A Fully Structure-Driven Performance Analysis of Sparse Matrix-Vector Multiplication

Sparse matrix-vector multiplication (SpMV) is an important kernel in many scientific, machine-learning, and other compute-intensive applications. Performance characteristics, however, depend on a complex combination of storage format, machine capabilities, and choices in code-generation. A deep understanding of the relative impact of these properties is important in itself, and also to better understanding the performance potential of alternative execution contexts such as web-based scientific computing, where the recent introduction ofWebAssembly offers the potential for low-level, near-native performance within a web browser. In this work we characterize the performance of SpMV operations for different sparse storage formats based on the sparse matrix structure and the machine architecture. We extract structural properties from 2000 real-life sparse matrices to understand their impact on the choice of storage format and also on the performance within those storage formats for both WebAssembly and native C. We extend this with new matrix features based on a "reuse-distance" concept to identify performance bottlenecks, and evaluate the effect of interaction between the matrix structure and hardware characteristics on SpMV performance. Our study provides valuable insights to scientific programmers and library developers to apply best practices and guide future optimization for SpMV in general, and in particular for web-based contexts with abstracted hardware and storage models.