tgamma
Section: C Library Functions (3)
Updated: 2023-02-10
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NAME
tgamma, tgammaf, tgammal - true gamma function
LIBRARY
Math library
(libm, -lm)
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 tha(x-1) eha-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 were added in glibc 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
|
STANDARDS
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 glibc 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.
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)
Index
- NAME
-
- LIBRARY
-
- SYNOPSIS
-
- DESCRIPTION
-
- RETURN VALUE
-
- ERRORS
-
- VERSIONS
-
- ATTRIBUTES
-
- STANDARDS
-
- NOTES
-
- BUGS
-
- SEE ALSO
-
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