  An algorithm for the evaluation of the complex exponential function is
proposed which is quasi-linear in time and linear in space. This algorithm is
based on a modified binary splitting method for the hypergeometric series and a
modified Karatsuba method for the fast evaluation of the exponential function.
The time complexity of this algorithm is equal to that of the ordinary
algorithm for the evaluation of the exponential function based on the series
expansion: O(M(n)log(n)^2).
