![]() | A major contributor to this article appears to have a
close connection with its subject. (April 2016) |
![]() | |
Class | pseudorandom number generator |
---|---|
Data structure | Array |
Worst-case performance | O(n) |
Best-case performance | O(n) |
Average performance | O(n) |
Worst-case space complexity | O(n) |
Optimal | Yes |
The MIXMAX generator is a family of pseudorandom number generators (PRNG) and is based on Anosov C-systems ( Anosov diffeomorphism) and Kolmogorov K-systems ( Kolmogorov automorphism). It was introduced in a 1986 preprint by G. Savvidy and N. Ter-Arutyunyan-Savvidy and published in 1991. [1]
A fast implementation in C/ C++ of the generator was developed by Konstantin Savvidy. [2] It is genuine 64-bit generator. The period of the generator is and the Kolmogorov entropy is for the matrix size . [3] That generator occupies less than 2 kb, and if a smaller generator state is required, a N = 17 version with less than 200 bytes memory requirement also exists.
The generator works on most 64-bit systems, including 64-bit Linux flavors and Intel Mac. It has also been tested on PPC and ARM architectures. The latest version also runs on 32-bit systems and on Windows. The generator is equally usable with C++ programs, [4] has been chosen as the default generator in CLHEP [5] for use in Geant4 [6] and there exists a ROOT interface [7] and a PYTHIA interface. [8] It has been recently tested extensively on very wide variety of platforms, as part of the CLHEP/Geant4 release. EU-funded MIXMAX project [9]
An analysis by L’Ecuyer, Wambergue and Bourceret, [10] see also, [11] showed that MIXMAX generators has a lattice structure when the produced random numbers are considered in n - dimensional space larger than the dimension N of the matrix generator, and only in that high dimensions n > N they lie on a set of parallel hyperplanes and determined the maximum distance between the covering hyperplanes.
![]() | A major contributor to this article appears to have a
close connection with its subject. (April 2016) |
![]() | |
Class | pseudorandom number generator |
---|---|
Data structure | Array |
Worst-case performance | O(n) |
Best-case performance | O(n) |
Average performance | O(n) |
Worst-case space complexity | O(n) |
Optimal | Yes |
The MIXMAX generator is a family of pseudorandom number generators (PRNG) and is based on Anosov C-systems ( Anosov diffeomorphism) and Kolmogorov K-systems ( Kolmogorov automorphism). It was introduced in a 1986 preprint by G. Savvidy and N. Ter-Arutyunyan-Savvidy and published in 1991. [1]
A fast implementation in C/ C++ of the generator was developed by Konstantin Savvidy. [2] It is genuine 64-bit generator. The period of the generator is and the Kolmogorov entropy is for the matrix size . [3] That generator occupies less than 2 kb, and if a smaller generator state is required, a N = 17 version with less than 200 bytes memory requirement also exists.
The generator works on most 64-bit systems, including 64-bit Linux flavors and Intel Mac. It has also been tested on PPC and ARM architectures. The latest version also runs on 32-bit systems and on Windows. The generator is equally usable with C++ programs, [4] has been chosen as the default generator in CLHEP [5] for use in Geant4 [6] and there exists a ROOT interface [7] and a PYTHIA interface. [8] It has been recently tested extensively on very wide variety of platforms, as part of the CLHEP/Geant4 release. EU-funded MIXMAX project [9]
An analysis by L’Ecuyer, Wambergue and Bourceret, [10] see also, [11] showed that MIXMAX generators has a lattice structure when the produced random numbers are considered in n - dimensional space larger than the dimension N of the matrix generator, and only in that high dimensions n > N they lie on a set of parallel hyperplanes and determined the maximum distance between the covering hyperplanes.