A more accurate Briggs method for the logarithm

A new approach for computing an expression of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a^{1/2^k}-1$\end{document} is presented that avoids the danger of subtractive cancellation in floating point arithmetic, where a is a complex number not belonging to the closed negative real axis and k is a nonnegative integer. We also derive a condition number for the problem. The algorithm therefore allows highly accurate numerical calculation of log(a) using Briggs’ method.