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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 .