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 .