  We present a comparison of major methodologies of fast generating mock halo
or galaxy catalogues. The comparison is done for two-point and the three-point
clustering statistics. The reference catalogues are drawn from the BigMultiDark
N-body simulation. Both friend-of-friends (including distinct halos only) and
spherical overdensity (including distinct halos and subhalos) catalogs have
been used with the typical number density of a large-volume galaxy surveys. We
demonstrate that a proper biasing model is essential for reproducing the power
spectrum at quasilinear and even smaller scales. With respect to various
clustering statistics a methodology based on perturbation theory and a
realistic biasing model leads to very good agreement with N-body simulations.
However, for the quadrupole of the correlation function or the power spectrum,
only the method based on semi-N-body simulation could reach high accuracy (1%
level) at small scales, i.e., r<25 Mpc/h or k>0.15 h/Mpc. Full N-body solutions
will remain indispensable to produce reference catalogues. Nevertheless, we
have demonstrated that the far more efficient approximate solvers can reach a
few percent accuracy in terms of clustering statistics at the scales
interesting for the large-scale structure analysis after calibration with a few
reference N-body calculations. This makes them useful for massive production
aimed at covariance studies, to scan large parameter spaces, and to estimate
uncertainties in data analysis techniques, such as baryon acoustic oscillation
reconstruction, redshift distortion measurements, etc.
