  We compare the efficiency of four different algorithms to compute the overlap
Dirac operator, both for the speed, i.e., time required to reach a desired
numerical accuracy, and for the adaptability, i.e., the scaling of speed with
the condition number of the (square of the) Wilson Dirac operator. Although
orthogonal polynomial expansions give good speeds at moderate condition number,
they are highly non-adaptable. One of the rational function expansions, the
Zolotarev approximation, is the fastest and is adaptable. The conjugate
gradient approximation is adaptable, self-tuning, and nearly as fast as the ZA.
