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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

       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    either  0.0  (if  representable),  or   an
       implementation-defined value shall be returned.

       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 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 .