erfc 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.
erfc, erfcf, erfcl — complementary error functions
Synopsis
#include <math.h> double erfc(double x); float erfcf(float x); long double erfcl(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 complementary error function 1.0  erf(x).
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 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 FloatingPoint option is not supported) an implementationdefined 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.
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
None.
Application Usage
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 underflowed.
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
erf(), 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 .
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/manpages/reporting_bugs.html .