# erfc

## 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.1‐2017 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.
    
           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.
    


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