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The goal of this paper is to provide a numerically fast and stabledescription for the microlensing amplification of an extended source (eitheruniform or limb-darkened) that holds in any amplification regime. We show thatour method of evaluating the amplification can be implemented into alight-curve fitting routine using the Levenberg-Marquardt algorithm. We comparethe accuracy and computation times to previous methods that either work in thehigh-amplification regime only, or require special treatments due to thesingularity of elliptic integrals.  In addition, we also provide the equations including finite lens effects inmicrolensing light curves. We apply our methods to the MACHO-1995-BLG-30 andthe 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-sourceand finite-source microlensing events in future large area microlensing surveysin a fast manner.

Finite source effects in microlensing: A precise, easy to implement, fast and numerical stable formalism