erfl(3p) — Linux manual page


ERF(3P)                   POSIX Programmer's Manual                  ERF(3P)

PROLOG         top

       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         top

       erf, erff, erfl — error functions

SYNOPSIS         top

       #include <math.h>

       double erf(double x);
       float erff(float x);
       long double erfl(long double x);

DESCRIPTION         top

       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         top

       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,

       If the IEC 60559 Floating-Point option is supported, 2 * x/sqrt(π)
       should be returned.

ERRORS         top

       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         top

   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

           #include <math.h>

           Phi(const double x1, const double x2)
               return ( erf(x2*M_SQRT1_2) − erf(x1*M_SQRT1_2) ) / 2;


       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         top




SEE ALSO         top

       erfc(3p), feclearexcept(3p), fetestexcept(3p), isnan(3p)

       The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
       of Error Conditions for Mathematical Functions, math.h(0p)

COPYRIGHT         top

       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 .

       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 .

IEEE/The Open Group                 2013                             ERF(3P)