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 vectory
.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)
anderf-1(x)
are the inverses toΦ(x)
anderf(x)
, respectively.The following figure illustrates the relationships among erf family functions (erf, erfc, cdfnorm).
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
+∞
+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 sizen
.- 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 sizen
.- 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 sizen
.USM API:
- y
Pointer
y
to the output vector of sizen
.- 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