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MIXMAX

   MIXMAX is the matrix-recursive random number generator introduced by my parents
   in:
   On the Monte Carlo Simulation of Physical Systems
   [8]J.Comput.Phys. 97, 566 (1991), [9](DOI link)
   Some of the algorithms used in this implementation, plus the theory behind the
   period is in my paper:
   [10]The MIXMAX random number generator
   Comp. Phys. Commun. 196 (2015) 161 [11](DOI link) [12](Arxiv link)
   Underlying MIXMAX is the theory of dynamical systems, more precisely of
   Kolmogorov's K-systems. Therefore, the floating point numbers generated by MIXMAX
   carry strong theoretical guarantees. This, and the fact that it passes all
   non-contrived tests of randomness, makes MIXMAX suitable for large scale
   Monte-Carlo simulations.
   The generator is now mature and has proven itself over the years. The more recent
   versions include the code for skipping, which we strongly suggest for seeding and
   parallelization of Monte-Carlo. It is guaranteed that even if the user seeds from
   sequential seeds, e.g. 1,2,3... the initial vectors are independent and are
   located on the MIXMAX trajectory at least 10^100 steps apart. This is vastly
   superior to the usual practice of choosing random or non-ramdom seeds and hoping
   that the generator would not produce a collision in the streams produced from
   different seeds. There is a rather detailed [13]Manual available.
   Please kindly let me know of your experiences.
   The latest release is 2.0, with a new combination of parameters (link to paper
   [14]here)! (September 1, 2017)
   The new release contains some small improvements to the C code, plus a new C++
   implementation,
   which contains among other conveniences a C++11 standard interface (std::random).
   Having said that, it will compile under slighly older compilers, e.g. g++4.6 with
   the -std=c++0x switch. The C version still compiles on gcc3.3, even on PPC and
   ARM. This version also includes a GSL interface out of the box. The software
   remains free, but it is no longer licensed under LGPL, so if you are interested
   to package it with some other software or distribution please contact me. If you
   are interested to reimplement it, modify it, code it in another computer language
   etc... read the papers and try coding it from there. This software retains my
   copyright.
   DOWNLOAD:
   [15]mixmax_release_200final.zip
   or the archived releases:
   [16]http://www.hepforge.org/downloads/mixmax
   If you got any version below 1.0, please switch! There are a number of
   improvements to speed, compared to the versions before 1.0.
   LATEST NEWS:
   [17]GEANT4 interface: the default random number generator is MIXMAX, as of
   version 10.4
   CLHEP starting with version 2.3.1.1[18] (presentation by Gabriele Cosmo)
   [19]ROOT TRandom starting with version 6.04 has a MIXMAX interface!
   GSL extension package: [20](here)
   PYTHIA8 plugin to its default Random Number Generator class: [21](here)
   Wikipedia page: [22]here
   The software has been verified and works fine on Apple's new CPU!
   Email me, Konstantin Savvidy, ksavvidis @at@ gmail.com

References

   1. https://mixmax.hepforge.org/
   2. http://www.hepforge.org/
   3. http://www.ippp.dur.ac.uk/
   4. https://mixmax.hepforge.org/
   5. https://mixmax.hepforge.org/svn/
   6. https://mixmax.hepforge.org/trac/report/3
   7. https://mixmax.hepforge.org/trac/wiki
   8. http://www.sciencedirect.com/science/article/pii/002199919190015D
   9. http://dx.doi.org/10.1016/0021-9991(91)90015-D
  10. http://arxiv.org/abs/1403.5355
  11. http://dx.doi.org/10.1016/j.cpc.2015.06.003
  12. http://arxiv.org/abs/1403.5355
  13. http://www.hepforge.org/archive/mixmax/MANUAL.pdf
  14. http://dx.doi.org/10.1016/j.chaos.2016.05.003
  15. http://www.hepforge.org/archive/mixmax/mixmax_release_200final.zip
  16. http://www.hepforge.org/downloads/mixmax
  17. https://cdcvs.fnal.gov/redmine/projects/g4/wiki/RNDM-Geant4104
  18. https://indico.cern.ch/event/731433/contributions/3015651/attachments/1679743/2698172/mixmax-CLHEP.pdf
  19. https://root.cern.ch/doc/master/classTRandom.html
  20. https://www.gnu.org/software/gsl/#extensions
  21. http://home.thep.lu.se/~torbjorn/doxygen/classMixMaxRndm.html
  22. https://en.wikipedia.org/wiki/MIXMAX_generator