erfcinv#

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

Description#

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

The inverse complementary error function is defined as given by:

\[\mathrm{erfcinv} (x) = \mathrm{erfinv} (1 - x)\]
\[\mathrm{erfinv} (x) = \mathrm{erf}^{-1} (x)\]
\[\mathrm{erf} (x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt\]

where erf(x) denotes the error function and erfinv(x) denotes the inverse error function.

The following figure illustrates the relationships among erfinv family functions (erfinv, erfcinv, cdfnorminv).

erfcinv Family Functions Relationship

erfcinv Family Functions Relationship#

Useful relations for these functions:

\[\mathrm{erfcinv} (x) = \mathrm{erfinv} (1 - x)\]
\[\mathrm{cdfnorminv} (x) = \sqrt{2} \mathrm{erfinv} (2x - 1) = \sqrt{2} \mathrm{erfcinv} (2 - 2x)\]

Argument

Result

Error Code

+1

+0

+2

-\(\infty\)

status::sing

-0

+\(\infty\)

status::sing

+0

+\(\infty\)

status::sing

a < -0

QNAN

status::errdom

a > +2

QNAN

status::errdom

+\(\infty\)

QNAN

status::errdom

-\(\infty\)

QNAN

status::errdom

QNAN

QNAN

SNAN

QNAN

API#

Syntax#

Buffer API

namespace oneapi::mkl::vm {

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

}

erfcinv supports the following precisions and devices:

T

Devices supported

sycl::half

GPU

_Float16

CPU

float

CPU and GPU

double

CPU and GPU

Input Parameters#

Buffer API

exec_queue

The queue where the routine will 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 will 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 y containing the output vector of size n.

return value (event)

Computation end event.

USM API

y

Pointer y to the output vector of size n.

return value (event)

Computation end event.

Examples#

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

share/doc/mkl/examples/sycl/vml/source/verfcinv.cpp