1.27 gamma, gammaf, lgamma, lgammaf, gamma_r, gammaf_r, lgamma_r, lgammaf_r, tgamma, and tgammaf—logarithmic and plain gamma functions

Synopsis

#include <math.h>
double gamma(double x);
float gammaf(float x);
double lgamma(double x);
float lgammaf(float x);
double gamma_r(double x, int *signgamp);
float gammaf_r(float x, int *signgamp);
double lgamma_r(double x, int *signgamp);
float lgammaf_r(float x, int *signgamp);
double tgamma(double x);
float tgammaf(float x);

Description
gamma calculates the natural logarithm of the gamma function of x. The gamma function (exp(gamma(x))) is a generalization of factorial, and retains the property that exp(gamma(N)) is equivalent to N*exp(gamma(N-1)). Accordingly, the results of the gamma function itself grow very quickly. gamma is defined as the natural log of the gamma function, rather than the gamma function itself, to extend the useful range of results representable.

The sign of the result is returned in the global variable signgam, which is declared in math.h.

gammaf performs the same calculation as gamma, but uses and returns float values.

lgamma and lgammaf are alternate names for gamma and gammaf. The use of lgamma instead of gamma is a reminder that these functions compute the log of the gamma function, rather than the gamma function itself.

The functions gamma_r, gammaf_r, lgamma_r, and lgammaf_r are just like gamma, gammaf, lgamma, and lgammaf, respectively, but take an additional argument. This additional argument is a pointer to an integer. This additional argument is used to return the sign of the result, and the global variable signgam is not used. These functions may be used for reentrant calls (but they will still set the global variable errno if an error occurs).

tgamma and tgammaf are the "true gamma" functions, returning the gamma function of x–without a logarithm. (They are apparently so named because of the prior existence of the old, poorly-named gamma functions which returned the log of gamma up through BSD 4.2.)

Returns
Normally, the computed result is returned.

When x is a nonpositive integer, gamma returns HUGE_VAL and errno is set to EDOM. If the result overflows, gamma returns HUGE_VAL and errno is set to ERANGE.

Portability
Neither gamma nor gammaf is ANSI C. It is better not to use either of these; use lgamma or tgamma instead.
lgamma, lgammaf, tgamma, and tgammaf are nominally C standard in terms of the base return values, although the signgam global for lgamma is not standard.