NAME

       lgamma, lgammaf, lgammal - log gamma function

SYNOPSIS

       #include <math.h>

       double lgamma(double x);
       float lgammaf(float x);
       long double lgammal(long double x);

       extern int signgam;

DESCRIPTION

       These functions shall compute

       The  argument  x  need not be a non-positive integer (Gamma(x) is defined over the reals, except the non-
       positive integers).

       The sign of Gamma(x) is returned in the external integer signgam.

       These functions need not be reentrant. A function that is not required to be reentrant is not required to
       be thread-safe.

       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.

RETURN VALUE

       Upon successful completion, these functions shall return the logarithmic gamma of x.

       If  x  is  a  non-positive integer, a pole error shall occur and lgamma(), lgammaf(), and lgammal() shall
       return +HUGE_VAL, +HUGE_VALF, and +HUGE_VALL, respectively.

       If the correct value would cause overflow, a  range  error  shall  occur  and  lgamma(),  lgammaf(),  and
       lgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL (having the same sign as the correct value),
       respectively.

       If x is NaN, a NaN shall be returned.

       If x is 1 or 2, +0 shall be returned.

       If x is ±Inf, +Inf shall be returned.

ERRORS

       These functions shall fail if:

       Pole Error
              The x argument is a negative integer or zero.

       If the integer expression (math_errhandling & MATH_ERRNO)  is  non-zero,  then  errno  shall  be  set  to
       [ERANGE].  If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-
       zero floating-point exception shall be raised.

       Range Error
              The result overflows.

       If the integer expression (math_errhandling & MATH_ERRNO)  is  non-zero,  then  errno  shall  be  set  to
       [ERANGE].  If  the  integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow
       floating-point exception shall be raised.

       The following sections are informative.

EXAMPLES

       None.

APPLICATION USAGE

       On error, the expressions (math_errhandling & MATH_ERRNO) and  (math_errhandling  &  MATH_ERREXCEPT)  are
       independent of each other, but at least one of them must be non-zero.

RATIONALE

       None.

FUTURE DIRECTIONS

       None.

SEE ALSO

       exp() , feclearexcept() , fetestexcept() , isnan() , the Base Definitions volume of IEEE Std 1003.1-2001,
       Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h>

COPYRIGHT

       Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition,
       Standard  for  Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers,
       Inc  and  The  Open Group. In the event of any discrepancy between this version and the original IEEE and
       The Open Group Standard, the original IEEE and The Open Group  Standard  is  the  referee  document.  The
       original Standard can be obtained online at http://www.opengroup.org/unix/online.html .