std::lgamma,std::lgammaf,std::lgammal (3) - Linux Man Pages
Defined in header <cmath>
float lgamma ( float arg ); (1) (since C++11)
float lgammaf( float arg );
double lgamma ( double arg ); (2) (since C++11)
long double lgamma ( long double arg ); (3) (since C++11)
long double lgammal( long double arg );
double lgamma ( IntegralType arg ); (4) (since C++11)
1-3) Computes the natural logarithm of the absolute value of the gamma_function of arg.
4) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to 2) (the argument is cast to double).
arg - value of a floating-point or Integral_type
If no errors occur, the value of the logarithm of the gamma function of arg, that is log
e-t dt|, is returned.
If a pole error occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.
If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.
Errors are reported as specified in math_errhandling.
If arg is zero or is an integer less than zero, a pole error may occur.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
* If the argument is 1, +0 is returned
* If the argument is 2, +0 is returned
* If the argument is ±0, +∞ is returned and FE_DIVBYZERO is raised
* If the argument is a negative integer, +∞ is returned and FE_DIVBYZERO is raised
* If the argument is ±∞, +∞ is returned.
* If the argument is NaN, NaN is returned
If arg is a natural number, std::lgamma(arg) is the logarithm of the factorial of arg-1.
The POSIX_version_of_lgamma is not thread-safe: each execution of the function stores the sign of the gamma function of arg in the static external variable signgam. Some implementations provide lgamma_r, which takes a pointer to user-provided storage for singgam as the second parameter, and is thread-safe.
There is a non-standard function named gamma in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of gamma executes lgamma, but 4.4BSD version of gamma executes tgamma.
// Run this code
Weisstein,_Eric_W._"Log_Gamma_Function." From MathWorld--A Wolfram Web Resource.