### NAME

lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam - log gamma function

### SYNOPSIS

#include <math.h>

double lgamma(double x); float lgammaf(float x); long double lgammal(long double x);

double lgamma_r(double x, int *signp); float lgammaf_r(float x, int *signp); long double lgammal_r(long double x, int *signp);

extern int signgam;

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

lgamma(): _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE || _ISOC99_SOURCE; or cc -std=c99 lgammaf(), lgammal(): _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE; or cc -std=c99 lgamma_r(), lgammaf_r(), lgammal_r(): _BSD_SOURCE || _SVID_SOURCE signgam: _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE

### DESCRIPTION

For the definition of the Gamma function, see tgamma(3).

The lgamma() function returns the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer signgam declared in <math.h>. It is 1 when the Gamma function is positive or zero, -1 when it is negative.

Since using a constant location signgam is not thread-safe, the functions lgamma_r() etc. have been introduced; they return the sign via the argument signp.

### RETURN VALUE

On success, these functions return the natural logarithm of Gamma(x).

If x is a NaN, a NaN is returned.

If x is 1 or 2, +0 is returned.

If x is positive infinity or negative infinity, positive infinity is returned.

If x is a non-positive integer, a pole error occurs, and the functions return +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL, respectively.

If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.

### ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:
Pole error: x is a non-positive integer
errno is set to ERANGE (but see BUGS). A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
Range error: result overflow
errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.

### CONFORMING TO

The lgamma() functions are specified in C99 and POSIX.1-2001. signgam is specified in POSIX.1-2001, but not in C99. The lgamma_r() functions are non-standard, but present on several other systems.

### BUGS

For a pole error, errno is set to EDOM; POSIX.1 says it should be set to ERANGE.