Bit-reversal permutation: Difference between revisions

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==Generalizations==
The generalization to [[radix]] <math>b</math> representations, for <math>b > 2</math>, and to <math>n=b^k</math>, is a '''digit-reversal permutation''', in which the base-<math>b</math> digits of the index of each element are reversed to obtain the permuted index. The same idea can also been generalized to [[mixed radix]] number systems. In such cases, the digit-reversal permutation should simultaneously reversesreverse the digits of each item and the bases of the number system, so that each reversed digit remains within the range defined by its base.<ref>{{citation
| last = Elster | first = Anne C.
| contribution = Fast bit-reversal algorithms
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TheSignificant performanceattention improvementhas ofbeen bit-reversalsgiven into bothimproving uniprocessorthe andperformance multiprocessorsof hasbit-reversal beenoperations paidwithin athe seriousfield attention inof high-performance computing fields. BecauseDeveloping architecture-aware algorithmalgorithms developmentis cancrucial bestfor utilizeenabling optimal use of hardware and system software resources, includingsuch as caches, TLBTLBs, and multicores, significantly accelerating themulticore computationprocessors.<ref>{{citation
| last1 = Zhang | first1 = Zhao
| last2 = Zhang | first2 = Xiaodong