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arXiv · 2601.00979

The cost of cyclic permutations and remainder sums in the Euclidean algorithm

Valentin Blomer·Kai-Uwe Bux
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Abstract

We discuss a modification to the Gries-Mills block swapping scheme for in-place rotation with average costs of 1.85 moves per element and worst case performance still at 3 moves per element. Analysis of the average case relies on the asymptotic behavior of the sum of remainders in the Euclidean algorithm.

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Valentin Blomer, Kai-Uwe Bux. 2026-01-02. The cost of cyclic permutations and remainder sums in the Euclidean algorithm. https://arxiv.org/abs/2601.00979

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