std::lgamma,std::lgammaf,std::lgammal (3) - Linux Manuals

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

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|∫∞
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);
  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

External links

Weisstein,_Eric_W._"Log_Gamma_Function." From MathWorld--A Wolfram Web Resource.