erfc

Computes the complementary error function value of vector elements.

Syntax

Buffer API:

namespace oneapi::mkl::vm {
  void erfc(queue& exec_queue,
  int64_t n,
  buffer<T,1>& a,
  buffer<T,1>& y,
  uint64_t mode = mode::not_defined,
  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 lib_mode = oneapi::mkl::vm::mode::not_defined, oneapi::mkl::vm::error_handler<T> eh = {});
}

USM API:

namespace oneapi::mkl::vm {
  event erfc(queue& exec_queue,
  int64_t n,
  T* a,
  T* y,
  vector_class<event> const & depends = {},
  uint64_t mode = mode::not_defined, 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,
  sycl::vector_class<cl::sycl::event> const & depends = {},
  oneapi::mkl::vm::mode lib_mode = oneapi::mkl::vm::mode::not_defined,
  oneapi::mkl::vm::error_handler<T> eh = {});
}

erfc supports the following precisions and devices:

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

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 Φ-1(x) and erf-1(x) are the inverses to Φ(x) and erf(x), respectively.

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

erfc Family Functions Relationship |

image5

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

+∞

+0

-∞

+2

QNAN

QNAN

SNAN

QNAN

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 a containing input vector of size n.

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 a to the input vector of size n.

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).

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 y containing the output vector of size n.

USM API:

y

Pointer y to the output vector of size n.

return value (event)

Function end event.

Example

An example of how to use erfccan be found in the Intel® oneMKL installation directory, under:

examples/dpcpp/vml/source/verfc.cpp