The Open Group Base Specifications Issue 7
IEEE Std 1003.1-2008, 2016 Edition
Copyright © 2001-2016 The IEEE and The Open Group

#### 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.1-2008 defers to the ISO C standard.

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

> 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.

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()/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 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.

End of informative text.

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