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      std::lgamma, std::lgammaf, std::lgammal

      From cppreference.com
      < cpp‎ | numeric‎ | math
       
      C++
       
      Numerics library
       
      Common mathematical functions
      Nearest integer floating point operations
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      Defined in header <cmath>
      (1)
      float       lgamma (float num );

      double      lgamma (double num );

      longdouble lgamma (longdouble num );
      		(until C++23)
      /*floating-point-type*/
                  lgamma (/*floating-point-type*/ num );
      		(since C++23)
      (constexpr since C++26)
      float       lgammaf(float num );
      		 (2)(since C++11)
      (constexpr since C++26)
      longdouble lgammal(longdouble num );
      		 (3)(since C++11)
      (constexpr since C++26)
      SIMD overload(since C++26)
      Defined in header <simd>
      template</*math-floating-point*/ V >

      constexpr/*deduced-simd-t*/<V>

                  lgamma (const V& v_num );
      		 (S) (since C++26)
      Defined in header <cmath>
      template<class Integer >
      double      lgamma ( Integer num );
      		 (A)(constexpr since C++26)
      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)
      S) The SIMD overload performs an element-wise std::lgamma on v_num.
      (See math-floating-point and deduced-simd-t for their definitions.)
      		(since C++26)
      A) Additional overloads are provided for all integer types, which are treated as double.
      		(since C++11)

      Contents

      [edit]Parameters

      num - floating-point or integer value

      [edit]Return value

      If no errors occur, the value of the logarithm of the gamma function of num, that is loge|∫∞
      0      tnum-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.

      [edit]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.

      [edit]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)).

      [edit]Example

      Run this code
      #include <cerrno>#include <cfenv>#include <cmath>#include <cstring>#include <iostream>   // #pragma STDC FENV_ACCESS ON   constdouble 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 valuesstd::cout<<"lgamma(1) = "<< std::lgamma(1)<<'\n'<<"lgamma(+Inf) = "<< std::lgamma(INFINITY)<<'\n';   // error handlingerrno=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

      [edit]See also

      (C++11)(C++11)(C++11)
      		 gamma function
      (function)[edit]
      C documentation for lgamma

      [edit]External links

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