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General matrix-matrix multiplications with double-precision real and complexentries (DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimizedfor square matrices but often show bad performance for tall & skinny matrices,which are much taller than wide. NVIDIA's current CUBLAS implementationdelivers only a fraction of the potential performance as indicated by theroofline model in this case. We describe the challenges and key characteristicsof an implementation that can achieve close to optimal performance. We furtherevaluate different strategies of parallelization and thread distribution, anddevise a flexible, configurable mapping scheme. To ensure flexibility and allowfor highly tailored implementations we use code generation combined withautotuning. For a large range of matrix sizes in the domain of interest weachieve at least 2/3 of the roofline performance and often substantiallyoutperform state-of-the art CUBLAS results on an NVIDIA Volta GPGPU.

Performance Engineering for Real and Complex Tall & Skinny Matrix Multiplication Kernels on GPUs