Name
tgamma, tgammaf, tgammal - true gamma functionLibrary
Math library ( libm ", " -lm )Synopsis
#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
These functions calculate the Gamma function ofx
. 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
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
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, and errno is set to ERANGE .
Attributes
For an explanation of the terms used in this section, see attributes(7).Interface | Attribute | Value |
T} | Thread safety | MT-Safe |
Standards
C11, POSIX.1-2008.History
glibc 2.1. C99, POSIX.1-2001.Notes
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
Before glibc 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity.Before glibc 2.19, the glibc implementation of these functions did not set errno 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 set to EDOM and an FE_INVALID exception raised), rather than a pole error.