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Abstract© 2015 IEEE. Many core systems are basically designed for applications having large data parallelism. Strassen Matrix Multiply (MM) can be formulated as a depth first (DFS) traversal of a recursion tree where all cores work in parallel on computing each of the NxN sub-matrices that reduces storage at the detriment of large data motion to gather and aggregate the results. We propose Strassen and Winograd algorithms (S-MM and W-MM) based on three optimizations: a set of basic algebra functions to reduce overhead, invoking efficient library (CUBLAS 5.5), and parameter-tuning of parametric kernel to improve resource occupancy. On GPUs, W-MM and S-MM with one recursion level outperform CUBLAS 5.5 Library with up to twice as faster for large arrays satisfying N>=2048 and N>=3072, respectively. Compared to NVIDIA SDK library, S-MM and W-MM achieved a speedup between 20x to 80x for the above arrays. The proposed approach can be used to enhance the performance of CUBLAS and MKL libraries.
CitationUl Hasan Khan A, Al-Mouhamed M, Fatayer A (2015) Optimizing strassen matrix multiply on GPUs. 2015 IEEE/ACIS 16th International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD). Available: http://dx.doi.org/10.1109/SNPD.2015.7176172.
SponsorsThe authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science & Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No.12-INF3008-04 as part of the National Science, Technology and Innovation Plan. We are also very thankful to King Abullah University of Science and Technology (KAUST) for providing access to their K20X GPU cluster to run the experiments.
Journal2015 IEEE/ACIS 16th International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD)