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PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT |
ERF(3P) POSIX Programmer's Manual ERF(3P)
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.
delim $$
erf, erff, erfl — error functions
#include <math.h>
double erf(double x);
float erff(float x);
long double erfl(long double x);
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:
${2 over sqrt pi} int from 0 to x e"^" " "{- t"^" 2" "} dt$
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.
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.
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.
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;
}
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.
None.
None.
erfc(3p), feclearexcept(3p), fetestexcept(3p), isnan(3p)
The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
of Error Conditions for Mathematical Functions, math.h(0p)
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.1-2008 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 .
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 .
IEEE/The Open Group 2013 ERF(3P)
Pages that refer to this page: math.h(0p), erfc(3p), erff(3p)