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# std::lgamma

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float lgamma( float arg ); | (1) | (since C++11)
double lgamma( double arg ); | (2) | (since C++11)
long double lgamma( long double arg ); | (3) | (since C++11)
double lgamma( Integral 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).

### [edit] Parameters

arg | - | value of a floating-point or Integral type

### [edit] Return value

If no errors occur, the value of the logarithm of the gamma function of `arg`, that is 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.

### [edit] 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

### [edit] 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`.

### [edit] 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);
    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

### [edit] See also

tgamma (C++11) | gamma function (function) [edit]
C documentation for lgamma

### [edit] External links

Weisstein, Eric W. "Log Gamma Function." From MathWorld--A Wolfram Web Resource.

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