Class template inversive_congruential

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## Class template inversive_congruential

boost::random::inversive_congruential

## Synopsis

    // In header: <boost/random/inversive_congruential.hpp>

    template<typename IntType, IntType a, IntType b, IntType p, IntType val>
    class inversive_congruential {
    public:
      // types
      typedef IntType result_type;

      // construct/copy/destruct
      inversive_congruential(IntType = 1);
      template<typename It> inversive_congruential(It &, It);

      // public member functions
      result_type min() const;
      result_type max() const;
      void seed(IntType = 1) ;
      template<typename It> void seed(It &, It) ;
      IntType operator()() ;

      // public static functions
      static bool validation(result_type) ;
      static const bool has_fixed_range;
      static const result_type min_value;
      static const result_type max_value;
      static const result_type multiplier;
      static const result_type increment;
      static const result_type modulus;
    };

## Description

Instantiations of class template `inversive_congruential` model a pseudo-random number generator . It uses the inversive congruential algorithm (ICG) described in

> "Inversive pseudorandom number generators: concepts, results and links", Peter Hellekalek, In: "Proceedings of the 1995 Winter Simulation Conference", C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman (editors), 1995, pp. 255-262. ftp://random.mat.sbg.ac.at/pub/data/wsc95.ps

The output sequence is defined by x(n+1) = (a*inv(x(n)) - b) (mod p), where x(0), a, b, and the prime number p are parameters of the generator. The expression inv(k) denotes the multiplicative inverse of k in the field of integer numbers modulo p, with inv(0) := 0.

The template parameter IntType shall denote a signed integral type large enough to hold p; a, b, and p are the parameters of the generators. The template parameter val is the validation value checked by validation.

| Note
The implementation currently uses the Euclidian Algorithm to compute the multiplicative inverse. Therefore, the inversive generators are about 10-20 times slower than the others (see section"performance"). However, the paper talks of only 3x slowdown, so the Euclidian Algorithm is probably not optimal for calculating the multiplicative inverse.

### `inversive_congruential` public construct/copy/destruct

1.     inversive_congruential(IntType y0 = 1);

   Constructs an inversive_congruential generator with `y0` as the initial state.

2.     template<typename It> inversive_congruential(It & first, It last);

### `inversive_congruential` public member functions

1.     result_type min() const;

2.     result_type max() const;

3.     void seed(IntType y0 = 1) ;

   Changes the current state to y0.

4.     template<typename It> void seed(It & first, It last) ;

5.     IntType operator()() ;

### `inversive_congruential` public static functions

1.     static bool validation(result_type x) ;