table of contents
std::lgamma,std::lgammaf,std::lgammal(3) | C++ Standard Libary | std::lgamma,std::lgammaf,std::lgammal(3) |
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
See also¶
tgamma
tgammaf
tgammal gamma function
(C++11) (function)
(C++11)
(C++11)
External links¶
Weisstein, Eric W. "Log Gamma Function." From MathWorld--A Wolfram Web Resource.
2022.07.31 | http://cppreference.com |