erf man page
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.
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.1‐2008 defers to the ISO C standard.
These functions shall compute the error function of their argument x, defined as:
$\frac{2}{\sqrt{\pi}}\underset{0}{\overset{x}{\int}}e\text{^}\text{}t\text{^}2\text{}dt$
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 nonzero or fetestexcept(FE_INVALID  FE_DIVBYZERO  FE_OVERFLOW  FE_UNDERFLOW) is nonzero, 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 implementationdefined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
If the IEC 60559 FloatingPoint 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 nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the underflow floatingpoint 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 nonzero.
Rationale
None.
Future Directions
None.
See Also
erfc(), feclearexcept(), fetestexcept(), isnan()
The Base Definitions volume of POSIX.1‐2008, Section 4.19, 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, 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.12008 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 http://www.unix.org/online.html .
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