🤖 AI Summary
This work addresses the limitations of conventional sparse matrix formats on GPUs for sparse matrix-vector multiplication (SpMV), which suffer from high memory overhead, frequent data movement, and insufficient support for flexible precision. The authors propose a precision-agnostic sparse storage format built upon the SELL structure, integrating column index delta encoding with a single-word packing scheme that compresses both index deltas and numerical values into a single word. This design enables dynamic bit-width allocation to accommodate custom floating-point formats. The approach substantially reduces memory footprint and improves memory access efficiency. Experimental results demonstrate a 1.63× speedup over cuSPARSE in FP16 mode, while a custom format achieves FP32-level accuracy with performance surpassing FP16 cuSPARSE. Furthermore, a mixed-precision preconditioned conjugate gradient (PCG) solver attains a 2.09× acceleration.
📝 Abstract
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.