erfcf (3p) - Linux Manuals

erfcf: complementary error functions


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


#include <math.h>

double erfc(double x);
float erfcf(float
long double erfcl(long double


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 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 complementary error function.

If the correct value would cause underflow and is not representable, a range error may occur and either 0.0 (if representable), or an implementation-defined value shall be returned.

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 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 non-zero.






Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. 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 .


erf(), feclearexcept(), fetestexcept(), isnan(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h>