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 .