  We compute the luminosity function (LF) and the formation rate of long gamma
ray bursts (GRBs) by fitting the observed differential peak flux distribution
obtained by the BATSE satellite in three different scenarios: i) GRBs follow
the cosmic star formation and their LF is constant in time; ii) GRBs follow the
cosmic star formation but the LF varies with redshift; iii) GRBs form
preferentially in low-metallicity environments. We find that the differential
peak flux number counts obtained by BATSE and by Swift can be reproduced using
the same LF and GRB formation rate, indicating that the two satellites are
observing the same GRB population. We then check the resulting redshift
distributions in the light of Swift 2-year data, focusing in particular on the
relatively large sample of GRBs detected at z>2.5. We show that models in which
GRBs trace the cosmic star formation and are described by a constant LF are
ruled out by the number of high-z Swift detections. This conclusion does not
depend on the redshift distribution of bursts that lack of optical
identification, nor on the existence of a decline in star formation rate at
z>2, nor on the adopted faint-end of the GRB LF. Swift observations can be
explained by assuming that the LF varies with redshift and/or that GRB
formation is limited to low-metallicity environments.
