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std::lgamma

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Defined in header <cmath>
float       lgamma( float arg );
(1) (since C++11)
double      lgamma( double arg );
(2) (since C++11)
long double lgamma( long double arg );
(3) (since C++11)
double      lgamma( Integral 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).

Contents

[edit] Parameters

arg - value of a floating-point or Integral type

[edit] Return value

If no errors occur, the value of the logarithm of the gamma function of arg, that is log
e
|
0
targ-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 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

[edit] 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.

[edit] Example

#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

[edit] See also

(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.