The external integer Fa signgam returns the sign of Gamma(x) .
lg = lgamma(x); g = signgam*exp(lg);
Only after Fn 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 Fn 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 Fn lgamma , have two choices:
#include <math.h> double gamma(x) double x; { return (lgamma(x)); }