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

^[CX] 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.1-2024 defers to the ISO C standard.

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

\( \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} d t\)

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.

^[MX] 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. ^[MXX]  If the IEC 60559 Floating-Point option is supported, 2* x/ sqrt() should be returned.

ERRORS

These functions may fail if:

Range Error

^[MX] 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.

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()/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

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

CHANGE HISTORY

First released in Issue 1. Derived from Issue 1 of the SVID.

Issue 5

The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

Issue 6

The erf() function is no longer marked as an extension.

The erfc() function is split out onto its own reference page.

The erff() and erfl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/22 is applied, adding the example to the EXAMPLES section.

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0092 [68] is applied.

Issue 8

Austin Group Defect 1178 is applied, joining two paragraphs in the RETURN VALUE section.