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(An announcement from HRF: May 28, 2024)
   We finished a free translation of the Patent Specification submitted to Japan Patnt Office. The translation is titled Random Number Generator on Computers with Moduluses Formed by Two Odd and Coprime Submoduluses. It is a little too heavy for the Lounge of HRF. The file is thus posted in Archives. Please go to the Archive by cricking the button, and download the pdf file on the top.
   The subjects discussed are the notorious, but magically able Sunzi theorem. Please think on our hard efforts to make the report readable. If this work will be helpful to your understanding, we Authors shall be all happy.

(Notices of HRF: February 4, 2024)
   (1) Nakazawa Ransu Laboratory (NRL) is renamed as Hirakata Ransu Factory (HRF). Scientific and Technological matters are controlled by Rpresentative Naoya Nakazawa; Representative Hiroshi Nakazawa is on general and advisory affairs.
   (2) We have shown that any random number generators are represened by multiplicative congruential (MC) generators. The Lounge of HRF below will give detailed arguments for this conclusion, as the direct consequences of requirements on random number generation problems on computers. In short, computers work with finite memories and specific requirements, and cannot treat real numbers in he sense of mathemaics. This restriction has a are concerned with arithmetic which is integral in very essence. So, we should be conscious of the natures assciated wih integers and rational numbers. In this sense the usual mathematical stand points based on real space and probability measures need intense revisions. Please see the note in Lounge A titled Representation theorem of Random Number Generators on Computers.
   We wish to help readers, as far as we can. with this and coming reports. Readers are wished to open-mindedly read the noticies in Louge of HRF, and to find to themselves new sceneries on random number problems.

    HRF will continue to sustain its hard efforts to present readers more and more clear oveview on subjects. Random numbers of the 20th Centuary saw a profusion of theories, but random numbers with sufficiently long periods was obained only by methods using primitive polynomials. Sorry to say, the method could not give a reliable examination of emitted random numbers. Other many methods , in so far as authors know, could not give a sufficiently large (about 2⁵⁰ or lrger) period. We could evade all these difficulties, happy to say. First of all, we found (around 2012) that the geometrical criterions of MC generators were not adequate. The adequate, corrected criterions thus followed but, sorry to say, introduced new type of difficulties, and we wasted years until we find possible ways out. The new criterions worked marvelously, and enabled us find 2 MC generators of high quality with periods as long as 2⁵³. But for the failures of 20th Centuary investigations, frankly speaking, these successes will not have been obtained. We are proud of our success, but we evenly thank predecessors for giving their hard efforts.

[Download] ezzz.pdf (93kBytes)

Lounge A of HRF (I)
Representation Theorem of
Random Number Generators on Computers

Naoya Nakazawa/ Hiroshi Nakazawa
(February 4, 2024)

All arguments presented are strictly limited to random number generators on computers. Please understand the physical or technological restrictions limit generators to work only in rational numbers. Neverthelss, we find convenient mechanisms such as the approximation theorem stated here, lattices formed by consecutive points of random numbers, the applicability of Sunzi theorem, the geometry of produced points, ensuing high speed computing, and so forth. Integer arithmetic apparently looks to have inconvenient restrictions compared to real number arithmetic, but the truth is different. Please feel these conveniences of integers.

[Download] a1.pdf (46.6kBytes)

Lounge A of HRF (II)
Disclosure: Two Excellent MC Generators

Naoya Nakazawa/ Hiroshi Nakazawa
(February 11, 2024)

This is a disclosure of 2 excellent MC random number generators discovered by NRL-HRF. They have periods 2⁵³ and 2⁵² respectively, which wll be used up in simulations on desktop computers in about a year or so. They excellently pass regular simplex criteria devised by NRL-HRF with hard efforts. These criteria were once granted patents of Russia, USA and Europe, then made open to all world. Here we disclose generators in the subroutine form in Fortran. Please experience their excellent statstical precision, by assemblying them into your simulation programs and computer games, enjoying the excellent generation speed at the same time. The metnod of high speed generation is now under the examination in Japan Patent Office.