cdfnorm

Computes the cumulative normal distribution function values of vector elements.

Syntax

Buffer API:

namespace oneapi::mkl::vm {

sycl::event cdfnorm(
        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 cdfnorm(
        sycl::queue& exec_queue,
        std::int64_t n,
        const T *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

cdfnorm supports the following precisions.

T
float
double

Description

The cdfnorm function computes the cumulative normal distribution function values for elements of the input vector a and writes them to the output vector y.

The cumulative normal distribution function is defined as given by:

\[\operatorname{cdfnorm}(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-\frac{t^2}{2}} \operatorname{d \!} x\]

Useful relations for these functions:

\[\operatorname{erf}(x) + \operatorname{erfc}(x) = 1\]

\[\begin{split}\operatorname{cdfnorm}(x) &= \frac{1}{2} \left( 1 + \operatorname{erf}\left(\frac{x}{\sqrt{2}}\right) \right) \\ &= 1 - \frac{1}{2} \operatorname{erfc}\left(\frac{x}{\sqrt{2}}\right)\end{split}\]

where \(\operatorname{erf}\) and \(\operatorname{erfc}\) are the error and complementary error functions, respectively.

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

cdfnorm Family Functions Relationship |

Argument	Result	Status code
a < underflow	+0	oneapi::mkl::vm::status::underflow
+∞	+1
-∞	+0
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