NAME

       tgamma, tgammaf, tgammal - compute gamma() function

SYNOPSIS

       #include <math.h>

       double tgamma(double x);
       float tgammaf(float x);
       long double tgammal(long double x);

DESCRIPTION

       These functions shall compute the gamma() function of x.

       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 Gamma( x).

       If  x  is  a  negative  integer,  a  domain  error  shall  occur,  and either a NaN (if supported), or an
       implementation-defined value shall be returned.

       If the correct value would cause overflow, a  range  error  shall  occur  and  tgamma(),  tgammaf(),  and
       tgammal()  shall  return  ±HUGE_VAL,  ±HUGE_VALF,  or ±HUGE_VALL, respectively, with the same sign as the
       correct value of the function.

       If x is NaN, a NaN shall be returned.

       If x is +Inf, x shall be returned.

       If x is ±0, a pole error shall occur, and tgamma(), tgammaf(),  and  tgammal()  shall  return  ±HUGE_VAL,
       ±HUGE_VALF, and ±HUGE_VALL, respectively.

       If  x  is -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined
       value shall be returned.

ERRORS

       These functions shall fail if:

       Domain Error
              The value of x is a negative integer,    or x is -Inf.

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

       Pole Error
              The value of x is 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 value 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

       For IEEE Std 754-1985 double, overflow happens when 0 < x < 1/DBL_MAX, and 171.7 < x.

       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

       This function is named tgamma() in order to avoid conflicts with  the  historical  gamma()  and  lgamma()
       functions.

FUTURE DIRECTIONS

       It is possible that the error response for a negative integer argument may be changed to a pole error and
       a return value of ±Inf.

SEE ALSO

       feclearexcept()  ,  fetestexcept()  ,  lgamma()  ,  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                                             TGAMMA(P)