  We review the theory of elliptic functions leading to Zolotarev's formula for
the sign function over the range (\epsilon \leq|x| \leq1). We show how Gauss'
arithmetico-geometric mean allows us to evaluate elliptic functions cheaply,
and thus to compute Zolotarev coefficients ``on the fly'' as a function of
(\epsilon). This in turn allows us to calculate the matrix functions (\sgn H),
(\sqrt H), and (1/\sqrt H) both quickly and accurately for any Hermitian matrix
(H) whose spectrum lies in the specified range.
