SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917462649339904 |
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| author | Xue, Weicheng Xu, Baisong Yang, Kai Liu, Yongxiang Fan, Dengdeng Xu, Pengxiang Tian, Yonghong |
| author_facet | Xue, Weicheng Xu, Baisong Yang, Kai Liu, Yongxiang Fan, Dengdeng Xu, Pengxiang Tian, Yonghong |
| contents | Modern AI accelerators provide high-throughput low-precision matrix engines, but their support for FP32 GEMM is often limited or inefficient. This work presents SGEMM-cube, a precision-recovery FP32 GEMM approximation on Ascend NPUs using FP16 Cube units. Rather than claiming bit-exact FP32 approximation, SGEMM-cube targets near-FP32 accuracy for inputs whose magnitudes are representable within the FP16 dynamic range. The method follows a two-component FP32-to-FP16 splitting strategy related to Ozaki-style and Ootomo-style schemes: each FP32 operand is represented by an FP16 high component and a scaled FP16 residual component, and the matrix product is reconstructed from the dominant high-high and high-low terms while omitting the low-low term. The main contribution of this paper is not a new splitting paradigm, but an architecture-specific realization and analysis of this precision-recovery scheme on Ascend NPUs. We analyze the effects of round-to-nearest conversion, underflow, residual scaling, and accumulation order under the Ascend execution model, and clarify the range and accuracy limitations of the approach. We further adapt standard high-performance GEMM techniques, including L1-aware blocking and double-buffered pipelining, to the software-managed memory hierarchy of Ascend NPUs. Experiments on Ascend 910A show that SGEMM-cube recovers substantially higher accuracy than native FP16 GEMM and approaches FP32 SGEMM accuracy for moderate-range inputs, while achieving up to 65.3 TFLOP/s, corresponding to 77\% of the FP32-equivalent peak defined by the three-GEMM decomposition cost. These results demonstrate that FP32-accuracy GEMM approximation can be made practical on FP16-only NPU matrix engines, provided that its range, error, and implementation constraints are explicitly managed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines Xue, Weicheng Xu, Baisong Yang, Kai Liu, Yongxiang Fan, Dengdeng Xu, Pengxiang Tian, Yonghong Distributed, Parallel, and Cluster Computing Modern AI accelerators provide high-throughput low-precision matrix engines, but their support for FP32 GEMM is often limited or inefficient. This work presents SGEMM-cube, a precision-recovery FP32 GEMM approximation on Ascend NPUs using FP16 Cube units. Rather than claiming bit-exact FP32 approximation, SGEMM-cube targets near-FP32 accuracy for inputs whose magnitudes are representable within the FP16 dynamic range. The method follows a two-component FP32-to-FP16 splitting strategy related to Ozaki-style and Ootomo-style schemes: each FP32 operand is represented by an FP16 high component and a scaled FP16 residual component, and the matrix product is reconstructed from the dominant high-high and high-low terms while omitting the low-low term. The main contribution of this paper is not a new splitting paradigm, but an architecture-specific realization and analysis of this precision-recovery scheme on Ascend NPUs. We analyze the effects of round-to-nearest conversion, underflow, residual scaling, and accumulation order under the Ascend execution model, and clarify the range and accuracy limitations of the approach. We further adapt standard high-performance GEMM techniques, including L1-aware blocking and double-buffered pipelining, to the software-managed memory hierarchy of Ascend NPUs. Experiments on Ascend 910A show that SGEMM-cube recovers substantially higher accuracy than native FP16 GEMM and approaches FP32 SGEMM accuracy for moderate-range inputs, while achieving up to 65.3 TFLOP/s, corresponding to 77\% of the FP32-equivalent peak defined by the three-GEMM decomposition cost. These results demonstrate that FP32-accuracy GEMM approximation can be made practical on FP16-only NPU matrix engines, provided that its range, error, and implementation constraints are explicitly managed. |
| title | SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2507.23387 |