lgamma(), lgamma_r(), lgammaf(), lgammaf_r(), lgammal(), lgammal_r()

Log gamma function

Synopsis:

#include <math.h>

double lgamma( double x );

double lgamma_r( double x,
                 int* signgamp);

float lgammaf( float x );

float lgammaf_r( float x,
                 int* signgamp);

long double lgammal( long double x );

long double lgammal_r( long double x,
                       int* signgamp);

Arguments:

x
An arbitrary number.
signgam
(lgamma_r(), lgammaf_r(), and lgammal_r() only) A pointer to a location where the function can store the sign of Γ(x).

Library:

libm

Use the -l m option to qcc to link against this library.

Description:

The lgamma*() and lgamma*_r() functions return the natural log (ln) of the Γ function. These functions return ln|Γ(x)|, where Γ(x) is defined as follows:

For x > 0:
For x < 1:
n / (Γ( 1-x ) * sin( nx ))

The results converge when x is between 0 and 1. The Γ function has the property:

Γ(N) = Γ(N-1)×N

The lgamma* functions compute the log because the Γ function grows very quickly.

The lgamma() and lgammaf() functions use the external integer signgam to return the sign of Γ(x), while lgamma_r() and lgammaf_r() use the user-allocated space addressed by signgamp.

Note: The signgam variable isn't set until lgamma() or lgammaf() returns. For example, don't use the expression:
g = signgam * exp( lgamma( x ));

to compute g = Γ(x)'. Instead, compute lgamma() first:

lg = lgamma(x); 
g = signgam * exp( lg );

Note that Γ(x) must overflow when x is large enough, underflow when -x is large enough, and generate a division by 0 exception at the singularities x a nonpositive integer.

To check for error situations, use feclearexcept() and fetestexcept():

Returns:

ln|Γ(x)|

Errors:

FE_DIVBYZERO
The x argument is a negative integer or 0.
FE_OVERFLOW
The result would cause an overflow.

Examples:

#include <stdio.h>
#include <fenv.h>
#include <inttypes.h>
#include <math.h>
#include <stdlib.h>

int main(int argc, char** argv) 
{
    double a, b;
    int except_flags;

    a = 0.5;
    feclearexcept(FE_ALL_EXCEPT);
    b = lgamma(a);
    except_flags = fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
    if(except_flags) {
        /* An error occurred; handle it appropriately. */
    }

    printf("lgamma(%f) = %f \n", a, b);

    return EXIT_SUCCESS;
}

produces the output:

lgamma(0.500000) = 0.572365 0

Classification:

lgamma(), lgammaf(), and lgammal() are ANSI, POSIX 1003.1; lgamma_r(), lgammaf_r(), and lgammal_r() are QNX Neutrino

Safety:  
Cancellation point No
Interrupt handler No
Signal handler No
Thread Yes