Host Distributions

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

Routine	Description
uniform (continuous)	Uniform continuous distribution on the interval [a,b)
gaussian	Normal (Gaussian) distribution
exponential	Exponential distribution
laplace	Laplace distribution (double exponential distribution)
weibull	Weibull distribution
cauchy	Cauchy distribution
rayleigh	Rayleigh distribution
lognormal	Lognormal distribution
gumbel	Gumbel (extreme value) distribution
gamma	Gamma distribution
beta	Beta distribution
chi_square	Chi-Square distribution
gaussian_mv	Normal Multivariate (Gaussian Multivariate) distribution

Table Discrete Distribution Generators

Type of Distribution	Description
uniform (discrete)	Uniform discrete distribution on the interval [a,b)
uniform_bits	Uniformly distributed bits in 32/64-bit chunks
bits	Bits of underlying BRNG integer recurrence
bernoulli	Bernoulli distribution
geometric	Geometric distribution
binomial	Binomial distribution
hypergeometric	Hypergeometric distribution
poisson	Poisson distribution
poisson_v	Poisson distribution with varying mean
negative_binomial	Negative binomial distribution, or Pascal distribution
multinomial	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 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

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

Parent topic: Random Number Generators Host Routines