[oneDPL][RNG][Spec] Added the extensions sections (uxlfoundation#492)

* [oneDPL][RNG][Spec] Added the extensions sections

* Applying the comments

* Applying changes from Alexey

* Fixing the lines lengthexey

* Fix of the line

* Applying the comments from Ruslan

source/elements/oneDPL/source/sycl_kernels_api.rst

@@ -14,14 +14,16 @@ CPU-based platform.
 
 .. _`C++ Standard`: https://isocpp.org/std/the-standard
 
+
 Random Number Generation
 ++++++++++++++++++++++++
 
 oneDPL provides a subset of the standard C++ pseudo-random number generation functionality
-suitable to use within SYCL kernels. The APIs are defined in the :code:`<oneapi/dpl/random>` header. 
+suitable to use within SYCL kernels. The APIs are defined in the :code:`<oneapi/dpl/random>` header.
 
 Supported functionality:
 ------------------------
+
 - Engine class templates:
  - ``linear_congruential_engine``
  - ``subtract_with_carry_engine``
@@ -46,17 +48,112 @@ Supported functionality:
  - ``cauchy_distribution``
  - ``extreme_value_distribution``
 
-Additionally, ``sycl::vec<>`` can be used as the result type for engines, engine adaptors, and distributions.
+``linear_congruential_engine`` and ``subtract_with_carry_engine`` satisfy the uniform random bit generator requirements.
 
 Limitations:
 ------------
+
 The following deviations from the `C++ Standard`_ may apply:
 
 - ``random_device`` and ``seed_seq`` classes and related APIs in other classes are not required;
 - ``operator>>()``, ``operator<<()``, ``operator==()`` are not required;
 - specifying the size of a random number engine's state is not required;
 - distributions are only required to operate with floating point types applicable to supported SYCL devices.
 
+Extensions:
+-----------
+
+As an extension to the `C++ Standard`_, ``sycl::vec<Type, N>`` can be used as the data type template parameter for
+engines, engine adaptors, and distributions, where ``Type`` is one of data types supported by the corresponding
+class template in the standard. For such template instantiations, the ``result_type`` is also defined to
+``sycl::vec<Type, N>``.
+
+Engines, engine adaptors, and distributions additionally define ``scalar_type``, equivalent to the following:
+
+- ``using scalar_type = typename result_type::element_type;`` if ``result_type`` is ``sycl::vec<Type, N>``,
+- otherwise, ``using scalar_type = result_type;``
+
+The ``scalar_type`` is used instead of ``result_type`` in all contexts where a scalar data type is expected, including
+
+- the type of configuration parameters and properties,
+- the seed value type,
+- the input parameters of constructors,
+- the return value type of ``min()`` and ``max()`` methods, etc.
+
+Since ``scalar_type`` is the same as ``result_type`` except for template instantiations with ``sycl::vec``,
+class templates still meet the applicable requirements of the `C++ Standard`_.
+
+When instantiated with ``sycl::vec<Type,N>``, ``linear_congruential_engine`` and ``subtract_with_carry_engine`` may not
+formally satisfy the uniform random bit generator requirements defined by the `C++ Standard`_. Instead, the following
+alternative requirements apply: for an engine object ``g`` of type ``G``,
+
+- ``G::scalar_type`` is an unsigned integral type same as ``sycl::vec<Type,N>::element_type``,
+- ``G::min()`` and ``G::max()`` return a value of ``G::scalar_type``,
+- for each index ``i`` in the range [``0``, ``N``), ``G::min() <= g()[i]`` and ``g()[i] <= G::max()``.
+
+Effectively, these engines satisfy the standard *uniform random bit generator* requirements for each element
+of a ``sycl::vec`` returned by their ``operator()``.
+
+Similarly, for a distribution object ``d`` of a type ``D`` that is a template instantiated with ``sycl::vec<Type,N>``:
+
+- ``D::scalar_type`` is the same as ``sycl::vec<Type,N>::element_type``,
+- ``D::min()`` and ``D::max()`` return a value of ``D::scalar_type``, and ``D::min() <= D::max()``,
+- ``operator()`` of a distribution returns a ``sycl::vec<Type,N>`` filled with random values
+ in the closed interval ``[D::min(), D::max()]``;
+
+The following engines and engine adaptors with predefined parameters are defined:
+
+.. code:: cpp
+
+ template <int N>
+ using minstd_rand0_vec = linear_congruential_engine<sycl::vec<::std::uint_fast32_t, N>, 16807, 0, 2147483647>;
+
+ template <int N>
+ using minstd_rand_vec = linear_congruential_engine<sycl::vec<uint_fast32_t, N>, 48271, 0, 2147483647>;
+
+ template <int N>
+ using ranlux24_base_vec = subtract_with_carry_engine<sycl::vec<uint_fast32_t, N>, 24, 10, 24>;
+
+ template <int N>
+ using ranlux48_base_vec = subtract_with_carry_engine<sycl::vec<uint_fast64_t, N>, 48, 5, 12>;
+
+ template <int N>
+ using ranlux24_vec = discard_block_engine<ranlux24_base_vec<N>, 223, 23>;
+
+ template <int N>
+ using ranlux48_vec = discard_block_engine<ranlux48_base_vec<N>, 389, 11>;
+
+Except for producing a ``sycl::vec`` of random values per invocation, the behavior of these engines is equivalent to
+the corresponding scalar engines, as described in the following table:
+
+.. container:: tablenoborder
+
+ .. list-table::
+ :header-rows: 1
+
+ * - Engines and engine adaptors based on ``sycl::vec<>``
+ - C++ standard analogue
+ - The 10000th scalar random value consecutively produced by a default-constructed object
+ * - ``minstd_rand0_vec``
+ - ``minstd_rand0``
+ - 1043618065
+ * - ``minstd_rand_vec``
+ - ``minstd_rand``
+ - 399268537
+ * - ``ranlux24_base_vec``
+ - ``ranlux24_base``
+ - 7937952
+ * - ``ranlux48_base_vec``
+ - ``ranlux48_base``
+ - 61839128582725
+ * - ``ranlux24_vec``
+ - ``ranlux24``
+ - 9901578
+ * - ``ranlux48_vec``
+ - ``ranlux48``
+ - 1112339016
+
+
 Function Objects
 ++++++++++++++++
 
@@ -75,5 +172,5 @@ The oneDPL function objects are defined in the :code:`<oneapi/dpl/functional>` h
  }
  }
 
-The :code:`oneapi::dpl::identity` class implements an identity operation. Its function operator 
+The :code:`oneapi::dpl::identity` class implements an identity operation. Its function operator
 receives an instance of a type and returns the argument unchanged.