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.
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 complementary error function 1.0 −
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
Upon successful completion, these functions shall return the value of
the complementary error function.
If the correct value would cause underflow, and is not representable,
a range error may occur, and erfc(), erfcf(), and erfcl() shall
return 0.0, or (if the IEC 60559 Floating-Point option is not
supported) an implementation-defined value no greater in magnitude
than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
If x is NaN, a NaN shall be returned.
If x is ±0, +1 shall be returned.
If x is −Inf, +2 shall be returned.
If x is +Inf, +0 shall be returned.
If the correct value would cause underflow and is representable, a
range error may occur and the correct value shall 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.
The erfc() function is provided because of the extreme loss of
relative accuracy if erf(x) is called for large x and the result
subtracted from 1.0.
Note for IEEE Std 754‐1985 double, 26.55 < x implies erfc(x) has
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.
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
IEEE/The Open Group 2013 ERFC(3P)