PackSELL: A Sparse Matrix Format for Precision-Agnostic High-Performance SpMV

TL;DR

PackSELL introduces a flexible sparse matrix format optimized for GPU-based SpMV, reducing memory use and boosting performance across various precisions, including non-IEEE formats.

Contribution

It presents a novel, configurable sparse matrix format that improves GPU SpMV efficiency and supports diverse data representations, including custom formats.

Findings

PackSELL outperforms cuSPARSE SELL-based kernel by up to 1.63× at FP16.

Configurable formats in PackSELL achieve FP32 accuracy with higher performance.

Using PackSELL in PCG solvers yields up to 2.09× speedup over full-precision implementations.

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.