#include <math.h> double lgamma(double x); float lgammaf(float x); long double lgammal(long double x); extern int signgam;
These functions shall compute $log_ e" " | Γ ( ^ x ) |$ where $Γ ( ^ x )$ is defined as $int from 0 to inf e"^" " "{ - t } t"^" " "{ x - 1 } dt$. The argument x need not be a non-positive integer ($Γ( ^ x )$ is defined over the reals, except the non-positive integers).
If x is NaN, -Inf, or a negative integer, the value of signgam is unspecified.
These functions need not be thread-safe.
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 non-positive integer, a pole error shall occur and lgamma(), lgammaf(), and lgammal() shall return +HUGE_VAL, +HUGE_VALF, and +HUGE_VALL, respectively.
If the correct value would cause overflow, a range error shall occur and lgamma(), lgammaf(), and lgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL (having the same sign as the correct value), respectively.
If x is NaN, a NaN shall be returned.
If x is 1 or 2, +0 shall be returned.
If x is ±Inf, +Inf shall be returned.
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.
The Base Definitions volume of POSIX.1-2008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>
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