tgamma(3) - Linux manual page (original) (raw)

tgamma(3) Library Functions Manual tgamma(3)

NAME top

   tgamma, tgammaf, tgammal - true gamma function

LIBRARY top

   Math library (_libm_, _-lm_)

SYNOPSIS top

   **#include <math.h>**

   **double tgamma(double** _x_**);**
   **float tgammaf(float** _x_**);**
   **long double tgammal(long double** _x_**);**

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)](../man7/math%5Ferror.7.html) 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](../man3/errno.3.html)_ is set to **EDOM**.  An invalid floating-point exception
          (**FE_INVALID**) is raised (but see BUGS).

   Pole error: _x_ is +0 or -0
          _[errno](../man3/errno.3.html)_ is set to **ERANGE**.  A divide-by-zero floating-point
          exception (**FE_DIVBYZERO**) is raised.

   Range error: result overflow
          _[errno](../man3/errno.3.html)_ 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, and _[errno](../man3/errno.3.html)_ is set to **ERANGE**.

ATTRIBUTES top

   For an explanation of the terms used in this section, see
   [attributes(7)](../man7/attributes.7.html).
   ┌──────────────────────────────────────┬───────────────┬─────────┐
   │ **Interface** │ **Attribute** │ **Value** │
   ├──────────────────────────────────────┼───────────────┼─────────┤
   │ **tgamma**(), **tgammaf**(), **tgammal**()       │ Thread safety │ MT-Safe │
   └──────────────────────────────────────┴───────────────┴─────────┘

STANDARDS top

   C11, POSIX.1-2008.

HISTORY top

   glibc 2.1.  C99, POSIX.1-2001.

NOTES top

   This function had to be called "true gamma function" since there
   is already a function [gamma(3)](../man3/gamma.3.html) that returns something else (see
   [gamma(3)](../man3/gamma.3.html) for details).

BUGS top

   Before glibc 2.18, the glibc implementation of these functions did
   not set _[errno](../man3/errno.3.html)_ to **EDOM** when _x_ is negative infinity.

   Before glibc 2.19, the glibc implementation of these functions did
   not set _[errno](../man3/errno.3.html)_ to **ERANGE** on an underflow range error.

   In glibc versions 2.3.3 and earlier, an argument of +0 or -0
   incorrectly produced a domain error (_[errno](../man3/errno.3.html)_ set to **EDOM** and an
   **FE_INVALID** exception raised), rather than a pole error.

SEE ALSO top

   [gamma(3)](../man3/gamma.3.html), [lgamma(3)](../man3/lgamma.3.html)

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Linux man-pages 6.10 2024-07-23 tgamma(3)

Pages that refer to this page:gamma(3), lgamma(3)