# tgammaf

```TGAMMA(3)                  Linux Programmer's Manual                 TGAMMA(3)

NAME
tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS
#include <math.h>

double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);

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

tgamma(), tgammaf(), tgammal():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

DESCRIPTION
These functions calculate the Gamma function of x.

The Gamma function is defined by

Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt

It  is  defined  for every real number except for nonpositive integers.
For nonnegative integral m one has

Gamma(m+1) = m!

and, more generally, for all x:

Gamma(x+1) = x * Gamma(x)

Furthermore, the following is valid for all values  of  x  outside  the
poles:

Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

RETURN VALUE
On success, these functions return Gamma(x).

If x is a NaN, a NaN is returned.

If x is positive infinity, positive infinity is returned.

If x is a negative integer, or is negative infinity, a domain error oc-
curs, and a NaN is returned.

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

If the result underflows, a range error occurs, and the  functions  re-
turn 0, with the correct mathematical sign.

If  x  is  -0  or  +0,  a  pole  error occurs, and the functions return
HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign  as
the 0.

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:

Domain error: x is a negative integer, or negative infinity
errno is set  to  EDOM.   An  invalid  floating-point  exception
(FE_INVALID) is raised (but see BUGS).

Pole error: x is +0 or -0
errno  is set to ERANGE.  A divide-by-zero floating-point excep-
tion (FE_DIVBYZERO) is raised.

Range error: result overflow
errno is set to ERANGE.  An  overflow  floating-point  exception
(FE_OVERFLOW) is raised.

glibc  also  gives the following error which is not specified in C99 or
POSIX.1-2001.

Range error: result underflow
An underflow floating-point exception (FE_UNDERFLOW) is  raised,
and errno is set to ERANGE.

VERSIONS
These functions first appeared in glibc in version 2.1.

ATTRIBUTES
For  an  explanation  of  the  terms  used  in  this  section,  see at-
tributes(7).

+-------------------------------+---------------+---------+
|Interface                      | Attribute     | Value   |
+-------------------------------+---------------+---------+
|tgamma(), tgammaf(), tgammal() | Thread safety | MT-Safe |
+-------------------------------+---------------+---------+
CONFORMING TO
C99, POSIX.1-2001, POSIX.1-2008.

NOTES
This function had to be called "true gamma function" since there is al-
ready a function gamma(3) that returns something else (see gamma(3) for
details).

BUGS
Before version 2.18, the glibc implementation of  these  functions  did
not set errno to EDOM when x is negative infinity.

Before  glibc 2.19, the glibc implementation of these functions did not
set errno to ERANGE on an underflow range error.  x

In glibc versions 2.3.3 and earlier, an argument of  +0  or  -0  incor-
rectly produced a domain error (errno set to EDOM and an FE_INVALID ex-
ception raised), rather than a pole error.