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We continue the line of research started in "Broadword Implementation ofRank/Select Queries" proposing broadword (a.k.a. SWAR, "SIMD Within ARegister") algorithms for finding matching closed parentheses and the k-th farclosed parenthesis. Our algorithms work in time O(log w) on a word of w bits,and contain no branch and no test instruction. On 64-bit (and wider)architectures, these algorithms make it possible to avoid costly tabulations,while providing a very significant speedup with respect to for-loopimplementations.

Broadword Implementation of Parenthesis Queries