  We present a new parallel implementation of the PINpointing Orbit
Crossing-Collapsed HIerarchical Objects (PINOCCHIO) algorithm, a quick tool,
based on Lagrangian Perturbation Theory, for the hierarchical build-up of Dark
Matter halos in cosmological volumes. To assess its ability to predict halo
correlations on large scales, we compare its results with those of an N-body
simulation of a 3 Gpc/h box sampled with 2048^3 particles taken from the MICE
suite, matching the same seeds for the initial conditions. Thanks to the FFTW
libraries and to the relatively simple design, the code shows very good scaling
properties. The CPU time required by PINOCCHIO is a tiny fraction (~1/2000) of
that required by the MICE simulation. Varying some of PINOCCHIO numerical
parameters allows one to produce a universal mass function that lies in the
range allowed by published fits, although it underestimates the MICE mass
function of FoF halos in the high mass tail. We compare the matter-halo and the
halo-halo power spectra with those of the MICE simulation and find that these
2-point statistics are well recovered on large scales. In particular, when
catalogs are matched in number density, agreement within ten per cent is
achieved for the halo power spectrum. At scales k>0.1 h/Mpc, the inaccuracy of
the Zel'dovich approximation in locating halo positions causes an underestimate
of the power spectrum that can be modeled as a Gaussian factor with a damping
scale of d=3 Mpc/h at z=0, decreasing at higher redshift. Finally, a remarkable
match is obtained for the reduced halo bispectrum, showing a good description
of nonlinear halo bias. Our results demonstrate the potential of PINOCCHIO as
an accurate and flexible tool for generating large ensembles of mock galaxy
surveys, with interesting applications for the analysis of large galaxy
redshift surveys.
