[bug #60026] Incorporate MIXMAX random number extension into GSL

[Patrick Alken]

URL:
  <https://savannah.gnu.org/bugs/?60026>

                 Summary: Incorporate MIXMAX random number extension into GSL
                 Project: GNU Scientific Library
            Submitted by: psa
            Submitted on: Tue 09 Feb 2021 04:09:05 AM UTC
                Category: None
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

from savvidy =at= inp =dot= demokritos =dot= gr

We have news on MIXMAX PRNG. 

1.It was fully implemented at CERN into the CLHEP/Geant4 software
a toolkit for the simulation of the passage of particles through matter as
default generator:

                    https://proj-clhep.web.cern.ch/proj-clhep/    (see Notes)

2.Became a part of the CMS Simulation Software at CERN:

            
https://indico.cern.ch/event/731433/contributions/3015654/attachments/1680131/2698971/CMSsim.pdf
  (see Pages 13-17)
            
https://indico.cern.ch/event/587955/contributions/2937635/attachments/1679273/2706817/PosterCMS_SIM_v4.pdf


3.It was recently used by NASA  in their design of the new mission to the Sun
    with the neutrino telescope  - a Solar Neutrino Spacecraft - the article
is attached (see page 13)

The authors of this project stated that: 

" Early in this project, the random number generation functions available in
standard C++ packages proved unsuitable for use;

they produce values which fall into a regular pattern of magnitude and will
generally avoid generating numbers very near zero or one.

For these reasons, the MIXMAX family of pseudo-random number generators have
been utilised here. Based off on Anosov C-systems—

a mathematical function group with useful instabilities in their structure—
this family of generators allows for the most random numerical

output in the shortest computational time [7] ".

We think that the problems with C++ packages above were connected with the
resolution power of the generators.
In a simple terms -  the MIXMAX is genuine 64 bit generator and have superior
resolution power. 

Please let me know if there were questions regarding MIXMAX.




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