NAME

lgamma - log gamma function

SYNOPSIS

#include <math.h>

double lgamma(x)

double x;

DESCRIPTION

Lgamma returns ln|Gamma(x)|.

The external integer signgam returns the sign of Gamma(x) .

IDIOSYNCRASIES

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

nonpositive integer.

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

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, can add the following program
to

your others:

#include <math.h>

double gamma(x)

double x;

{

return (lgamma(x));

}

SEE ALSO

libm(3)