Advantages and disadvantages of the non-approximated numerical implementation of the Rayleigh-Sommerfeld diffraction integral (RSD) are revisited. In this work, it is shown that as trade-off for its large computation load, the non-approximated RSD removes any limitation on the propagation range and does not introduce any artifact in the computed wave field. A non-approximated GPU implementation of the RSD is contrasted with the angular spectrum, the Fresnel transform, and a fast Fourier transform implementation of the RSD. The forecasted phase shift introduced in the propagated wave fields as light is diffracted on complementary apertures and utilized as a metric to quantify the performance of the tested methods. An application to numerical reconstructions with arbitrary shape and size of digital recorded holograms from digital lensless holographic microscopy is presented.