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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 .

IEEE/The Open Group                                   2003                                             LGAMMA(P)