.. _expint1:

expint1
=======


Computes the element-wise exponential integral of vector elements.


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

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

The ``expint1(a)`` function computes the exponential integral of vector
elements of the input vector ``a`` and writes them to the output
vector ``y``.


For positive real values ``x``, this can be written as:


.. math::

   E_1(x) =
   \int_x^{\infty}
      \frac{e^{-t}}{t} dt =
   \int_1^{\infty}
      \frac{e^{-xt}}{t} dt

For negative real values ``x``, the result is defined as NAN.


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

   * -  Argument
     -  Result
     -  Error Code
   * -  ``x`` < +0
     -  QNAN
     -  ``status::errdom``
   * -  +0
     -  +\ :math:`\infty`
     -  ``status::sing``
   * -  -0
     -  +\ :math:`\infty`
     -  ``status::sing``
   * -  +\ :math:`\infty`
     -  +0
     -   
   * -  -\ :math:`\infty`
     -  QNAN
     -  ``status::errdom``
   * -  QNAN
     -  QNAN
     -   
   * -  SNAN
     -  QNAN
     -   


API
***


Syntax
------

**Buffer API**


.. code-block:: cpp

   namespace oneapi::mkl::vm {

   sycl::event expint1(sycl::queue & exec_queue,
         std::int64_t n,
         sycl::buffer<T> & a,
         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 expint1(sycl::queue & exec_queue,
         sycl::buffer<T> & a,
         oneapi::mkl::slice sa,
         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 expint1(sycl::queue & exec_queue,
         std::int64_t n,
         T const * a,
         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 expint1(sycl::queue & exec_queue,
         T const * a,
         oneapi::mkl::slice sa,
         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 = {});

   }




``expint1`` supports the following precisions and devices:


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

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


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 input vector.


sa
   Slice selector for ``a``. 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 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.


**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 input vector.


sa
   Slice selector for ``a``. 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 ``expint1`` can be found in the |O-MKL|
installation directory, under:


.. code-block::


   examples/dpcpp/vml/source/vexpint1.cpp