TSM2X: High-performance tall-and-skinny matrix–matrix multiplication on GPUs

Linear algebra operations have been widely used in big data analytics and scientific computations. Many works done on optimizing linear GPUs with regular-shaped input. However, few focus fully utilizing GPU resources when the input is not regular-shaped. Current optimizations do consider memory bandwidth computing power; therefore, they can only achieve sub-optimal performance. In this paper, we propose two efficient algorithms -- TSM2R TSM2L for classes of tall-and-skinny matrix-matrix multiplications GPUs. Both them operation at least one matrices tall-and-skinny. Specifically, designed a large matrix multiplying matrix, while small matrix. We implement our proposed test several modern NVIDIA micro-architectures. Experiments show that, compared to current state-of-the-art works, (1) speeds up computation by 1.1x~3x improves utilization power 8%~47.6% 7%~37.3%, respectively, size relatively or medium; (2) 1.1x~3.5x improve 55% small.