Empirical Installation of Linear Algebra Shared-Memory Subroutines for Auto-Tuning

The final publication is available at Springer via http://dx.doi.org/10.1007/s10766-013-0249-6The introduction of auto-tuning techniques in linear algebra shared-memory routines is analyzed. Information obtained in the installation of the routines is used at running time to take some decisions to reduce the total execution time. The study is carried out with routines at different levels (matrix multiplication, LU and Cholesky factorizations and linear systems symmetric or general routines) and with calls to routines in the LAPACK and PLASMA libraries with multithread implementations. Medium NUMA and large cc-NUMA systems are used in the experiments. This variety of routines, libraries and systems allows us to obtain general conclusions about the methodology to use for linear algebra shared-memory routines auto-tuning. Satisfactory execution times are obtained with the proposed methodology.Partially supported by Fundacion Seneca, Consejeria de Educacion de la Region de Murcia, 08763/PI/08, PROMETEO/2009/013 from Generalitat Valenciana, the Spanish Ministry of Education and Science through TIN2012-38341-C04-03, and the High-Performance Computing Network on Parallel Heterogeneus Architectures (CAPAP-H). The authors gratefully acknowledge the computer resources and assistance provided by the Supercomputing Centre of the Scientific Park Foundation of Murcia and by the Centre de Supercomputacio de Catalunya.Cámara, J.; Cuenca, J.; Giménez, D.; García, LP.; Vidal Maciá, AM. (2014). Empirical Installation of Linear Algebra Shared-Memory Subroutines for Auto-Tuning. International Journal of Parallel Programming. 42(3):408-434. https://doi.org/10.1007/s10766-013-0249-6408434423Agullo, E., Demmel, J., Dongarra, J., Hadri, B., Kurzak, J., Langou, J., Ltaief, H., Luszczek, P., Tomov, S.: Numerical linear algebra on emerging architectures: the PLASMA and MAGMA projects. J. Phys. Conf. Ser. 180(1), 1–5 (2009)Alberti, P., Alonso, P., Vidal, A.M., Cuenca, J., Giménez, D.: Designing polylibraries to speed up linear algebra computations. Int. J. High Perform. Comput. Netw. 1/2/3(1), 75–84 (2004)Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J.J., Du Croz, J., Grenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., D. Sorensen, S.: LAPACK User’s Guide. Society for Industrial and Applied Mathematics, Philadelphia (1995)Bernabé, G., Cuenca, J., Giménez, D.: Optimization techniques for 3D-FWT on systems with manycore GPUs and multicore CPUs. In: ICCS (2013)Buttari, A., Langou, J., Kurzak, J., Dongarra, J.: A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Comput. 35(1), 38–53 (2009)Cámara, J., Cuenca, J., Giménez, D., Vidal. A.M.: Empirical autotuning of two-level parallel linear algebra routines on large cc-NUMA systems. In: ISPA (2012)Caron, E., Desprez, F., Suter, F.: Parallel extension of a dynamic performance forecasting tool. Scalable Comput. Pract. Exp. 6(1), 57–69 (2005)Chen, Z., Dongarra, J., Luszczek, P., Roche, K.: Self adapting software for numerical linear algebra and LAPACK for clusters. Parallel Comput. 29, 1723–1743 (2003)Cuenca, J., Giménez, D., González, J.: Achitecture of an automatic tuned linear algebra library. Parallel Comput. 30(2), 187–220 (2004)Cuenca, J., García, L.P., Giménez, D.: Improving linear algebra computation on NUMA platforms through auto-tuned nested parallelism. In: Proceedings of the 2012 EUROMICRO Conference on Parallel, Distributed and Network Processing (2012)Frigo, M.: FFTW: An adaptive software architecture for the FFT. In: Proceedings of the ICASSP Conference, vol. 3, p. 1381 (1998)Golub, G., Van Loan, C.F.: Matrix Computations, 3rd edn. The John Hopkins University Press, Baltimore (1996)Im, E.-J., Yelick, K., Vuduc, R.: Sparsity: optimization framework for sparse matrix kernels. Int. J. High Perform. Comput. Appl. (IJHPCA) 18(1), 135–158 (2004)Intel MKL web page.: http://software.intel.com/en-us/intel-mkl/Jerez, S., Montávez, J.-P., Giménez, D.: Optimizing the execution of a parallel meteorology simulation code. In: Proceedings of the 23rd IEEE International Parallel and Distributed Processing Symposium. IEEE (2009)Katagiri, T., Kise, K., Honda, H., Yuba, T.: Fiber: a generalized framework for auto-tuning software. Springer LNCS 2858, 146–159 (2003)Katagiri, T., Kise, K., Honda, H., Yuba, T.: ABCLib-DRSSED: a parallel eigensolver with an auto-tuning facility. Parallel Comput. 32(3), 231–250 (2006)Kurzak, J., Tomov, S., Dongarra, J.: Autotuning gemm kernels for the FERMI GPU. IEEE Trans. Parallel Distrib. Syst. 23(11), 2045–2057 (2012)Lastovetsky, A.L., Reddy, R., Higgins, R.: Building the functional performance model of a processor. In: SAC, pp. 746–753 (2006)Li, J., Skjellum, A., Falgout, R.D.: A poly-algorithm for parallel dense matrix multiplication on two-dimensional process grid topologies. Concurrency Pract. Exp. 9(5), 345–389 (1997)Naono, K., Teranishi, K., Cavazos, J., Suda, R., (eds.): Software Automatic Tuning. From Concepts to State-of-the-Art Results. Springer, Berlin (2010)Nath, R., Tomov, S., Dongarra, J.: An improved MAGMA gemm for FERMI graphics processing units. IJHPCA 24(4), 511–515 (2010)Petitet, A., Blackford, L.S., Dongarra, J., Ellis, B., Fagg, G.E., Roche, K., Vadhiyar, S.S.: Numerical libraries and the grid. IJHPCA 15(4), 359–374 (2001)PLASMA.: http://icl.cs.utk.edu/plasma/Püschel, M., Moura, J.M.F., Singer, B., Xiong, J., Johnson, J.R., Padua, D.A., Veloso, M.M., Johnson, R.W.: Spiral: a generator for platform-adapted libraries of signal processing algorithms. IJHPCA 18(1), 21–45 (2004)Seshagiri, L., Wu, M.-S., Sosonkina, M., Zhang, Z., Gordon, M.S., Schmidt, M.W.: Enhancing adaptive middleware for quantum chemistry applications with a database framework. In: IPDPS Workshops, pp. 1–8 (2010)Tanaka, T., Katagiri, T., Yuba, T.: d-Spline based incremental parameter estimation in automatic performance tuning. In: PARA, pp. 986–995 (2006)Vuduc, R., Demmel, J., Bilmes, J.: Statistical models for automatic performance tuning. In: International Conference on Computational Science (1), pp. 117–126 (2001)Whaley, R.C., Petitet, A., Dongarra, J.: Automated empirical optimizations of software and the ATLAS project. Parallel Comput. 27(1–2), 3–35 (2001