A parallel compensated Horner scheme for SIMD architecture

Stef Graillat (1) , Youness Ibrahimy , Clothilde Jeangoudoux , Christoph Lauter

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

A parallel algorithm for accurate polynomial evaluation is proposed for SIMD architectures. This is a parallelized version of the compensated Horner scheme using error-free transformations. The proposed parallel algorithm in this paper is fast and is designed to achieve a result as if computed in twice the working precision and then rounded to the working precision. Numerical results are presented showing the performance of this new parallel algorithm.

Mots clés: polynomial evaluation; compensated algorithms; error-free transformations; Horner scheme; rounding errors; parallel algorithms; SIMD; AVX

Domaines: Arithmétique des ordinateurs

Stef Graillat, Youness Ibrahimy, Clothilde Jeangoudoux, Christoph Lauter. A parallel compensated Horner scheme for SIMD architecture. 2023. ⟨hal-04180645⟩