Bibliography

For more information about the VS functionality, refer to the following publications:

  • VS RNG

    [AVX]

    Intel. Intel® Advanced Vector Extensions Programming Reference. (https://software.intel.com/file/36945)

    [Bratley88]

    Bratley P. and Fox B.L. Implementing Sobol’s Quasirandom Sequence Generator, ACM Transactions on Mathematical Software, Vol. 14, No. 1, Pages 88-100, March 1988.

    [Bratley92]

    Bratley P., Fox B.L., and Niederreiter H. Implementation and Tests of Low-Discrepancy Sequences, ACM Transactions on Modeling and Computer Simulation, Vol. 2, No. 3, Pages 195-213, July 1992.

    [Coddington94]

    Coddington, P. D. Analysis of Random Number Generators Using Monte Carlo Simulation. Int. J. Mod. Phys. C-5, 547, 1994.

    [IntelSWMan]

    Intel. Intel® 64 and IA-32 Architectures Software Developer’s Manual. 3 vols. (https://software.intel.com/content/www/us/en/develop/articles/intel-sdm.html)

    [L’Ecuyer99]

    L’Ecuyer, Pierre. Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure. Mathematics of Computation, 68, 225, 249-260, 1999.

    [L’Ecuyer99a]

    L’Ecuyer, Pierre. Good Parameter Sets for Combined Multiple Recursive Random Number Generators. Operations Research, 47, 1, 159-164, 1999.

    [Kirkpatrick81]

    Kirkpatrick, S., and Stoll, E. A Very Fast Shift-Register Sequence Random Number Generator. Journal of Computational Physics, V. 40. 517-526, 1981.

    [Matsumoto98]

    Matsumoto, M., and Nishimura, T. Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, Pages 3-30, January 1998.

    [Matsumoto00]

    Matsumoto, M., and Nishimura, T. Dynamic Creation of Pseudorandom Number Generators, 56-69, in: Monte Carlo and Quasi-Monte Carlo Methods 1998, Ed. Niederreiter, H. and Spanier, J., Springer 2000, http://www.math.sci.hiroshima-u.ac.jp/%7Em-mat/MT/DC/dc.html.

    [NAG]

    NAG Numerical Libraries. http://www.nag.co.uk/numeric/numerical_libraries.asp

    [Saito08]

    Saito, M., and Matsumoto, M. SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator. Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, Pages 607 – 622, 2008.

    http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/earticles.html

    [Salmon11]

    Salmon, John K., Morales, Mark A., Dror, Ron O., and Shaw, David E., Parallel Random Numbers: As Easy as 1, 2, 3. SC ‘11 Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, 2011.

    [Sobol76]

    Sobol, I.M., and Levitan, Yu.L. The production of points uniformly distributed in a multidimensional cube. Preprint 40, Institute of Applied Mathematics, USSR Academy of Sciences, 1976 (In Russian).

    [VS Notes]

    Intel® oneMKL Vector Statistics Notes, a document present on the Intel® oneMKL product at https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-documentation.html

  • VM

    [IEEE754]

    IEEE Standard for Binary Floating-Point Arithmetic. ANSI/IEEE Std 754-2008.