On the asymptotic analysis of the Euclidean algorithm

Authors:
G. H. Norton
Affiliations:
Centre for Communications Research, Faculty of Engineering, University of Bristol, University Walk, Bristol BS8 ITR, U.K.
Venue:
Journal of Symbolic Computation
Year:
1990

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Abstract

Let N=2 and @e 0. For uniformly distributed integers in the interval [1, N], the Euclidean algorithm requires an average of 12ln@?2@p^2(ln@?N-12+@z^'(2)@z^'(2))+C-12+O(N^@e^-^1^/^6) divisions, where C is Porter's constant.