erfcinv¶

Computes the inverse complementary error function value of vector elements.

Syntax

Buffer API:

namespace oneapi::mkl::vm {

sycl::event erfcinv(
        sycl::queue& exec_queue,
        std::int64_t n,
        sycl::buffer<T,1>& a,
        sycl::buffer<T,1>& y,
        oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined,
        oneapi::mkl::vm::error_handler<T> errhandler = {});

} // namespace oneapi::mkl::vm

USM API:

namespace oneapi::mkl::vm {

sycl::event erfcinv(
        sycl::queue& exec_queue,
        std::int64_t n,
        T* a,
        T* y,
        sycl::vector_class<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

erfcinv supports the following precisions.

T
`float`
`double`

Description

The erfcinv(a) function computes the inverse complimentary 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:

\[\operatorname{erfcinv}(x) = \operatorname{erfinv}(1 - x)\]

Useful relations for these functions:

\[\operatorname{erfcinv}(x) = \operatorname{erfinv}(1 - x)\]

\[\begin{split}\operatorname{cdfnorminv}(x) &= \sqrt{2} \operatorname{erfinv}(2x - 1) \\ &= \sqrt{2} \operatorname{erfcinv}(2 - 2x)\end{split}\]

\[\operatorname{erfinv}(x) = \operatorname{erf}^{-1}(x)\]

\[\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \operatorname{d \!} t\]

where \(\operatorname{erf}(x)\) denotes the error function and \(\operatorname{erfinv}(x)\) denotes the inverse error function.

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

erfcinv Family Functions Relationship |

Argument	Result	Status code
+1	+0
+2	-∞	`oneapi::mkl::vm::status::sing`
-0	+∞	`oneapi::mkl::vm::status::sing`
+0	+∞	`oneapi::mkl::vm::status::sing`
a < -0	QNAN	`oneapi::mkl::vm::status::errdom`
a > +2	QNAN	`oneapi::mkl::vm::status::errdom`
+∞	QNAN	`oneapi::mkl::vm::status::errdom`
-∞	QNAN	`oneapi::mkl::vm::status::errdom`
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.
mode: Overrides the global VM mode setting for this function call. See set_mode function for possible values and their description. This is an optional parameter. The default value is oneapi::mkl::vm::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.
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 oneapi::mkl::vm::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.

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): Event, signifying availability of computed output and status code(s).

Exceptions

For list of generated exceptions please refer to Exceptions

Parent topic: VM Mathematical Functions

erfc erfinv

oneAPI Specification 1.1-provisional-rev-1 documentation

erfcinv¶