ERFC(3P) POSIX Programmer's Manual ERFC(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.
erfc, erfcf, erfcl — complementary error functions
double erfc(double x);
float erfcf(float x);
long double erfcl(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 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 has
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
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
Note for IEEE Std 754‐1985 double, 26.55 < x implies erfc(x) has under‐
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 ALSOerf(), 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 ERFC(3P)