Contents

erfc

Computes the element-wise complementary error function of vector elements.

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:

\mathrm{erfc} (x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}dt

Useful relations:

\mathrm{erfc} (x) = 1 - \mathrm{erf} (x)

\Phi (x) = \frac{1}{2} \mathrm{erf} (\frac{x}{\sqrt{2}})

where

\Phi (x) = - \frac{1}{\sqrt{2\pi}} \int_0^x \exp (- frac{t^2}{2}) dt

is the cumulative normal distribution function.

\Phi^{-1} (x) = \sqrt{2} \mathrm{erf}^{-1} (2x - 1)

where \phi -1(x) and erf-1(x) are the inverses to \phi (x) and erf(x), respectively.

The following figure illustrates the relationships among erf family functions (erf, erfc, cdfnorm).

erfc Family Functions Relationship

erfc Family Functions Relationship

Useful relations for these functions:

\mathrm{erf} (x) + \mathrm{erfc} = 1

\mathrm{cdfnorm} (x) = \frac{1}{2} (1 + \mathrm{erf} (\frac{x}{\sqrt{2}})) = 1 - frac{1}{2} \mathrm{erfc} (\frac{x}{\sqrt{2}})

Argument

Result

Error Code

a > underflow

+0

status::underflow

+\infty

+0

-\infty

+2

QNAN

QNAN

SNAN

QNAN

API

Syntax

Buffer API

namespace oneapi::mkl::vm {

sycl::event erfc(sycl::queue & exec_queue,
      std::int64_t n,
      sycl::buffer<T> & a,
      sycl::buffer<T> & y,
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});

}

namespace oneapi::mkl::vm {

sycl::event erfc(sycl::queue & exec_queue,
      sycl::buffer<T> & a,
      oneapi::mkl::slice sa,
      sycl::buffer<T> & y,
      oneapi::mkl::slice sy,
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});

}

USM API

namespace oneapi::mkl::vm {

sycl::event erfc(sycl::queue & exec_queue,
      std::int64_t n,
      T const * a,
      T * y,
      std::vector<cl::sycl::event> const & depends = {},
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});

}

namespace oneapi::mkl::vm {

sycl::event erfc(sycl::queue & exec_queue,
      T const * a,
      oneapi::mkl::slice sa,
      T * y,
      oneapi::mkl::slice sy,
      std::vector<cl::sycl::event> const & depends = {},
      oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
      oneapi::mkl::vm::error_handler<T> errhandler = {});

}

erfc supports the following precisions and devices:

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

Input Parameters

Buffer API

exec_queue

The queue where the routine should be executed.

n

Specifies the number of elements to be calculated.

a

The buffer containing the input vector.

sa

Slice selector for a. See Data Types for a description of the oneMKL slice type.

sy

Slice selector for y. See Data Types for a description of the oneMKL slice type.

mode

Overrides the global VM mode setting for this function call. See the set_mode function for possible values and their description. This is an optional parameter. The default value is mode::not_defined.

errhandler

Sets local error handling mode for this function call. See the create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.

USM API

exec_queue

The queue where the routine should be executed.

n

Specifies the number of elements to be calculated.

a

Pointer to the input vector.

sa

Slice selector for a. See Data Types for a description of the oneMKL slice type.

sy

Slice selector for y. See Data Types for a description of the oneMKL slice type.

depends

Vector of dependent events (to wait for input data to be ready). This is an optional parameter. The default is an empty vector.

mode

Overrides the global VM mode setting for this function call. See the set_mode function for possible values and their description. This is an optional parameter. The default value is mode::not_defined.

errhandler

Sets local error handling mode for this function call. See the ref:create_error_handler function for arguments and their descriptions. This is an optional parameter. The local error handler is disabled by default.

Output Parameters

Buffer API

y

The buffer containing the output vector.

return value (event)

Computation end event.

USM API

y

Pointer to the output vector.

return value (event)

Computation end event.

Examples

An example of how to use erfc can be found in the oneMKL installation directory, under:

examples/dpcpp/vml/source/verfc.cpp
erf cdfnorm