LGAMMA(3M) BSD LGAMMA(3M)
NAME
lgamma - log gamma function
SYNOPSIS
#include <math.h>
double lgamma(x)
double x;
DESCRIPTION
lgamma returns ln|G(x)|.
The external integer signgam returns the sign of G(x) .
IDIOSYNCRASIES
Do not use the expression signgam*exp(lgamma(x)) to compute g := G(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
G(x) must overflow when x is large enough, underflow when -x is large
enough, and spawn a division by 0 when x is a nonpositive integer.
Only in the UNIX math library for C was the name "gamma" ever attached to
lnG. Elsewhere, for instance in IBM*'s FORTRAN library, the name GAMMA
belongs to G and the name ALGAMA to lnG 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(G(|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 G(x) be
computed without conditional expressions. Programmers should not assume
that lgamma has settled down.
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, have two choices:
o Use the old math library, libom.
o Add the following program to your others:
#include <math.h>
double gamma(x)
double x;
{
return (lgamma(x));
}
NOTES
*IBM is a registered trademark of International Business Machines Corp.