关键词：阻塞矩阵乘法算法；二维通信结构；高维环连接；带宽成本
摘 要：Blocked matrix multiplication algorithms such as Cannon's algorithm and SUMMA havea 2-dimensional communication structure. We introduce a generalized 'Split-Dimensional' version of Cannon's algorithm (SD-Cannon) with higher-dimensional and bidirectional communication structure.This algorithm is useful for higher-dimensional torus interconnects that can achieve more injection bandwidth than single-link bandwidth. On a bidirectional torus network of dimension d, SD-Cannon can lower the algorithmic bandwidth cost by a factor of up to d. With rectangular collectives, SUMMA also achieves the lower bandwidth cost but has a higher latency cost. We use Charm++ virtualization to eciently map SD-Cannon on unbalanced and odd-dimensional torus network partitions. Our per-formance study on Blue Gene/P demonstrates that an MPI version of SD-Cannon can exploit multiple communication links and improve performance.