Fast multiple precision exp(x) with precomputations

Joris van der Hoeven (1, 2) , Fredrik Johansson (3, 4)

1 CNRS - Centre National de la Recherche Scientifique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 IMB - Institut de Mathématiques de Bordeaux
4 CANARI - Analyse cryptographique et arithmétique

What is the most efficient way to compute the exponential function when allowing for the precomputation of lookup tables? In this paper we study this question as a function of the working precision and analyze both classical and asymptotically fast approaches. We present new complexity results, discuss efficient parameter choices and point out improvements that lead to speedups over existing implementations.

Keywords: Elementary functions; Multiple-precision arithmetic; Table-based methods; FFT

Domains: Computer Science [cs]; Mathematics [math]

Joris van der Hoeven, Fredrik Johansson. Fast multiple precision exp(x) with precomputations. 2024. ⟨hal-04454093v2⟩