Notes for Intel® oneAPI Math Kernel Library Vector Statistics
ID
772987
Date
6/30/2025
Public
3D Spheres Test
Birthday Spacing Test
Bitstream Test
Rank of 31x31 Binary Matrices Test
Rank of 32x32 Binary Matrices Test
Rank of 6x8 Binary Matrices Test
Count-the-1's Test (Stream of Bits)
Count-the-1's Test (Stream of Specific Bytes)
Craps Test
Parking Lot Test
Self-Avoiding Random Walk Test
Template Test
Uniform (VSL_RNG_METHOD_UNIFORM_STD/VSL_RNG_METHOD_UNIFORM_STD_ACCURATE)
Gaussian (VSL_RNG_METHOD_GAUSSIAN_BOXMULLER)
Gaussian (VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2)
Gaussian (VSL_RNG_METHOD_GAUSSIAN_ICDF)
GaussianMV (VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER)
GaussianMV (VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER2)
GaussianMV (VSL_RNG_METHOD_GAUSSIANMV_ICDF)
Exponential (VSL_RNG_METHOD_EXPONENTIAL_ICDF/VSL_RNG_METHOD_EXPONENTIAL_ICDF_ACCURATE)
Laplace (VSL_RNG_METHOD_LAPLACE_ICDF)
Weibull (VSL_RNG_METHOD_WEIBULL_ICDF/ VSL_RNG_METHOD_WEIBULL_ICDF_ACCURATE)
Cauchy (VSL_RNG_METHOD_CAUCHY_ICDF)
Rayleigh (VSL_RNG_METHOD_RAYLEIGH_ICDF/ VSL_RNG_METHOD_RAYLEIGH_ICDF_ACCURATE)
Lognormal (VSL_RNG_METHOD_LOGNORMAL_ BOXMULLER2/VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2_ACCURATE)
Lognormal (VSL_RNG_METHOD_LOGNORMAL_ICDF/VSL_RNG_METHOD_LOGNORMAL_ICDF_ACCURATE)
Gumbel (VSL_RNG_METHOD_GUMBEL_ICDF)
Gamma (VSL_RNG_METHOD_GAMMA_GNORM/ VSL_RNG_METHOD_GAMMA_GNORM_ACCURATE)
Beta (VSL_RNG_METHOD_BETA_CJA/ VSL_RNG_METHOD_BETA_CJA_ACCURATE)
ChiSquare (VSL_RNG_METHOD_CHISQUARE_CHI2GAMMA)
Uniform (VSL_RNG_METHOD_UNIFORM_STD)
UniformBits (VSL_RNG_METHOD_UNIFORMBITS_STD)
UniformBits32 (VSL_RNG_METHOD_UNIFORMBITS32_STD)
UniformBits64 (VSL_RNG_METHOD_UNIFORMBITS64_STD)
Bernoulli (VSL_RNG_METHOD_BERNOULLI_ICDF)
Geometric (VSL_RNG_METHOD_GEOMETRIC_ICDF)
Binomial (VSL_RNG_METHOD_BINOMIAL_BTPE)
Hypergeometric (VSL_RNG_METHOD_HYPERGEOMETRIC_H2PE)
Poisson (VSL_RNG_METHOD_POISSON_PTPE)
Poisson (VSL_RNG_METHOD_POISSON_POISNORM)
PoissonV (VSL_RNG_METHOD_POISSONV_POISNORM)
NegBinomial (VSL_RNG_METHOD_NEGBINOMIAL_NBAR)
Multinomial (VSL_RNG_METHOD_MULTINOMIAL_MULTPOISSON)
One-Level (Threshold) Testing
To test K subsequences u1, u2, ..., un; un +1, un +2, ..., u2n; ...; u(K-1)n+1, u(K-1)n+2, ..., uKn of the original sequence, p-values p1, p2, ..., pK are computed. For a subsequence u(j-1)n+1, u(j -1)n+2, ..., ujn the test j fails if the value pj falls outside the interval (pl, ph) ⊂ (0, 1). The sequence u1, u2, ..., uKn is considered suspicious when r or more test iterations failed.
Threshold testing for the VS generators was done with the following variable settings:
ten iterations (K=10)
the interval (pl, ph) equal to (0.05, 0.95)
r = 5.
The chance to reject a 'good' sequence in this case is 0.16349374% ≅ 0.2%.
Parent topic: Interpreting Test Results