TGAMMA(3P)						     POSIX Programmer's Manual							TGAMMA(3P)

PROLOG

       This  manual page is part of the POSIX Programmer's Manual.  The Linux implementation of this interface may differ (consult the correspond-
       ing Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

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

       The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here
       and the ISO C standard is unintentional. This volume of POSIX.1-2008 defers to the ISO C standard.

       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 may occur and either a NaN (if supported) or an implementation-defined value shall be returned.
       On systems that support the IEC 60559 Floating-Point option, a domain error shall occur and a NaN shall be returned.

       If x is +-0, tgamma(), tgammaf(), and tgammal() shall return +-HUGE_VAL, +-HUGE_VALF, and +-HUGE_VALL, respectively.  On systems that  sup-
       port the IEC 60559 Floating-Point option, a pole error shall occur; otherwise, a pole error may occur.

       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 the correct value would cause underflow, and is not representable, a range error may occur, and tgamma(), tgammaf(), and tgammal() shall
       return  0.0,  or  (if  IEC  60559  Floating-Point  is  not supported) an implementation-defined value no greater in magnitude than DBL_MIN,
       FLT_MIN, and LDBL_MIN, respectively.

       If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.

       If x is NaN, a NaN shall be returned.

       If x is +Inf, x shall be returned.

       If x is -Inf, a domain error shall occur, and a NaN 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.

       These functions may fail if:

       Domain Error
		   The value of x is a negative integer.

		   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 result underflows.

		   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 underflow 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 POSIX.1-2008, Section 4.19, 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, 2013 Edition, Standard for Information Technol-
       ogy -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, Copyright (C)  2013  by	the  Institute	of
       Electrical and Electronics Engineers, Inc and The Open Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) 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 Stan-
       dard is the referee document. The original Standard can be obtained online at http://www.unix.org/online.html .

       Any typographical or formatting errors that appear in this page are most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .

IEEE
/The Open Group						       2013								TGAMMA(3P)