NAME

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

LIBRARY

       Math library (libm, -lm)

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():
           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

       lgammaf(), lgammal():
           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

       lgamma_r(), lgammaf_r(), lgammal_r():
           /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

       signgam:
           _XOPEN_SOURCE
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

DESCRIPTION

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

       The  lgamma(),  lgammaf(),  and  lgammal()  functions  return 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(),
       lgammaf_r(),  and  lgammal_r() 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 nonpositive 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 nonpositive 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.

STANDARDS

       The  lgamma()  functions are specified in C99, POSIX.1-2001, and POSIX.1-2008.  signgam is
       specified in POSIX.1-2001 and POSIX.1-2008, but not in C99.  The lgamma_r() functions  are
       nonstandard, but present on several other systems.

BUGS

       In  glibc  2.9 and earlier, when a pole error occurs, errno is set to EDOM; instead of the
       POSIX-mandated ERANGE.  Since glibc 2.10, glibc does the right thing.

SEE ALSO

       tgamma(3)