Abstract:We give faster methods to compute discrete convolutions. We assume that all the inputs are packed, that is, strings are packed into words such that each word is packed with [Formula: see text] characters, where w is the length of a machine word and ∑ is the alphabet. The output of our methods is also packed, that is, each word of the output contains more than one element of the result. The approach is based on the word-level parallelism and the FFT. Given two strings with m and n ( n ≥ m ) characters that are … Show more
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