LGAMMA(3M) Mathematical Library Functions LGAMMA(3M)
NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, gamma,
gammaf, gammal, gamma_r, gammaf_r, gammal_r - log gamma function
SYNOPSIS
c99 [
flag... ]
file...
-lm [
library... ]
#include <math.h>
extern int signgam;
double lgamma(
double x);
float lgammaf(
float x);
long double lgammal(
long double x);
double gamma(
double x);
float gammaf(
float x);
long double gammal(
long double x);
double lgamma_r(
double x,
int *signgamp);
float lgammaf_r(
float x,
int *signgamp);
long double lgammal_r(
long double x,
int *signgamp);
double gamma_r(
double x,
int *signgamp);
float gammaf_r(
float x,
int *signgamp);
long double gammal_r(
long double x,
int *signgamp);
DESCRIPTION
These functions return
ln||~(x)|
where
|~(x) = integral from 0 to +Infinity of pow(t,x-1)*exp(-t) dt
for x > 0 and
|~(x) = n/(|~(1-x)sin(nx))
for x < 1.
These functions use the external integer
signgam to return the sign
of
|~(x) while
lgamma_r() and
gamma_r() use the user-allocated space
addressed by
signgamp.
RETURN VALUES
Upon successful completion, these functions return the logarithmic
gamma of
x.
If
x is a non-positive integer, a pole error occurs and these
functions return +
HUGE_VAL, +
HUGE_VALF, and +
HUGE_VALL, respectively.
If
x is NaN, a NaN is returned.
If
x is 1 or 2, +0 shall be returned.
If
x is +-Inf, +Inf is returned.
ERRORS
These functions will fail if:
Pole Error The
x argument is a negative integer or 0.
If the integer expression (
math_errhandling &
MATH_ERREXCEPT) is non-zero, then the divide-by-zero
floating-point exception is raised.
USAGE
An application wanting to check for exceptions should call
feclearexcept(
FE_ALL_EXCEPT) before calling these functions. On
return, if
fetestexcept(
FE_INVALID |
FE_DIVBYZERO |
FE_OVERFLOW |
FE_UNDERFLOW) is non-zero, an exception has been raised. An
application should either examine the return value or check the
floating point exception flags to detect exceptions.
In the case of
lgamma(), do not use the expression
signgam*exp(lgamma(x)) to compute
`g := |~(x)'
Instead compute
lgamma() first:
lg = lgamma(x); g = signgam*exp(lg); only after
lgamma() has returned can
signgam be correct. Note that
|~(x) must overflow when
x is large enough, underflow when -
x is
large enough, and generate a division by 0 exception at the
singularities
x a nonpositive integer.
ATTRIBUTES
See
attributes(7) for descriptions of the following attributes:
+----------------------------+-----------------------------+
| ATTRIBUTE TYPE | ATTRIBUTE VALUE |
+----------------------------+-----------------------------+
|Interface Stability | See below. |
+----------------------------+-----------------------------+
|MT-Level | See below. |
+----------------------------+-----------------------------+
The
lgamma(),
lgammaf(),
lgammal(), and
gamma() functions are
Standard. The
lgamma_r(),
lgammaf_r(),
lgammal_r(),
gamma_r(),
gammaf_r(), and
gammal_r(), functions are Stable.
The
lgamma(),
lgammaf(),
lgammal(),
gamma(),
gammaf(), and
gammal() functions are Unsafe in multithreaded applications. The
lgamma_r(),
lgammaf_r(),
lgammal_r(),
gamma_r(),
gammaf_r(), and
gammal_r() functions are MT-Safe and should be used instead.
SEE ALSO
math.h(3HEAD),
exp(3M),
feclearexcept(3M),
fetestexcept(3M),
isnan(3M),
attributes(7),
standards(7)NOTES
When compiling multithreaded applications, the
_REENTRANT flag must
be defined on the compile line. This flag should only be used in
multithreaded applications.
SunOS 5.11 July 12, 2006 LGAMMA(3M)
