A UNIFIED SPARSE MATRIX DATA FORMAT FOR EFFICIENT GENERAL SPARSE MATRIX-VECTOR MULTIPLICATION ON MODERN PROCESSORS WITH WIDE SIMD UNITS

Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi-and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELLC-sigma, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from general-purpose graphics processing units and vector computer programming. We discuss the advantages of SELL-C-sigma compared to established formats like Compressed Row Storage and ELLPACK and show its suitability on a variety of hardware platforms (Intel Sandy Bridge, Intel Xeon Phi, and Nvidia Tesla K20) for a wide range of test matrices from different application areas. Using appropriate performance models we develop deep insight into the data transfer properties of the SELL-C-sigma spMVM kernel. SELL-C-sigma comes with two tuning parameters whose performance impact across the range of test matrices is studied and for which reasonable choices are proposed. This leads to a hardware-independent ("catch-all") sparse matrix format, which achieves very high efficiency for all test matrices across all hardware platforms.