Legacy Document

erfc

You can use the erfc function to perform the complementary error function.

double_t erfc (double_t x);

x

Any floating-point number.

DESCRIPTION

The erfc function computes the complementary error of its argument. This function is antisymmetric.

$erfc(x)\; =\; 1.0+-erf(x)$

For large positive numbers (around 10), use the function call erfc(x) instead of the expression 1.0 - erf(x). The call erfc(x) produces a more exact result.

EXCEPTIONS

When x is finite and nonzero, either the result of $erfc(x)$ is exact or it raises one of the following exceptions:

• inexact (if the result must be rounded or an underflow occurs)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-36 shows the results when the argument to the erfc function is a zero, a NaN, or an Infinity.

Special cases for the erfc function

Operation	Result	Exceptions raised
$erfc(+0)$	+1	None
$erfc(-0)$	+1	None
$erfc(NaN)$	NaN	None[60]
$erfc(+$ )	+0	None
$erfc(-$ )	+2	None

EXAMPLES

z = erfc(-INFINITY); /* z = 1 - erf() = 1 - -1 = +2.0 */
z = erfc(0.0);       /* z = 1 - erf(0) = 1 - 0 = 1.0 */

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[60] If the NaN is a signaling NaN, the invalid exception is raised.