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

       erfc, erfcf, erfcl — complementary error functions

SYNOPSIS

       #include <math.h>

       double erfc(double x);
       float erfcf(float x);
       long double erfcl(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 complementary error function 1.0 − erf(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 the value  of  the  complementary
       error function.

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

       If x is NaN, a NaN shall be returned.

       If x is ±0, +1 shall be returned.

       If x is −Inf, +2 shall be returned.

       If x is +Inf, +0 shall be returned.

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

ERRORS

       These functions may fail if:

       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

       The erfc() function is provided because of the extreme loss of relative accuracy if erf(x)
       is called for large x and the result subtracted from 1.0.

       Note for IEEE Std 754‐1985 double, 26.55 < x implies erfc(x) has underflowed.

       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

       None.

FUTURE DIRECTIONS

       None.

SEE ALSO

       erf(), feclearexcept(), fetestexcept(), isnan()

       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 .