[oneMath][RNG] Make number of generators for MT2203 be implementation defined (#618)

* Made the number of engines to be implementation defined

* engines -> generators

* Update engines-basic-random-number-generators.rst

* fixed the link

Author: andreyfe1

source/elements/oneMath/source/domains/rng/host_api/engines-basic-random-number-generators.rst

@@ -40,7 +40,7 @@ Host Engines (Basic Random Number Generators)
          * -                      \ :ref:`onemath_rng_mt19937`\
            -     Mersenne Twister pseudorandom number generator       ``MT19937``\ :ref:`[Matsumoto98] <onemath_rng_bibliography>`      with period length 2\ :sup:`19937`-1 of the produced sequence
          * -                      \ :ref:`onemath_rng_mt2203`\
-           -     Set of 6024 Mersenne Twister pseudorandom number       generators      ``MT2203``\ :ref:`[Matsumoto98] <onemath_rng_bibliography>`,      :ref:`[Matsumoto00] <onemath_rng_bibliography>`.      Each of them generates a sequence of period length equal to      2\ :sup:`2203`-1. Parameters of the generators provide mutual      independence of the corresponding sequences.
+           -     Set of Mersenne Twister pseudorandom number       generators      ``MT2203``\ :ref:`[Matsumoto98] <onemath_rng_bibliography>`,      :ref:`[Matsumoto00] <onemath_rng_bibliography>`.      Each of them generates a sequence of period length equal to      2\ :sup:`2203`-1. Parameters of the generators provide mutual      independence of the corresponding sequences.
          * -                      \ :ref:`onemath_rng_sfmt19937`\
            -     SIMD-oriented Fast Mersenne Twister pseudorandom       number generator      ``SFMT19937``\ :ref:`[Saito08] <onemath_rng_bibliography>`      with a period length equal to 2\ :sup:`19937`-1 of the produced      sequence.
          * -                      \ :ref:`onemath_rng_sobol`\
@@ -62,8 +62,8 @@ Host Engines (Basic Random Number Generators)
    description of these functions can be found in the :ref:`onemath_rng_service_routines` section.
 
 
-   In addition, the MT2203 pseudorandom number generator is a set of 6024
-   generators designed to create up to 6024 independent random
+   In addition, the MT2203 pseudorandom number generator is a set of
+   generators designed to create independent random
    sequences, which might be used in parallel Monte Carlo simulations.
    Another generator that has the same feature is Wichmann-Hill. It
    allows creating up to 273 independent random streams. The properties
@@ -107,7 +107,7 @@ Host Engines (Basic Random Number Generators)
       SFMT19937 [Saito08] with a period length equal to
       2\ :sup:`19937`-1 of the produced sequence.
    -  :ref:`onemath_rng_mt2203`
-      Set of 6024 Mersenne Twister pseudorandom number generators MT2203
+      Set of Mersenne Twister pseudorandom number generators MT2203
       [Matsumoto98], [Matsumoto00]. Each of them generates a sequence of
       period length equal to 2\ :sup:`2203`-1. Parameters of the
       generators provide mutual independence of the corresponding

source/elements/oneMath/source/domains/rng/host_api/onemath-rng-mt2203.rst

@@ -7,19 +7,21 @@
 mt2203
 ======
 
-The mt2203 engine is the set of 6024 Mersenne Twister pseudorandom number generators MT2203 [:ref:`Matsumoto98 <onemath_rng_bibliography>`], [:ref:`Matsumoto00 <onemath_rng_bibliography>`].
+The mt2203 engine is the set of Mersenne Twister pseudorandom number generators MT2203 [:ref:`Matsumoto98 <onemath_rng_bibliography>`], [:ref:`Matsumoto00 <onemath_rng_bibliography>`].
+Coefficients are obtained by `the following tool`_. The amount of generators in the set (denoted `n_engines`) is implementation defined.
 
 .. _onemath_rng_mt2203_description:
 
 .. rubric:: Description
 
-The set of 6024 basic pseudorandom number generators MT2203 is a natural addition to the MT19937 generator. MT2203 generators are intended for use in large scale Monte Carlo simulations performed on multi-processor computer systems.
+The set of basic pseudorandom number generators MT2203 is a natural addition to the MT19937 generator.
+MT2203 generators are intended for use in large scale Monte Carlo simulations performed on multi-processor computer systems.
 
 .. container:: section
 
     .. rubric:: Generation algorithm
 
-    For :math:`j = 1,..., 6024`:
+    For :math:`j = 1,..., n_engines`:
 
     :math:`x_{n, j} =x_{n - (69 - 34), j} \oplus ( (x_{n - 69, j} \& 0xFFFFFFE0) | (x_{n + 69 + 1, j} \& 0x1F) ) A_{j}`
 
@@ -140,14 +142,14 @@ class mt2203
             The initial conditions of the generator state. The initialization algorithm described in [:ref:`MT2203 <onemath_rng_bibliography>`].
 
         engine_idx
-            The index of the set 1, ..., 6024.
+            The index of the set 1, ..., n_engines.
 
     .. container:: section
 
         .. rubric:: Throws
 
         oneapi::math::invalid_argument
-            Exception is thrown when :math:`idx > 6024`
+            Exception is thrown when :math:`idx > n_engines`
 
     .. _`mt2203(sycl::queue queue, std::initializer_list<std::uint32_t> seed)`:
 
@@ -182,7 +184,7 @@ class mt2203
             The initial conditions of the generator state. The initialization algorithm described in [:ref:`MT2203 <onemath_rng_bibliography>`].
 
         engine_idx
-            The index of the set 1, ..., 6024.
+            The index of the set 1, ..., n_engines.
 
     .. _`mt2203(const mt2203& other)`:
 
@@ -237,3 +239,5 @@ class mt2203
             Valid ``mt2203`` 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`
+
+.. _`the following tool`: https://www.math.sci.hiroshima-u.ac.jp/m-mat/MT/DC/dc.html