Stream-K: Work-centric Parallel Decomposition for Dense Matrix-Matrix Multiplication on the GPU

Muhammad Osama; Duane Merrill; Cris Cecka; Michael Garland; John D. Owens

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arXiv · 2301.03598

Stream-K: Work-centric Parallel Decomposition for Dense Matrix-Matrix Multiplication on the GPU

Muhammad Osama·Duane Merrill·Cris Cecka·Michael Garland·John D. Owens

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Abstract

We introduce Stream-K, a work-centric parallelization of matrix multiplication (GEMM) and related computations in dense linear algebra. Whereas contemporary decompositions are primarily tile-based, our method operates by partitioning an even share of the aggregate inner loop iterations among physical processing elements. This provides a near-perfect utilization of computing resources, regardless of how efficiently the output tiling for any given problem quantizes across the underlying processing elements. On GPU processors, our Stream-K parallelization of GEMM produces a peak speedup of up to 14$\times$ and 6.7$\times$, and an average performance response that is both higher and more consistent across 32,824 GEMM problem geometries than state-of-the-art math libraries such as CUTLASS and cuBLAS. Furthermore, we achieve this performance from a single tile size configuration per floating-point precision, whereas today's math libraries employ complex kernel-selection heuristics to select from a large ensemble of kernel variants.

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Muhammad Osama, Duane Merrill, Cris Cecka, Michael Garland, John D. Owens. 2023-01-09. Stream-K: Work-centric Parallel Decomposition for Dense Matrix-Matrix Multiplication on the GPU. https://arxiv.org/abs/2301.03598

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