.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation
..
.. SPDX-License-Identifier: CC-BY-4.0

.. _onemath_rng_r250:

r250
====

The 32-bit generalized feedback shift register pseudorandom number generator GFSR(250,103) :ref:`[Kirkpatrick81] <onemath_rng_bibliography>`.

.. _onemath_rng_r250_description:

.. rubric:: Description

Feedback shift register generators possess ample theoretical foundation and were initially intended for cryptographic and communication applications. The stream state is the array of 250 32-bit integers.

.. container:: section

    .. rubric:: Generation algorithm


    :math:`x_n=x_{n-103} \oplus x_{n-250}`

    :math:`u_n=x_n / 2 ^ {32}`


.. _onemath_rng_r250_description_syntax:

class r250
----------

.. rubric:: Syntax

.. code-block:: cpp

    namespace oneapi::math::rng {
    class r250 {
    public:
        static constexpr std::uint32_t default_seed = 1;

        r250(sycl::queue queue, std::uint32_t seed = default_seed);

        r250(sycl::queue queue, std::vector<std::uint32_t> seed);

        r250(const r250& other);

        r250(r250&& other);

        r250& operator=(const r250& other);

        r250& operator=(r250&& other);

        ~r250();
    };
    }

.. container:: section

    .. rubric:: Class Members

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

        * - Routine
          - Description
        * - `r250(sycl::queue queue, std::uint32_t seed = default_seed)`_
          - Constructor for common seed initialization of the engine
        * - `r250(sycl::queue queue, std::vector<std::uint32_t> seed)`_
          - Constructor for extended seed initialization of the engine
        * - `r250(const r250& other)`_
          - Copy constructor
        * - `r250(r250&& other)`_
          - Move constructor
        * - `r250& operator=(const r250& other)`_
          - Copy assignment operator
        * - `r250& operator=(r250&& other)`_
          - Move assignment operator

.. container:: section

    .. rubric:: Constructors

    .. _`r250(sycl::queue queue, std::uint32_t seed = default_seed)`:

    .. code-block:: cpp
    
        r250::r250(sycl::queue queue, std::uint32_t seed = default_seed)

    .. container:: section

        .. rubric:: Input Parameters

        queue
            Valid sycl::queue object, calls of the :ref:`oneapi::math::rng::generate()<onemath_rng_generate>` routine submits kernels in this queue to obtain random numbers from a given engine.

        seed
            The initial conditions of the generator state, assume :math:`x_{-250} = seed`. If :math:`seed = 0`, assume :math:`seed = 1`. Other values in state are initialized according to recurrent correlation :math:`x_{n+1} = 69069x_{n}(mod \ 2 ^ {32})`. Then the values :math:`x_{7k-247}, k = 0, 1, ..., 31` are interpreted as a binary matrix of size 32 x 32 and diagonal bits are set to 0, the under-diagonal bits to 0.

    .. _`r250(sycl::queue queue, std::vector<std::uint32_t> seed)`:

    .. code-block:: cpp
    
        r250::r250(sycl::queue queue, std::vector<std::uint32_t> seed)

    .. container:: section

        .. rubric:: Input Parameters

        queue
            Valid ``sycl::queue`` object, calls of the :ref:`oneapi::math::rng::generate()<onemath_rng_generate>` routine submits kernels in this queue to obtain random numbers from a given engine.

        seed
            The initial conditions of the generator state
            if :math:`n \geqslant 0: x_{k-250} = seed[k], k = 0, 1, ..., 249`

    .. _`r250(const r250& other)`:

    .. code-block:: cpp
    
        r250::r250(const r250& other)

    .. container:: section

        .. rubric:: Input Parameters

        other
            Valid ``r250`` object. The ``queue`` and state of the other engine is copied and applied to the current engine.

    .. _`r250(r250&& other)`:

    .. code-block:: cpp

        r250::r250(r250&& other)

    .. container:: section

        .. rubric:: Input Parameters

        other
            Valid ``r250`` object. The ``queue`` and state of the other engine is moved to the current engine.

    .. _`r250& operator=(const r250& other)`:

    .. code-block:: cpp

        r250::r250& operator=(const r250& other)

    .. container:: section

        .. rubric:: Input Parameters

        other
            Valid ``r250`` object. The ``queue`` and state of the other engine is copied and applied to the current engine.

    .. _`r250& operator=(r250&& other)`:

    .. code-block:: cpp

        r250::r250& operator=(r250&& other)

    .. container:: section

        .. rubric:: Input Parameters

        other
            Valid ``r250`` r-value object. The ``queue`` and state of the other engine is moved to the current engine.

**Parent topic:** :ref:`onemath_rng_engines_basic_random_number_generators`