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Distributed-memory matrix multiplication (MM) is a key element of algorithmsin many domains (machine learning, quantum physics). Conventional algorithmsfor dense MM rely on regular/uniform data decomposition to ensure load balance.These traits conflict with the irregular structure (block-sparse or rank-sparsewithin blocks) that is increasingly relevant for fast methods in quantumphysics. To deal with such irregular data we present a new MM algorithm basedon Scalable Universal Matrix Multiplication Algorithm (SUMMA). The novelfeatures are: (1) multiple-issue scheduling of SUMMA iterations, and (2)fine-grained task-based formulation. The latter eliminates the need forexplicit internodal synchronization; with multiple-iteration scheduling thisallows load imbalance due to nonuniform matrix structure. For square MM withuniform and nonuniform block sizes (the latter simulates matrices with generalirregular structure) we found excellent performance in weak and strong-scalingregimes, on commodity and high-end hardware.

Task-Based Algorithm for Matrix Multiplication: A Step Towards Block-Sparse Tensor Computing