.. _oneapi-mkl-rng-device-uniform-discrete:

oneapi::mkl::rng::device::uniform (Discrete)
============================================


Generates random numbers uniformly distributed over the interval ``[a, b)``.


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

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

The ``oneapi::mkl::rng::device::uniform`` class object is used in ``oneapi::mkl::rng::device::generate`` functions to provide random numbers uniformly distributed over the interval ``[a, b)``, where ``a, b`` are the left and right bounds of the interval respectively, and ``a, b∈Z; a < b``.


The probability distribution is given by:

.. math::

   P(X = k) = \frac{1}{b-a},
   k \in \{a, a + 1, \ldots, b-1\}

The cumulative distribution function is as follows:

.. math::

   F_{a, b}(x) =
   \begin{cases}
       0, & x < a \\
       \frac{x-a + 1}{b-a}, & a \leq x < b \\
       1, & x \geq b
   \end{cases},
   x \in R


API
***


Syntax
------

.. code-block:: cpp


   template<typename Type, typename Method>
   class uniform<std::(u)int32_t, Method> {
   public:
   using method_type = Method;
   using result_type = Type;
   uniform(): uniform((Type)0,
                 std::is_same<Method,
                 uniform_method::standard>::value ? (1 << 23) :
                 std::numeric_limits<Type>::max()){};
   explicit uniform(Type a, Type b);
   explicit uniform(const param_type& pt);
   Type a() const;
   Type b() const;
   param_type param() const;
   void param(const param_type& pt);
   };


Include Files
-------------

- ``oneapi/mkl/rng/device.hpp``


Template Parameters
-------------------

.. list-table::
   :header-rows: 0

   * - ``typename Method``
     - Generation method. The specific values are as follows:

       ``oneapi::mkl::rng::device::uniform_method::standard``

       ``oneapi::mkl::rng::device::uniform_method::accurate``

       See brief descriptions of the methods in :ref:`distributions-template-parameter-method`.


.. note::
   The ``oneapi::mkl::rng::device::uniform_method::standard`` uses the ``s`` BRNG type. This might cause the produced numbers to have incorrect statistics (due to rounding error) when :math:`(abs(b – a) > 2^{23} || abs(b) > 2^{23} || abs(a) > 2^{23})`. To get proper statistics for this case, use the ``oneapi::mkl::rng::device::uniform_method::accurate`` method instead.


Input Parameters
----------------

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

   * - Name
     - Type
     - Description
   * - c
     - ``std::int32_t``

       ``std::uint32_t``
     - Left bound ``a``
   * - d
     - ``std::int32_t``

       ``std::uint32_t``
     - Right bound ``b``