368 lines
13 KiB
C++
368 lines
13 KiB
C++
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/* boost random/mersenne_twister.hpp header file
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*
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* Copyright Jens Maurer 2000-2001
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id: mersenne_twister.hpp 60755 2010-03-22 00:45:06Z steven_watanabe $
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*
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* Revision history
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* 2001-02-18 moved to individual header files
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*/
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#ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
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#define BOOST_RANDOM_MERSENNE_TWISTER_HPP
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#include <iostream>
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#include <algorithm> // std::copy
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#include <stdexcept>
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#include <boost/config.hpp>
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#include <boost/limits.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/integer_traits.hpp>
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#include <boost/cstdint.hpp>
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#include <boost/random/linear_congruential.hpp>
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#include <boost/detail/workaround.hpp>
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#include <boost/random/detail/config.hpp>
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#include <boost/random/detail/ptr_helper.hpp>
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#include <boost/random/detail/seed.hpp>
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namespace boost {
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namespace random {
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/**
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* Instantiations of class template mersenne_twister model a
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* \pseudo_random_number_generator. It uses the algorithm described in
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*
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* @blockquote
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* "Mersenne Twister: A 623-dimensionally equidistributed uniform
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* pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura,
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* ACM Transactions on Modeling and Computer Simulation: Special Issue on
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* Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
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* @endblockquote
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*
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* @xmlnote
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* The boost variant has been implemented from scratch and does not
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* derive from or use mt19937.c provided on the above WWW site. However, it
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* was verified that both produce identical output.
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* @endxmlnote
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*
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* The seeding from an integer was changed in April 2005 to address a
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* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
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*
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* The quality of the generator crucially depends on the choice of the
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* parameters. User code should employ one of the sensibly parameterized
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* generators such as \mt19937 instead.
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*
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* The generator requires considerable amounts of memory for the storage of
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* its state array. For example, \mt11213b requires about 1408 bytes and
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* \mt19937 requires about 2496 bytes.
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*/
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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class mersenne_twister
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{
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public:
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typedef UIntType result_type;
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BOOST_STATIC_CONSTANT(int, word_size = w);
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BOOST_STATIC_CONSTANT(int, state_size = n);
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BOOST_STATIC_CONSTANT(int, shift_size = m);
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BOOST_STATIC_CONSTANT(int, mask_bits = r);
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BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
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BOOST_STATIC_CONSTANT(int, output_u = u);
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BOOST_STATIC_CONSTANT(int, output_s = s);
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BOOST_STATIC_CONSTANT(UIntType, output_b = b);
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BOOST_STATIC_CONSTANT(int, output_t = t);
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BOOST_STATIC_CONSTANT(UIntType, output_c = c);
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BOOST_STATIC_CONSTANT(int, output_l = l);
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BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
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/**
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* Constructs a @c mersenne_twister and calls @c seed().
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*/
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mersenne_twister() { seed(); }
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/**
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* Constructs a @c mersenne_twister and calls @c seed(value).
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, value)
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{ seed(value); }
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template<class It> mersenne_twister(It& first, It last) { seed(first,last); }
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/**
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* Constructs a mersenne_twister and calls @c seed(gen).
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*
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* @xmlnote
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* The copy constructor will always be preferred over
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* the templated constructor.
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* @endxmlnote
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*/
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BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Generator, gen)
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{ seed(gen); }
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// compiler-generated copy ctor and assignment operator are fine
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/** Calls @c seed(result_type(5489)). */
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void seed() { seed(UIntType(5489)); }
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/**
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* Sets the state x(0) to v mod 2w. Then, iteratively,
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* sets x(i) to (i + 1812433253 * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
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* for i = 1 .. n-1. x(n) is the first value to be returned by operator().
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, value)
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{
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// New seeding algorithm from
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// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
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// In the previous versions, MSBs of the seed affected only MSBs of the
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// state x[].
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const UIntType mask = ~0u;
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x[0] = value & mask;
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for (i = 1; i < n; i++) {
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// See Knuth "The Art of Computer Programming" Vol. 2, 3rd ed., page 106
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x[i] = (1812433253UL * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
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}
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}
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/**
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* Sets the state of this mersenne_twister to the values
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* returned by n invocations of gen.
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*
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* Complexity: Exactly n invocations of gen.
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*/
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BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Generator, gen)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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BOOST_STATIC_ASSERT(!std::numeric_limits<result_type>::is_signed);
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#endif
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// I could have used std::generate_n, but it takes "gen" by value
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for(int j = 0; j < n; j++)
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x[j] = gen();
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i = n;
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}
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template<class It>
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void seed(It& first, It last)
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{
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int j;
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for(j = 0; j < n && first != last; ++j, ++first)
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x[j] = *first;
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i = n;
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if(first == last && j < n)
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throw std::invalid_argument("mersenne_twister::seed");
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}
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result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return 0; }
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result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
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{
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// avoid "left shift count >= with of type" warning
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result_type res = 0;
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for(int j = 0; j < w; ++j)
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res |= (1u << j);
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return res;
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}
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result_type operator()();
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static bool validation(result_type v) { return val == v; }
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#ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
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#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
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template<class CharT, class Traits>
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friend std::basic_ostream<CharT,Traits>&
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operator<<(std::basic_ostream<CharT,Traits>& os, const mersenne_twister& mt)
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{
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for(int j = 0; j < mt.state_size; ++j)
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os << mt.compute(j) << " ";
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return os;
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}
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template<class CharT, class Traits>
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friend std::basic_istream<CharT,Traits>&
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operator>>(std::basic_istream<CharT,Traits>& is, mersenne_twister& mt)
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{
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for(int j = 0; j < mt.state_size; ++j)
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is >> mt.x[j] >> std::ws;
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// MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
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// value parameter "n" available from the class template scope, so use
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// the static constant with the same value
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mt.i = mt.state_size;
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return is;
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}
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#endif
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friend bool operator==(const mersenne_twister& x, const mersenne_twister& y)
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{
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for(int j = 0; j < state_size; ++j)
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if(x.compute(j) != y.compute(j))
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return false;
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return true;
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}
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friend bool operator!=(const mersenne_twister& x, const mersenne_twister& y)
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{ return !(x == y); }
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#else
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// Use a member function; Streamable concept not supported.
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bool operator==(const mersenne_twister& rhs) const
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{
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for(int j = 0; j < state_size; ++j)
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if(compute(j) != rhs.compute(j))
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return false;
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return true;
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}
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bool operator!=(const mersenne_twister& rhs) const
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{ return !(*this == rhs); }
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#endif
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private:
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/// \cond hide_private_members
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// returns x(i-n+index), where index is in 0..n-1
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UIntType compute(unsigned int index) const
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{
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// equivalent to (i-n+index) % 2n, but doesn't produce negative numbers
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return x[ (i + n + index) % (2*n) ];
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}
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void twist(int block);
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/// \endcond
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// state representation: next output is o(x(i))
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// x[0] ... x[k] x[k+1] ... x[n-1] x[n] ... x[2*n-1] represents
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// x(i-k) ... x(i) x(i+1) ... x(i-k+n-1) x(i-k-n) ... x[i(i-k-1)]
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// The goal is to always have x(i-n) ... x(i-1) available for
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// operator== and save/restore.
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UIntType x[2*n];
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int i;
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};
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#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
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// A definition is required even for integral static constants
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const bool mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::has_fixed_range;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::state_size;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::shift_size;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::mask_bits;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::parameter_a;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_u;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_s;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_b;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_t;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const UIntType mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_c;
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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const int mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::output_l;
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#endif
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/// \cond hide_private_members
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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void mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::twist(int block)
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{
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const UIntType upper_mask = (~0u) << r;
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const UIntType lower_mask = ~upper_mask;
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if(block == 0) {
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for(int j = n; j < 2*n; j++) {
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UIntType y = (x[j-n] & upper_mask) | (x[j-(n-1)] & lower_mask);
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x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0);
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}
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} else if (block == 1) {
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// split loop to avoid costly modulo operations
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{ // extra scope for MSVC brokenness w.r.t. for scope
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for(int j = 0; j < n-m; j++) {
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UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask);
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x[j] = x[j+n+m] ^ (y >> 1) ^ (y&1 ? a : 0);
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}
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}
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for(int j = n-m; j < n-1; j++) {
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UIntType y = (x[j+n] & upper_mask) | (x[j+n+1] & lower_mask);
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x[j] = x[j-(n-m)] ^ (y >> 1) ^ (y&1 ? a : 0);
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}
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// last iteration
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UIntType y = (x[2*n-1] & upper_mask) | (x[0] & lower_mask);
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x[n-1] = x[m-1] ^ (y >> 1) ^ (y&1 ? a : 0);
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i = 0;
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}
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}
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/// \endcond
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template<class UIntType, int w, int n, int m, int r, UIntType a, int u,
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int s, UIntType b, int t, UIntType c, int l, UIntType val>
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inline typename mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::result_type
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mersenne_twister<UIntType,w,n,m,r,a,u,s,b,t,c,l,val>::operator()()
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{
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if(i == n)
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twist(0);
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else if(i >= 2*n)
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twist(1);
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// Step 4
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UIntType z = x[i];
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++i;
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z ^= (z >> u);
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z ^= ((z << s) & b);
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z ^= ((z << t) & c);
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z ^= (z >> l);
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return z;
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}
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} // namespace random
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/**
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* The specializations \mt11213b and \mt19937 are from
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*
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* @blockquote
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* "Mersenne Twister: A 623-dimensionally equidistributed
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* uniform pseudo-random number generator", Makoto Matsumoto
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* and Takuji Nishimura, ACM Transactions on Modeling and
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* Computer Simulation: Special Issue on Uniform Random Number
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* Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
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* @endblockquote
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*/
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typedef random::mersenne_twister<uint32_t,32,351,175,19,0xccab8ee7,11,
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7,0x31b6ab00,15,0xffe50000,17, 0xa37d3c92> mt11213b;
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/**
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* The specializations \mt11213b and \mt19937 are from
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*
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* @blockquote
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* "Mersenne Twister: A 623-dimensionally equidistributed
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* uniform pseudo-random number generator", Makoto Matsumoto
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* and Takuji Nishimura, ACM Transactions on Modeling and
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* Computer Simulation: Special Issue on Uniform Random Number
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* Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
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* @endblockquote
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*/
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typedef random::mersenne_twister<uint32_t,32,624,397,31,0x9908b0df,11,
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7,0x9d2c5680,15,0xefc60000,18, 3346425566U> mt19937;
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} // namespace boost
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BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
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#endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP
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