text: /* boost random/linear_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.
   *
   * $Id$
   *
   * Revision history
   *  2001-02-18  moved to individual header files
   */
  
  #ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
  #define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
  
  #include <iostream>
  #include <stdexcept>
  #include <boost/assert.hpp>
  #include <boost/config.hpp>
  #include <boost/cstdint.hpp>
  #include <boost/limits.hpp>
  #include <boost/static_assert.hpp>
  #include <boost/integer/static_log2.hpp>
  #include <boost/mpl/if.hpp>
  #include <boost/type_traits/is_arithmetic.hpp>
  #include <boost/random/detail/config.hpp>
  #include <boost/random/detail/const_mod.hpp>
  #include <boost/random/detail/seed.hpp>
  #include <boost/random/detail/seed_impl.hpp>
  #include <boost/detail/workaround.hpp>
  
  #include <boost/random/detail/disable_warnings.hpp>
  
  namespace boost {
  namespace random {
  
  /**
   * Instantiations of class template linear_congruential_engine model a
   * \pseudo_random_number_generator. Linear congruential pseudo-random
   * number generators are described in:
   *
   *  @blockquote
   *  "Mathematical methods in large-scale computing units", D. H. Lehmer,
   *  Proc. 2nd Symposium on Large-Scale Digital Calculating Machines,
   *  Harvard University Press, 1951, pp. 141-146
   *  @endblockquote
   *
   * Let x(n) denote the sequence of numbers returned by some pseudo-random
   * number generator. Then for the linear congruential generator,
   * x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are
   * x(0), a, c, m. The template parameter IntType shall denote an integral
   * type. It must be large enough to hold values a, c, and m. The template
   * parameters a and c must be smaller than m.
   *
   * Note: The quality of the generator crucially depends on the choice of
   * the parameters. User code should use one of the sensibly parameterized
   * generators such as minstd_rand instead.
   */
  template<class IntType, IntType a, IntType c, IntType m>
  class linear_congruential_engine
  {
  public:
      typedef IntType result_type;
  
      // Required for old Boost.Random concept
      BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
  
      BOOST_STATIC_CONSTANT(IntType, multiplier = a);
      BOOST_STATIC_CONSTANT(IntType, increment = c);
      BOOST_STATIC_CONSTANT(IntType, modulus = m);
      BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
      
      BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer);
      BOOST_STATIC_ASSERT(m == 0 || a < m);
      BOOST_STATIC_ASSERT(m == 0 || c < m);
      
      /**
       * Constructs a @c linear_congruential_engine, using the default seed
       */
      linear_congruential_engine() { seed(); }
  
      /**
       * Constructs a @c linear_congruential_engine, seeding it with @c x0.
       */
      BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine,
                                                 IntType, x0)
      { seed(x0); }
      
      /**
       * Constructs a @c linear_congruential_engine, seeding it with values
       * produced by a call to @c seq.generate().
       */
      BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine,
                                               SeedSeq, seq)
      { seed(seq); }
  
      /**
       * Constructs a @c linear_congruential_engine  and seeds it
       * with values taken from the itrator range [first, last)
       * and adjusts first to point to the element after the last one
       * used.  If there are not enough elements, throws @c std::invalid_argument.
       *
       * first and last must be input iterators.
       */
      template<class It>
      linear_congruential_engine(It& first, It last)
      {
          seed(first, last);
      }
  
      // compiler-generated copy constructor and assignment operator are fine
  
      /**
       * Calls seed(default_seed)
       */
      void seed() { seed(default_seed); }
  
      /**
       * If c mod m is zero and x0 mod m is zero, changes the current value of
       * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero,
       * distinct seeds in the range [1,m) will leave the generator in distinct
       * states. If c is not zero, the range is [0,m).
       */
      BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0_)
      {
          // Work around a msvc 12/14 optimizer bug, which causes
          // the line _x = 1 to run unconditionally sometimes.
          // Creating a local copy seems to make it work.
          IntType x0 = x0_;
          // wrap _x if it doesn't fit in the destination
          if(modulus == 0) {
              _x = x0;
          } else {
              _x = x0 % modulus;
          }
          // handle negative seeds
          if(_x <= 0 && _x != 0) {
              _x += modulus;
          }
          // adjust to the correct range
          if(increment == 0 && _x == 0) {
              _x = 1;
          }
          BOOST_ASSERT(_x >= (min)());
          BOOST_ASSERT(_x <= (max)());
      }
  
      /**
       * Seeds a @c linear_congruential_engine using values from a SeedSeq.
       */
      BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq)
      { seed(detail::seed_one_int<IntType, m>(seq)); }
  
      /**
       * seeds a @c linear_congruential_engine with values taken
       * from the itrator range [first, last) and adjusts @c first to
       * point to the element after the last one used.  If there are
       * not enough elements, throws @c std::invalid_argument.
       *
       * @c first and @c last must be input iterators.
       */
      template<class It>
      void seed(It& first, It last)
      { seed(detail::get_one_int<IntType, m>(first, last)); }
  
      /**
       * Returns the smallest value that the @c linear_congruential_engine
       * can produce.
       */
      static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
      { return c == 0 ? 1 : 0; }
      /**
       * Returns the largest value that the @c linear_congruential_engine
       * can produce.
       */
      static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
      { return modulus-1; }
  
      /** Returns the next value of the @c linear_congruential_engine. */
      IntType operator()()
      {
          _x = const_mod<IntType, m>::mult_add(a, _x, c);
          return _x;
      }
    
      /** Fills a range with random values */
      template<class Iter>
      void generate(Iter first, Iter last)
      { detail::generate_from_int(*this, first, last); }
  
      /** Advances the state of the generator by @c z. */
      void discard(boost::uintmax_t z)
      {
          typedef const_mod<IntType, m> mod_type;
          IntType b_inv = mod_type::invert(a-1);
          IntType b_gcd = mod_type::mult(a-1, b_inv);
          if(b_gcd == 1) {
              IntType a_z = mod_type::pow(a, z);
              _x = mod_type::mult_add(a_z, _x, 
                  mod_type::mult(mod_type::mult(c, b_inv), a_z - 1));
          } else {
              // compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd)
              // we're storing the intermediate result / b_gcd
              IntType a_zm1_over_gcd = 0;
              IntType a_km1_over_gcd = (a - 1) / b_gcd;
              boost::uintmax_t exponent = z;
              while(exponent != 0) {
                  if(exponent % 2 == 1) {
                      a_zm1_over_gcd =
                          mod_type::mult_add(
                              b_gcd,
                              mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd),
                              mod_type::add(a_zm1_over_gcd, a_km1_over_gcd));
                  }
                  a_km1_over_gcd = mod_type::mult_add(
                      b_gcd,
                      mod_type::mult(a_km1_over_gcd, a_km1_over_gcd),
                      mod_type::add(a_km1_over_gcd, a_km1_over_gcd));
                  exponent /= 2;
              }
              
              IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1);
              IntType num = mod_type::mult(c, a_zm1_over_gcd);
              b_inv = mod_type::invert((a-1)/b_gcd);
              _x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num));
          }
      }
  
      friend bool operator==(const linear_congruential_engine& x,
                             const linear_congruential_engine& y)
      { return x._x == y._x; }
      friend bool operator!=(const linear_congruential_engine& x,
                             const linear_congruential_engine& y)
      { return !(x == y); }
      
  #if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS)
      /** Writes a @c linear_congruential_engine to a @c std::ostream. */
      template<class CharT, class Traits>
      friend std::basic_ostream<CharT,Traits>&
      operator<<(std::basic_ostream<CharT,Traits>& os,
                 const linear_congruential_engine& lcg)
      {
          return os << lcg._x;
      }
  
      /** Reads a @c linear_congruential_engine from a @c std::istream. */
      template<class CharT, class Traits>
      friend std::basic_istream<CharT,Traits>&
      operator>>(std::basic_istream<CharT,Traits>& is,
                 linear_congruential_engine& lcg)
      {
          lcg.read(is);
          return is;
      }
  #endif
  
  private:
  
      /// \cond show_private
  
      template<class CharT, class Traits>
      void read(std::basic_istream<CharT, Traits>& is) {
          IntType x;
          if(is >> x) {
              if(x >= (min)() && x <= (max)()) {
                  _x = x;
              } else {
                  is.setstate(std::ios_base::failbit);
              }
          }
      }
  
      /// \endcond
  
      IntType _x;
  };
  
  #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  //  A definition is required even for integral static constants
  template<class IntType, IntType a, IntType c, IntType m>
  const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range;
  template<class IntType, IntType a, IntType c, IntType m>
  const IntType linear_congruential_engine<IntType,a,c,m>::multiplier;
  template<class IntType, IntType a, IntType c, IntType m>
  const IntType linear_congruential_engine<IntType,a,c,m>::increment;
  template<class IntType, IntType a, IntType c, IntType m>
  const IntType linear_congruential_engine<IntType,a,c,m>::modulus;
  template<class IntType, IntType a, IntType c, IntType m>
  const IntType linear_congruential_engine<IntType,a,c,m>::default_seed;
  #endif
  
  /// \cond show_deprecated
  
  // provided for backwards compatibility
  template<class IntType, IntType a, IntType c, IntType m, IntType val = 0>
  class linear_congruential : public linear_congruential_engine<IntType, a, c, m>
  {
      typedef linear_congruential_engine<IntType, a, c, m> base_type;
  public:
      linear_congruential(IntType x0 = 1) : base_type(x0) {}
      template<class It>
      linear_congruential(It& first, It last) : base_type(first, last) {}
  };
  
  /// \endcond
  
  /**
   * The specialization \minstd_rand0 was originally suggested in
   *
   *  @blockquote
   *  A pseudo-random number generator for the System/360, P.A. Lewis,
   *  A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2,
   *  1969, pp. 136-146
   *  @endblockquote
   *
   * It is examined more closely together with \minstd_rand in
   *
   *  @blockquote
   *  "Random Number Generators: Good ones are hard to find",
   *  Stephen K. Park and Keith W. Miller, Communications of
   *  the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 
   *  @endblockquote
   */
  typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0;
  
  /** The specialization \minstd_rand was suggested in
   *
   *  @blockquote
   *  "Random Number Generators: Good ones are hard to find",
   *  Stephen K. Park and Keith W. Miller, Communications of
   *  the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
   *  @endblockquote
   */
  typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand;
  
  
  #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
  /**
   * Class @c rand48 models a \pseudo_random_number_generator. It uses
   * the linear congruential algorithm with the parameters a = 0x5DEECE66D,
   * c = 0xB, m = 2**48. It delivers identical results to the @c lrand48()
   * function available on some systems (assuming lcong48 has not been called).
   *
   * It is only available on systems where @c uint64_t is provided as an
   * integral type, so that for example static in-class constants and/or
   * enum definitions with large @c uint64_t numbers work.
   */
  class rand48 
  {
  public:
      typedef boost::uint32_t result_type;
  
      BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
      /**
       * Returns the smallest value that the generator can produce
       */
      static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
      /**
       * Returns the largest value that the generator can produce
       */
      static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION ()
      { return 0x7FFFFFFF; }
    
      /** Seeds the generator with the default seed. */
      rand48() : lcf(cnv(static_cast<uint32_t>(1))) {}
      /**
       * Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e.
       */
      BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0)
      { seed(x0); }
      /**
       * Seeds the generator with values produced by @c seq.generate().
       */
      BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq)
      { seed(seq); }
      /**
       * Seeds the generator using values from an iterator range,
       * and updates first to point one past the last value consumed.
       */
      template<class It> rand48(It& first, It last) : lcf(first, last) { }
  
      // compiler-generated copy ctor and assignment operator are fine
  
      /** Seeds the generator with the default seed. */
      void seed() { seed(static_cast<uint32_t>(1)); }
      /**
       * Changes the current value x(n) of the generator to (x0 << 16) | 0x330e.
       */
      BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0)
      { lcf.seed(cnv(x0)); }
      /**
       * Seeds the generator using values from an iterator range,
       * and updates first to point one past the last value consumed.
       */
      template<class It> void seed(It& first, It last) { lcf.seed(first,last); }
      /**
       * Seeds the generator with values produced by @c seq.generate().
       */
      BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq)
      { lcf.seed(seq); }
  
      /**  Returns the next value of the generator. */
      uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); }
      
      /** Advances the state of the generator by @c z. */
      void discard(boost::uintmax_t z) { lcf.discard(z); }
    
      /** Fills a range with random values */
      template<class Iter>
      void generate(Iter first, Iter last)
      {
          for(; first != last; ++first) {
              *first = (*this)();
          }
      }
  
  #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
      /**  Writes a @c rand48 to a @c std::ostream. */
      template<class CharT,class Traits>
      friend std::basic_ostream<CharT,Traits>&
      operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r)
      { os << r.lcf; return os; }
  
      /** Reads a @c rand48 from a @c std::istream. */
      template<class CharT,class Traits>
      friend std::basic_istream<CharT,Traits>&
      operator>>(std::basic_istream<CharT,Traits>& is, rand48& r)
      { is >> r.lcf; return is; }
  #endif
  
      /**
       * Returns true if the two generators will produce identical
       * sequences of values.
       */
      friend bool operator==(const rand48& x, const rand48& y)
      { return x.lcf == y.lcf; }
      /**
       * Returns true if the two generators will produce different
       * sequences of values.
       */
      friend bool operator!=(const rand48& x, const rand48& y)
      { return !(x == y); }
  private:
      /// \cond show_private
      typedef random::linear_congruential_engine<uint64_t,
          // xxxxULL is not portable
          uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32),
          0xB, uint64_t(1)<<48> lcf_t;
      lcf_t lcf;
  
      static boost::uint64_t cnv(boost::uint32_t x)
      { return (static_cast<uint64_t>(x) << 16) | 0x330e; }
      /// \endcond
  };
  #endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */
  
  } // namespace random
  
  using random::minstd_rand0;
  using random::minstd_rand;
  using random::rand48;
  
  } // namespace boost
  
  #include <boost/random/detail/enable_warnings.hpp>
  
  #endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
  