.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_rng_distributions: Host Distributions ================== .. container:: oneMath RNG routines are used to generate random numbers with different types of distribution. Each function group is introduced below by the type of underlying distribution and contains a short description of its functionality, as well as specifications of the call sequence and the explanation of input and output parameters. `Table Continuous Distribution Generators`_ and `Table Discrete Distribution Generators`_ list the random number generator routines with data types and output distributions, and sets correspondence between data types of the generator routines and the basic random number generators. _`Table Continuous Distribution Generators` .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Routine - Description * - \ :ref:`onemath_rng_uniform_continuous`\ - Uniform continuous distribution on the interval [``a,b``) * - \ :ref:`onemath_rng_gaussian`\ - Normal (Gaussian) distribution * - \ :ref:`onemath_rng_exponential`\ - Exponential distribution * - \ :ref:`onemath_rng_laplace`\ - Laplace distribution (double exponential distribution) * - \ :ref:`onemath_rng_weibull`\ - Weibull distribution * - \ :ref:`onemath_rng_cauchy`\ - Cauchy distribution * - \ :ref:`onemath_rng_rayleigh`\ - Rayleigh distribution * - \ :ref:`onemath_rng_lognormal`\ - Lognormal distribution * - \ :ref:`onemath_rng_gumbel`\ - Gumbel (extreme value) distribution * - \ :ref:`onemath_rng_gamma`\ - Gamma distribution * - \ :ref:`onemath_rng_beta`\ - Beta distribution * - \ :ref:`onemath_rng_chi_square`\ - Chi-Square distribution * - \ :ref:`onemath_rng_gaussian_mv`\ - Normal Multivariate (Gaussian Multivariate) distribution _`Table Discrete Distribution Generators` .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Type of Distribution - Description * - \ :ref:`onemath_rng_uniform_discrete`\ - Uniform discrete distribution on the interval [``a,b``) * - \ :ref:`onemath_rng_uniform_bits`\ - Uniformly distributed bits in 32/64-bit chunks * - \ :ref:`onemath_rng_bits`\ - Bits of underlying BRNG integer recurrence * - \ :ref:`onemath_rng_bernoulli`\ - Bernoulli distribution * - \ :ref:`onemath_rng_geometric`\ - Geometric distribution * - \ :ref:`onemath_rng_binomial`\ - Binomial distribution * - \ :ref:`onemath_rng_hypergeometric`\ - Hypergeometric distribution * - \ :ref:`onemath_rng_poisson`\ - Poisson distribution * - \ :ref:`onemath_rng_poisson_v`\ - Poisson distribution with varying mean * - \ :ref:`onemath_rng_negative_binomial`\ - Negative binomial distribution, or Pascal distribution * - \ :ref:`onemath_rng_multinomial`\ - Multinomial distribution .. container:: section .. rubric:: Modes of random number generation The library provides two modes of random number generation, accurate and fast. Accurate generation mode is intended for applications that are highly demanding to accuracy of calculations. When used in this mode, the generators produce random numbers lying completely within the definitional domain for all values of the distribution parameters. For example, random numbers obtained from the generator of continuous distribution that is uniform on interval [``a``,\ ``b``] belong to this interval irrespective of what ``a`` and ``b`` values may be. Fast mode provides high performance generation and also guarantees that generated random numbers belong to the definitional domain except for some specific values of distribution parameters. The generation mode is set by specifying the relevant value of the method parameter in generator routines. The list of distributions that support accurate mode of generation is given in the table below. _`Table Distribution Generators with Accurate Method` .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Distribution - Method * - \ :ref:`onemath_rng_uniform_continuous`\ - `oneapi::math::rng::unform_method::accurate` * - \ :ref:`onemath_rng_exponential`\ - `oneapi::math::rng::exponential_method::icdf_accurate` * - \ :ref:`onemath_rng_weibull`\ - `oneapi::math::rng::weibull_method::icdf_accurate` * - \ :ref:`onemath_rng_rayleigh`\ - `oneapi::math::rng::rayleigh_method::icdf_accurate` * - \ :ref:`onemath_rng_lognormal`\ - `oneapi::math::rng::lognormal_method::box_muller2_accurate`, `oneapi::math::rng::lognormal_method::icdf_accurate` * - \ :ref:`onemath_rng_gamma`\ - `oneapi::math::rng::gamma_method::marsaglia_accurate` * - \ :ref:`onemath_rng_beta`\ - `oneapi::math::rng::beta_method::cja_accurate`   **Parent topic:** :ref:`onemath_rng_manual_offload_routines` .. toctree:: :hidden: distributions-template-parameter-onemath-rng-method-values onemath-rng-uniform-continuous onemath-rng-gaussian onemath-rng-exponential onemath-rng-laplace onemath-rng-weibull onemath-rng-cauchy onemath-rng-rayleigh onemath-rng-lognormal onemath-rng-gumbel onemath-rng-gamma onemath-rng-beta onemath-rng-chi_square onemath-rng-gaussian_mv onemath-rng-uniform-discrete onemath-rng-uniform_bits onemath-rng-bits onemath-rng-bernoulli onemath-rng-geometric onemath-rng-binomial onemath-rng-hypergeometric onemath-rng-poisson onemath-rng-poisson_v onemath-rng-negbinomial onemath-rng-multinomial