/* boost random/mersenne_twister.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: mersenne_twister.hpp 60755 2010-03-22 00:45:06Z steven_watanabe $ | |
* | |
* Revision history | |
* 2001-02-18 moved to individual header files | |
*/ | |
#ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP | |
#define BOOST_RANDOM_MERSENNE_TWISTER_HPP | |
#include <iostream> | |
#include <algorithm> // std::copy | |
#include <stdexcept> | |
#include <boost/config.hpp> | |
#include <boost/limits.hpp> | |
#include <boost/static_assert.hpp> | |
#include <boost/integer_traits.hpp> | |
#include <boost/cstdint.hpp> | |
#include <boost/random/linear_congruential.hpp> | |
#include <boost/detail/workaround.hpp> | |
#include <boost/random/detail/config.hpp> | |
#include <boost/random/detail/ptr_helper.hpp> | |
#include <boost/random/detail/seed.hpp> | |
namespace boost { | |
namespace random { | |
/** | |
* Instantiations of class template mersenne_twister model a | |
* \pseudo_random_number_generator. It uses the algorithm described in | |
* | |
* @blockquote | |
* "Mersenne Twister: A 623-dimensionally equidistributed uniform | |
* pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura, | |
* ACM Transactions on Modeling and Computer Simulation: Special Issue on | |
* Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30. | |
* @endblockquote | |
* | |
* @xmlnote | |
* The boost variant has been implemented from scratch and does not | |
* derive from or use mt19937.c provided on the above WWW site. However, it | |
* was verified that both produce identical output. | |
* @endxmlnote | |
* | |
* The seeding from an integer was changed in April 2005 to address a | |
* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>. | |
* | |
* The quality of the generator crucially depends on the choice of the | |
* parameters. User code should employ one of the sensibly parameterized | |
* generators such as \mt19937 instead. | |
* | |
* The generator requires considerable amounts of memory for the storage of | |
* its state array. For example, \mt11213b requires about 1408 bytes and | |
* \mt19937 requires about 2496 bytes. | |
*/ | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
class mersenne_twister | |
{ | |
public: | |
typedef UIntType result_type; | |
BOOST_STATIC_CONSTANT(int, word_size = w); | |
BOOST_STATIC_CONSTANT(int, state_size = n); | |
BOOST_STATIC_CONSTANT(int, shift_size = m); | |
BOOST_STATIC_CONSTANT(int, mask_bits = r); | |
BOOST_STATIC_CONSTANT(UIntType, parameter_a = a); | |
BOOST_STATIC_CONSTANT(int, output_u = u); | |
BOOST_STATIC_CONSTANT(int, output_s = s); | |
BOOST_STATIC_CONSTANT(UIntType, output_b = b); | |
BOOST_STATIC_CONSTANT(int, output_t = t); | |
BOOST_STATIC_CONSTANT(UIntType, output_c = c); | |
BOOST_STATIC_CONSTANT(int, output_l = l); | |
BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); | |
/** | |
* Constructs a @c mersenne_twister and calls @c seed(). | |
*/ | |
mersenne_twister() { seed(); } | |
/** | |
* Constructs a @c mersenne_twister and calls @c seed(value). | |
*/ | |
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, value) | |
{ seed(value); } | |
template<class It> mersenne_twister(It& first, It last) { seed(first,last); } | |
/** | |
* Constructs a mersenne_twister and calls @c seed(gen). | |
* | |
* @xmlnote | |
* The copy constructor will always be preferred over | |
* the templated constructor. | |
* @endxmlnote | |
*/ | |
BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Generator, gen) | |
{ seed(gen); } | |
// compiler-generated copy ctor and assignment operator are fine | |
/** Calls @c seed(result_type(5489)). */ | |
void seed() { seed(UIntType(5489)); } | |
/** | |
* Sets the state x(0) to v mod 2w. Then, iteratively, | |
* sets x(i) to (i + 1812433253 * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup> | |
* for i = 1 .. n-1. x(n) is the first value to be returned by operator(). | |
*/ | |
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, value) | |
{ | |
// New seeding algorithm from | |
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html | |
// In the previous versions, MSBs of the seed affected only MSBs of the | |
// state x[]. | |
const UIntType mask = ~0u; | |
x[0] = value & mask; | |
for (i = 1; i < n; i++) { | |
// See Knuth "The Art of Computer Programming" Vol. 2, 3rd ed., page 106 | |
x[i] = (1812433253UL * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask; | |
} | |
} | |
/** | |
* Sets the state of this mersenne_twister to the values | |
* returned by n invocations of gen. | |
* | |
* Complexity: Exactly n invocations of gen. | |
*/ | |
BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Generator, gen) | |
{ | |
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS | |
BOOST_STATIC_ASSERT(!std::numeric_limits<result_type>::is_signed); | |
#endif | |
// I could have used std::generate_n, but it takes "gen" by value | |
for(int j = 0; j < n; j++) | |
x[j] = gen(); | |
i = n; | |
} | |
template<class It> | |
void seed(It& first, It last) | |
{ | |
int j; | |
for(j = 0; j < n && first != last; ++j, ++first) | |
x[j] = *first; | |
i = n; | |
if(first == last && j < n) | |
throw std::invalid_argument("mersenne_twister::seed"); | |
} | |
result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return 0; } | |
result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const | |
{ | |
// avoid "left shift count >= with of type" warning | |
result_type res = 0; | |
for(int j = 0; j < w; ++j) | |
res |= (1u << j); | |
return res; | |
} | |
result_type operator()(); | |
static bool validation(result_type v) { return val == v; } | |
#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, const mersenne_twister& mt) | |
{ | |
for(int j = 0; j < mt.state_size; ++j) | |
os << mt.compute(j) << " "; | |
return os; | |
} | |
template<class CharT, class Traits> | |
friend std::basic_istream<CharT,Traits>& | |
operator>>(std::basic_istream<CharT,Traits>& is, mersenne_twister& mt) | |
{ | |
for(int j = 0; j < mt.state_size; ++j) | |
is >> mt.x[j] >> std::ws; | |
// MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template | |
// value parameter "n" available from the class template scope, so use | |
// the static constant with the same value | |
mt.i = mt.state_size; | |
return is; | |
} | |
#endif | |
friend bool operator==(const mersenne_twister& x, const mersenne_twister& y) | |
{ | |
for(int j = 0; j < state_size; ++j) | |
if(x.compute(j) != y.compute(j)) | |
return false; | |
return true; | |
} | |
friend bool operator!=(const mersenne_twister& x, const mersenne_twister& y) | |
{ return !(x == y); } | |
#else | |
// Use a member function; Streamable concept not supported. | |
bool operator==(const mersenne_twister& rhs) const | |
{ | |
for(int j = 0; j < state_size; ++j) | |
if(compute(j) != rhs.compute(j)) | |
return false; | |
return true; | |
} | |
bool operator!=(const mersenne_twister& rhs) const | |
{ return !(*this == rhs); } | |
#endif | |
private: | |
/// \cond hide_private_members | |
// returns x(i-n+index), where index is in 0..n-1 | |
UIntType compute(unsigned int index) const | |
{ | |
// equivalent to (i-n+index) % 2n, but doesn't produce negative numbers | |
return x[ (i + n + index) % (2*n) ]; | |
} | |
void twist(int block); | |
/// \endcond | |
// state representation: next output is o(x(i)) | |
// x[0] ... x[k] x[k+1] ... x[n-1] x[n] ... x[2*n-1] represents | |
// x(i-k) ... x(i) x(i+1) ... x(i-k+n-1) x(i-k-n) ... x[i(i-k-1)] | |
// The goal is to always have x(i-n) ... x(i-1) available for | |
// operator== and save/restore. | |
UIntType x[2*n]; | |
int i; | |
}; | |
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION | |
// A definition is required even for integral static constants | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const bool mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::has_fixed_range; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::state_size; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::shift_size; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::mask_bits; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::parameter_a; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_u; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_s; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_b; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_t; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_c; | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_l; | |
#endif | |
/// \cond hide_private_members | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
void mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::twist(int block) | |
{ | |
const UIntType upper_mask = (~0u) << r; | |
const UIntType lower_mask = ~upper_mask; | |
if(block == 0) { | |
for(int j = n; j < 2*n; j++) { | |
UIntType y = (x[j-n] & upper_mask) | (x[j-(n-1)] & lower_mask); | |
x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0); | |
} | |
} else if (block == 1) { | |
// split loop to avoid costly modulo operations | |
{ // extra scope for MSVC brokenness w.r.t. for scope | |
for(int j = 0; j < n-m; j++) { | |
UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask); | |
x[j] = x[j+n+m] ^ (y >> 1) ^ (y&1 ? a : 0); | |
} | |
} | |
for(int j = n-m; j < n-1; j++) { | |
UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask); | |
x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0); | |
} | |
// last iteration | |
UIntType y = (x[2*n-1] & upper_mask) | (x[0] & lower_mask); | |
x[n-1] = x[m-1] ^ (y >> 1) ^ (y&1 ? a : 0); | |
i = 0; | |
} | |
} | |
/// \endcond | |
template<class UIntType, int w, int n, int m, int r, UIntType a, int u, | |
int s, UIntType b, int t, UIntType c, int l, UIntType val> | |
inline typename mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::result_type | |
mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::operator()() | |
{ | |
if(i == n) | |
twist(0); | |
else if(i >= 2*n) | |
twist(1); | |
// Step 4 | |
UIntType z = x[i]; | |
++i; | |
z ^= (z >> u); | |
z ^= ((z << s) & b); | |
z ^= ((z << t) & c); | |
z ^= (z >> l); | |
return z; | |
} | |
} // namespace random | |
/** | |
* The specializations \mt11213b and \mt19937 are from | |
* | |
* @blockquote | |
* "Mersenne Twister: A 623-dimensionally equidistributed | |
* uniform pseudo-random number generator", Makoto Matsumoto | |
* and Takuji Nishimura, ACM Transactions on Modeling and | |
* Computer Simulation: Special Issue on Uniform Random Number | |
* Generation, Vol. 8, No. 1, January 1998, pp. 3-30. | |
* @endblockquote | |
*/ | |
typedef random::mersenne_twister<uint32_t,32,351,175,19,0xccab8ee7,11, | |
7,0x31b6ab00,15,0xffe50000,17, 0xa37d3c92> mt11213b; | |
/** | |
* The specializations \mt11213b and \mt19937 are from | |
* | |
* @blockquote | |
* "Mersenne Twister: A 623-dimensionally equidistributed | |
* uniform pseudo-random number generator", Makoto Matsumoto | |
* and Takuji Nishimura, ACM Transactions on Modeling and | |
* Computer Simulation: Special Issue on Uniform Random Number | |
* Generation, Vol. 8, No. 1, January 1998, pp. 3-30. | |
* @endblockquote | |
*/ | |
typedef random::mersenne_twister<uint32_t,32,624,397,31,0x9908b0df,11, | |
7,0x9d2c5680,15,0xefc60000,18, 3346425566U> mt19937; | |
} // namespace boost | |
BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937) | |
#endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP |