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

## Synopsis

#include <math.h> double lgamma(doublex); float lgammaf(floatx); long double lgammal(long doublex); double lgamma_r(doublex, int *signp); float lgammaf_r(floatx, int *signp); long double lgammal_r(long doublex, int *signp); extern intsigngam;

`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 versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

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

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

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

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

/* Since glibc 2.19: */ _DEFAULT_SOURCE

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

*signgam*:

_XOPEN_SOURCE

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

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

## Description

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*.

## Return Value

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.

## 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:

- 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.

## Conforming to

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.

## Bugs

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.

## See Also

## Colophon

This page is part of release 5.04 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/.

## Referenced By

The man pages lgammaf(3), lgammaf_r(3), lgammal(3), lgammal_r(3), lgamma_r(3) and signgam(3) are aliases of lgamma(3).