Distributed and heterogeneous tensor–vector contraction algorithms for high performance computing

Abstract

The tensor–vector contraction (TVC) is the most memory-bound operation of its class and a core component of the higher-order power method (HOPM). This paper brings distributed-memory parallelization to a native TVC algorithm for dense tensors that overall remains oblivious to contraction mode, tensor splitting, and tensor order. Similarly, we propose a novel distributed HOPM, namely dHOPM${}_3$, that can save up to one order of magnitude of streamed memory and is about twice as costly in terms of data movement as a distributed TVC operation (dTVC) when using task-based parallelization. The numerical experiments carried out in this work on three different architectures featuring multicore and accelerators confirm that the performances of dTVC and dHOPM${}_3$ remain relatively close to the peak system memory bandwidth (50%–80%, depending on the architecture) and on par with STREAM benchmark figures. On strong scalability scenarios, our native multicore implementations of these two algorithms can achieve similar and sometimes even greater performance figures than those based upon state-of-the-art CUDA batched kernels. Finally, we demonstrate that both computation and communication can benefit from mixed precision arithmetic also in cases where the hardware does not support low precision data types natively.