.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_rng_engines_basic_random_number_generators: Host Engines (Basic Random Number Generators) ============================================= .. container:: oneMKL RNG provides pseudorandom, quasi-random, and non-deterministic random number generators for Data Parallel C++: .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Routine - Description * - \ :ref:`onemkl_rng_default_engine`\ - The default random engine * - \ :ref:`onemkl_rng_mrg32k3a`\ - The combined multiple recursive pseudorandom number generator ``MRG32k3a``\ :ref:`[L'Ecuyer99a] `\ * - \ :ref:`onemkl_rng_philox4x32x10`\ - Philox4x32-10 counter-based pseudorandom number generator with a period of 2\ :sup:`128`\ ``PHILOX4X32X10``\ :ref:`[Salmon11] `\ * - \ :ref:`onemkl_rng_mcg31m1`\ - The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 231 -1) :ref:`[L'Ecuyer99] `\ * - \ :ref:`onemkl_rng_r250`\ - The 32-bit generalized feedback shift register pseudorandom number generator ``GFSR(250,103)``\ :ref:`[Kirkpatrick81] `\ * - \ :ref:`onemkl_rng_mcg59`\ - The 59-bit multiplicative congruential pseudorandom number generator ``MCG(13``\ :sup:`13`\ ``, 2``\ :sup:`59`) from NAG Numerical Libraries :ref:`[NAG] `\ * - \ :ref:`onemkl_rng_wichmann_hill`\ - Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries :ref:`[NAG] `\ * - \ :ref:`onemkl_rng_mt19937`\ - Mersenne Twister pseudorandom number generator ``MT19937``\ :ref:`[Matsumoto98] ` with period length 2\ :sup:`19937`-1 of the produced sequence * - \ :ref:`onemkl_rng_mt2203`\ - Set of 6024 Mersenne Twister pseudorandom number generators ``MT2203``\ :ref:`[Matsumoto98] `, :ref:`[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 sequences. * - \ :ref:`onemkl_rng_sfmt19937`\ - SIMD-oriented Fast Mersenne Twister pseudorandom number generator ``SFMT19937``\ :ref:`[Saito08] ` with a period length equal to 2\ :sup:`19937`-1 of the produced sequence. * - \ :ref:`onemkl_rng_sobol`\ - Sobol quasi-random number generator :ref:`[Sobol76] `, :ref:`[Bratley88] `, which works in arbitrary dimension. * - \ :ref:`onemkl_rng_niederreiter`\ - Niederreiter quasi-random number generator :ref:`[Bratley92] `, which works in arbitrary dimension. * - \ :ref:`onemkl_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] `. * - \ :ref:`onemkl_rng_nondeterministic`\ - Non-deterministic random number generator \ For some basic generators, oneMKL 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:`onemkl_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 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 `]. **Parent topic:** :ref:`onemkl_rng_manual_offload_routines` .. container:: - :ref:`onemkl_rng_default_engine` The default random engine (implementation defined) - :ref:`onemkl_rng_mrg32k3a` The combined multiple recursive pseudorandom number generator MRG32k3a [ L'Ecuyer99a] - :ref:`onemkl_rng_philox4x32x10` A Philox4x32-10 counter-based pseudorandom number generator. [Salmon11]. - :ref:`onemkl_rng_mcg31m1` The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 231 -1) [L'Ecuyer99] - :ref:`onemkl_rng_mcg59` The 59-bit multiplicative congruential pseudorandom number generator MCG(1313, 259) from NAG Numerical Libraries [NAG]. - :ref:`onemkl_rng_r250` The 32-bit generalized feedback shift register pseudorandom number generator GFSR(250,103)[Kirkpatrick81]. - :ref:`onemkl_rng_wichmann_hill` Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries [NAG]. - :ref:`onemkl_rng_mt19937` Mersenne Twister pseudorandom number generator MT19937 [Matsumoto98] with period length 2\ :sup:`19937`-1 of the produced sequence. - :ref:`onemkl_rng_sfmt19937` SIMD-oriented Fast Mersenne Twister pseudorandom number generator SFMT19937 [Saito08] with a period length equal to 2\ :sup:`19937`-1 of the produced sequence. - :ref:`onemkl_rng_mt2203` Set of 6024 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 sequences.. - :ref:`onemkl_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[Salmon11]. - :ref:`onemkl_rng_sobol` Sobol quasi-random number generator [Sobol76], [Bratley88], which works in arbitrary dimension. - :ref:`onemkl_rng_niederreiter` Niederreiter quasi-random number generator [Bratley92], which works in arbitrary dimension. - :ref:`onemkl_rng_nondeterministic` Non-deterministic random number generator. .. toctree:: :hidden: mkl-rng-default_engine mkl-rng-mrg32k3a mkl-rng-philox4x32x10 mkl-rng-mcg31m1 mkl-rng-mcg59 mkl-rng-r250 mkl-rng-wichmann_hill mkl-rng-mt19937 mkl-rng-sfmt19937 mkl-rng-mt2203 mkl-rng-ars5 mkl-rng-sobol mkl-rng-niederreiter mkl-rng-nondeterministic