std::lgamma, std::lgammaf, std::lgammal
<cmath>
double lgamma ( double num );
lgamma ( /*floating-point-type*/ num );
(constexpr since C++26)
(constexpr since C++26)
(constexpr since C++26)
<simd>
constexpr /*deduced-simd-t*/<V>
<cmath>
double lgamma ( Integer num );
std::lgamma
for all cv-unqualified floating-point types as the type of the parameter.(since C++23)std::lgamma
on v_num.- (See math-floating-point and deduced-simd-t for their definitions.)
[edit] Parameters
[edit] 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.
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 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.
[edit] 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)).
[edit] 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"; }
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