SELL_C_sigma swMATH ID: 11232 Software Authors: Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard; Fehske, Holger; Bishop, Alan R. Description: 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. Homepage: http://blogs.fau.de/essex/files/2012/11/SELL-C-sigma.pdf Keywords: sparse matrix; sparse matrix-vector multiplication; data format; performance model; numerical examples; algorithm; single instruction multiple data Related Software: SparseMatrix; CUDA; CUSPARSE; yaSpMV; CUSP; clSpMV; ITER-REF; FEAST; OpenCL; FEniCS; CRAFT; ELSI; ELPA; STRUMPACK; CholQR; CIRR; ITPACK; LightSpMV; CSR5; COFFEE Cited in: 11 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A unified sparse matrix data format for efficient general sparse matrix-vector multiplication on modern processors with wide SIMD units. Zbl 1307.65055Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard; Fehske, Holger; Bishop, Alan R. 2014 all top 5 Cited by 61 Authors 3 Fehske, Holger 3 Hager, Georg 3 Kreutzer, Moritz 3 Wellein, Gerhard 2 Alvermann, Andreas 2 Basermann, Achim 2 Gao, Jiaquan 2 He, Guixia 2 Röhrig-Zöllner, Melven 2 Thies, Jonas 1 Bernaschi, Massimo 1 Bishop, Alan Reginald 1 Bisson, Mauro 1 Bungartz, Hans-Joachim 1 Carbogno, Christian 1 Dziekonski, A. 1 Ernst, Dominik 1 Fantozzi, Carlo 1 Futamura, Yasunori 1 Galgon, Martin 1 Grasser, Tibor 1 Huber, Sarah E. 1 Huckle, Thomas Kilian 1 Ida, Akihiro 1 Imakura, Akira 1 Janna, Carlo 1 Jüngel, Ansgar 1 Kawai, Masatoshi 1 Köcher, Simone 1 Krasnopolsky, Boris I. 1 Kus, Pavel 1 Lang, Bruno 1 Lederer, Hermann 1 Manin, Valeriy 1 Marek, Andreas 1 Mironowicz, Piotr 1 Mohr, Marcus 1 Morhammer, Andreas 1 Mrozowski, M. 1 Nakajima, Kengo 1 Nemec, Lydia 1 Pieper, Andreas 1 Pikle, Nileshchandra K. 1 Qi, Panpan 1 Reuter, Karsten 1 Rippl, Michael 1 Rüde, Ulrich 1 Rudolf, Florian 1 Rupp, Karl 1 Sakurai, Tetsuya 1 Sathe, Shailesh R. 1 Scheffler, Matthias 1 Scheurer, Christoph 1 Selberherr, Siegfried 1 Shahzad, Faisal 1 Simoes Brambila, Danilo 1 Tillet, Philippe 1 Vyavhare, Arvind Y. 1 Weinbub, Josef 1 Weismüller, J. 1 Wohlmuth, Barbara I. all top 5 Cited in 6 Serials 5 SIAM Journal on Scientific Computing 2 Mathematical Problems in Engineering 1 Applied Numerical Mathematics 1 Japan Journal of Industrial and Applied Mathematics 1 Lobachevskii Journal of Mathematics 1 Sādhanā Cited in 3 Fields 10 Numerical analysis (65-XX) 1 Partial differential equations (35-XX) 1 Fluid mechanics (76-XX) Citations by Year