Cascading GEMM: High Precision from Low Precision
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913628152659968 |
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| author | Parikh, Devangi N. van de Geijn, Robert A. Henry, Greg M. |
| author_facet | Parikh, Devangi N. van de Geijn, Robert A. Henry, Greg M. |
| contents | This paper lays out insights and opportunities for implementing higher-precision matrix-matrix multiplication (GEMM) from (in terms of) lower-precision high-performance GEMM. The driving case study approximates double-double precision (FP64x2) GEMM in terms of double precision (FP64) GEMM, leveraging how the BLAS-like Library Instantiation Software (BLIS) framework refactors the Goto Algorithm. With this, it is shown how approximate FP64x2 GEMM accuracy can be cast in terms of ten ``cascading'' FP64 GEMMs. Promising results from preliminary performance and accuracy experiments are reported. The demonstrated techniques open up new research directions for more general cascading of higher-precision computation in terms of lower-precision computation for GEMM-like functionality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cascading GEMM: High Precision from Low Precision Parikh, Devangi N. van de Geijn, Robert A. Henry, Greg M. Mathematical Software G.4 This paper lays out insights and opportunities for implementing higher-precision matrix-matrix multiplication (GEMM) from (in terms of) lower-precision high-performance GEMM. The driving case study approximates double-double precision (FP64x2) GEMM in terms of double precision (FP64) GEMM, leveraging how the BLAS-like Library Instantiation Software (BLIS) framework refactors the Goto Algorithm. With this, it is shown how approximate FP64x2 GEMM accuracy can be cast in terms of ten ``cascading'' FP64 GEMMs. Promising results from preliminary performance and accuracy experiments are reported. The demonstrated techniques open up new research directions for more general cascading of higher-precision computation in terms of lower-precision computation for GEMM-like functionality. |
| title | Cascading GEMM: High Precision from Low Precision |
| topic | Mathematical Software G.4 |
| url | https://arxiv.org/abs/2303.04353 |