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arXiv · 1606.03881

Length of the continued logarithm algorithm on rational inputs

Jeffrey Shallit
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Abstract

The continued logarithm algorithm was introduced by Gosper around 1978, and recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I show that the continued logarithm algorithm terminates in at most 2 log_2 p + O(1) steps on input a rational number p/q >= 1. Furthermore, this bound is tight, up to an additive constant.

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Jeffrey Shallit. 2016-06-21. Length of the continued logarithm algorithm on rational inputs. https://arxiv.org/abs/1606.03881

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