lgamma, lgammaf, lgammal

Header: <math.h>

1-3) Computes the natural logarithm of the absolute value of the gamma function of arg.

# Declarations

float lgammaf( float arg );

(since C99)

double lgamma( double arg );

(since C99)

long double lgammal( long double arg );

(since C99)

#define lgamma( arg )

(since C99)

# Parameters

# 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}|)loge|∫∞0targ-1 e-t dt|, is returned.

# Notes

If arg is a natural number, 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

#include <errno.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
// #pragma STDC FENV_ACCESS ON
 
int main(void)
{
    printf("lgamma(10) = %f, log(9!) = %f\n", lgamma(10),
                                              log(2 * 3 * 4 * 5 * 6 * 7 * 8 * 9));
    const double pi = acos(-1);
    printf("lgamma(0.5) = %f, log(sqrt(pi)) = %f\n", log(sqrt(pi)), lgamma(0.5));
    // special values
    printf("lgamma(1) = %f\n", lgamma(1));
    printf("lgamma(+Inf) = %f\n", lgamma(INFINITY));
 
    // error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);
    printf("lgamma(0) = %f\n", lgamma(0));
    if (errno == ERANGE)
        perror("    errno == ERANGE");
    if (fetestexcept(FE_DIVBYZERO))
        puts("    FE_DIVBYZERO raised");
}

# See also