Performance and efficiency investigations of SIMD programs of Coulomb solvers on multi-and many-core systems with vector units

Vectorization is a key technology to increase the performance and efficiency of computer systems, however the performance increase usually strongly depends on the specific application program. In this article, we introduce SIMD program versions of a Coulomb solver based on manual vectorization as well as automatic vectorization using the Intel C Compiler. The implementation uses the latest Advanced Vector Extensions with 512-bit vector size (AVX-512). The comparison of the performance results visualizes the reduction of the execution time achieved by the manual vectorization as well as the automatic vectorization compared to the code without vectorization. The automatic vectorization achieves a good speed up that should be sufficient for most use cases. However, we also show that the manual vectorization is able to outperform the automatic vectorization. The control over the instructions used by the manual vectorization can reduce the amount of expensive vector reduction operations which are introduced by the automatic vectorization.