|TGAMMA(3)||Linux Programmer's Manual||TGAMMA(3)|
double tgamma(double x); float tgammaf(float x); long double tgammal(long double x);
Link with -lm.
tgamma(), tgammaf(), tgammal():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
The Gamma function is defined by
It is defined for every real number except for nonpositive integers. For nonnegative integral m one has
and, more generally, for all x:
Furthermore, the following is valid for all values of x outside the poles:
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.
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.
|tgamma (), tgammaf (), tgammal ()||Thread safety||MT-Safe|
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.