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Fast multidimensional convolution can be performed naively in quadratic timeand can often be performed more efficiently via the Fourier transform; however,when the dimensionality is large, these algorithms become more challenging. Amethod is proposed for performing exact hypercube convolution in sub-quadratictime. The method outperforms FFTPACK, called via numpy, and FFTW, called viapyfftw) for hypercube convolution. Embeddings in hypercubes can be paired withsub-quadratic hypercube convolution method to construct sub-quadraticalgorithms for variants of vector convolution.

An exact, cache-localized algorithm for the sub-quadratic convolution of hypercubes