  The extreme computational costs of calculating the sign of the Wilson matrix
within the overlap operator have so far prevented four dimensional dynamical
overlap simulations on realistic lattice sizes, because the computational power
required to invert the overlap operator, the time consuming part of the Hybrid
Monte Carlo algorithm, is too high. In this series of papers we introduced the
optimal approximation of the sign function and have been developing
preconditioning and relaxation techniques which reduce the time needed for the
inversion of the overlap operator by over a factor of four, bringing the
simulation of dynamical overlap fermions on medium-size lattices within the
range of Teraflop-computers.
  In this paper we adapt the HMC algorithm to overlap fermions. We approximate
the matrix sign function using the Zolotarev rational approximation, treating
the smallest eigenvalues of the Wilson operator exactly within the fermionic
force. We then derive the fermionic force for the overlap operator, elaborating
on the problem of Dirac delta-function terms from zero crossings of eigenvalues
of the Wilson operator. The crossing scheme proposed shows energy violations
which are better than O($\Delta\tau^2$) and thus are comparable with the
violations of the standard leapfrog algorithm over the course of a trajectory.
We explicitly prove that our algorithm satisfies reversibility and area
conservation. Finally, we test our algorithm on small $4^4$, $6^4$, and $8^4$
lattices at large masses.
