368 lines
13 KiB
C++
368 lines
13 KiB
C++
/* 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
|