  We describe some "unrestricted" algorithms which are useful for the
computation of elementary and special functions when the precision required is
not known in advance. Several general classes of algorithms are identified and
illustrated by examples. The topics include: power series methods, use of
halving identities, asymptotic expansions, continued fractions, recurrence
relations, Newton's method, numerical contour integration, and the
arithmetic-geometric mean. Most of the algorithms discussed are implemented in
the MP package (arXiv:1004.3173).
