A simple and fast algorithm for computing exponentials of power series

TL;DR

This paper presents a straightforward and efficient algorithm for computing exponentials of truncated power series, reducing computational complexity with a low constant factor.

Contribution

It introduces a simple, fast algorithm for power series exponentials that improves upon previous methods by minimizing polynomial multiplications.

Findings

Algorithm achieves faster computation of power series exponentials.

Reduces the number of polynomial multiplications needed.

Simplifies implementation compared to existing methods.

Abstract

As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.