NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | VERSIONS | ATTRIBUTES | CONFORMING TO | NOTES | BUGS | SEE ALSO | COLOPHON

TGAMMA(3)                 Linux Programmer's Manual                TGAMMA(3)

NAME         top

       tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS         top

       #include <math.h>

       double tgamma(double x);
       float tgammaf(float x);
       long double tgammal(long double x);

       Link with -lm.

   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

       tgamma(), tgammaf(), tgammal():
           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

DESCRIPTION         top

       These functions calculate the Gamma function of x.

       The Gamma function is defined by

           Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt

       It is defined for every real number except for nonpositive integers.
       For nonnegative integral m one has

           Gamma(m+1) = m!

       and, more generally, for all x:

           Gamma(x+1) = x * Gamma(x)

       Furthermore, the following is valid for all values of x outside the
       poles:

           Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

RETURN VALUE         top

       On success, these functions return Gamma(x).

       If x is a NaN, a NaN is returned.

       If x is positive infinity, positive infinity is returned.

       If x is a negative integer, or is negative infinity, a domain error
       occurs, and a NaN is returned.

       If the result overflows, a range error occurs, and the functions
       return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the
       correct mathematical sign.

       If the result underflows, a range error occurs, and the functions
       return 0, with the correct mathematical sign.

       If x is -0 or +0, a pole error occurs, and the functions return
       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign
       as the 0.

ERRORS         top

       See math_error(7) for information on how to determine whether an
       error has occurred when calling these functions.

       The following errors can occur:

       Domain error: x is a negative integer, or negative infinity
              errno is set to EDOM.  An invalid floating-point exception
              (FE_INVALID) is raised (but see BUGS).

       Pole error: x is +0 or -0
              errno is set to ERANGE.  A divide-by-zero floating-point
              exception (FE_DIVBYZERO) is raised.

       Range error: result overflow
              errno is set to ERANGE.  An overflow floating-point exception
              (FE_OVERFLOW) is raised.

       glibc also gives the following error which is not specified in C99 or
       POSIX.1-2001.

       Range error: result underflow
              An underflow floating-point exception (FE_UNDERFLOW) is
              raised.

              errno is not set for this case.

VERSIONS         top

       These functions first appeared in glibc in version 2.1.

ATTRIBUTES         top

       For an explanation of the terms used in this section, see
       attributes(7).

       ┌───────────────────────────────┬───────────────┬─────────┐
       │Interface                      Attribute     Value   │
       ├───────────────────────────────┼───────────────┼─────────┤
       │tgamma(), tgammaf(), tgammal() │ Thread safety │ MT-Safe │
       └───────────────────────────────┴───────────────┴─────────┘

CONFORMING TO         top

       C99, POSIX.1-2001, POSIX.1-2008.

NOTES         top

       This function had to be called "true gamma function" since there is
       already a function gamma(3) that returns something else (see gamma(3)
       for details).

BUGS         top

       Before version 2.18, the glibc implementation of these functions did
       not set errno to EDOM when x is negative infinity.

       In glibc versions 2.3.3 and earlier, an argument of +0 or -0
       incorrectly produced a domain error (errno set to EDOM and an
       FE_INVALID exception raised), rather than a pole error.

SEE ALSO         top

       gamma(3), lgamma(3)

COLOPHON         top

       This page is part of release 4.08 of the Linux man-pages project.  A
       description of the project, information about reporting bugs, and the
       latest version of this page, can be found at
       https://www.kernel.org/doc/man-pages/.

GNU                              2016-03-15                        TGAMMA(3)