williamr@2: /* boost random/mersenne_twister.hpp header file
williamr@2:  *
williamr@2:  * Copyright Jens Maurer 2000-2001
williamr@2:  * Distributed under the Boost Software License, Version 1.0. (See
williamr@2:  * accompanying file LICENSE_1_0.txt or copy at
williamr@2:  * http://www.boost.org/LICENSE_1_0.txt)
williamr@2:  *
williamr@2:  * See http://www.boost.org for most recent version including documentation.
williamr@2:  *
williamr@2:  * $Id: mersenne_twister.hpp,v 1.20 2005/07/21 22:04:31 jmaurer Exp $
williamr@2:  *
williamr@2:  * Revision history
williamr@2:  *  2001-02-18  moved to individual header files
williamr@2:  */
williamr@2: 
williamr@2: #ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
williamr@2: #define BOOST_RANDOM_MERSENNE_TWISTER_HPP
williamr@2: 
williamr@2: #include <iostream>
williamr@2: #include <algorithm>     // std::copy
williamr@2: #include <stdexcept>
williamr@2: #include <boost/config.hpp>
williamr@2: #include <boost/limits.hpp>
williamr@2: #include <boost/static_assert.hpp>
williamr@2: #include <boost/integer_traits.hpp>
williamr@2: #include <boost/cstdint.hpp>
williamr@2: #include <boost/random/linear_congruential.hpp>
williamr@2: #include <boost/detail/workaround.hpp>
williamr@2: #include <boost/random/detail/ptr_helper.hpp>
williamr@2: 
williamr@2: namespace boost {
williamr@2: namespace random {
williamr@2: 
williamr@2: // http://www.math.keio.ac.jp/matumoto/emt.html
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: class mersenne_twister
williamr@2: {
williamr@2: public:
williamr@2:   typedef UIntType result_type;
williamr@2:   BOOST_STATIC_CONSTANT(int, word_size = w);
williamr@2:   BOOST_STATIC_CONSTANT(int, state_size = n);
williamr@2:   BOOST_STATIC_CONSTANT(int, shift_size = m);
williamr@2:   BOOST_STATIC_CONSTANT(int, mask_bits = r);
williamr@2:   BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
williamr@2:   BOOST_STATIC_CONSTANT(int, output_u = u);
williamr@2:   BOOST_STATIC_CONSTANT(int, output_s = s);
williamr@2:   BOOST_STATIC_CONSTANT(UIntType, output_b = b);
williamr@2:   BOOST_STATIC_CONSTANT(int, output_t = t);
williamr@2:   BOOST_STATIC_CONSTANT(UIntType, output_c = c);
williamr@2:   BOOST_STATIC_CONSTANT(int, output_l = l);
williamr@2: 
williamr@2:   BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
williamr@2:   
williamr@2:   mersenne_twister() { seed(); }
williamr@2: 
williamr@2: #if defined(__SUNPRO_CC) && (__SUNPRO_CC <= 0x520)
williamr@2:   // Work around overload resolution problem (Gennadiy E. Rozental)
williamr@2:   explicit mersenne_twister(const UIntType& value)
williamr@2: #else
williamr@2:   explicit mersenne_twister(UIntType value)
williamr@2: #endif
williamr@2:   { seed(value); }
williamr@2:   template<class It> mersenne_twister(It& first, It last) { seed(first,last); }
williamr@2: 
williamr@2:   template<class Generator>
williamr@2:   explicit mersenne_twister(Generator & gen) { seed(gen); }
williamr@2: 
williamr@2:   // compiler-generated copy ctor and assignment operator are fine
williamr@2: 
williamr@2:   void seed() { seed(UIntType(5489)); }
williamr@2: 
williamr@2: #if defined(__SUNPRO_CC) && (__SUNPRO_CC <= 0x520)
williamr@2:   // Work around overload resolution problem (Gennadiy E. Rozental)
williamr@2:   void seed(const UIntType& value)
williamr@2: #else
williamr@2:   void seed(UIntType value)
williamr@2: #endif
williamr@2:   {
williamr@2:     // New seeding algorithm from 
williamr@2:     // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
williamr@2:     // In the previous versions, MSBs of the seed affected only MSBs of the
williamr@2:     // state x[].
williamr@2:     const UIntType mask = ~0u;
williamr@2:     x[0] = value & mask;
williamr@2:     for (i = 1; i < n; i++) {
williamr@2:       // See Knuth "The Art of Computer Programming" Vol. 2, 3rd ed., page 106
williamr@2:       x[i] = (1812433253UL * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
williamr@2:     }
williamr@2:   }
williamr@2: 
williamr@2:   // For GCC, moving this function out-of-line prevents inlining, which may
williamr@2:   // reduce overall object code size.  However, MSVC does not grok
williamr@2:   // out-of-line definitions of member function templates.
williamr@2:   template<class Generator>
williamr@2:   void seed(Generator & gen)
williamr@2:   {
williamr@2: #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
williamr@2:     BOOST_STATIC_ASSERT(!std::numeric_limits<result_type>::is_signed);
williamr@2: #endif
williamr@2:     // I could have used std::generate_n, but it takes "gen" by value
williamr@2:     for(int j = 0; j < n; j++)
williamr@2:       x[j] = gen();
williamr@2:     i = n;
williamr@2:   }
williamr@2: 
williamr@2:   template<class It>
williamr@2:   void seed(It& first, It last)
williamr@2:   {
williamr@2:     int j;
williamr@2:     for(j = 0; j < n && first != last; ++j, ++first)
williamr@2:       x[j] = *first;
williamr@2:     i = n;
williamr@2:     if(first == last && j < n)
williamr@2:       throw std::invalid_argument("mersenne_twister::seed");
williamr@2:   }
williamr@2:   
williamr@2:   result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return 0; }
williamr@2:   result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
williamr@2:   {
williamr@2:     // avoid "left shift count >= with of type" warning
williamr@2:     result_type res = 0;
williamr@2:     for(int i = 0; i < w; ++i)
williamr@2:       res |= (1u << i);
williamr@2:     return res;
williamr@2:   }
williamr@2: 
williamr@2:   result_type operator()();
williamr@2:   static bool validation(result_type v) { return val == v; }
williamr@2: 
williamr@2: #ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
williamr@2: 
williamr@2: #ifndef BOOST_NO_MEMBER_TEMPLATE_FRIENDS
williamr@2:   template<class CharT, class Traits>
williamr@2:   friend std::basic_ostream<CharT,Traits>&
williamr@2:   operator<<(std::basic_ostream<CharT,Traits>& os, const mersenne_twister& mt)
williamr@2:   {
williamr@2:     for(int j = 0; j < mt.state_size; ++j)
williamr@2:       os << mt.compute(j) << " ";
williamr@2:     return os;
williamr@2:   }
williamr@2: 
williamr@2:   template<class CharT, class Traits>
williamr@2:   friend std::basic_istream<CharT,Traits>&
williamr@2:   operator>>(std::basic_istream<CharT,Traits>& is, mersenne_twister& mt)
williamr@2:   {
williamr@2:     for(int j = 0; j < mt.state_size; ++j)
williamr@2:       is >> mt.x[j] >> std::ws;
williamr@2:     // MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
williamr@2:     // value parameter "n" available from the class template scope, so use
williamr@2:     // the static constant with the same value
williamr@2:     mt.i = mt.state_size;
williamr@2:     return is;
williamr@2:   }
williamr@2: #endif
williamr@2: 
williamr@2:   friend bool operator==(const mersenne_twister& x, const mersenne_twister& y)
williamr@2:   {
williamr@2:     for(int j = 0; j < state_size; ++j)
williamr@2:       if(x.compute(j) != y.compute(j))
williamr@2:         return false;
williamr@2:     return true;
williamr@2:   }
williamr@2: 
williamr@2:   friend bool operator!=(const mersenne_twister& x, const mersenne_twister& y)
williamr@2:   { return !(x == y); }
williamr@2: #else
williamr@2:   // Use a member function; Streamable concept not supported.
williamr@2:   bool operator==(const mersenne_twister& rhs) const
williamr@2:   {
williamr@2:     for(int j = 0; j < state_size; ++j)
williamr@2:       if(compute(j) != rhs.compute(j))
williamr@2:         return false;
williamr@2:     return true;
williamr@2:   }
williamr@2: 
williamr@2:   bool operator!=(const mersenne_twister& rhs) const
williamr@2:   { return !(*this == rhs); }
williamr@2: #endif
williamr@2: 
williamr@2: private:
williamr@2:   // returns x(i-n+index), where index is in 0..n-1
williamr@2:   UIntType compute(unsigned int index) const
williamr@2:   {
williamr@2:     // equivalent to (i-n+index) % 2n, but doesn't produce negative numbers
williamr@2:     return x[ (i + n + index) % (2*n) ];
williamr@2:   }
williamr@2:   void twist(int block);
williamr@2: 
williamr@2:   // state representation: next output is o(x(i))
williamr@2:   //   x[0]  ... x[k] x[k+1] ... x[n-1]     x[n]     ... x[2*n-1]   represents
williamr@2:   //  x(i-k) ... x(i) x(i+1) ... x(i-k+n-1) x(i-k-n) ... x[i(i-k-1)]
williamr@2:   // The goal is to always have x(i-n) ... x(i-1) available for
williamr@2:   // operator== and save/restore.
williamr@2: 
williamr@2:   UIntType x[2*n]; 
williamr@2:   int i;
williamr@2: };
williamr@2: 
williamr@2: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
williamr@2: //  A definition is required even for integral static constants
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const bool mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::has_fixed_range;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::state_size;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::shift_size;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::mask_bits;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::parameter_a;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_u;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_s;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_b;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_t;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_c;
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_l;
williamr@2: #endif
williamr@2: 
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: void mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::twist(int block)
williamr@2: {
williamr@2:   const UIntType upper_mask = (~0u) << r;
williamr@2:   const UIntType lower_mask = ~upper_mask;
williamr@2: 
williamr@2:   if(block == 0) {
williamr@2:     for(int j = n; j < 2*n; j++) {
williamr@2:       UIntType y = (x[j-n] & upper_mask) | (x[j-(n-1)] & lower_mask);
williamr@2:       x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0);
williamr@2:     }
williamr@2:   } else if (block == 1) {
williamr@2:     // split loop to avoid costly modulo operations
williamr@2:     {  // extra scope for MSVC brokenness w.r.t. for scope
williamr@2:       for(int j = 0; j < n-m; j++) {
williamr@2:         UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask);
williamr@2:         x[j] = x[j+n+m] ^ (y >> 1) ^ (y&1 ? a : 0);
williamr@2:       }
williamr@2:     }
williamr@2:     
williamr@2:     for(int j = n-m; j < n-1; j++) {
williamr@2:       UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask);
williamr@2:       x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0);
williamr@2:     }
williamr@2:     // last iteration
williamr@2:     UIntType y = (x[2*n-1] & upper_mask) | (x[0] & lower_mask);
williamr@2:     x[n-1] = x[m-1] ^ (y >> 1) ^ (y&1 ? a : 0);
williamr@2:     i = 0;
williamr@2:   }
williamr@2: }
williamr@2: 
williamr@2: template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
williamr@2:   int s, UIntType b, int t, UIntType c, int l, UIntType val>
williamr@2: inline typename mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::result_type
williamr@2: mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::operator()()
williamr@2: {
williamr@2:   if(i == n)
williamr@2:     twist(0);
williamr@2:   else if(i >= 2*n)
williamr@2:     twist(1);
williamr@2:   // Step 4
williamr@2:   UIntType z = x[i];
williamr@2:   ++i;
williamr@2:   z ^= (z >> u);
williamr@2:   z ^= ((z << s) & b);
williamr@2:   z ^= ((z << t) & c);
williamr@2:   z ^= (z >> l);
williamr@2:   return z;
williamr@2: }
williamr@2: 
williamr@2: } // namespace random
williamr@2: 
williamr@2: 
williamr@2: typedef random::mersenne_twister<uint32_t,32,351,175,19,0xccab8ee7,11,
williamr@2:   7,0x31b6ab00,15,0xffe50000,17, 0xa37d3c92> mt11213b;
williamr@2: 
williamr@2: // validation by experiment from mt19937.c
williamr@2: typedef random::mersenne_twister<uint32_t,32,624,397,31,0x9908b0df,11,
williamr@2:   7,0x9d2c5680,15,0xefc60000,18, 3346425566U> mt19937;
williamr@2: 
williamr@2: } // namespace boost
williamr@2: 
williamr@2: BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
williamr@2: 
williamr@2: #endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP