#include <math.h> 

 double lgamma(x)  double x; 

Lgamma returns ln\||\(*G(x)| where \(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x-1\s10\d e\u\s8-t\s10\d dt for x > 0 and

 \(*G(x) = \(*p/(\(*G(1-x)\|sin(\(*px)) for x < 1. \}
Lgamma returns ln\||\(*G(x)|.

The external integer signgam returns the sign of \(*G(x) .

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 zero when x is a nonpositive integer.

Only in the UNIX math library for C was the name gamma ever attached to ln\(*G. Elsewhere, for instance in IBM's FORTRAN library, the name GAMMA belongs to \(*G and the name ALGAMA to ln\(*G 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:

#include <math.h>
double gamma(x)
double x;
{

return (lgamma(x));

}