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.1‐2008 defers to the ISO C standard.

       These functions shall compute the error function of their argument x, defined as:

--

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 [x1,x2] with x1≤x2.

       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.

SEE ALSO

       erfc(), 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 .

IEEE/The Open Group                                   2013                                           ERF(3POSIX)