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ERF(3P)                    POSIX Programmer's Manual                   ERF(3P)
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:
              _Ie^ -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(n)
       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(n)/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 Electri-
       cal 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.ker-
       nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group                  2013                              ERF(3P)