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

Parameters

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 | ∫ ∞0 t num-1 e ^-t d t | , 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

#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";
}

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

External links