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.

       delim $$

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:

              ${2 over sqrt pi} int from 0 to x e"^" " "{- t"^" 2" "} dt$

       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 [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 .