.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_rng_engines_basic_random_number_generators: Host Engines (Basic Random Number Generators) ============================================= .. container:: oneMath 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:`onemath_rng_default_engine`\ - The default random engine * - \ :ref:`onemath_rng_mrg32k3a`\ - The combined multiple recursive pseudorandom number generator ``MRG32k3a``\ :ref:`[L'Ecuyer99a] `\ * - \ :ref:`onemath_rng_philox4x32x10`\ - Philox4x32-10 counter-based pseudorandom number generator with a period of 2\ :sup:`128`\ ``PHILOX4X32X10``\ :ref:`[Salmon11] `\ * - \ :ref:`onemath_rng_mcg31m1`\ - The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 231 -1) :ref:`[L'Ecuyer99] `\ * - \ :ref:`onemath_rng_r250`\ - The 32-bit generalized feedback shift register pseudorandom number generator ``GFSR(250,103)``\ :ref:`[Kirkpatrick81] `\ * - \ :ref:`onemath_rng_mcg59`\ - The 59-bit multiplicative congruential pseudorandom number generator ``MCG(13``\ :sup:`13`\ ``, 2``\ :sup:`59`) from NAG Numerical Libraries :ref:`[NAG] `\ * - \ :ref:`onemath_rng_wichmann_hill`\ - Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries :ref:`[NAG] `\ * - \ :ref:`onemath_rng_mt19937`\ - Mersenne Twister pseudorandom number generator ``MT19937``\ :ref:`[Matsumoto98] ` with period length 2\ :sup:`19937`-1 of the produced sequence * - \ :ref:`onemath_rng_mt2203`\ - Set of 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:`onemath_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:`onemath_rng_sobol`\ - Sobol quasi-random number generator :ref:`[Sobol76] `, :ref:`[Bratley88] `, which works in arbitrary dimension. * - \ :ref:`onemath_rng_niederreiter`\ - Niederreiter quasi-random number generator :ref:`[Bratley92] `, which works in arbitrary dimension. * - \ :ref:`onemath_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:`onemath_rng_nondeterministic`\ - Non-deterministic random number generator \ For some basic generators, oneMath 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:`onemath_rng_service_routines` section. 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 of the generators designed for parallel computations are discussed in detail in [:ref:`Coddington94 `]. **Parent topic:** :ref:`onemath_rng_manual_offload_routines` .. container:: - :ref:`onemath_rng_default_engine` The default random engine (implementation defined) - :ref:`onemath_rng_mrg32k3a` The combined multiple recursive pseudorandom number generator MRG32k3a [ L'Ecuyer99a] - :ref:`onemath_rng_philox4x32x10` A Philox4x32-10 counter-based pseudorandom number generator. [Salmon11]. - :ref:`onemath_rng_mcg31m1` The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 231 -1) [L'Ecuyer99] - :ref:`onemath_rng_mcg59` The 59-bit multiplicative congruential pseudorandom number generator MCG(1313, 259) from NAG Numerical Libraries [NAG]. - :ref:`onemath_rng_r250` The 32-bit generalized feedback shift register pseudorandom number generator GFSR(250,103)[Kirkpatrick81]. - :ref:`onemath_rng_wichmann_hill` Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries [NAG]. - :ref:`onemath_rng_mt19937` Mersenne Twister pseudorandom number generator MT19937 [Matsumoto98] with period length 2\ :sup:`19937`-1 of the produced sequence. - :ref:`onemath_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:`onemath_rng_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 sequences.. - :ref:`onemath_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:`onemath_rng_sobol` Sobol quasi-random number generator [Sobol76], [Bratley88], which works in arbitrary dimension. - :ref:`onemath_rng_niederreiter` Niederreiter quasi-random number generator [Bratley92], which works in arbitrary dimension. - :ref:`onemath_rng_nondeterministic` Non-deterministic random number generator. .. toctree:: :hidden: onemath-rng-default_engine onemath-rng-mrg32k3a onemath-rng-philox4x32x10 onemath-rng-mcg31m1 onemath-rng-mcg59 onemath-rng-r250 onemath-rng-wichmann_hill onemath-rng-mt19937 onemath-rng-sfmt19937 onemath-rng-mt2203 onemath-rng-ars5 onemath-rng-sobol onemath-rng-niederreiter onemath-rng-nondeterministic