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

Log gamma function


#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);


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



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


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 > 0.0:
For x < 1.0:
n / (Γ( 1-x ) * sin( nx ))

The results converge when x is between 0.0 and 1.0. 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(). For example:



If: These functions return: Errors:
x is 1.0 or 2.0 0.0
x is a non-positive integer Inf FE_DIVBYZERO
x is ±Inf Inf
x is NaN NaN
The correct value would cause overflow Inf FE_OVERFLOW

These functions raise FE_INEXACT if the FPU reports that the result can't be exactly represented as a floating-point number.


#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;
    b = lgamma(a);
    except_flags = fetestexcept(FE_ALL_EXCEPT);
    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


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

Cancellation point No
Interrupt handler No
Signal handler No
Thread Yes