Faster exponentials of power series

arXiv preprint (November 2009).


We describe a new algorithm for computing exp f where f is a power series in C[[x]]. If M(n) denotes the cost of multiplying polynomials of degree n, the new algorithm costs (2.1666... + o(1)) M(n) to compute exp f to order n. This improves on the previous best result, namely (2.333... + o(1)) M(n).

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