LGAMMA(3M)LGAMMA(3M)NAMElgamma - log gamma function
SYNOPSIS
#include <math.h>
double lgamma(x)
double x;
DESCRIPTION
Lgamma returns ln|Γ(x)|.
The external integer signgam returns the sign of Γ(x) .
IDIOSYNCRASIES
Do not use the expression signgam∗exp(lgamma(x)) to compute g := Γ(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
Γ(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
lnΓ. Elsewhere, for instance in IBM's FORTRAN library, the name GAMMA
belongs to Γ and the name ALGAMA to lnΓ 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(Γ(|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 inaccu‐
rate values when x is almost a negative integer, and lets Γ(x) be com‐
puted 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:
1) Use the old math library, libom.
2) Add the following program to your others:
#include <math.h>
double gamma(x)
double x;
{
return (lgamma(x));
}
DIAGNOSTICS
The reserved operand is returned on a VAX for negative integer argu‐
ments, errno is set to ERANGE; for very large arguments over/underflows
will occur inside the lgamma routine.
SEE ALSOmath(3M), infnan(3M)4.3 Berkeley Distribution May 12, 1986 LGAMMA(3M)
