A More Accurate Briggs Method for the Logarithm

A new approach for computing an expression of the form $a^{1/2^k}-1$ 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