GAMMA: Exploiting Gustavson’s Algorithm to Accelerate Sparse Matrix Multiplication

Sparse matrix-sparse matrix multiplication (spMspM) is at the heart of a wide range of scientific and machine learning applications. spMspM is inefficient on general-purpose architectures, making accelerators attractive. However, prior spMspM accelerators use inner- or outer-product dataflows that suffer poor input or output reuse, leading to high traffic and poor performance. These prior accelerators have not explored Gustavson’s algorithm, an alterna- tive spMspM dataflow that does not suffer from these problems but features irregular memory access patterns that prior accelerators do not support.

We present Gamma, an spMspM accelerator that uses Gustavson’s algorithm to address the challenges of prior work. Gamma performs spMspM’s computation using specialized processing elements with simple high-radix mergers, and performs many merges in parallel to achieve high throughput. Gamma uses a novel on-chip storage structure that combines features of both caches and explicitly man- aged buffers. This structure captures Gustavson’s irregular reuse patterns and streams thousands of concurrent sparse fibers (i.e., lists of coordinates and values for rows or columns) with explicitly decoupled data movement. Gamma features a new dynamic scheduling algorithm to achieve high utilization despite irregularity. We also present new preprocessing algorithms that boost Gamma’s efficiency and versatility. As a result, Gamma outperforms prior accelerators by gmean 2.1×, and reduces memory traffic by gmean 2.2× and by up to 13×.