v?Erfc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

v?Erfc

Computes the complementary error function value of vector elements.

Syntax

call vserfc ( n , a , y )

call vserfci(n, a, inca, y, incy)

call vmserfc ( n , a , y , mode )

call vmserfci(n, a, inca, y, incy, mode)

call vderfc ( n , a , y )

call vderfci(n, a, inca, y, incy)

call vmderfc ( n , a , y , mode )

call vmderfci(n, a, inca, y, incy, mode)

Include Files

mkl_vml.f90

Input Parameters

Name	Type	Description
`n`	INTEGER , INTENT(IN)	Specifies the number of elements to be calculated.
`a`	Fortran 77: DOUBLE PRECISION for `vderfc` , `vmderfc`Fortran 90: REAL , INTENT(IN) for `vserfc` , `vmserfc`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vderfc` , `vmderfc`	Array that specifies the input vector `a` .
`inca` , `incy`	INTEGER, INTENT(IN)	Specifies increments for the elements of `a` and `y` .
`mode`	INTEGER(KIND=8) , INTENT(IN)	Overrides global VM mode setting for this function call. See vmlSetMode (Sets a new mode for VM functions according to the mode parameter and stores the previous VM mode to oldmode.) for possible values and their description.

Output Parameters

Name	Type	Description
`y`	Fortran 77: DOUBLE PRECISION for `vderfc` , `vmderfc`Fortran 90: REAL , INTENT(OUT) for `vserfc` , `vmserfc`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vderfc` , `vmderfc`	Array that specifies the output vector `y` .

Description

vsErfc vdErfc vmsErfc vmdErfc

The Erfc function computes the complementary error function values for elements of the input vector a and writes them to the output vector y .

The complementary error function is defined as follows:

Useful relations:

where

is the cumulative normal distribution function.

where Φ^{-1}(x) and erf^{-1}(x) are the inverses to Φ(x) and erf(x) respectively.

See also Figure “Erf Family Functions Relationship” in Erf function description for Erfc function relationship with the other functions of Erf family.

Special Values for Real Function v?Erfc(x)

Argument	Result	VM Error Status	Exception
X > underflow	+0	VML_STATUS_UNDERFLOW	UNDERFLOW
∞	+0
∞	+2
QNAN	QNAN
SNAN	QNAN		INVALID

NOTE:

Erf
CdfNorm

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?Erfc

Syntax

Include Files

Input Parameters

Output Parameters

Description