erfc(x): Complementary Error¶

Complementary error function.

Declaration¶

Syntax¶

retval = erfc(x)
elemental real function erfc(x)

Arguments¶

x the input value must be of type real.

Return values¶

The return value is of type real and of the same kind as of the input parameter x. erfc(x) returns \(1 - erf(x)\).

Description¶

erf(x) computes the error function of x. The result lies in the range:

\(0 \leq erf (x) \leq 2\)

It is calculated using:

\(\frac{2}{\sqrt\pi}\int_{x}^{\infty}e^{-t^2}dt\)

It is used in instances when the large loss of relative accuracy occurs if erf(x) is called for large x and the result is subtracted from 1.

Types¶

Supported argument types is real.

interface erfc
    module procedure serfc, derfc
end interface

contains

elemental real(sp) function serfc(x)
real(sp), intent(in) :: x
end function

elemental real(dp) function derfc(x)
real(dp), intent(in) :: x
end function

Examples¶

program intrinsics_erfc
	print *, erfc(1.0)
end program

Result:

0.1572992057