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Performance of stencil computations can be significantly improved through smart implementations that improve memory locality, computation reuse, or parallelize the computation. Unfortunately, efficient implementations are hard to obtain because they often involve non-traditional transformations, which means that they cannot be produced by optimizing the reference stencil with a compiler. In fact, many stencils are produced by code generators that were tediously handcrafted.
Solar-Lezama et al. (Sun,) studied this question.