SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines

[2507.23387] SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Distributed, Parallel, and Cluster Computing arXiv:2507.23387 (cs) [Submitted on 31 Jul 2025 ( v1 ), last revised 15 Aug 2026 (this version, v5)] Title: SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines Authors: Weicheng Xue , Baisong Xu , Kai Yang , Yongxiang Liu , Dengdeng Fan , Pengxiang Xu , Yonghong Tian View a PDF of the paper titled SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines, by Weicheng Xue and 6 other authors View PDF HTML (experimental) Abstract: Modern AI accelerators provide high-throughput low-precision matrix engines, but often lack efficient support for FP32 GEMM. This paper presents SGEMM-cube, an FP32-accuracy GEMM approximation for Ascend NPUs built on FP16 Cube units. Following the fixed-length two-word splitting of Ootomo and Yokota, each FP32 operand is represented by an FP16 high component and a scaled FP16 residual. The product is reconstructed from three FP16 GEMMs while omitting the residual-residual term; the method therefore targets FP32-level accuracy rather than bit-exact emulation. Under an RN FP32-accumulation model, we provide a componentwise error analysis showing that the omitted term is no larger than the rounding error of a short FP32 inner product and that, for practically relevant inner-product lengths, the overall error is dominated by ordinary FP32 accumulation. We further analyze residual underflow and scaling under round-to-nearest conversion, compare two accumulation orders, and adapt L1-aware blocking and double buffering to Ascend's software-managed memory hierarchy. On Ascend 910A, SGEMM-cube is substantially more accurate than native FP16 GEMM, is comparable to the tested OpenBLAS FP32 SGEMM baseline for the evaluated input distributions and exponent range, and reaches 65.3\,TFLOP/s, or 77\% of the three-GEMM FP32-equivalent peak. Subjects: Distributed, Parallel, and Cluster Computing (cs.DC) Cite as: arXiv:2507.23387 [cs.DC] (or arXiv:2507.23387v5 [cs.DC] for this version) https://doi.org/10.48550/arXiv.2507.23387 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Weicheng Xue [ view email ] [v1] Thu, 31 Jul 2025 10:02:26 UTC (692 KB) [v2] Fri, 1 Aug 2025 03:43:24 UTC (694 KB) [v3] Tue, 19 Aug 2025 09:13:13 UTC (779 KB) [v4] Wed, 6 May 2026 12:03:33 UTC (791 KB) [v5] Sat, 15 Aug 2026 13:15:55 UTC (787 KB) Full-text links: Access Paper: View a PDF of the paper titled SGEMM-cube: Precision-Recovery FP32 GEMM Approximation on Ascend NPUs with FP16 Matrix Engines, by Weicheng Xue and 6 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.DC < prev | next > new | recent | 2025-07 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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