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**NAME**

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

**SYNOPSIS**

#include<math.h>doublelgamma(doublex);floatlgammaf(floatx);longdoublelgammal(longdoublex);doublelgamma_r(doublex,int*signp);floatlgammaf_r(floatx,int*signp);longdoublelgammal_r(longdoublex,int*signp);externintsigngam;Link with-lm. Feature Test Macro Requirements for glibc (seefeature_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_SOURCElgammaf(),lgammal(): _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || /* Since glibc 2.19: */ _DEFAULT_SOURCE || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCElgamma_r(),lgammaf_r(),lgammal_r(): /* Since glibc 2.19: */ _DEFAULT_SOURCE || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCEsigngam: _XOPEN_SOURCE || /* Since glibc 2.19: */ _DEFAULT_SOURCE || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

**DESCRIPTION**

For the definition of the Gamma function, seetgamma(3). Thelgamma(),lgammaf(), andlgammal() functions return the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integersigngamdeclared in<math.h>. It is 1 when the Gamma function is positive or zero, -1 when it is negative. Since using a constant locationsigngamis not thread-safe, the functionslgamma_r(),lgammaf_r(), andlgammal_r() have been introduced; they return the sign via the argumentsignp.

**RETURN** **VALUE**

On success, these functions return the natural logarithm of Gamma(x). Ifxis a NaN, a NaN is returned. Ifxis 1 or 2, +0 is returned. Ifxis positive infinity or negative infinity, positive infinity is returned. Ifxis 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 returnHUGE_VAL,HUGE_VALF, orHUGE_VALL, respectively, with the correct mathematical sign.

**ERRORS**

Seemath_error(7) for information on how to determine whether an error has occurred when calling these functions. The following errors can occur: Pole error:xis a nonpositive integererrnois set toERANGE(but see BUGS). A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised. Range error: result overflowerrnois set toERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.

**CONFORMING** **TO**

Thelgamma() functions are specified in C99, POSIX.1-2001, and POSIX.1-2008.signgamis specified in POSIX.1-2001 and POSIX.1-2008, but not in C99. Thelgamma_r() functions are nonstandard, but present on several other systems.

**BUGS**

In glibc 2.9 and earlier, when a pole error occurs,errnois set toEDOM; instead of the POSIX-mandatedERANGE. Since version 2.10, glibc does the right thing.

**SEE** **ALSO**

tgamma(3)

**COLOPHON**

This page is part of release 4.15 of the Linuxman-pagesproject. 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/. 2017-09-15 LGAMMA(3)