Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works are focusing on fully utilizing GPU resources when the input is not regular-shaped. Current optimizations lack of considering fully utilizing the memory bandwidth and computing power, therefore they could only achieve sub-optimal performance. In this paper, we propose two efficient irregular-shaped matrix-matrix multiplication (GEMM) algorithms on GPUs, called TSM2 and ISM2. Both of them focus on optimizing GEMMs with various input sizes where at least one of the matrices is tall-and-skinny. We implement our proposed algorithms and test on several modern Nvidia GPU micro-architectures. Experiments show that compared to state of the art, our TSM2 speeds up the computation by 1.1x~3x and improves the memory bandwidth utilization and computing power utilization by 8%~47.6% and 7%~37.3%, respectively, when the size of regular matrix is relatively large or medium. Moreover, our ISM2 speeds up the GEMM by 1.1x~3.5x and improve the memory bandwidth utilization by up to 55% when the size of regular matrix is relatively small.
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