PackSELL: A Sparse Matrix Format for Precision-Agnostic High-Performance SpMV
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917409558888448 |
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| author | Suzuki, Kengo Iwashita, Takeshi |
| author_facet | Suzuki, Kengo Iwashita, Takeshi |
| contents | We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta encoding of column indices and a novel packing scheme that stores each index-delta-value pair in a single word, thereby reducing memory footprint and data movement. This design further enables fine-grained control over the bit allocation between deltas and values, allowing flexible data representations, including non-IEEE formats. Experimental results show that, when configured for half precision (FP16), the PackSELL-based SpMV kernel outperforms the cuSPARSE SELL-based kernel by up to $1.63\times$. Moreover, with configurations using customized formats, PackSELL achieves FP32-level accuracy while exceeding the performance of FP16 cuSPARSE. These benefits extend to sparse linear solvers; for example, a mixed-precision preconditioned conjugate gradient (PCG) solver using PackSELL achieves up to a $2.09\times$ speedup over the standard full-precision PCG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13433 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PackSELL: A Sparse Matrix Format for Precision-Agnostic High-Performance SpMV Suzuki, Kengo Iwashita, Takeshi Distributed, Parallel, and Cluster Computing Numerical Analysis 68W10, 65F50 F.2.1; I.1.2; G.1.3 We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta encoding of column indices and a novel packing scheme that stores each index-delta-value pair in a single word, thereby reducing memory footprint and data movement. This design further enables fine-grained control over the bit allocation between deltas and values, allowing flexible data representations, including non-IEEE formats. Experimental results show that, when configured for half precision (FP16), the PackSELL-based SpMV kernel outperforms the cuSPARSE SELL-based kernel by up to $1.63\times$. Moreover, with configurations using customized formats, PackSELL achieves FP32-level accuracy while exceeding the performance of FP16 cuSPARSE. These benefits extend to sparse linear solvers; for example, a mixed-precision preconditioned conjugate gradient (PCG) solver using PackSELL achieves up to a $2.09\times$ speedup over the standard full-precision PCG. |
| title | PackSELL: A Sparse Matrix Format for Precision-Agnostic High-Performance SpMV |
| topic | Distributed, Parallel, and Cluster Computing Numerical Analysis 68W10, 65F50 F.2.1; I.1.2; G.1.3 |
| url | https://arxiv.org/abs/2604.13433 |