Length of the continued logarithm algorithm on rational inputs
Number Theory
2016-06-22 v2 Data Structures and Algorithms
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.
Cite
@article{arxiv.1606.03881,
title = {Length of the continued logarithm algorithm on rational inputs},
author = {Jeffrey Shallit},
journal= {arXiv preprint arXiv:1606.03881},
year = {2016}
}