#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);
These functions shall compute the gamma() function of x.
An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
Upon successful completion, these functions shall return Gamma( x).
If x is a negative integer, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.
If the correct value would cause overflow, a range error shall occur and tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same sign as the correct value of the function.
If x is NaN, a NaN shall be returned.
If x is +Inf, x shall be returned.
If x is ±0, a pole error shall occur, and tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.
If x is -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.
These functions shall fail if:
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
then errno shall be set to [ERANGE]. If the
integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the divide-by-zero floating-point exception shall be
raised.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.
The following sections are informative.
For IEEE Std 754-1985 double, overflow happens when 0 < x < 1/DBL_MAX, and 171.7 < x.
On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.
This function is named tgamma() in order to avoid conflicts with the historical gamma() and lgamma() functions.
It is possible that the error response for a negative integer argument may be changed to a pole error and a return value of ±Inf.
feclearexcept(), fetestexcept(), lgamma(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h>