TGAMMA
Section: Linux Programmer's Manual (3)
Updated: 2017-09-15
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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^(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 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 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 exception
(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
attributes(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 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
man-pages
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/man-pages/.
Index
- NAME
-
- SYNOPSIS
-
- DESCRIPTION
-
- RETURN VALUE
-
- ERRORS
-
- VERSIONS
-
- ATTRIBUTES
-
- CONFORMING TO
-
- NOTES
-
- BUGS
-
- SEE ALSO
-
- COLOPHON
-
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|
- Running on 
-
:
: 