JP4669979B2 - 一様独立乱数生成方法 - Google Patents
一様独立乱数生成方法 Download PDFInfo
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- G—PHYSICS
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- G06F7/58—Random or pseudo-random number generators
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- G06F7/586—Pseudo-random number generators using an integer algorithm, e.g. using linear congruential method
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Description
段落0007の状況の大きな転換は非特許文献5、6(2004)において発見された。発明の開示の文献1、2にも述べられたとおり、0からz−1までの値を取る整数の作る任意の列の十分な長さTの部分について、その各数は(素数pや2iの形とは限らない)一般の自然数の法d、そしてdと素な適当な乗数zに基づく乗算合同法数列の対応する数で一様な誤差1/zで近似される区間[0、1)の数列を与える、という認識から得られた。この発見は、一様独立乱数列が自然物理現象に基づくものであろうと、或いはどのような計算方式に基づいて生成されたものであろうとすべて、素数と限らない合成数dを法とする乗算合同法の数列によって近似表現される、という事実を示すものである。認識は乗算合同法乱数発生方法の合成数への一般化に対応する数理構造の再考と、乗数の新しい選択基準の発見とを迫るものとなった。本特許に関わる研究は、この動機から誘発された。
【非特許文献1】D.H.Lehmer,“Mathemtical methods in large scale computing units.”Annals Comp.Lab.Harvard,Vol.26(1951),pp.141−146.
【非特許文献2】
【非特許文献3】
【非特許文献4】M.Matsumoto and T.Nishimura,“Mersenne Twister;A 623−dimensionally equidistributed uniform pseudorandom number generator,”ACM Transactions on Modeling and Computer Simulation,Vol,4(1994),254−266.
【非特許文献5】H.Nakazawa,“Coset representation of uniform and independent random number sequences I.Cosets associated with periodic sequences,”(August,2004,インターネット発表),(URL)http://www10.plala.or.jp/h−nkzw/.
【発明の開示】
[1]中澤宏,中澤直也,“長周期で高精度の一様独立乱数の設計:数の連が作る点列幾何の直積群構造及び格子構造に基づく制御.”
(March 9,2008,インターネット発表,0309.pdf),(URL)http://www10.plala.or.jp/h−nkzw/.
[2]中澤宏,中澤直也,“長周期で高精度の一様独立乱数の設計:数の連が作る点列幾何の直積群構造及び格子構造に基づく制御.”
(March 9−July 4,2008,インターネット発表,309704j.pdf),(URL)http://www10.plala.or.jp/h−nkzw/.
[2]H.Nakazawa and N.Nakazawa,“Designs of Uniform and Independent Random Numbers with Long Period and High Precision.”(March 9−July 8,2008,インターネット発表),(URL)http://www10.plala.or.jp/h−nkzw/.
Claims (1)
- 情報処理装置上の一様独立乱数生成方法であって、生成手順として
2つの異なる奇素数p1、p2で整数q1=(p1−1)/2及びq2=(p2−1)/2が互いに素であり、かつq1、q2の1つは偶数、他は奇数であるものを選ぶステップ、
整数dを前記奇素数p1、p2の積d=p1p2と選ぶステップ、
前記奇素数p1、p2をそれぞれ法とする原始根z1、z2を選ぶステップ、
前記p1、p2、z1、z2が与える連立合同式
整数nで前記dとは素な任意のものを選ぶステップ、
前記dと素な整数の作る法dの既約剰余群の中で前記zが生成し前記nから出発する巡回列、即ち整数列{n1、n2、n3、・・・}であって線形漸化合同式
一様独立乱数を与える実数列{u1、u2、u3、・・・}を除法等式
を有する方法、或いは前記法dの既約剰余群と同型な群を用いて前記の一様独立乱数列{u1、u2、u3、・・・}を得る上記諸ステップと同等な方法。
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JP2008220460A JP4669979B2 (ja) | 2008-08-02 | 2008-08-02 | 一様独立乱数生成方法 |
US12/379,964 US8443021B2 (en) | 2008-08-02 | 2009-03-05 | Method of generating random numbers |
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Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
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JP2012203898A (ja) * | 2011-03-28 | 2012-10-22 | Hiroshi Nakazawa | 一様独立乱数生成方法ii |
Families Citing this family (7)
Publication number | Priority date | Publication date | Assignee | Title |
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CN103135961A (zh) * | 2011-11-28 | 2013-06-05 | 中泽宏 | 基于具有两个奇素因子的模数生成乘同余随机数的方法 |
CN103197912B (zh) * | 2013-03-21 | 2016-02-10 | 北京理工大学 | 一种用于深空通信协议编码的均匀随机数生成方法 |
US20140337399A1 (en) * | 2013-05-13 | 2014-11-13 | Hiroshi Nakazawa | Method of generating random numbers iii |
US9778913B2 (en) | 2013-07-08 | 2017-10-03 | Hiroshi Nakazawa | Method of generating uniform and independent random numbers |
JP2015035197A (ja) * | 2013-07-08 | 2015-02-19 | 宏 中澤 | 一様独立乱数生成方法 |
JP2015118680A (ja) * | 2013-12-16 | 2015-06-25 | 宏 中澤 | 乱数乗算合同法の高次スペクトル検定方法 |
US20170004506A1 (en) * | 2015-06-14 | 2017-01-05 | Tender Armor, Llc | Security for electronic transactions and user authentication |
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US4944009A (en) * | 1988-02-25 | 1990-07-24 | Massachusetts Institute Of Technology | Pseudo-random sequence generator |
US6691141B2 (en) * | 2001-04-13 | 2004-02-10 | Science Applications International Corp. | Method and apparatus for generating random number generators |
US7149763B2 (en) * | 2002-09-09 | 2006-12-12 | Gemplus | Method for generating a random prime number within a predetermined interval |
US7921145B2 (en) * | 2007-05-22 | 2011-04-05 | Harris Corporation | Extending a repetition period of a random sequence |
US8588412B2 (en) * | 2008-05-23 | 2013-11-19 | Red Hat, Inc. | Mechanism for generating pseudorandom number sequences |
US20120290632A1 (en) * | 2011-05-11 | 2012-11-15 | Hiroshi Nakazawa | Method of generating random numbers ii |
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JP2012203898A (ja) * | 2011-03-28 | 2012-10-22 | Hiroshi Nakazawa | 一様独立乱数生成方法ii |
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