Cascading GEMM: High Precision from Low Precision
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, leveragin...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
07.03.2023
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2303.04353 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Parikh, Devangi N Henry, Greg M van de Geijn, Robert A |
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| BackLink | https://doi.org/10.48550/arXiv.2303.04353$$DView paper in arXiv |
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| Snippet | This paper lays out insights and opportunities for implementing
higher-precision matrix-matrix multiplication (GEMM) from (in terms of)
lower-precision... |
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| Title | Cascading GEMM: High Precision from Low Precision |
| URI | https://arxiv.org/abs/2303.04353 |
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