  Soft or collinear photon emission potentially poses numerical problems in the
phase-space integration of radiative processes. In this paper, a general
subtraction formalism is presented that removes such singularities from the
integrand of the numerical integration and adds back the analytically
integrated contributions that have been subtracted. The method is a
generalization of the dipole formalism of Catani and Seymour, which was
formulated for NLO QCD processes with massless unpolarized particles. The
presented formalism allows for arbitrary mass and helicity configurations in
processes with charged fermions and any other neutral particles. Particular
attention is paid to the limit of small fermion masses, in which collinear
singularities cause potentially large corrections. The actual application and
the efficiency of the formalism are demonstrated by the discussion of photonic
corrections to the processes \gamma \gamma --> t \bar t (\gamma), e^- \gamma
--> e^- \gamma (\gamma), and \mu^+ \mu^- --> \nu_e \bar\nu_e (\gamma).
