v?ErfInv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

v?ErfInv

Computes inverse error function value of vector elements.

Syntax

vhErfInv ( n , a , y ) ;

vhErfInvI(n, a, inca, y, incy);

vmhErfInv ( n , a , y , mode ) ;

vmhErfInvI(n, a, inca, y, incy, mode);

vsErfInv ( n , a , y ) ;

vsErfInvI(n, a, inca, y, incy);

vmsErfInv ( n , a , y , mode ) ;

vmsErfInvI(n, a, inca, y, incy, mode);

vdErfInv ( n , a , y ) ;

vdErfInvI(n, a, inca, y, incy);

vmdErfInv ( n , a , y , mode ) ;

vmdErfInvI(n, a, inca, y, incy, mode);

Include Files

mkl.h

Input Parameters

Name	Type	Description
`n`	const MKL_INT	Specifies the number of elements to be calculated.
`a`	const _Float16* for `vhErfInv` , `vmhErfInv` const float* for `vsErfInv` , `vmsErfInv` const double* for `vdErfInv` , `vmdErfInv`	Pointer to an array that contains the input vector `a` .
`inca` , `incy`	const MKL_INT	Specifies increments for the elements of `a` and `y` .
`mode`	const MKL_INT64	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`	_Float16* for `vhErfInv` , `vmhErfInv` float* for `vsErfInv` , `vmsErfInv` double* for `vdErfInv` , `vmdErfInv`	Pointer to an array that contains the output vector `y` .

Description

vsErfInv vdErfInv vmsErfInv vmdErfInv

The ErfInv function computes the inverse error function values for elements of the input vector a and writes them to the output vector y

y = erf^{-1}(a) ,

where erf(x) is the error function defined as given by:

Useful relations:

where erfc is the complementary error function.

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.

Figure “ErfInv Family Functions Relationship” illustrates the relationships among ErfInv family functions ( ErfInv , ErfcInv , CdfNormInv ).

ErfInv Family Functions Relationship

Sparse Matrices That Can be Solved With PARDISO

Useful relations for these functions:

Special Values for Real Function v?ErfInv(x)

Argument	Result	VM Error Status	Exception
+0	+0
-0	-0
+1	∞	VML_STATUS_SING	ZERODIVIDE
-1	∞	VML_STATUS_SING	ZERODIVIDE
`\(\|X\| > 1\)`	QNAN	VML_STATUS_ERRDOM	INVALID
∞	QNAN	VML_STATUS_ERRDOM	INVALID
∞	QNAN	VML_STATUS_ERRDOM	INVALID
QNAN	QNAN
SNAN	QNAN		INVALID

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for C

v?ErfInv

Syntax

Include Files

Input Parameters

Output Parameters

Description

ErfInv Family Functions Relationship