std::lgamma,std::lgammaf,std::lgammal(3)

NAME
std::lgamma,std::lgammaf,std::lgammal - std::lgamma,std::lgammaf,std::lgammal

Synopsis
   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).

Parameters
   arg - value of a floating-point or Integral type

Return value
   If no errors occur, the value of the logarithm of the gamma function of arg, that is
   \(\log_{e}|{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}|\)log
   e|∫∞
   0targ-1
   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.

Error handling
   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

Notes
   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.

Example
// Run this code
 #include <iostream>
 #include <cmath>
 #include <cerrno>
 #include <cstring>
 #include <cfenv>
 // #pragma STDC FENV_ACCESS ON
 const double pi = std::acos(-1); // or std::numbers::pi since C++20
 int main()
 {
     std::cout << "lgamma(10) = " << std::lgamma(10)
               << ", log(9!) = " << std::log(2*3*4*5*6*7*8*9) << '\n'
               << "lgamma(0.5) = " << std::lgamma(0.5)
               << " , log(sqrt(pi)) = " << std::log(std::sqrt(pi)) << '\n';
     // special values
     std::cout << "lgamma(1) = " << std::lgamma(1) << '\n'
               << "lgamma(+Inf) = " << std::lgamma(INFINITY) << '\n';
     // error handling
     errno = 0;
     std::feclearexcept(FE_ALL_EXCEPT);
     std::cout << "lgamma(0) = " << std::lgamma(0) << '\n';
     if (errno == ERANGE)
         std::cout << " errno == ERANGE: " << std::strerror(errno) << '\n';
     if (std::fetestexcept(FE_DIVBYZERO))
         std::cout << " FE_DIVBYZERO raised\n";
 }

Output:
 lgamma(10) = 12.8018, log(9!) = 12.8018
 lgamma(0.5) = 0.572365 , log(sqrt(pi)) = 0.572365
 lgamma(1) = 0
 lgamma(+Inf) = inf
 lgamma(0) = inf
     errno == ERANGE: Numerical result out of range
     FE_DIVBYZERO raised

See also
   tgamma
   tgammaf
   tgammal gamma function
   (C++11) (function)
   (C++11)
   (C++11)

External links
   Weisstein, Eric W. "Log Gamma Function." From MathWorld--A Wolfram Web Resource.