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

4) Type-generic macro: If arg has type long double, lgammal is called. Otherwise, if arg has integer type or the type double, lgamma is called. Otherwise, lgammaf is called.

Parameters

Return value

If no errors occur, the value of the logarithm of the gamma function of arg, that is loge|∫∞
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, 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");
}

lgamma(10) = 12.801827, log(9!) = 12.801827
lgamma(0.5) = 0.572365, log(sqrt(pi)) = 0.572365
lgamma(1) = 0.000000
lgamma(+Inf) = inf
lgamma(0) = inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised

References

See also

External links