# erf

## 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



           erf, erff, erfl — error functions
    


## SYNOPSIS



           #include <math.h>
    
           double erf(double _x_);
           float erff(float _x_);
           long double erfl(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 error function of their argument
           _x_ , defined as:
    
                  _√__ 2 _‾_ π __x_ 0∫ _e^_ − _t^_ 2 _dt_
    
           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 error function.
    
           If _x_ is NaN, a NaN shall be returned.
    
           If _x_ is ±0, ±0 shall be returned.
    
           If _x_ is ±Inf, ±1 shall be returned.
    
           If the correct value would cause underflow, a range error may
           occur, and _erf_(), _erff_(), and _erfl_() shall return an
           implementation-defined value no greater in magnitude than DBL_MIN,
           FLT_MIN, and LDBL_MIN, respectively.
    
           If the IEC 60559 Floating-Point option is supported, 2 * _x_ /_sqrt_(π)
           should 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



       **Computing the Probability for a Normal Variate**
           This example shows how to use _erf_() to compute the probability
           that a normal variate assumes a value in the range [_x_ 1,_x_ 2] with
           _x_ 1≤ _x_ 2.
    
           This example uses the constant M_SQRT1_2 which is part of the XSI
           option.
    
               #include <math.h>
    
               double
               Phi(const double x1, const double x2)
               {
                   return ( erf(x2*M_SQRT1_2) - erf(x1*M_SQRT1_2) ) / 2;
               }
    


## APPLICATION USAGE



           Underflow occurs when |_x_ | < DBL_MIN * (_sqrt_(π)/2).
    
           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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