Matrix Multiplication on High-Density Multi-GPU Architectures: Theoretical and Experimental Investigations

Matrix multiplication (MM) is one of the core problems in the high performance computing domain and its efficiency impacts performances of almost all matrix problems. The high-density multi-GPU architecture escalates the complexities of such classical problem, though it greatly exceeds the capacities of previous homogeneous multicore architectures. In order to fully exploit the potential of such multi-accelerator architectures for multiplying matrices, we systematically evaluate the performances of two prevailing tilebased MM algorithms, standard and Strassen. We use a high-density multi-GPU server, CS-Storm which can support up to eight NVIDIA GPU cards and we test three generations of GPU cards which are K20Xm, K40m and K80. Our results show that (1) Strassen is often faster than standard method on multicore architecture but it is not beneficial for small enough matrices. (2) Strassen is more efficient than standard algorithm on low-density GPU solutions but it quickly loses its superior on high-density GPU solutions. This is a result of more additions needed in Strassen than in standard algorithm. Experimental results indicate that: though Strassen needs less arithmetic operations than standard algorithm, the heterogeneity of computing resources is a key factor of determining the best-practice algorithm.