LGAMMA(3) Linux Programmer's Manual LGAMMA(3)NAME
lgamma - log gamma function
SYNOPSIS
#include <math.h>
double lgamma(double x);
float lgammaf(float x);
long double lgammal(long double x);
double lgamma_r(double x, int *signp);
float lgammaf_r(float x, int *signp);
long double lgammal_r(long double x, int *signp);
DESCRIPTION
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)
For x < 0.5 one can use
Gamma(x) * Gamma(1-x) = PI/sin(PI*x)
The lgamma() function returns 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 nega-
tive.
Since using a constant location signgam is not thread-safe, the functions lgamma_r() etc. have been introduced; they return this sign via
the parameter signp.
For nonpositive integer values of x, lgamma() returns HUGE_VAL, sets errno to ERANGE and raises the zero divide exception. (Similarly,
lgammaf() returns HUGE_VALF and lgammal() returns HUGE_VALL.)
ERRORS
An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error
has occurred.
ERANGE Invalid argument - nonpositive integer value of x.
CONFORMING TO
C99, SVID 3, BSD 4.3
SEE ALSO tgamma(3)
2002-08-10 LGAMMA(3)
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LGAMMA(3) Linux Programmer's Manual LGAMMA(3)NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam - log gamma function
SYNOPSIS
#include <math.h>
double lgamma(double x);
float lgammaf(float x);
long double lgammal(long double x);
double lgamma_r(double x, int *signp);
float lgammaf_r(float x, int *signp);
long double lgammal_r(long double x, int *signp);
extern int signgam;
Link with -lm.
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
lgamma(): _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE || _ISOC99_SOURCE; or cc -std=c99
lgammaf(), lgammal(): _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE; or cc -std=c99
lgamma_r(), lgammaf_r(), lgammal_r(): _BSD_SOURCE || _SVID_SOURCE
signgam: _BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE
DESCRIPTION
For the definition of the Gamma function, see tgamma(3).
The lgamma() function returns 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 nega-
tive.
Since using a constant location signgam is not thread-safe, the functions lgamma_r() etc. 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 and POSIX.1-2001. signgam is specified in POSIX.1-2001, but not in C99. The lgamma_r() func-
tions are nonstandard, but present on several other systems.
BUGS
For a pole error, errno is set to EDOM; POSIX.1 says it should be set to ERANGE.
SEE ALSO tgamma(3)COLOPHON
This page is part of release 3.25 of the Linux man-pages project. A description of the project, and information about reporting bugs, can
be found at http://www.kernel.org/doc/man-pages/.
2008-08-05 LGAMMA(3)