Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/31/2023
Public

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v?Erfc

Computes the complementary error function value of vector elements.

Syntax

vsErfc( n, a, y );

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

vmsErfc( n, a, y, mode );

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

vdErfc( n, a, y );

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

vmdErfc( n, a, y, mode );

vmdErfcI(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 float* for vsErfc, vmsErfc

const double* for vdErfc, vmdErfc

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 for possible values and their description.

Output Parameters

Name

Type

Description

y

float* for vsErfc, vmsErfc

double* for vdErfc, vmdErfc

Pointer to an array that contains the output vector y.

Description

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:


Equation

Useful relations:

Equation

Equation

where

Equation

is the cumulative normal distribution function.

Equation

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

See Also