.. _remainder:

remainder
=========

Computes the element-wise remainder of vector ``a`` elements divided by vector ``b`` elements, that is nearest to zero.


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

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

The ``remainder(a)`` function computes the remainder of each element
of vector ``a``, with respect to the corresponding elements of vector
``b``: compute the values of ``n`` such that

``n = ai - n*bi``

where ``n`` is the integer nearest to the exact value of
``a``\ :sub:`i`/``b``\ :sub:`i`. If two integers are equally close to
``a``\ :sub:`i`/``b``\ :sub:`i`, ``n`` is the even one. If ``n`` is
zero, it has the same sign as ``a``\ :sub:`i`.


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

   * -  Argument 1
     -  Argument 2
     -  Result
     -  VM Error Status

   * -  ``a`` not NAN
     -  ±0
     -  NAN
     -  status::errdom
   * -  :math:`\pm \infty`
     -  ``b`` not NAN
     -  NAN
     -   
   * -  ±0
     -  ``b``\ ≠ 0, not NAN
     -  ±0
     -   
   * -  ``a`` finite
     -  :math:`\pm \infty`
     -  ``a``
     -   
   * -  NAN
     -  ``b``
     -  NAN
     -   
   * -  ``a``
     -  NAN
     -  NAN
     -   


API
***


Syntax
------

**Buffer API**

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event remainder(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,
         oneapi::mkl::vm::error_handler<T> errhandler = {});

   }

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event remainder(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,
         oneapi::mkl::vm::error_handler<T> errhandler = {});

   }

**USM API**

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event remainder(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,
         oneapi::mkl::vm::error_handler<T> errhandler = {});

   }

.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event remainder(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,
         oneapi::mkl::vm::error_handler<T> errhandler = {});

   }

``remainder`` 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``.


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.


**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``.


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 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 ``remainder`` can be found in the |O-MKL|
installation directory, under:


.. code-block::

   examples/dpcpp/vml/source/vremainder.cpp