Abstract
The matrix powers kernel, used in communication-avoiding Krylov subspace methods, requires runtime auto-tuning for best performance. We demonstrate how the SEJITS (Selective Embedded Just-In-Time Specialization) approach can be used to deliver a high-performance and performance-portable implementation of the matrix powers kernel to application authors, while separating their high-level concerns from those of auto-tuner implementers involving low-level optimizations. The benefits of delivering this kernel in the form of a specializer, rather than a traditional library, are discussed. Performance of the matrix powers kernel specializer is evaluated in the context of a communication-avoiding conjugate gradient (CA-CG) solver, which compares favorably to traditional CG.
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References
Mohiyuddin, M., Hoemmen, M., Demmel, J., Yelick, K.: Minimizing communication in sparse matrix solvers. In: Supercomputing 2009, Portland, OR (November 2009)
Catanzaro, B., Kamil, S., Lee, Y., Asanović, K., Demmel, J., Keutzer, K., Shalf, J., Yelick, K., Fox, A.: SEJITS: Getting productivity and performance with selective embedded JIT specialization. In: Workshop on Programming Models for Emerging Architectures, PMEA 2009, Raleigh, NC (October 2009)
Kamil, S.: Asp: A SEJITS implementation for Python, https://github.com/shoaibkamil/asp/wiki
Kamil, S., Coetzee, D., Fox, A.: Bringing parallel performance to Python with domain-specific selective embedded just-in-time specialization. In: Proceedings of the 10th Python in Science Conference, SciPy 2011, Austin, TX (2011)
Intel: Math Kernel Library, http://software.intel.com/en-us/articles/intel-mkl/
Carson, E., Demmel, J., Knight, N.: Hypergraph partitioning for computing matrix powers (October 2010), http://www.cs.berkeley.edu/~knight/cdk_CSC11_abstract.pdf
Catalyürek, Ü.V.: Partitioning Tools for Hypergraph, http://bmi.osu.edu/~umit/software.html
Hoemmen, M.: Communication-avoiding Krylov subspace methods. PhD thesis, EECS Department, University of California, Berkeley (April 2010)
Davis, T., Hu, Y.: The University of Florida sparse matrix collection, http://www.cise.ufl.edu/research/sparse/matrices
Bilmes, J., Asanović, K., Chin, C.W., Demmel, J.: Optimizing matrix multiply using PHiPAC: a Portable, High-Performance, ANSI C coding methodology. In: Proceedings of International Conference on Supercomputing, Vienna, Austria (July 1997)
Vuduc, R., Demmel, J.W., Yelick, K.A.: OSKI: A library of automatically tuned sparse matrix kernels. Journal of Physics Conference Series 16(i), 521–530 (2005)
Püschel, M., Moura, J.M.F., Johnson, J., Padua, D., Veloso, M., Singer, B., Xiong, J., Franchetti, F., Gacic, A., Voronenko, Y., Chen, K., Johnson, R.W., Rizzolo, N.: SPIRAL: Code generation for DSP transforms. Proceedings of the IEEE, Special Issue on “Program Generation, Optimization, and Adaptation” 93(2), 232–275 (2005)
Kamil, S., Chan, C., Oliker, L., Shalf, J., Williams, S.: An auto-tuning framework for parallel multicore stencil computations. In: IPDPS 2010, pp. 1–12 (2010)
Tang, Y., Chowdhury, R.A., Kuszmaul, B.C., Luk, C.K., Leiserson, C.E.: The Pochoir stencil compiler. In: Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2011, pp. 117–128. ACM, New York (2011)
Katagiri, T., Kise, K., Honda, H., Yuba, T.: ABCLibScript: a directive to support specification of an auto-tuning facility for numerical software. Parallel Comput. 32(1), 92–112 (2006)
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Morlan, J., Kamil, S., Fox, A. (2013). Auto-tuning the Matrix Powers Kernel with SEJITS. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science - VECPAR 2012. VECPAR 2012. Lecture Notes in Computer Science, vol 7851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38718-0_36
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DOI: https://doi.org/10.1007/978-3-642-38718-0_36
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