Parallel Vectorized Algorithms for Computing Trigonometric Sums Using AVX-512 Extensions

The aim of this paper is to show that Goertzel and Reinsch algorithms for computing trigonometric sums can be efficiently vectorized using Intel AVX-512 intrinsics in order to utilize SIMD extensions of modern processors. Numerical experiments show that the new vectorized implementations of the algorithms using only one core achieve very good speedup over their sequential versions. The new algorithms have been parallelized using OpenMP in order to utilize multiple cores. For sufficiently large problem sizes, the parallel implementations of the algorithms achieve reasonable speedup against the vectorized ones.