  The article shows how two choices are possible whenever computing the
geometric mean, and the repetition of this process can in general yield
2-to-the power N different values when the choices are compounded in the first
N steps of evaluation of the arithmetic-geometric mean. This happens not only
in the simple AGM involved in the computation of the complete elliptic integral
of the first kind, but also in analogous methods for the computation of the
complete and incomplete elliptic integrals of the first and second kind.
