Direct methods based on the origin-free modulus sum function (S) were first adapted in 1994 to the processing of intensity data from density functions with positive and negative scatterers. Nevertheless, that implementation used phase relationships explicitly with the inherent limitation introduced by the time consuming manipulation of quartets. This limitation was removed with the introduction of the S-FFT algorithm (maximising S with only Fourier transforms) and its posterior adaptation S2-FFT for non-positive definite density functions. In the present work both algorithms are reformulated into a generalized one, thus simplifying their implementation in the XLENS® program. The resulting unified S-FFT algorithm is highly effective for crystal structures with at least one medium-heavy scatterer in the unit cell. We have successfully applied it on neutron diffraction data of compounds with negative Fermi lengths.