tgamma, tgammaf, tgammal - true gamma function
Math library (libm
, -lm
)
#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)):
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)
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.
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
The following errors can occur:
x
is a negative integer, or negative
infinityerrno
is set to EDOM. An invalid
floating-point exception (FE_INVALID) is raised (but
see BUGS).
x
is +0 or -0errno
is set to ERANGE. A divide-by-zero
floating-point exception (FE_DIVBYZERO) is raised.
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.
An underflow floating-point exception (FE_UNDERFLOW)
is raised, and errno
is set to ERANGE.
For an explanation of the terms used in this section, see attributes(7).
Interface | Attribute | Value |
Thread safety | MT-Safe |
C11, POSIX.1-2008.
glibc 2.1. C99, POSIX.1-2001.
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.