Programming parallel dense matrix factorizations with look-ahead and OpenMP

[EN] We investigate a parallelization strategy for dense matrix factorization (DMF) algorithms, using OpenMP, that departs from the legacy (or conventional) solution, which simply extracts concurrency from a multi-threaded version of basic linear algebra subroutines (BLAS). The proposed approach is also different from the more sophisticated runtime-based implementations, which decompose the operation into tasks and identify dependencies via directives and runtime support. Instead, our strategy attains high performance by explicitly embedding a static look-ahead technique into the DMF code, in order to overcome the performance bottleneck of the panel factorization, and realizing the trailing update via a cache-aware multi-threaded implementation of the BLAS. Although the parallel algorithms are specified with a high level of abstraction, the actual implementation can be easily derived from them, paving the road to deriving a high performance implementation of a considerable fraction of linear algebra package (LAPACK) functionality on any multicore platform with an OpenMP-like runtime.The researchers from Universidad Jaume I were supported by the CICYT Projects TIN2014-53495-R and TIN2017-82972-R of the MINECO and FEDER, and the H2020 EU FETHPC Project 671602 "INTERTWinE". The researchers from Universidad Complutense de Madrid were supported by the CICYT Project TIN2015-65277-R of the MINECO and FEDER. Sandra Catalan was supported during part of this time by the FPU program of the Ministerio de Educacion, Cultura y Deporte. Adrian Castello was supported by the ValI+D 2015 FPI program of the Generalitat Valenciana.Catalán, S.; Castelló, A.; Igual, FD.; Rodríguez-Sánchez, R.; Quintana Ortí, ES. (2020). Programming parallel dense matrix factorizations with look-ahead and OpenMP. Cluster Computing. 23(1):359-375. https://doi.org/10.1007/s10586-019-02927-zS359375231Anderson, E., Bai, Z., Susan Blackford, L., Demmel, J., Dongarra, J.J., Croz, J.D., Hammarling, S., Greenbaum, A., McKenney, A., Sorensen, D.C.: LAPACK Users’ guide. SIAM, 3rd edition (1999)Badia, R.M., Herrero, J.R., Labarta, J., Pérez, J.M., Quintana-Ortí, E.S., Quintana-Ortí, G.: Parallelizing dense and banded linear algebra libraries using SMPSs. Conc. Comp. 21, 2438–2456 (2009)Bientinesi, P., Gunnels, J.A., Myers, M.E., Quintana-Ortí, E.S., van de Geijn, R.A.: The science of deriving dense linear algebra algorithms. ACM Trans. Math. Softw. 31(1), 1–26 (2005)Bischof, C.H., Lang, B., Sun, X.: Algorithm 807: the SBR toolbox–software for successive band reduction. ACM Trans. Math. Softw. 26(4), 602–616 (2000)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)Castelló, A., Mayo, R., Sala, K., Beltran, V., Balaji, P., Peña, A.J.: On the adequacy of lightweight thread approaches for high-level parallel programming models. Future Gener. Comput. Syst. 84, 22–31 (2018)Castelló, A., Peña, A.J., Seo, S., Mayo, R., Balaji, P., Quintana-Ortí, E.S.: A review of lightweight thread approaches for high performance computing. In: Proceedings of the IEEE International Conference on Cluster Computing, Taipei, Taiwan (September 2016)Castelló, A., Seo, S., Mayo, R., Balaji, P., Quintana-Ortí, E.S., Peña, A.J.: GLT: a unified API for lightweight thread libraries. In: Proceedings of the IEEE International European Conference on Parallel and Distributed Computing, Santiago de Compostela, Spain (August 2017)Castelló, A., Seo, S., Mayo, R., Balaji, P., Quintana-Ortí, E.S., Peña, A.J.: GLTO: on the adequacy of lightweight thread approaches for OpenMP implementations. In: Proceedings of the International Conference on Parallel Processing, Bristol, UK (August 2017)Catalán, S, Herrero, JR., Quintana-Ortí, E.S., Rodríguez-Sánchez, R., van de Geijn, R.A.: A case for malleable thread-level linear algebra libraries: The LU factorization with partial pivoting. CoRR (2016) arXiv:1611.06365Catalán, S., Igual, F.D., Mayo, R., Rguez-Sánchez, R.: Architecture-aware configuration and scheduling of matrix multiplication on asymmetric multicore processors. Clust. Comput. 19(3), 1037–1051 (2016)Chameleon project. http://project.inria.fr/chameleon/Demmel, J.: Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Paris (1997)Dongarra, J.J., Croz, J.D., Hammarling, S., Duff, I.: A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Softw. 16(1), 1–17 (1990)FLAME project home page. http://www.cs.utexas.edu/users/flame/Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)Goto, K., van de Geijn, R.A.: Anatomy of high-performance matrix multiplication. ACM Trans. Math. Softw. 34(3), 12:1–12:25 (2008)Goto, K., van de Geijn, R.: High performance implementation of the level-3 BLAS. ACM Trans. Math. Softw. 35(1), 4:1–4:14 (2008)Grosser, B., Lang, B.: Efficient parallel reduction to bidiagonal form. Parallel Comput. 25(8), 969–986 (1999)Gunter, B.C., van de Geijn, R.A.: Parallel out-of-core computation and updating the QR factorization. ACM Trans. Math. Soft. 31(1), 60–78 (2005)IBM. Engineering and Scientific Subroutine Library. http://www-03.ibm.com/systems/power/software/essl/ (2015)Intel. Math Kernel Library. https://software.intel.com/en-us/intel-mkl (2015)OmpSs project home page. http://pm.bsc.es/ompsshttp://www.openblas.net (2015)OpenMP API specification for parallel programming. http://www.openmp.org (2017)PLASMA project home page. http://icl.cs.utk.edu/plasmaQuintana-Ortí, E.S., van de Geijn, R.A.: Updating an LU factorization with pivoting. ACM Trans. Math. Softw. 35(2), 11:1–11:16 (2008)Quintana-Ortí, G., Quintana-Ortí, E.S., van de Geijn, R.A., Van Zee, F.G., Chan, E.: Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Trans. Math. Softw. 36(3), 14:1–14:26 (2009)Rodríguez-Sánchez, R., Catalán, Sandra, H., José, R., Quintana-Ortí, E.S., Tomás, A.E.: Two-sided reduction to compact band forms with look-ahead (2017) CoRR, arXiv:1709.00302Seo, S., Amer, A., Balaji, P., Bordage, C., Bosilca, G., Brooks, A., Carns, P., Castelló, A., Genet, D., Herault, T., Iwasaki, S., Jindal, P., Kale, S., Krishnamoorthy, S., Lifflander, J., Lu, H., Meneses, E., Snir, M., Sun, Y., Taura, K., Beckman, P.: Argobots: a lightweight low-level threading and tasking framework. IEEE Trans. Parallel Distrib. Syst. PP(99), 1–1 (2017)Smith, T.M., van de Geijn, R., Smelyanskiy, M., Hammond, J.R., Van Zee, F.G.: Anatomy of high-performance many-threaded matrix multiplication. In: Proceedings of IEEE 28th International Parallel and Distributed Processing Symposium, IPDPS’14, pp. 1049–1059 (2014)StarPU project. http://runtime.bordeaux.inria.fr/StarPU/Stein, D., Shah, D.: Implementing lightweight threads. In: USENIX Summer (1992)Strazdins, P.: A comparison of lookahead and algorithmic blocking techniques for parallel matrix factorization. Technical Report TR-CS-98-07, Department of Computer Science, The Australian National University, Canberra 0200 ACT, Australia (1998)Van Zee, F.G., van de Geijn, R.A.: BLIS: a framework for rapidly instantiating BLAS functionality. ACM Trans. Math. Softw. 41(3), 14:1–14:33 (2015)Whaley, C.R., Dongarra, J.J.: Automatically tuned linear algebra software. In: Proceedings of SC’98 (1998)Van Zee, F.G., Smith, T.M., Marker, B., Low, T., Van De Geijn, R.A., Igual, F.D., Smelyanskiy, M., Zhang, X., Kistler, M., Austel, V., Gunnels, J.A., Killough, L.: The BLIS framework: experiments in portability. ACM Trans. Math. Softw. 42(2), 12:1–12:19 (2016

Integration and exploitation of intra-routine malleability in BLIS

[EN] Malleability is a property of certain applications (or tasks) that, given an external request or autonomously, can accommodate a dynamic modification of the degree of parallelism being exploited at runtime. Malleability improves resource usage (core occupation) on modern multicore architectures for applications that exhibit irregular and divergent execution paths and heavily depend on the underlying library performance to attain high performance. The integration of malleability within high-performance instances of the Basic Linear Algebra Subprograms (BLAS) is nonexistent, and, in addition, it is difficult to attain given the rigidity of current application programming interfaces (APIs). In this paper, we overcome these issues presenting the integration of a malleability mechanism within BLIS, a high-performance and portable framework to implement BLAS-like operations. For this purpose, we leverage low-level (yet simple) APIs to integrate on-demand malleability across all Level-3 BLAS routines, and we demonstrate the performance benefits of this approach by means of a higher-level dense matrix operation: the LU factorization with partial pivoting and look-aheadThe researchers from Universidad Complutense de Madrid were supported by the EU (FEDER) and Spanish MINECO (TIN2015-65277-R, RTI2018-093684-B-I00), and by Spanish CM (S2018/TCS-4423). The researcher from Universitat Poliecnica de Valencia was supported by the Spanish MINECO (TIN2017-82972-R)Rodríguez-Sánchez, R.; Igual, FD.; Quintana-Ortí, ES. (2020). Integration and exploitation of intra-routine malleability in BLIS. The Journal of Supercomputing (Online). 76(4):2860-2875. https://doi.org/10.1007/s11227-019-03078-zS28602875764Augonnet C, Thibault S, Namyst R, Wacrenier PA (2011) StarPU: a unified platform for task scheduling on heterogeneous multicore architectures. Concurr Comput Pract Exp Spec Issue Euro Par 2009(23):187–198Catalán S, Castelló A, Igual FD, Rodríguez-Sánchez R, Quintana-Ortí ES (2019) Programming parallel dense matrix factorizations with look-ahead and OpenMP. Cluster Comput. https://doi.org/10.1007/s10586-019-02927-zCatalán S, Herrero JR, Quintana-Ortí ES, Rodríguez-Sánchez R, Van De Geijn R (2019) A case for malleable thread-level linear algebra libraries: the LU factorization with partial pivoting. IEEE Access 7:17617–17633Catalán S, Igual FD, Mayo R, Rodríguez-Sánchez R, Quintana-Ortí ES (2016) Architecture-aware configuration and scheduling of matrix multiplication on asymmetric multicore processors. Cluster Comput 19(3):1037–1051Chan E, Van Zee FG, Bientinesi P, Quintana-Ortí ES, Quintana-Ortí G, van de Geijn R (2008)Supermatrix: A multithreaded runtime scheduling system for algorithms-by-blocks. In: Proceedings of the 13th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. ACM, New York, pp 123–132Corporation I (2019) Intel ® math kernel library developer reference. Tech rep, Intel Corporation. https://software.intel.com/sites/default/files/mkl-2019-developer-reference-c_2.pdf. Accessed 13 Nov 2019Dolz MF, Igual FD, Ludwig T, Piñuel L, Quintana-Ortí ES (2015) Balancing task- and data-level parallelism to improve performance and energy consumption of matrix computations on the intel xeon phi. Comput Electr Eng 46:95–111Dongarra JJ, Du Croz J, Hammarling S, Duff IS (1990) A set of level 3 basic linear algebra subprograms. ACM Trans Math Softw 16(1):1–17Duran A, Ayguadé E, Badia RM, Labarta J, Martinell L, Martorell X, Planas J (2011) OmpSs: a proposal for programming heterogeneous multi-core architectures. Parallel Process Lett 21(2):173–193Gates M, Luszczek P, Abdelfattah A, Kurzak J, Dongarra J, Arturov K, Cecka C, Freitag C (2018) C++ API for BLAS and LAPACK. Tech Rep 2, ICL-UT-17-03 (2017). Revision 21 Feb 2018Guennebaud G, Jacob B et al (2019) Eigen v3. http://eigen.tuxfamily.org. Accessed 13 Nov 2019LAPACK project home page. http://www.netlib.org/lapack. Accessed 13 Nov 2019Leung J, Kelly L, Anderson JH (2004) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press Inc, Boca Raton, FLSmith TM, van de Geijn RA, Smelyanskiy M, Hammond JR, Van Zee FG (2014) Anatomy of high-performance many-threaded matrix multiplication. In: 28th IEEE International Parallel & Distributed Processing SymposiumStrazdins P (1998) A comparison of lookahead and algorithmic blocking techniques for parallel matrix factorization. Tech Rep TR-CS-98-07, Department of Computer Science, The Australian National University, Canberra 0200 ACT, AustraliaWhaley RC, Petitet A, Dongarra JJ (2001) Automated empirical optimization of software and the ATLAS project. Parallel Comput 27(1–2):3–35Van Zee FG, Implementing high-performance complex matrix multiplication via the 1m method. ACM Trans Math Softw (submitted)Van Zee FG, van de Geijn RA (2015) BLIS: a framework for rapidly instantiating BLAS functionality. ACM Trans Math Softw 41(3):14:1–14:33Van Zee FG, Parikh DN, van de Geijn RA, Supporting mixed-domain mixed-precision matrix multiplication within the BLIS framework. ACM Trans Math Softw (submitted)Van Zee FG, Smith T (2017) Implementing high-performance complex matrix multiplication via the 3m and 4m methods. ACM Trans Math Softw 44(1):7:1–7:36Van Zee FG, Smith T, Igual FD, Smelyanskiy M, Zhang X, Kistler M, Austel V, Gunnels J, Low TM, Marker B, Killough L, van de Geijn RA (2016) The BLIS framework: experiments in portability. ACM Trans Math Softw 42(2):12:1–12:1