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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  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 imple-
       mentation-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 Electri-
       cal  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.ker-
       nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group                  2013                           TGAMMA(3P)