.. _atan2pi:

atan2pi
=======


Computes the element-wise four-quadrant arctangent of vector ``a`` elements divided by vector ``b`` elements, divided by pi.


.. contents::
    :local:
    :depth: 1

Description
***********

The ``atan2pi(a,b)`` function computes the four-quadrant inverse tangent
of the ratios of the corresponding elements of two vectors divided by
:math:`\infty`.


For the elements of the output vector ``y``, the function computers
the four-quadrant arctangent of ``a``\ :sub:`i`/``b``\ :sub:`i`, with
the result divided by :math:`\infty`.


.. tabularcolumns:: |\Y{0.25}|\Y{0.25}|\Y{0.25}|\Y{0.25}|

.. list-table::
   :header-rows: 1
   :class: longtable

   * -  Argument 1
     -  Argument 2
     -  Result
     -  Error Code
   * -  -\ :math:`\infty`
     -  -\ :math:`\infty`
     -  -3/4
     -
   * -  -\ :math:`\infty`
     -  ``b`` < +0
     -  -1/2
     -
   * -  -\ :math:`\infty`
     -  -0
     -  +1/2
     -
   * -  -\ :math:`\infty`
     -  +0
     -  -1/2
     -
   * -  -\ :math:`\infty`
     -  ``x`` > +0
     -  -1/2
     -
   * -  -\ :math:`\infty`
     -  +\ :math:`\infty`
     -  -1/4
     -
   * -  ``a`` < +0
     -  -\ :math:`\infty`
     -  -1
     -
   * -  ``a`` < +0
     -  -0
     -  -1/2
     -
   * -  ``a`` < +0
     -  +0
     -  -1/2
     -
   * -  ``a`` < +0
     -  +\ :math:`\infty`
     -  -0
     -
   * -  -0
     -  -\ :math:`\infty`
     -  -1
     -
   * -  -0
     -  ``b`` < +0
     -  -1
     -
   * -  -0
     -  -0
     -  -1
     -
   * -  -0
     -  +0
     -  -0
     -
   * -  -0
     -  ``b`` > +0
     -  -0
     -
   * -  -0
     -  +\ :math:`\infty`
     -  -0
     -
   * -  +0
     -  -\ :math:`\infty`
     -  +1
     -
   * -  +0
     -  ``b`` < +0
     -  +1
     -
   * -  +0
     -  -0
     -  +1
     -
   * -  +0
     -  +0
     -  +0
     -
   * -  +0
     -  ``b`` > +0
     -  +0
     -
   * -  +0
     -  +\ :math:`\infty`
     -  +0
     -
   * -  ``a`` > +0
     -  -\ :math:`\infty`
     -  +1
     -
   * -  ``a`` > +0
     -  -0
     -  +1/2
     -
   * -  ``x`` > +0
     -  +0
     -  +1/2
     -
   * -  ``a`` > +0
     -  +\ :math:`\infty`
     -  +1/4
     -
   * -  +\ :math:`\infty`
     -  -\ :math:`\infty`
     -  +3/4
     -
   * -  +\ :math:`\infty`
     -  ``b`` < +0
     -  +1/2
     -
   * -  +\ :math:`\infty`
     -  -0
     -  +1/2
     -
   * -  +\ :math:`\infty`
     -  +0
     -  +1/2
     -
   * -  +\ :math:`\infty`
     -  ``b`` > +0
     -  +1/2
     -
   * -  +\ :math:`\infty`
     -  +\ :math:`\infty`
     -  +1/4
     -
   * -  ``a`` > +0
     -  QNAN
     -  QNAN
     -
   * -  ``a`` > +0
     -  SNAN
     -  QNAN
     -
   * -  QNAN
     -  ``b`` > +0
     -  QNAN
     -
   * -  SNAN
     -  ``x`` > +0
     -  QNAN
     -
   * -  QNAN
     -  QNAN
     -  QNAN
     -
   * -  QNAN
     -  SNAN
     -  QNAN
     -
   * -  SNAN
     -  QNAN
     -  QNAN
     -
   * -  SNAN
     -  SNAN
     -  QNAN
     -


The ``atan2pi(a,b)`` function does not generate any errors.


API
***


Syntax
------

**Buffer API**


.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event atan2pi(sycl::queue & exec_queue,
         std::int64_t n,
         sycl::buffer<T> & a,
         sycl::buffer<T> & b,
         sycl::buffer<T> & y,
         oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined);

   }

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event atan2pi(sycl::queue & exec_queue,
         sycl::buffer<T> & a,
         oneapi::mkl::slice sa,
         sycl::buffer<T> & b,
         oneapi::mkl::slice sb,
         sycl::buffer<T> & y,
         oneapi::mkl::slice sy,
         oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined);

   }

**USM API**

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event atan2pi(sycl::queue & exec_queue,
         std::int64_t n,
         T const * a,
         T const * b,
         T * y,
         std::vector<cl::sycl::event> const & depends = {},
         oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined);

   }

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event atan2pi(sycl::queue & exec_queue,
         T const * a,
         oneapi::mkl::slice sa,
         T const * b,
         oneapi::mkl::slice sb,
         T * y,
         oneapi::mkl::slice sy,
         std::vector<cl::sycl::event> const & depends = {},
         oneapi::mkl::vm::mode mode = oneapi::mkl::vm::mode::not_defined);

   }





``atan2pi`` supports the following precisions and devices:

.. list-table::
   :header-rows: 1

   * -  T
     -  Devices supported
   * -  ``float``
     -  Host, CPU, and GPU
   * -  ``double``
     -  Host, CPU, and GPU


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 containing the 1st input vector.


sa
   Slice selector for ``a``. See :ref:`data-types` for a description of the |O-MKL| slice type.


b
   The buffer containing the 2nd input vector.


sb
   Slice selector for ``b``. See :ref:`data-types` for a description of the |O-MKL| slice type.


sy
   Slice selector for ``y``. See :ref:`data-types` for a description of the |O-MKL| slice type.


mode
   Overrides the global VM mode setting for this function call. See :ref:`set_mode` function for possible values and their description. This is an optional parameter. The default value is ``mode::not_defined``.


**USM API**


exec_queue
   The queue where the routine should be executed.


n
   Specifies the number of elements to be calculated.


a
   Pointer to the 1st input vector.


sa
   Slice selector for ``a``. See :ref:`data-types` for a description of the |O-MKL| slice type.


b
   Pointer to the 2nd input vector.


sb
   Slice selector for ``b``. See :ref:`data-types` for a description of the |O-MKL| slice type.


sy
   Slice selector for ``y``. See :ref:`data-types` for a description of the |O-MKL| 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 :ref:`set_mode` function for possible values and their description. This is an optional parameter. The default value is ``mode::not_defined``.


Output Parameters
-----------------

**Buffer API**


y
   The buffer containing the output vector.


return value (event)
   Computation end event.


**USM API**


y
   Pointer to the output vector.


return value (event)
   Computation end event.


Examples
********

An example of how to use ``atan2pi`` can be found in the |O-MKL|
installation directory, under:

.. code-block::

   examples/dpcpp/vml/source/vatan2pi.cpp