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

Since C++26

Header: <cmath>

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)

# Declarations

float lgamma ( float num );
double lgamma ( double num );
long double lgamma ( long double num );

(until C++23)

/*floating-point-type*/
lgamma ( /*floating-point-type*/ num );

(since C++23) (constexpr since C++26)

float lgammaf( float num );

(since C++11) (constexpr since C++26)

long double lgammal( long double num );

(since C++11) (constexpr since C++26)

SIMD overload (since C++26)

template< /*math-floating-point*/ V >
constexpr /*deduced-simd-t*/<V>
lgamma ( const V& v_num );

(since C++26)

Additional overloads (since C++11)

template< class Integer >
double lgamma ( Integer num );

(constexpr since C++26)

# 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}|)loge|∫∞0tnum-1 e-t dt|, 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(num)).

# Example

#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";
}