography and Residue Arithmetic #Digital Filter Design and Implementation #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1402.2991

openalex publication_date 2014/02/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we improve the usual relative error bound for the computation of xⁿ 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.

Related

• On Sound Relative Error Bounds for Floating-Point Arithmetic
• Effective Quadratic Error Bounds for Floating-Point Algorithms Computing the Hypotenuse Function
• Deterministic and Probabilistic Error Bounds for Floating Point Summation Algorithms
• Floating point numbers are real numbers
• Mechanizing Olver's Error Arithmetic