text: /* boost random/inversive_congruential.hpp header file
   *
   * Copyright Jens Maurer 2000-2001
   * Distributed under the Boost Software License, Version 1.0. (See
   * accompanying file LICENSE_1_0.txt or copy at
   * http://www.boost.org/LICENSE_1_0.txt)
   *
   * See http://www.boost.org for most recent version including documentation.
   *
   * $Id: inversive_congruential.hpp 60755 2010-03-22 00:45:06Z steven_watanabe $
   *
   * Revision history
   *  2001-02-18  moved to individual header files
   */
  
  #ifndef BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
  #define BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
  
  #include <iostream>
  #include <cassert>
  #include <stdexcept>
  #include <boost/config.hpp>
  #include <boost/static_assert.hpp>
  #include <boost/random/detail/config.hpp>
  #include <boost/random/detail/const_mod.hpp>
  
  namespace boost {
  namespace random {
  
  // Eichenauer and Lehn 1986
  /**
   * Instantiations of class template @c inversive_congruential model a
   * \pseudo_random_number_generator. It uses the inversive congruential
   * algorithm (ICG) described in
   *
   *  @blockquote
   *  "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
   *  @endblockquote
   *
   * 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.
   *
   * @xmlnote
   * 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.
   * @endxmlnote
   */
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  class inversive_congruential
  {
  public:
    typedef IntType result_type;
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
    static const bool has_fixed_range = true;
    static const result_type min_value = (b == 0 ? 1 : 0);
    static const result_type max_value = p-1;
  #else
    BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
  #endif
    BOOST_STATIC_CONSTANT(result_type, multiplier = a);
    BOOST_STATIC_CONSTANT(result_type, increment = b);
    BOOST_STATIC_CONSTANT(result_type, modulus = p);
  
    result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return b == 0 ? 1 : 0; }
    result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return p-1; }
  
    /**
     * Constructs an inversive_congruential generator with
     * @c y0 as the initial state.
     */
    explicit inversive_congruential(IntType y0 = 1) : value(y0)
    {
      BOOST_STATIC_ASSERT(b >= 0);
      BOOST_STATIC_ASSERT(p > 1);
      BOOST_STATIC_ASSERT(a >= 1);
      if(b == 0) 
        assert(y0 > 0); 
    }
    template<class It> inversive_congruential(It& first, It last)
    { seed(first, last); }
  
    /** Changes the current state to y0. */
    void seed(IntType y0 = 1) { value = y0; if(b == 0) assert(y0 > 0); }
    template<class It> void seed(It& first, It last)
    {
      if(first == last)
        throw std::invalid_argument("inversive_congruential::seed");
      value = *first++;
    }
    IntType operator()()
    {
      typedef const_mod<IntType, p> do_mod;
      value = do_mod::mult_add(a, do_mod::invert(value), b);
      return value;
    }
  
    static bool validation(result_type x) { return val == x; }
  
  #ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
  
  #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
    template<class CharT, class Traits>
    friend std::basic_ostream<CharT,Traits>&
    operator<<(std::basic_ostream<CharT,Traits>& os, inversive_congruential x)
    { os << x.value; return os; }
  
    template<class CharT, class Traits>
    friend std::basic_istream<CharT,Traits>&
    operator>>(std::basic_istream<CharT,Traits>& is, inversive_congruential& x)
    { is >> x.value; return is; }
  #endif
  
    friend bool operator==(inversive_congruential x, inversive_congruential y)
    { return x.value == y.value; }
    friend bool operator!=(inversive_congruential x, inversive_congruential y)
    { return !(x == y); }
  #else
    // Use a member function; Streamable concept not supported.
    bool operator==(inversive_congruential rhs) const
    { return value == rhs.value; }
    bool operator!=(inversive_congruential rhs) const
    { return !(*this == rhs); }
  #endif
  private:
    IntType value;
  };
  
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  //  A definition is required even for integral static constants
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const bool inversive_congruential<IntType, a, b, p, val>::has_fixed_range;
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const typename inversive_congruential<IntType, a, b, p, val>::result_type inversive_congruential<IntType, a, b, p, val>::min_value;
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const typename inversive_congruential<IntType, a, b, p, val>::result_type inversive_congruential<IntType, a, b, p, val>::max_value;
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const typename inversive_congruential<IntType, a, b, p, val>::result_type inversive_congruential<IntType, a, b, p, val>::multiplier;
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const typename inversive_congruential<IntType, a, b, p, val>::result_type inversive_congruential<IntType, a, b, p, val>::increment;
  template<class IntType, IntType a, IntType b, IntType p, IntType val>
  const typename inversive_congruential<IntType, a, b, p, val>::result_type inversive_congruential<IntType, a, b, p, val>::modulus;
  #endif
  
  } // namespace random
  
  /**
   * The specialization hellekalek1995 was suggested in
   *
   *  @blockquote
   *  "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
   *  @endblockquote
   */
  typedef random::inversive_congruential<int32_t, 9102, 2147483647-36884165,
    2147483647, 0> hellekalek1995;
  
  } // namespace boost
  
  #endif // BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
  