Tuning a Finite Difference Computation for Parallel Vector Processors

Current CPU and GPU architectures heavily use data and instruction parallelism at different levels. Floating point operations are organised in vector instructions of increasing vector length. For reasons of performance it is mandatory to use the vector instructions efficiently. Several ways of tuning a model problem finite difference stencil computation are discussed. The combination of vectorisation and an interleaved data layout, cache aware algorithms, loop unrolling, parallelisation and parameter tuning lead to optimised implementations at a level of 90% peak performance of the floating point pipelines on recent Intel Sandy Bridge and AMD Bulldozer CPU cores, both with AVX vector instructions as well as on Nvidia Fermi/ Kepler GPU architectures. Furthermore, we present numbers for parallel multi-core/ multi-processor and multi-GPU configurations. They represent regularly more than an order of speed up compared to a standard implementation. The analysis may also explain deficiencies of automatic vectorisation for linear data layout and serve as a foundation of efficient implementations of more complex expressions.