Provided by: manpages-posix-dev_2013a-2_all bug

PROLOG

       This  manual  page  is part of the POSIX Programmer's Manual.  The Linux implementation of
       this interface may differ (consult the corresponding 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 support 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 Technology -- 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 Standard 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 .