# NAME

erfc, erfcf, erfcl - complementary error function

# LIBRARY

Math library (`libm`, `-lm`)

# SYNOPSIS

``````#include <math.h>
double erfc(double x);
float erfcf(float x);
long double erfcl(long double x);``````

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

erfc():

``````    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE``````

erfcf(), erfcl():

``````    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE``````

# DESCRIPTION

These functions return the complementary error function of `x`, that is, 1.0 - erf(x).

# RETURN VALUE

On success, these functions return the complementary error function of `x`, a value in the range [0,2].

If `x` is a NaN, a NaN is returned.

If `x` is +0 or -0, 1 is returned.

If `x` is positive infinity, +0 is returned.

If `x` is negative infinity, +2 is returned.

If the function result underflows and produces an unrepresentable value, the return value is 0.0.

If the function result underflows but produces a representable (i.e., subnormal) value, that value is returned, and a range error occurs.

# ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

Range error: result underflow (result is subnormal)

An underflow floating-point exception (FE_UNDERFLOW) is raised.

These functions do not set `errno`.

# ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

 Interface Attribute Value erfc(), erfcf(), erfcl() Thread safety MT-Safe

# STANDARDS

C11, POSIX.1-2008.

# HISTORY

C99, POSIX.1-2001.

The variant returning `double` also conforms to SVr4, 4.3BSD.

# NOTES

The erfc(), erfcf(), and erfcl() functions are provided to avoid the loss accuracy that would occur for the calculation 1-erf(x) for large values of `x` (for which the value of erf(x) approaches 1).