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The bit reversal permutation has also been used to devise lower bounds in distributed computation. [8] The Van der Corput sequence, a low-discrepancy sequence of numbers in the unit interval, is formed by reinterpreting the indexes of the bit-reversal permutation as the fixed-point binary representations of dyadic rational numbers.
16-bit Gray code permutation G multiplied with the bit-reversal permutation B G has 2 fixed points, 1 2-cycle and 3 4-cycles B has 4 fixed points and 6 2-cycles GB has 2 fixed points and 2 7-cycles P * (1,2,3,4) T = (4,1,3,2) T Permutation of four elements with 1 fixed point and 1 3-cycle
The best-known reordering technique involves explicit bit reversal for in-place radix-2 algorithms. Bit reversal is the permutation where the data at an index n, written in binary with digits b 4 b 3 b 2 b 1 b 0 (e.g. 5 digits for N=32 inputs), is transferred to the index with reversed digits b 0 b 1 b 2 b 3 b 4.
Even and odd permutations—see Parity of a permutation; ... Bit-reversal permutation; Claw-free permutation; Heap's algorithm; Permutation automaton; Schreier vector;
Bit-reversal permutation — particular permutation of vectors with 2 m entries used in many FFTs. Butterfly diagram; Twiddle factor — the trigonometric constant coefficients that are multiplied by the data; Cyclotomic fast Fourier transform — for FFT over finite fields
Bit-reversal permutation; Boustrophedon transform; C. Cayley's theorem; Change ringing; Circular permutation in proteins; Claw-free permutation; Computing the permanent;
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Permuting the vertices on each level of the Stern–Brocot tree by a bit-reversal permutation produces a different tree, the Calkin–Wilf tree, in which the children of each number a / b are the two numbers a / a + b and a + b / b . Like the Stern–Brocot tree, the Calkin–Wilf tree contains each positive rational ...