Finite source effects in microlensing: A precise, easy to implement,
  fast and numerical stable formalism
  The goal of this paper is to provide a numerically fast and stable
description for the microlensing amplification of an extended source (either
uniform or limb-darkened) that holds in any amplification regime. We show that
our method of evaluating the amplification can be implemented into a
light-curve fitting routine using the Levenberg-Marquardt algorithm. We compare
the accuracy and computation times to previous methods that either work in the
high-amplification regime only, or require special treatments due to the
singularity of elliptic integrals.
  In addition, we also provide the equations including finite lens effects in
microlensing light curves. We apply our methods to the MACHO-1995-BLG-30 and
the OGLE-2003-BLG-262 events and obtain results consistent to former studies.
We derive an upper limit for the OGLE-2003-BLG-262 event lens size.
  We conclude that our method allows to simultaneously search for point-source
and finite-source microlensing events in future large area microlensing surveys
in a fast manner.
