The Open Group Base Specifications Issue 6
IEEE Std 1003.1, 2004 Edition
Copyright © 2001-2004 The IEEE and The Open Group, All Rights reserved.
A newer edition of this document exists here


erf, erff, erfl - error functions


#include <math.h>

double erf(double
float erff(float
long double erfl(long double


[CX] [Option Start] 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 IEEE Std 1003.1-2001 defers to the ISO C standard. [Option End]

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.


Upon successful completion, these functions shall return the value of the error function.

[MX] [Option Start] 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 x is subnormal, a range error may occur, and 2 * x/ sqrt() should be returned. [Option End]


These functions may fail if:

Range Error
[MX] [Option Start] 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. [Option End]

The following sections are informative.


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 an XSI extension.

#include <math.h>

double 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()/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.






erfc(), feclearexcept(), fetestexcept(), isnan(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h>


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.

End of informative text.

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