lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam - log gamma function

**#include <math.h>**

**double lgamma(double** *x***);
float lgammaf(float**

long double lgammal(long double

**double lgamma_r(double** *x***, int ****signp***);
float lgammaf_r(float**

long double lgammal_r(long double

**extern int** *signgam***;**

Link with *-lm*.

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

**lgamma**():

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

**lgammaf**(), **lgammal**():

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

**lgamma_r**(), **lgammaf_r**(), **lgammal_r**():

/* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

*signgam*:

_XOPEN_SOURCE

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

For the definition of the Gamma function, see **tgamma(3)**.

The **lgamma**(), **lgammaf**(), and **lgammal**() functions return the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer *signgam* declared in *<math.h>*. It is 1 when the Gamma function is positive or zero, -1 when it is negative.

Since using a constant location *signgam* is not thread-safe, the functions **lgamma_r**(), **lgammaf_r**(), and **lgammal_r**() have been introduced; they return the sign via the argument *signp*.

On success, these functions return the natural logarithm of Gamma(x).

If *x* is a NaN, a NaN is returned.

If *x* is 1 or 2, +0 is returned.

If *x* is positive infinity or negative infinity, positive infinity is returned.

If *x* is a nonpositive integer, a pole error occurs, and the functions return +**HUGE_VAL**, +**HUGE_VALF**, or +**HUGE_VALL**, respectively.

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.

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

The following errors can occur:

Pole error: *x* is a nonpositive integer

*errno* is set to **ERANGE** (but see BUGS). 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.

The **lgamma**() functions are specified in C99, POSIX.1-2001, and POSIX.1-2008. *signgam* is specified in POSIX.1-2001 and POSIX.1-2008, but not in C99. The **lgamma_r**() functions are nonstandard, but present on several other systems.

In glibc 2.9 and earlier, when a pole error occurs, *errno* is set to **EDOM**; instead of the POSIX-mandated **ERANGE**. Since version 2.10, glibc does the right thing.

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