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.