.. _engines-basic-random-number-generators:

Engines (Basic Random Number Generators)
========================================


|O-MKL| RNG provides pseudorandom, quasi-random, and
non-deterministic random number generators for Data Parallel C++:

.. tabularcolumns:: |\Y{0.4}|\Y{0.6}|

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

   * -  Routine
     -  Description
   * -  :ref:`oneapi-mkl-rng-mrg32k3a`
     -  The combined multiple recursive pseudorandom number generator ``MRG32k3a`` :ref:`[L'Ecuyer99a] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-philox4x32x10`
     -  Philox4x32-10 counter-based pseudorandom number generator with a period of 2\ :sup:`128`  ``PHILOX4X32X10`` :ref:`[Salmon11] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-mcg31m1`
     -  The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 2\ :sup:`32` -1) :ref:`[L'Ecuyer99a] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-r250`
     -  The 32-bit generalized feedback shift register pseudorandom number generator ``GFSR(250,103)`` :ref:`[Kirkpatrick81] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-mcg59`
     -  The 59-bit multiplicative congruential pseudorandom number generator ``MCG(13``\ :sup:`13`\ ``, 2``\ :sup:`59`) from NAG Numerical Libraries :ref:`[NAG] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-wichmann_hill`
     -  Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries :ref:`[NAG] <bibliography>`
   * -  :ref:`oneapi-mkl-rng-mt19937`
     -  Mersenne Twister pseudorandom number generator ``MT19937``:ref:`[Matsumoto98] <bibliography>` with period length 2\ :sup:`19937`-1 of the produced sequence
   * -  :ref:`oneapi-mkl-rng-mt2203`
     -   Set of 6024 Mersenne Twister pseudorandom number generators ``MT2203`` :ref:`[Matsumoto98] <bibliography>`, :ref:`[Matsumoto00] <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:`oneapi-mkl-rng-sfmt19937`
     -  SIMD-oriented Fast Mersenne Twister pseudorandom number generator ``SFMT19937`` :ref:`[Saito08] <bibliography>` with a period length equal to 2\ :sup:`19937`-1 of the produced sequence.
   * -  :ref:`oneapi-mkl-rng-sobol`
     -  Sobol quasi-random number generator :ref:`[Sobol76] <bibliography>`, :ref:`[Bratley88] <bibliography>`, which works in arbitrary dimension.
   * -  :ref:`oneapi-mkl-rng-niederreiter`
     -   Niederreiter quasi-random number generator :ref:`[Bratley92] <bibliography>`, which works in arbitrary dimension.
   * -  :ref:`oneapi-mkl-rng-ars5`
     -  ARS-5 counter-based pseudorandom number generator with a period of 2\ :sup:`128`, which uses instructions from the AES-NI set ``ARS5`` :ref:`[Salmon11] <bibliography>`.
   * -  :ref:`oneapi-mkl-rng-nondeterministic`
     -  Non-deterministic random number generator (RDRAND-based) :ref:`[AVX] <bibliography>`, :ref:`[IntelSWMan] <bibliography>`

For some basic generators, |O-MKL| RNG provides two methods of creating independent states in multiprocessor computations, which are the leapfrog method and the block-splitting method. These sequence splitting methods are also useful in sequential Monte Carlo. The description of these functions can be found in the :ref:`service-routines` section.


In addition, MT2203 pseudorandom number generator is a set of 6024 generators designed to create up to 6024 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 of the generators designed for parallel computations are discussed in detail in :ref:`[Coddington94] <bibliography>`.


See :ref:`VS Notes <bibliography>` for the detailed description.

.. toctree::
   :maxdepth: 1
   :hidden:

   oneapi-mkl-rng-mrg32k3a
   oneapi-mkl-rng-philox4x32x10
   oneapi-mkl-rng-mcg31m1
   oneapi-mkl-rng-mcg59
   oneapi-mkl-rng-r250
   oneapi-mkl-rng-wichmann_hill
   oneapi-mkl-rng-mt19937
   oneapi-mkl-rng-sfmt19937
   oneapi-mkl-rng-mt2203
   oneapi-mkl-rng-ars5
   oneapi-mkl-rng-sobol
   oneapi-mkl-rng-niederreiter
   oneapi-mkl-rng-nondeterministic