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

External links

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