ERF(3P) POSIX Programmer's Manual ERF(3P)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
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,
__∫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
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,
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
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
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.
SEE ALSOerfc(), feclearexcept(), fetestexcept(), isnan()
The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
Error Conditions for Mathematical Functions, <math.h>
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 Electri‐
cal 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 .
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IEEE/The Open Group 2013 ERF(3P)