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Inversive congruential generators are a type of nonlinear congruential pseudorandom number generator, which use the modular multiplicative inverse (if it exists) to generate the next number in a sequence. The standard formula for an inversive congruential generator, modulo some prime ''q'' is: :+ c) \mod q || if |- | || if |} Such a generator is denoted symbolically as ICG(q,a,c,seed) and is said to be an ICG with parameters ''q'',''a'',''c'' and seed ''seed''. ==Period== The sequence must have after finitely many steps and since the next element depends only on its direct predecessor also etc. The maximum length that the period ''T'' for a function modulo ''q'' can have is . If the polynomial (polynomial ring over ) is primitive, then the sequence will have the maximum length. Such polynomials are called inversive maximal period (IMP) polynomials. The sufficient condition for maximum sequence period is a proper choice of parameters ''a'' and ''c'' according to the algorithm described in.〔 Eichenauer-Herrmann, Lehn, Grothe and Niederreiter have shown that inversive congruential generators have good uniformity properties, in particular with regard to lattice structure and serial correlations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「inversive congruential generator」の詳細全文を読む スポンサード リンク
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