Towards efficient tile low-rank GEMM computation on sunway many-core processors

Tile low-rank general matrix multiplication (TLR GEMM) is a novel method of matrix multiplication on large data-sparse matrices, which can significantly reduce storage footprint and arithmetic complexity under given accuracy. To implement high-performance TLR GEMM on Sunway many-core processor, the following challenges remain to be addressed: 1) design an efficient parallel scheme; 2) provide an efficient kernel library of math functions commonly used in TLR GEMM. This paper proposes swTLR GEMM, an efficient implementation of TLR GEMM. We assign LR GEMM computation to a single computing processing element (CPE) and use grouped task queue to process different data tiles of the TLR matrix. Moreover, we implement an efficient kernel library (swLR Kernels) for low-rank matrix operations. To scale to massive (CGs), we organize the CGs into the CG grid and partition the matrices into blocks accordingly. We also apply Cannon’s algorithm to enable efficient communication when processing the matrix blocks across CGs simultaneously. The experiment results show that the DGEMM kernel in swLR Kernels achieves 102\(\times\) speedup on average. In terms of overall performance, swTLR GEMM-LLD and swTLR GEMM-LLL achieve 91\(\times\) and 20.1\(\times\) speedup on average, respectively. In addition, our implementation of swTLR GEMM exhibits good scalability when running on 1,024 CGs of Sunway processors (66,560 cores in total).