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 SELL-C-σ, 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-σ 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-σ spMVM kernel. SELL-C-σ 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.
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References in zbMATH (referenced in 5 articles , 1 standard article )
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- Mironowicz, P.; Dziekonski, A.; Mrozowski, M.: A task-scheduling approach for efficient sparse symmetric matrix-vector multiplication on a GPU (2015)
- Röhrig-Zöllner, Melven; Thies, Jonas; Kreutzer, Moritz; Alvermann, Andreas; Pieper, Andreas; Basermann, Achim; Hager, Georg; Wellein, Gerhard; Fehske, Holger: Increasing the performance of the Jacobi-Davidson method by blocking (2015)
- Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard; Fehske, Holger; Bishop, Alan R.: A unified sparse matrix data format for efficient general sparse matrix-vector multiplication on modern processors with wide SIMD units (2014)