TGAMMA
Section: Linux Programmer's Manual (3)
Updated: 20170915
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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);
Link with lm.
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^(x1) 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 occurs,
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 mathematical sign.
If the result underflows,
a range error occurs,
and the functions return 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 floatingpoint exception
(FE_INVALID)
is raised (but see BUGS).
 Pole error: x is +0 or 0

errno
is set to
ERANGE.
A dividebyzero floatingpoint exception
(FE_DIVBYZERO)
is raised.
 Range error: result overflow

errno
is set to
ERANGE.
An overflow floatingpoint exception
(FE_OVERFLOW)
is raised.
glibc also gives the following error which is not specified
in C99 or POSIX.12001.
 Range error: result underflow

An underflow floatingpoint 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
attributes(7).
Interface  Attribute  Value

tgamma(),
tgammaf(),
tgammal()
 Thread safety  MTSafe

CONFORMING TO
C99, POSIX.12001, POSIX.12008.
NOTES
This function had to be called "true gamma function"
since there is already 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 incorrectly produced a domain error
(errno
set to
EDOM
and an
FE_INVALID
exception raised), rather than a pole error.
SEE ALSO
gamma(3),
lgamma(3)
COLOPHON
This page is part of release 4.13 of the Linux
manpages
project.
A description of the project,
information about reporting bugs,
and the latest version of this page,
can be found at
https://www.kernel.org/doc/manpages/.
Index
 NAME

 SYNOPSIS

 DESCRIPTION

 RETURN VALUE

 ERRORS

 VERSIONS

 ATTRIBUTES

 CONFORMING TO

 NOTES

 BUGS

 SEE ALSO

 COLOPHON
