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:

--

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.1‐2017, Section 4.20, Treatment of Error Conditions
       for Mathematical Functions, <math.h>

COPYRIGHT

       Portions of this text are reprinted and  reproduced  in  electronic  form  from  IEEE  Std
       1003.1-2017,  Standard  for  Information Technology -- Portable Operating System Interface
       (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C)  2018  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 .

       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 .