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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;

       Link with -lm.

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

       lgamma():
           _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE || _ISOC99_SOURCE ||
           _POSIX_C_SOURCE >= 200112L;
           or cc -std=c99
       lgammaf(), lgammal():
           _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE ||
           _POSIX_C_SOURCE >= 200112L;
           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 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.

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 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 version 2.10, glibc does the right thing.

SEE ALSO

       tgamma(3)

COLOPHON

       This  page  is  part of release 3.35 of the Linux man-pages project.  A description of the
       project, and information about reporting bugs, can be found at  http://man7.org/linux/man-
       pages/.

                                            2010-09-11                                  LGAMMA(3)