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 /* 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/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 += 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 BOOST_CONSTEXPR 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 BOOST_CONSTEXPR 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 BOOST_CONSTEXPR uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
     /**
      * Returns the largest value that the generator can produce
      */
     static BOOST_CONSTEXPR 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

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