tgamma, tgammaf, tgammal

Parameters

Return value

If no errors occur, the value of the gamma function of arg, that is \(\Gamma(\mathtt{arg}) = \displaystyle\int_0^\infty\!\! t^{\mathtt{arg}-1} e^{-t}\, dt\) ∫ ∞
0 t arg-1
e ^-t dt

If a domain error occurs, an implementation-defined value (NaN where supported) 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.

If a range error due to underflow occurs, the correct value (after rounding) 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 or a domain error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

• If the argument is ±0, ±∞ is returned and FE_DIVBYZERO is raised.
• If the argument is a negative integer, NaN is returned and FE_INVALID is raised.
• If the argument is -∞, NaN is returned and FE_INVALID is raised.
• If the argument is +∞, +∞ is returned.
• If the argument is NaN, NaN is returned.

Notes

If arg is a natural number, tgamma(arg) is the factorial of arg - 1

For IEEE-compatible type double, overflow happens if 0 < x < 1 / DBL_MAX or if x > 171.7

POSIX requires

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("tgamma(10) = %f, 9!=%f\n", tgamma(10), 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9.0);
    printf("tgamma(0.5) = %f, sqrt(pi) = %f\n", tgamma(0.5), sqrt(acos(-1)));
 
    // special values
    printf("tgamma(+Inf) = %f\n", tgamma(INFINITY));
 
    // error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);
    printf("tgamma(-1) = %f\n", tgamma(-1));
    if (errno == ERANGE)
        perror("    errno == ERANGE");
    else
        if (errno == EDOM)   perror("    errno == EDOM");
    if (fetestexcept(FE_DIVBYZERO))
        puts("    FE_DIVBYZERO raised");
    else if (fetestexcept(FE_INVALID))
        puts("    FE_INVALID raised");
}

tgamma(10) = 362880.000000, 9!=362880.000000
tgamma(0.5) = 1.772454, sqrt(pi) = 1.772454
tgamma(+Inf) = inf
tgamma(-1) = nan
    errno == EDOM: Numerical argument out of domain
    FE_INVALID raised

References

See also

External links