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Inversive congruential generator : ウィキペディア英語版
Inversive congruential generator
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 x_i\ne 0
|-
| x_= c || if x_i=0
|}
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 (x_n)_ must have x_i=x_j after finitely many steps and since the next element depends only on its direct predecessor also x_=x_ etc. The maximum length that the period ''T'' for a function modulo ''q'' can have is . If the polynomial f(x)=x^2-cx-a \in \mathbb F_q() (polynomial ring over \mathbb F_q) 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)
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