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Perfect Trees and Bitreversal Permutations
, 1999
"... A famous algorithm is the Fast Fourier Transform, or FFT. An efficient iterative version of the FFT algorithm performs as a first step a bitreversal permutation of the input list. The bitreversal permutation swaps elements whose indices have binary representations that are the reverse of each othe ..."
Abstract

Cited by 4 (2 self)
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A famous algorithm is the Fast Fourier Transform, or FFT. An efficient iterative version of the FFT algorithm performs as a first step a bitreversal permutation of the input list. The bitreversal permutation swaps elements whose indices have binary representations that are the reverse of each other. Using an amortized approach this operation can be made to run in linear time on a randomaccess machine. An intriguing question is whether a lineartime implementation is also feasible on a pointer machine, that is in a purely functional setting. We show that the answer to this question is in the affirmative. In deriving a solution we employ several advanced programming language concepts such as nested datatypes, associated fold and unfold operators, rank2 types, and polymorphic recursion. 1 Introduction A bitreversal permutation operates on lists whose length is n = 2 k for some natural number k and swaps elements whose indices have binary representations that are the reverse of eac...