Developer Reference for Intel® oneAPI Math Kernel Library for C
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Distribution Generators
oneMKLVS 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.
Type of Distribution |
Data Types |
BRNG Data Type |
Description |
|---|---|---|---|
s, d |
s, d |
Uniform continuous distribution on the interval [a,b) |
|
s, d |
s, d |
Normal (Gaussian) distribution |
|
s, d |
s, d |
Normal (Gaussian) multivariate distribution |
|
s, d |
s, d |
Exponential distribution |
|
s, d |
s, d |
Laplace distribution (double exponential distribution) |
|
s, d |
s, d |
Weibull distribution |
|
s, d |
s, d |
Cauchy distribution |
|
s, d |
s, d |
Rayleigh distribution |
|
s, d |
s, d |
Lognormal distribution |
|
s, d |
s, d |
Gumbel (extreme value) distribution |
|
s, d |
s, d |
Gamma distribution |
|
s, d |
s, d |
Beta distribution |
|
s, d |
s, d |
Chi-Square distribution |
Type of Distribution |
Data Types |
BRNG Data Type |
Description |
|---|---|---|---|
i |
d |
Uniform discrete distribution on the interval [a,b) |
|
i |
i |
Underlying BRNG integer recurrence |
|
i |
i |
Uniformly distributed bits in 32-bit chunks |
|
i |
i |
Uniformly distributed bits in 64-bit chunks |
|
i |
s |
Bernoulli distribution |
|
i |
s |
Geometric distribution |
|
i |
d |
Binomial distribution |
|
i |
d |
Hypergeometric distribution |
|
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 |
|
i |
s |
Poisson distribution with varying mean |
|
i |
d |
Negative binomial distribution, or Pascal distribution |
|
i |
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.
Type of Distribution |
Data Types |
|---|---|
s, d |
|
s, d |
|
s, d |
|
s, d |
|
s, d |
|
s, d |
|
s, d |
See additional details about accurate and fast mode of random number generation in VS Notes.
New method names
The current version of oneMKL has a modified structure of VS RNG method names. (SeeRNG 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 VS random number generators.
RNG |
Legacy Method Name |
New Method Name |
|---|---|---|
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 |
|
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 |
|
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 |
|
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 |
|
VSL_METHOD_SLAPLACE_ICDF, VSL_METHOD_DLAPLACEL_ICDF |
VSL_RNG_METHOD_LAPLACE_ICDF |
|
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 |
|
VSL_METHOD_SCAUCHY_ICDF, VSL_METHOD_DCAUCHY_ICDF |
VSL_RNG_METHOD_CAUCHY_ICDF |
|
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 |
|
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 |
|
VSL_METHOD_SLOGNORMAL_ICDF, VSL_METHOD_DLOGNORMAL_ICDF, VSL_METHOD_SLOGNORMAL_ICDF_ACCURATE, VSL_METHOD_DLOGNORMAL_ICDF_ACCURATE |
VSL_RNG_METHOD_LOGNORMAL_ICDF, VSL_RNG_METHOD_LOGNORMAL_ICDF_ACCURATE |
|
VSL_METHOD_SGUMBEL_ICDF, VSL_METHOD_DGUMBEL_ICDF |
VSL_RNG_METHOD_GUMBEL_ICDF |
|
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 |
|
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 |
RNG |
Legacy Method Name |
New Method Name |
|---|---|---|
VSL_METHOD_IUNIFORM_STD |
VSL_RNG_METHOD_UNIFORM_STD |
|
VSL_METHOD_IUNIFORMBITS_STD |
VSL_RNG_METHOD_UNIFORMBITS_STD |
|
VSL_METHOD_IBERNOULLI_ICDF |
VSL_RNG_METHOD_BERNOULLI_ICDF |
|
VSL_METHOD_IGEOMETRIC_ICDF |
VSL_RNG_METHOD_GEOMETRIC_ICDF |
|
VSL_METHOD_IBINOMIAL_BTPE |
VSL_RNG_METHOD_BINOMIAL_BTPE |
|
VSL_METHOD_IHYPERGEOMETRIC_H2PE |
VSL_RNG_METHOD_HYPERGEOMETRIC_H2PE |
|
VSL_METHOD_IPOISSON_PTPE, VSL_METHOD_IPOISSON_POISNORM |
VSL_RNG_METHOD_POISSON_PTPE, VSL_RNG_METHOD_POISSON_POISNORM |
|
VSL_METHOD_IPOISSONV_POISNORM |
VSL_RNG_METHOD_POISSONV_POISNORM |
|
VSL_METHOD_INEGBINOMIAL_NBAR |
VSL_RNG_METHOD_NEGBINOMIAL_NBAR |