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

Time- and space-efficient evaluation of the complex exponential function using series expansion