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Distributions

oneMKL 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. The following tables 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.

Type of Distribution	Data Types	BRNG Data Type	Description
oneapi::mkl::rng::uniform (Continuous)	s, d	s, d	Uniform continuous distribution on the interval [a,b)
oneapi::mkl::rng::gaussian	s, d	s, d	Normal (Gaussian) distribution
oneapi::mkl::rng::gaussian_mv	s, d	s, d	Normal (Gaussian) multivariate distribution
oneapi::mkl::rng::exponential	s, d	s, d	Exponential distribution
oneapi::mkl::rng::laplace	s, d	s, d	Laplace distribution (double exponential distribution)
oneapi::mkl::rng::weibull	s, d	s, d	Weibull distribution
oneapi::mkl::rng::cauchy	s, d	s, d	Cauchy distribution
oneapi::mkl::rng::rayleigh	s, d	s, d	Rayleigh distribution
oneapi::mkl::rng::lognormal	s, d	s, d	Lognormal distribution
oneapi::mkl::rng::gumbel	s, d	s, d	Gumbel (extreme value) distribution
oneapi::mkl::rng::gamma	s, d	s, d	Gamma distribution
oneapi::mkl::rng::gamma	s, d	s, d	Beta distribution
oneapi::mkl::rng::chi_square	s, d	s, d	Chi-Square distribution

Type of Distribution	Data Types	BRNG Data Type	Description
oneapi::mkl::rng::uniform (Discrete)	i	GPU: s for oneapi::mkl::rng::uniform_method::standard, d for oneapi::mkl::rng::method::accurate CPU/Host: d for both methods	Uniform discrete distribution on the interval [a,b)
oneapi::mkl::rng::uniform_bits	i	i	Uniformly distributed bits in 32-bit chunks
	i	i	Uniformly distributed bits in 64-bit chunks
oneapi::mkl::rng::bits	i	i	Bits of underlying BRNG integer recurrence
oneapi::mkl::rng::bernoulli	i	s	Bernoulli distribution
oneapi::mkl::rng::geometric	i	s	Geometric distribution
oneapi::mkl::rng::binomial	i	d	Binomial distribution
oneapi::mkl::rng::hypergeometric	i	d	Hypergeometric distribution
oneapi::mkl::rng::poisson	i	s (for ) oneapi::mkl::rng::poisson_method::gaussian_icdf_based s (for distribution parameter ) and d (for ) (for oneapi::mkl::rng::poisson_method::ptpe)	Poisson distribution
oneapi::mkl::rng::poisson_v	i	d	Poisson distribution with varying mean
oneapi::mkl::rng::negative_binomial	i	d	Negative binomial distribution, or Pascal distribution
oneapi::mkl::rng::multinomial	i	CPU - s GPU - d	Multinomial distribution

Modes of Random Number Generation

The library provides two modes of random number generation, accurate and fast. Accurate generation mode is intended for the applications that are highly demanding to accuracy of calculations. When used in this mode, the generators produce random numbers lying completely within 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 of 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 relevant value of the method parameter in generator routines. List of distributions that support accurate mode of generation is given in the table below.

Distribution	Distribution Method
oneapi::mkl::rng::uniform (Discrete)	oneapi::mkl::rng::unform_method::accurate
oneapi::mkl::rng::exponential	oneapi::mkl::rng::exponential_method::icdf_accurate
oneapi::mkl::rng::weibull	oneapi::mkl::rng::weibull_method::icdf_accurate
oneapi::mkl::rng::rayleigh	oneapi::mkl::rng::rayleigh_method::icdf_accurate
oneapi::mkl::rng::lognormal	oneapi::mkl::rng::lognormal_method::icdf_accurate oneapi::mkl::rng::lognormal_method::box_muller2_accurate
oneapi::mkl::rng::gamma	oneapi::mkl::rng::gamma_method::marsaglia_accurate
oneapi::mkl::rng::gamma	oneapi::mkl::rng::beta_method::cja_accurate

oneapi::mkl::rng::get_state_size Distributions Template Parameter Method