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Current architectures are now equipped with matrix computation units designedto enhance AI and high-performance computing applications. Within thesearchitectures, two fundamental instruction types are matrix multiplication andvector outer product, with the latter being lighter due to its vector inputs.This characteristic not only allows for the development of flexible algorithmsbeyond dense linear algebra computations but also offers greater potential forimplementation optimization. Stencil computations, commonly found in scientificand engineering applications, involve nested loops. This paper introduces anovel stencil algorithm leveraging vector outer products. Unlike previousapproaches, this algorithm emerges from the stencil definition in scatter modeand is initially formulated using vector outer product expressions. Theimplementation integrates a series of optimizations to enhance memory referencepatterns, execution pipeline efficiency, and data reuse. These optimizationsconsider various algorithmic options and data sharing among input vectors.Evaluation conducted on a simulator demonstrates that our proposed designachieves significant speedup compared to vectorized stencil algorithms.

Stencil Matrixization