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 /* boost random/subtract_with_carry.hpp header file
  *
  * Copyright Jens Maurer 2002
  * 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
  *  2002-03-02  created
  */
 
 #ifndef BOOST_RANDOM_SUBTRACT_WITH_CARRY_HPP
 #define BOOST_RANDOM_SUBTRACT_WITH_CARRY_HPP
 
 #include <boost/config/no_tr1/cmath.hpp>         // std::pow
 #include <iostream>
 #include <algorithm>     // std::equal
 #include <stdexcept>
 #include <boost/config.hpp>
 #include <boost/limits.hpp>
 #include <boost/cstdint.hpp>
 #include <boost/static_assert.hpp>
 #include <boost/integer/static_log2.hpp>
 #include <boost/integer/integer_mask.hpp>
 #include <boost/detail/workaround.hpp>
 #include <boost/random/detail/config.hpp>
 #include <boost/random/detail/seed.hpp>
 #include <boost/random/detail/operators.hpp>
 #include <boost/random/detail/seed_impl.hpp>
 #include <boost/random/detail/generator_seed_seq.hpp>
 #include <boost/random/linear_congruential.hpp>
 
 
 namespace boost {
 namespace random {
 
 namespace detail {
    
 struct subtract_with_carry_discard
 {
     template<class Engine>
     static void apply(Engine& eng, boost::uintmax_t z)
     {
         typedef typename Engine::result_type IntType;
         const std::size_t short_lag = Engine::short_lag;
         const std::size_t long_lag = Engine::long_lag;
         std::size_t k = eng.k;
         IntType carry = eng.carry;
         if(k != 0) {
             // increment k until it becomes 0.
             if(k < short_lag) {
                 std::size_t limit = (short_lag - k) < z?
                     short_lag : (k + static_cast<std::size_t>(z));
                 for(std::size_t j = k; j < limit; ++j) {
                     carry = eng.do_update(j, j + long_lag - short_lag, carry);
                 }
             }
             std::size_t limit = (long_lag - k) < z?
                 long_lag : (k + static_cast<std::size_t>(z));
             std::size_t start = (k < short_lag ? short_lag : k);
             for(std::size_t j = start; j < limit; ++j) {
                 carry = eng.do_update(j, j - short_lag, carry);
             }
         }
 
         k = ((z % long_lag) + k) % long_lag;
 
         if(k < z) {
             // main loop: update full blocks from k = 0 to long_lag
             for(std::size_t i = 0; i < (z - k) / long_lag; ++i) {
                 for(std::size_t j = 0; j < short_lag; ++j) {
                     carry = eng.do_update(j, j + long_lag - short_lag, carry);
                 }
                 for(std::size_t j = short_lag; j < long_lag; ++j) {
                     carry = eng.do_update(j, j - short_lag, carry);
                 }
             }
 
             // Update the last partial block
             std::size_t limit = short_lag < k? short_lag : k; 
             for(std::size_t j = 0; j < limit; ++j) {
                 carry = eng.do_update(j, j + long_lag - short_lag, carry);
             }
             for(std::size_t j = short_lag; j < k; ++j) {
                 carry = eng.do_update(j, j - short_lag, carry);
             }
         }
         eng.carry = carry;
         eng.k = k;
     }
 };
 
 }
 
 /**
  * Instantiations of @c subtract_with_carry_engine model a
  * \pseudo_random_number_generator.  The algorithm is
  * described in
  *
  *  @blockquote
  *  "A New Class of Random Number Generators", George
  *  Marsaglia and Arif Zaman, Annals of Applied Probability,
  *  Volume 1, Number 3 (1991), 462-480.
  *  @endblockquote
  */
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 class subtract_with_carry_engine
 {
 public:
     typedef IntType result_type;
     BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
     BOOST_STATIC_CONSTANT(std::size_t, long_lag = r);
     BOOST_STATIC_CONSTANT(std::size_t, short_lag = s);
     BOOST_STATIC_CONSTANT(uint32_t, default_seed = 19780503u);
 
     // Required by the old Boost.Random concepts
     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
     // Backwards compatibility
     BOOST_STATIC_CONSTANT(result_type, modulus = (result_type(1) << w));
     
     BOOST_STATIC_ASSERT(std::numeric_limits<result_type>::is_integer);
 
     /**
      * Constructs a new @c subtract_with_carry_engine and seeds
      * it with the default seed.
      */
     subtract_with_carry_engine() { seed(); }
     /**
      * Constructs a new @c subtract_with_carry_engine and seeds
      * it with @c value.
      */
     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(subtract_with_carry_engine,
                                                IntType, value)
     { seed(value); }
     /**
      * Constructs a new @c subtract_with_carry_engine and seeds
      * it with values produced by @c seq.generate().
      */
     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(subtract_with_carry_engine,
                                              SeedSeq, seq)
     { seed(seq); }
     /**
      * Constructs a new @c subtract_with_carry_engine and seeds
      * it with values from a range.  first is updated to point
      * one past the last value consumed.  If there are not
      * enough elements in the range to fill the entire state of
      * the generator, throws @c std::invalid_argument.
      */
     template<class It> subtract_with_carry_engine(It& first, It last)
     { seed(first,last); }
 
     // compiler-generated copy ctor and assignment operator are fine
 
     /** Seeds the generator with the default seed. */
     void seed() { seed(default_seed); }
     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(subtract_with_carry_engine,
                                         IntType, value)
     {
         typedef linear_congruential_engine<uint32_t,40014,0,2147483563> gen_t;
         gen_t intgen(static_cast<boost::uint32_t>(value == 0 ? default_seed : value));
         detail::generator_seed_seq<gen_t> gen(intgen);
         seed(gen);
     }
 
     /** Seeds the generator with values produced by @c seq.generate(). */
     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(subtract_with_carry, SeedSeq, seq)
     {
         detail::seed_array_int<w>(seq, x);
         carry = (x[long_lag-1] == 0);
         k = 0;
     }
 
     /**
      * Seeds the generator with values from a range.  Updates @c first to
      * point one past the last consumed value.  If the range does not
      * contain enough elements to fill the entire state of the generator,
      * throws @c std::invalid_argument.
      */
     template<class It>
     void seed(It& first, It last)
     {
         detail::fill_array_int<w>(first, last, x);
         carry = (x[long_lag-1] == 0);
         k = 0;
     }
 
     /** Returns the smallest value that the generator can produce. */
     static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
     { return 0; }
     /** Returns the largest value that the generator can produce. */
     static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
     { return boost::low_bits_mask_t<w>::sig_bits; }
 
     /** Returns the next value of the generator. */
     result_type operator()()
     {
         std::size_t short_index =
             (k < short_lag)?
                 (k + long_lag - short_lag) :
                 (k - short_lag);
         carry = do_update(k, short_index, carry);
         IntType result = x[k];
         ++k;
         if(k >= long_lag)
             k = 0;
         return result;
     }
 
     /** Advances the state of the generator by @c z. */
     void discard(boost::uintmax_t z)
     {
         detail::subtract_with_carry_discard::apply(*this, z);
     }
 
     /** Fills a range with random values. */
     template<class It>
     void generate(It first, It last)
     { detail::generate_from_int(*this, first, last); }
  
     /** Writes a @c subtract_with_carry_engine to a @c std::ostream. */
     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, subtract_with_carry_engine, f)
     {
         for(unsigned int j = 0; j < f.long_lag; ++j)
             os << f.compute(j) << ' ';
         os << f.carry;
         return os;
     }
 
     /** Reads a @c subtract_with_carry_engine from a @c std::istream. */
     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, subtract_with_carry_engine, f)
     {
         for(unsigned int j = 0; j < f.long_lag; ++j)
             is >> f.x[j] >> std::ws;
         is >> f.carry;
         f.k = 0;
         return is;
     }
 
     /**
      * Returns true if the two generators will produce identical
      * sequences of values.
      */
     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(subtract_with_carry_engine, x_, y)
     {
         for(unsigned int j = 0; j < r; ++j)
             if(x_.compute(j) != y.compute(j))
                 return false;
         return true;
     }
 
     /**
      * Returns true if the two generators will produce different
      * sequences of values.
      */
     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(subtract_with_carry_engine)
 
 private:
     /// \cond show_private
     // returns x(i-r+index), where index is in 0..r-1
     IntType compute(unsigned int index) const
     {
         return x[(k+index) % long_lag];
     }
 
     friend struct detail::subtract_with_carry_discard;
 
     IntType do_update(std::size_t current, std::size_t short_index, IntType carry_)
     {
         IntType delta;
         IntType temp = x[current] + carry_;
         if (x[short_index] >= temp) {
             // x(n) >= 0
             delta =  x[short_index] - temp;
             carry_ = 0;
         } else {
             // x(n) < 0
             delta = modulus - temp + x[short_index];
             carry_ = 1;
         }
         x[current] = delta;
         return carry_;
     }
     /// \endcond
 
     // state representation; next output (state) is x(i)
     //   x[0]  ... x[k] x[k+1] ... x[long_lag-1]     represents
     //  x(i-k) ... x(i) x(i+1) ... x(i-k+long_lag-1)
     // speed: base: 20-25 nsec
     // ranlux_4: 230 nsec, ranlux_7: 430 nsec, ranlux_14: 810 nsec
     // This state representation makes operator== and save/restore more
     // difficult, because we've already computed "too much" and thus
     // have to undo some steps to get at x(i-r) etc.
 
     // state representation: next output (state) is x(i)
     //   x[0]  ... x[k] x[k+1]          ... x[long_lag-1]     represents
     //  x(i-k) ... x(i) x(i-long_lag+1) ... x(i-k-1)
     // speed: base 28 nsec
     // ranlux_4: 370 nsec, ranlux_7: 688 nsec, ranlux_14: 1343 nsec
     IntType x[long_lag];
     std::size_t k;
     IntType carry;
 };
 
 #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
 //  A definition is required even for integral static constants
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const bool subtract_with_carry_engine<IntType, w, s, r>::has_fixed_range;
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const IntType subtract_with_carry_engine<IntType, w, s, r>::modulus;
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_engine<IntType, w, s, r>::word_size;
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_engine<IntType, w, s, r>::long_lag;
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_engine<IntType, w, s, r>::short_lag;
 template<class IntType, std::size_t w, std::size_t s, std::size_t r>
 const uint32_t subtract_with_carry_engine<IntType, w, s, r>::default_seed;
 #endif
 
 
 // use a floating-point representation to produce values in [0..1)
 /**
  * Instantiations of \subtract_with_carry_01_engine model a
  * \pseudo_random_number_generator.  The algorithm is
  * described in
  *
  *  @blockquote
  *  "A New Class of Random Number Generators", George
  *  Marsaglia and Arif Zaman, Annals of Applied Probability,
  *  Volume 1, Number 3 (1991), 462-480.
  *  @endblockquote
  */
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 class subtract_with_carry_01_engine
 {
 public:
     typedef RealType result_type;
     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
     BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
     BOOST_STATIC_CONSTANT(std::size_t, long_lag = r);
     BOOST_STATIC_CONSTANT(std::size_t, short_lag = s);
     BOOST_STATIC_CONSTANT(boost::uint32_t, default_seed = 19780503u);
 
     BOOST_STATIC_ASSERT(!std::numeric_limits<result_type>::is_integer);
 
     /** Creates a new \subtract_with_carry_01_engine using the default seed. */
     subtract_with_carry_01_engine() { init_modulus(); seed(); }
     /** Creates a new subtract_with_carry_01_engine and seeds it with value. */
     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(subtract_with_carry_01_engine,
                                                boost::uint32_t, value)
     { init_modulus(); seed(value); }
     /**
      * Creates a new \subtract_with_carry_01_engine and seeds with values
      * produced by seq.generate().
      */
     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(subtract_with_carry_01_engine,
                                              SeedSeq, seq)
     { init_modulus(); seed(seq); }
     /**
      * Creates a new \subtract_with_carry_01_engine and seeds it with values
      * from a range.  Advances first to point one past the last consumed
      * value.  If the range does not contain enough elements to fill the
      * entire state, throws @c std::invalid_argument.
      */
     template<class It> subtract_with_carry_01_engine(It& first, It last)
     { init_modulus(); seed(first,last); }
 
 private:
     /// \cond show_private
     void init_modulus()
     {
 #ifndef BOOST_NO_STDC_NAMESPACE
         // allow for Koenig lookup
         using std::pow;
 #endif
         _modulus = pow(RealType(2), RealType(word_size));
     }
     /// \endcond
 
 public:
     // compiler-generated copy ctor and assignment operator are fine
 
     /** Seeds the generator with the default seed. */
     void seed() { seed(default_seed); }
 
     /** Seeds the generator with @c value. */
     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(subtract_with_carry_01_engine,
                                         boost::uint32_t, value)
     {
         typedef linear_congruential_engine<uint32_t, 40014, 0, 2147483563> gen_t;
         gen_t intgen(value == 0 ? default_seed : value);
         detail::generator_seed_seq<gen_t> gen(intgen);
         seed(gen);
     }
 
     /** Seeds the generator with values produced by @c seq.generate(). */
     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(subtract_with_carry_01_engine,
                                       SeedSeq, seq)
     {
         detail::seed_array_real<w>(seq, x);
         carry = (x[long_lag-1] ? result_type(0) : result_type(1 / _modulus));
         k = 0;
     }
 
     /**
      * Seeds the generator with values from a range.  Updates first to
      * point one past the last consumed element.  If there are not
      * enough elements in the range to fill the entire state, throws
      * @c std::invalid_argument.
      */
     template<class It>
     void seed(It& first, It last)
     {
         detail::fill_array_real<w>(first, last, x);
         carry = (x[long_lag-1] ? result_type(0) : result_type(1 / _modulus));
         k = 0;
     }
 
     /** Returns the smallest value that the generator can produce. */
     static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
     { return result_type(0); }
     /** Returns the largest value that the generator can produce. */
     static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
     { return result_type(1); }
 
     /** Returns the next value of the generator. */
     result_type operator()()
     {
         std::size_t short_index =
             (k < short_lag) ?
                 (k + long_lag - short_lag) :
                 (k - short_lag);
         carry = do_update(k, short_index, carry);
         RealType result = x[k];
         ++k;
         if(k >= long_lag)
             k = 0;
         return result;
     }
 
     /** Advances the state of the generator by @c z. */
     void discard(boost::uintmax_t z)
     { detail::subtract_with_carry_discard::apply(*this, z); }
 
     /** Fills a range with random values. */
     template<class Iter>
     void generate(Iter first, Iter last)
     { detail::generate_from_real(*this, first, last); }
 
     /** Writes a \subtract_with_carry_01_engine to a @c std::ostream. */
     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, subtract_with_carry_01_engine, f)
     {
         std::ios_base::fmtflags oldflags =
             os.flags(os.dec | os.fixed | os.left); 
         for(unsigned int j = 0; j < f.long_lag; ++j)
             os << (f.compute(j) * f._modulus) << ' ';
         os << (f.carry * f._modulus);
         os.flags(oldflags);
         return os;
     }
     
     /** Reads a \subtract_with_carry_01_engine from a @c std::istream. */
     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, subtract_with_carry_01_engine, f)
     {
         RealType value;
         for(unsigned int j = 0; j < long_lag; ++j) {
             is >> value >> std::ws;
             f.x[j] = value / f._modulus;
         }
         is >> value;
         f.carry = value / f._modulus;
         f.k = 0;
         return is;
     }
 
     /** Returns true if the two generators will produce identical sequences. */
     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(subtract_with_carry_01_engine, x_, y)
     {
         for(unsigned int j = 0; j < r; ++j)
             if(x_.compute(j) != y.compute(j))
                 return false;
         return true;
     }
 
     /** Returns true if the two generators will produce different sequences. */
     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(subtract_with_carry_01_engine)
 
 private:
     /// \cond show_private
     RealType compute(unsigned int index) const
     {
         return x[(k+index) % long_lag];
     }
 
     friend struct detail::subtract_with_carry_discard;
 
     RealType do_update(std::size_t current, std::size_t short_index, RealType carry_)
     {
         RealType delta = x[short_index] - x[current] - carry_;
         if(delta < 0) {
             delta += RealType(1);
             carry_ = RealType(1)/_modulus;
         } else {
             carry_ = 0;
         }
         x[current] = delta;
         return carry_;
     }
     /// \endcond
     std::size_t k;
     RealType carry;
     RealType x[long_lag];
     RealType _modulus;
 };
 
 #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
 //  A definition is required even for integral static constants
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 const bool subtract_with_carry_01_engine<RealType, w, s, r>::has_fixed_range;
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_01_engine<RealType, w, s, r>::word_size;
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_01_engine<RealType, w, s, r>::long_lag;
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 const std::size_t subtract_with_carry_01_engine<RealType, w, s, r>::short_lag;
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 const uint32_t subtract_with_carry_01_engine<RealType, w, s, r>::default_seed;
 #endif
 
 
 /// \cond show_deprecated
 
 template<class IntType, IntType m, unsigned s, unsigned r, IntType v>
 class subtract_with_carry :
     public subtract_with_carry_engine<IntType,
         boost::static_log2<m>::value, s, r>
 {
     typedef subtract_with_carry_engine<IntType,
         boost::static_log2<m>::value, s, r> base_type;
 public:
     subtract_with_carry() {}
     BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(subtract_with_carry, Gen, gen)
     { seed(gen); }
     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(subtract_with_carry,
                                                IntType, val)
     { seed(val); }
     template<class It>
     subtract_with_carry(It& first, It last) : base_type(first, last) {}
     void seed() { base_type::seed(); }
     BOOST_RANDOM_DETAIL_GENERATOR_SEED(subtract_with_carry, Gen, gen)
     {
         detail::generator_seed_seq<Gen> seq(gen);
         base_type::seed(seq);
     }
     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(subtract_with_carry, IntType, val)
     { base_type::seed(val); }
     template<class It>
     void seed(It& first, It last) { base_type::seed(first, last); }
 };
 
 template<class RealType, int w, unsigned s, unsigned r, int v = 0>
 class subtract_with_carry_01 :
     public subtract_with_carry_01_engine<RealType, w, s, r>
 {
     typedef subtract_with_carry_01_engine<RealType, w, s, r> base_type;
 public:
     subtract_with_carry_01() {}
     BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(subtract_with_carry_01, Gen, gen)
     { seed(gen); }
     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(subtract_with_carry_01,
                                                uint32_t, val)
     { seed(val); }
     template<class It>
     subtract_with_carry_01(It& first, It last) : base_type(first, last) {}
     void seed() { base_type::seed(); }
     BOOST_RANDOM_DETAIL_GENERATOR_SEED(subtract_with_carry_01, Gen, gen)
     {
         detail::generator_seed_seq<Gen> seq(gen);
         base_type::seed(seq);
     }
     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(subtract_with_carry_01, uint32_t, val)
     { base_type::seed(val); }
     template<class It>
     void seed(It& first, It last) { base_type::seed(first, last); }
 };
 
 /// \endcond
 
 namespace detail {
 
 template<class Engine>
 struct generator_bits;
 
 template<class RealType, std::size_t w, std::size_t s, std::size_t r>
 struct generator_bits<subtract_with_carry_01_engine<RealType, w, s, r> > {
     static std::size_t value() { return w; }
 };
 
 template<class RealType, int w, unsigned s, unsigned r, int v>
 struct generator_bits<subtract_with_carry_01<RealType, w, s, r, v> > {
     static std::size_t value() { return w; }
 };
 
 }
 
 } // namespace random
 } // namespace boost
 
 #endif // BOOST_RANDOM_SUBTRACT_WITH_CARRY_HPP

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