We study a general class of Euclidean algorithms which
compute the greatest common divisor [gcd], and we perform
probabilistic analyses of their main parameters. We view an
algorithm as a dynamical system restricted to rational inputs, and
combine tools imported from dynamics, such as transfer operators,
with various tools of analytic combinatorics: generating
functions, Dirichlet series, Tauberian theorems, Perron's formula
and quasi-powers theorems. Such dynamical analyses can be used to
perform the average-case analysis of algorithms, but also
(dynamical) analysis in distribution.
Mathematics Subject Classification: Primary: 68Q25, 68W40, 37E05, 37C30, 11M41; Secondary: 47A.