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 num );
   double lgamma ( double num ); (until C++23)
   long double lgamma ( long double num );
   /* floating-point-type */ (since C++23)
               lgamma ( /* floating-point-type */ num (constexpr since C++26)
   ); (1)
   float lgammaf( float num ); (2) (since C++11)
                        (constexpr since C++26)
   long double lgammal( long double num ); (3) (since C++11)
                        (constexpr since C++26)
   Additional overloads (since C++11)
   Defined in header <cmath>
   template< class Integer > (A) (constexpr since C++26)
   double lgamma ( Integer num );
   1-3) Computes the natural logarithm of the absolute value of the gamma function of
   num.
   The library provides overloads of std::lgamma for all cv-unqualified floating-point
   types as the type of the parameter.
   (since C++23)
   A) Additional overloads are provided for all integer types, which are (since C++11)
   treated as double.

Parameters
   num - floating-point or integer value

Return value
   If no errors occur, the value of the logarithm of the gamma function of num, that is
   \(\log_{e}|{\int_0^\infty t^{num-1} e^{-t} \mathsf{d}t}|\)log
   e|∫∞
   0tnum-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 num 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 num is a natural number, std::lgamma(num) is the logarithm of the factorial of
   num - 1.
   The POSIX version of lgamma is not thread-safe: each execution of the function
   stores the sign of the gamma function of num 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.
   The additional overloads are not required to be provided exactly as (A). They only
   need to be sufficient to ensure that for their argument num of integer type,
   std::lgamma(num) has the same effect as std::lgamma(static_cast<double>(num)).

Example
// Run this code
 #include <cerrno>
 #include <cfenv>
 #include <cmath>
 #include <cstring>
 #include <iostream>
 // #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(std::tgamma(10))
               << ", exp(lgamma(10)) = " << std::exp(std::lgamma(10)) << '\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, exp(lgamma(10)) = 362880
 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)
   C documentation for
   lgamma

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