lgamma - log gamma function
Lgamma returns ln|Gamma(x)|.
The external integer signgam returns the sign of Gamma(x) .
Do not use the expression signgam*exp(lgamma(x)) to compute g :=
Gamma(x). Instead use a program like this (in C):
lg = lgamma(x); g = signgam*exp(lg);
Only after lgamma has returned
can signgam be correct. Note too
that Gamma(x) must overflow when x is large enough, underflow when
-x is large enough, and spawn a division by zero when x is a
Only in the UNIX math library
for C was the name gamma ever
attached to lnGamma. Elsewhere, for instance in IBM’s FORTRAN
library, the name GAMMA belongs to Gamma and the name ALGAMA to
lnGamma in single precision; in double the names are DGAMMA and
DLGAMA. Why should C be different?
Archaeological records suggest
that C’s gamma originally delivered
ln(Gamma(|x|)). Later, the program gamma was changed to cope with
negative arguments x in a more conventional way, but the
documentation did not reflect that change correctly. The most
recent change corrects inaccurate values when x is almost a
negative integer, and lets Gamma(x) be computed without conditional
expressions. Programmers should not assume that lgamma has settled
At some time in the future, the
name gamma will be rehabilitated
and used for the gamma function, just as is done in FORTRAN. The
reason for this is not so much compatibility with FORTRAN as a
desire to achieve greater speed for smaller values of |x| and
greater accuracy for larger values.
Meanwhile, programmers who have
to use the name gamma in its former
sense, for what is now lgamma, can add the following program to