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:

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

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.1-2017, 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 .