Further analysis of the binary Euclidean algorithm

Abstract

The binary Euclidean algorithm is a variant of the classical Euclidean algorithm. It avoids multiplications and divisions, except by powers of two, so is potentially faster than the classical algorithm on a binary machine. We describe the binary algorithm and consider its average case behaviour. In particular, we correct some errors in the literature, discuss some results of Vall\'ee, and describe a numerical computation which supports a conjecture of Vall\'ee.