lgamma, lgammaf, lgammal

Parameters

Return value

If no errors occur, the value of the logarithm of the gamma function of arg , that is \(\log_{e}|{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}|\) log e | ∫ ∞0 t arg-1 e ^-t d t | , 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