#include <math.h> double tgamma(double x); float tgammaf(float x); long double tgammal(long double x);
These functions shall compute $Γ ( ^ x )$ where $Γ ( ^ x )$ is defined as $int from 0 to inf e"^" " "{ - t } t"^" " "{ x - 1 } dt$.
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.
If x is a negative integer, a domain error may occur and either a NaN (if supported) or an implementation-defined value shall be returned. On systems that support the IEC 60559 Floating-Point option, a domain error shall occur and a NaN shall be returned.
If x is ±0, tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively. On systems that support the IEC 60559 Floating-Point option, a pole error shall occur; otherwise, a pole error may occur.
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 the correct value would cause underflow, and is not representable, a range error may occur, and tgamma(), tgammaf(), and tgammal() shall return 0.0, or (if IEC 60559 Floating-Point is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.
If x is subnormal and 1/x is representable, 1/x should be returned.
If x is NaN, a NaN shall be returned.
If x is +Inf, x shall be returned.
If x is -Inf, a domain error shall occur, and a NaN shall be returned.
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.
These functions may 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 underflow floating-point exception shall be raised.
The following sections are informative.
The Base Definitions volume of POSIX.1-2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h>
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