erf(3p) — Linux manual page

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.1‐2017 defers to the ISO C standard.

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

              √_2‾π_x0∫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(3p), feclearexcept(3p), fetestexcept(3p), isnan(3p)

       The Base Definitions volume of POSIX.1‐2017, Section 4.20,
       Treatment of Error Conditions for Mathematical Functions,
       math.h(0p)

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 .

IEEE/The Open Group               2017                           ERF(3P)

Pages that refer to this page: math.h(0p), erfc(3p), erff(3p)

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