Distribution Generators

Intel MKL VSL 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 for both Fortran and C-interface 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.

Continuous Distribution Generators
Type of Distribution	Data Types	BRNG Data Type	Description
Uniform	s, d	s, d	Uniform continuous distribution on the interval [`a,b`].
Gaussian	s, d	s, d	Normal (Gaussian) distribution.
GaussianMV	s, d	s, d	Multivariate normal (Gaussian) distribution.
Exponential	s, d	s, d	Exponential distribution.
Laplace	s, d	s, d	Laplace distribution (double exponential distribution).
Weibull	s, d	s, d	Weibull distribution.
Cauchy	s, d	s, d	Cauchy distribution.
Rayleigh	s, d	s, d	Rayleigh distribution.
Lognormal	s, d	s, d	Lognormal distribution.
Gumbel	s, d	s, d	Gumbel (extreme value) distribution.
Gamma	s, d	s, d	Gamma distribution.
Beta	s, d	s, d	Beta distribution.

Discrete Distribution Generators
Type of Distribution	Data Types	BRNG Data Type	Description
Uniform	i	d	Uniform discrete distribution on the interval [`a,b`).
UniformBits	i	i	Generator of integer random values with uniform bit distribution.
Bernoulli	i	s	Bernoulli distribution.
Geometric	i	s	Geometric distribution.
Binomial	i	d	Binomial distribution.
Hypergeometric	i	d	Hypergeometric distribution.
Poisson	i	s (for VSL_RNG_METHOD_POISSON_POISNORM) s (for distribution parameter λ≥ 27) and d (for λ < 27) (for VSL_RNG_METHOD_POISSON_PTPE)	Poisson distribution.
PoissonV	i	s	Poisson distribution with varying mean.
NegBinomial	i	d	Negative binomial distribution, or Pascal 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 guaranties 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 Generators Supporting Accurate Mode
Type of Distribution	Data Types
Uniform	s, d
Exponential	s, d
Weibull	s, d
Rayleigh	s, d
Lognormal	s, d
Gamma	s, d
Beta	s, d

See additional details about accurate and fast mode of random number generation in VSL Notes.

New method names

The current version of Intel MKL has a modified structure of VSL RNG method names. (See RNG Naming Conventions for details.) The old names are kept for backward compatibility. The tables below set correspondence between the new and legacy method names for VSL random number generators.

Method Names for Continuous Distribution Generators
RNG	Legacy Method Name	New Method Name
Uniform	VSL_METHOD_SUNIFORM_STD, VSL_METHOD_DUNIFORM_STD, VSL_METHOD_SUNIFORM_STD_ACCURATE, VSL_METHOD_DUNIFORM_STD_ACCURATE	VSL_RNG_METHOD_UNIFORM_STD, VSL_RNG_METHOD_UNIFORM_STD_ACCURATE
Gaussian	VSL_METHOD_SGAUSSIAN_BOXMULLER, VSL_METHOD_SGAUSSIAN_BOXMULLER2, VSL_METHOD_SGAUSSIAN_ICDF, VSL_METHOD_DGAUSSIAN_BOXMULLER, VSL_METHOD_DGAUSSIAN_BOXMULLER2, VSL_METHOD_DGAUSSIAN_ICDF	VSL_RNG_METHOD_GAUSSIAN_BOXMULLER, VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2, VSL_RNG_METHOD_GAUSSIAN_ICDF
GaussianMV	VSL_METHOD_SGAUSSIANMV_BOXMULLER, VSL_METHOD_SGAUSSIANMV_BOXMULLER2, VSL_METHOD_SGAUSSIANMV_ICDF, VSL_METHOD_DGAUSSIANMV_BOXMULLER, VSL_METHOD_DGAUSSIANMV_BOXMULLER2, VSL_METHOD_DGAUSSIANMV_ICDF	VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER, VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER2, VSL_RNG_METHOD_GAUSSIANMV_ICDF
Exponential	VSL_METHOD_SEXPONENTIAL_ICDF, VSL_METHOD_DEXPONENTIAL_ICDF, VSL_METHOD_SEXPONENTIAL_ICDF_ACCURATE, VSL_METHOD_DEXPONENTIAL_ICDF_ACCURATE	VSL_RNG_METHOD_EXPONENTIAL_ICDF, VSL_RNG_METHOD_EXPONENTIAL_ICDF_ACCURATE
Laplace	VSL_METHOD_SLAPLACE_ICDF, VSL_METHOD_DLAPLACEL_ICDF	VSL_RNG_METHOD_LAPLACE_ICDF
Weibull	VSL_METHOD_SWEIBULL_ICDF, VSL_METHOD_DWEIBULL_ICDF, VSL_METHOD_SWEIBULL_ICDF_ACCURATE, VSL_METHOD_DWEIBULL_ICDF_ACCURATE	VSL_RNG_METHOD_WEIBULL_ICDF, VSL_RNG_METHOD_WEIBULL_ICDF_ACCURATE
Cauchy	VSL_METHOD_SCAUCHY_ICDF, VSL_METHOD_DCAUCHY_ICDF	VSL_RNG_METHOD_CAUCHY_ICDF
Rayleigh	VSL_METHOD_SRAYLEIGH_ICDF, VSL_METHOD_DRAYLEIGH_ICDF, VSL_METHOD_SRAYLEIGH_ICDF_ACCURATE, VSL_METHOD_DRAYLEIGH_ICDF_ACCURATE	VSL_RNG_METHOD_RAYLEIGH_ICDF, VSL_RNG_METHOD_RAYLEIGH_ICDF_ACCURATE
Lognormal	VSL_METHOD_SLOGNORMAL_BOXMULLER2, VSL_METHOD_DLOGNORMAL_BOXMULLER2, VSL_METHOD_SLOGNORMAL_BOXMULLER2_ACCURATE, VSL_METHOD_DLOGNORMAL_BOXMULLER2_ACCURATE	VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2, VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2_ACCURATE
Gumbel	VSL_METHOD_SGUMBEL_ICDF, VSL_METHOD_DGUMBEL_ICDF	VSL_RNG_METHOD_GUMBEL_ICDF
Gamma	VSL_METHOD_SGAMMA_GNORM, VSL_METHOD_DGAMMA_GNORM, VSL_METHOD_SGAMMA_GNORM_ACCURATE, VSL_METHOD_DGAMMA_GNORM_ACCURATE	VSL_RNG_METHOD_GAMMA_GNORM, VSL_RNG_METHOD_GAMMA_GNORM_ACCURATE
Beta	VSL_METHOD_SBETA_CJA, VSL_METHOD_DBETA_CJA, VSL_METHOD_SBETA_CJA_ACCURATE, VSL_METHOD_DBETA_CJA_ACCURATE	VSL_RNG_METHOD_BETA_CJA, VSL_RNG_METHOD_BETA_CJA_ACCURATE

Method Names for Discrete Distribution Generators
RNG	Legacy Method Name	New Method Name
Uniform	VSL_METHOD_IUNIFORM_STD	VSL_RNG_METHOD_UNIFORM_STD
UniformBits	VSL_METHOD_IUNIFORMBITS_STD	VSL_RNG_METHOD_UNIFORMBITS_STD
Bernoulli	VSL_METHOD_IBERNOULLI_ICDF	VSL_RNG_METHOD_BERNOULLI_ICDF
Geometric	VSL_METHOD_IGEOMETRIC_ICDF	VSL_RNG_METHOD_GEOMETRIC_ICDF
Binomial	VSL_METHOD_IBINOMIAL_BTPE	VSL_RNG_METHOD_BINOMIAL_BTPE
Hypergeometric	VSL_METHOD_IHYPERGEOMETRIC_H2PE	VSL_RNG_METHOD_HYPERGEOMETRIC_H2PE
Poisson	VSL_METHOD_IPOISSON_PTPE, VSL_METHOD_IPOISSON_POISNORM	VSL_RNG_METHOD_POISSON_PTPE, VSL_RNG_METHOD_POISSON_POISNORM
PoissonV	VSL_METHOD_IPOISSONV_POISNORM	VSL_RNG_METHOD_POISSONV_POISNORM
NegBinomial	VSL_METHOD_INEGBINOMIAL_NBAR	VSL_RNG_METHOD_NEGBINOMIAL_NBAR