Abstract
The general matrix-matrix multiplication (GEMM) is the most important numerical kernel in dense linear algebra, and is the key component for obtaining high performance in most LAPACK routines. As batched computations on relatively small problems continue to gain interest in many scientific applications, a need arises for a high performance GEMM kernel for batches of small matrices. Such a kernel should be well designed and tuned to handle small sizes, and to maintain high performance for realistic test cases found in the higher level LAPACK routines, and scientific computing applications in general.
This paper presents a high performance batched GEMM kernel on Graphics Processing Units (GPUs). We address batched problems with both fixed and variable sizes, and show that specialized GEMM designs and a comprehensive autotuning process are needed to handle problems of small sizes. For most performance tests reported in this paper, the proposed kernels outperform state-of-the-art approaches using a K40c GPU.
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Acknowledgment
This work is based upon work supported by the National Science Foundation under Grants No. ACI-1339822 and CSR 1514286, NVIDIA, the Department of Energy (LLNL subcontract under DOE contract DE-AC52-07NA27344), and in part by the Russian Scientific Foundation, Agreement N14-11-00190.
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Abdelfattah, A., Haidar, A., Tomov, S., Dongarra, J. (2016). Performance, Design, and Autotuning of Batched GEMM for GPUs. In: Kunkel, J., Balaji, P., Dongarra, J. (eds) High Performance Computing. ISC High Performance 2016. Lecture Notes in Computer Science(), vol 9697. Springer, Cham. https://doi.org/10.1007/978-3-319-41321-1_2
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