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편집 파일: mersenne_twister.hpp

/* boost random/mersenne_twister.hpp header file * * Copyright Jens Maurer 2000-2001 * Copyright Steven Watanabe 2010 * 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 * 2013-10-14 fixed some warnings with Wshadow (mgaunard) * 2001-02-18 moved to individual header files */ #ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP #define BOOST_RANDOM_MERSENNE_TWISTER_HPP #include <iosfwd> #include <istream> #include <stdexcept> #include <boost/config.hpp> #include <boost/cstdint.hpp> #include <boost/integer/integer_mask.hpp> #include <boost/random/detail/config.hpp> #include <boost/random/detail/ptr_helper.hpp> #include <boost/random/detail/seed.hpp> #include <boost/random/detail/seed_impl.hpp> #include <boost/random/detail/generator_seed_seq.hpp> #include <boost/random/detail/polynomial.hpp> #include <boost/random/detail/disable_warnings.hpp> namespace boost { namespace random { /** * Instantiations of class template mersenne_twister_engine 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, std::size_t w, std::size_t n, std::size_t m, std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s, UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f> class mersenne_twister_engine { public: typedef UIntType result_type; BOOST_STATIC_CONSTANT(std::size_t, word_size = w); BOOST_STATIC_CONSTANT(std::size_t, state_size = n); BOOST_STATIC_CONSTANT(std::size_t, shift_size = m); BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r); BOOST_STATIC_CONSTANT(UIntType, xor_mask = a); BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u); BOOST_STATIC_CONSTANT(UIntType, tempering_d = d); BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s); BOOST_STATIC_CONSTANT(UIntType, tempering_b = b); BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t); BOOST_STATIC_CONSTANT(UIntType, tempering_c = c); BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l); BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f); BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u); // backwards compatibility BOOST_STATIC_CONSTANT(UIntType, parameter_a = a); BOOST_STATIC_CONSTANT(std::size_t, output_u = u); BOOST_STATIC_CONSTANT(std::size_t, output_s = s); BOOST_STATIC_CONSTANT(UIntType, output_b = b); BOOST_STATIC_CONSTANT(std::size_t, output_t = t); BOOST_STATIC_CONSTANT(UIntType, output_c = c); BOOST_STATIC_CONSTANT(std::size_t, output_l = l); // old Boost.Random concept requirements BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); /** * Constructs a @c mersenne_twister_engine and calls @c seed(). */ mersenne_twister_engine() { seed(); } /** * Constructs a @c mersenne_twister_engine and calls @c seed(value). */ BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine, UIntType, value) { seed(value); } template<class It> mersenne_twister_engine(It& first, It last) { seed(first,last); } /** * Constructs a mersenne_twister_engine and calls @c seed(gen). * * @xmlnote * The copy constructor will always be preferred over * the templated constructor. * @endxmlnote */ BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine, SeedSeq, seq) { seed(seq); } // compiler-generated copy ctor and assignment operator are fine /** Calls @c seed(default_seed). */ void seed() { seed(default_seed); } /** * Sets the state x(0) to v mod 2w. Then, iteratively, * sets x(i) to * (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2^w * for i = 1 .. n-1. x(n) is the first value to be returned by operator(). */ BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, 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 = (max)(); 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] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask; } normalize_state(); } /** * Seeds a mersenne_twister_engine using values produced by seq.generate(). */ BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq) { detail::seed_array_int<w>(seq, x); i = n; normalize_state(); } /** Sets the state of the generator using values from an iterator range. */ template<class It> void seed(It& first, It last) { detail::fill_array_int<w>(first, last, x); i = n; normalize_state(); } /** Returns the smallest value that the generator can produce. */ static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } /** Returns the largest value that the generator can produce. */ static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () { return boost::low_bits_mask_t<w>::sig_bits; } /** Produces the next value of the generator. */ result_type operator()(); /** 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 steps. Equivalent to * * @code * for(unsigned long long i = 0; i < z; ++i) { * gen(); * } * @endcode */ void discard(boost::uintmax_t z) { #ifndef BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD #define BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD 10000000 #endif if(z > BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD) { discard_many(z); } else { for(boost::uintmax_t j = 0; j < z; ++j) { (*this)(); } } } #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS /** Writes a mersenne_twister_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 mersenne_twister_engine& mt) { mt.print(os); return os; } /** Reads a mersenne_twister_engine from a @c std::istream */ template<class CharT, class Traits> friend std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& is, mersenne_twister_engine& mt) { for(std::size_t 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 /** * Returns true if the two generators are in the same state, * and will thus produce identical sequences. */ friend bool operator==(const mersenne_twister_engine& x_, const mersenne_twister_engine& y_) { if(x_.i < y_.i) return x_.equal_imp(y_); else return y_.equal_imp(x_); } /** * Returns true if the two generators are in different states. */ friend bool operator!=(const mersenne_twister_engine& x_, const mersenne_twister_engine& y_) { return !(x_ == y_); } private: /// \cond show_private void twist(); /** * Does the work of operator==. This is in a member function * for portability. Some compilers, such as msvc 7.1 and * Sun CC 5.10 can't access template parameters or static * members of the class from inline friend functions. * * requires i <= other.i */ bool equal_imp(const mersenne_twister_engine& other) const { UIntType back[n]; std::size_t offset = other.i - i; for(std::size_t j = 0; j + offset < n; ++j) if(x[j] != other.x[j+offset]) return false; rewind(&back[n-1], offset); for(std::size_t j = 0; j < offset; ++j) if(back[j + n - offset] != other.x[j]) return false; return true; } /** * Does the work of operator<<. This is in a member function * for portability. */ template<class CharT, class Traits> void print(std::basic_ostream<CharT, Traits>& os) const { UIntType data[n]; for(std::size_t j = 0; j < i; ++j) { data[j + n - i] = x[j]; } if(i != n) { rewind(&data[n - i - 1], n - i); } os << data[0]; for(std::size_t j = 1; j < n; ++j) { os << ' ' << data[j]; } } /** * Copies z elements of the state preceding x[0] into * the array whose last element is last. */ void rewind(UIntType* last, std::size_t z) const { const UIntType upper_mask = (~static_cast<UIntType>(0)) << r; const UIntType lower_mask = ~upper_mask; UIntType y0 = x[m-1] ^ x[n-1]; if(y0 & (static_cast<UIntType>(1) << (w-1))) { y0 = ((y0 ^ a) << 1) | 1; } else { y0 = y0 << 1; } for(std::size_t sz = 0; sz < z; ++sz) { UIntType y1 = rewind_find(last, sz, m-1) ^ rewind_find(last, sz, n-1); if(y1 & (static_cast<UIntType>(1) << (w-1))) { y1 = ((y1 ^ a) << 1) | 1; } else { y1 = y1 << 1; } *(last - sz) = (y0 & upper_mask) | (y1 & lower_mask); y0 = y1; } } /** * Converts an arbitrary array into a valid generator state. * First we normalize x[0], so that it contains the same * value we would get by running the generator forwards * and then in reverse. (The low order r bits are redundant). * Then, if the state consists of all zeros, we set the * high order bit of x[0] to 1. This function only needs to * be called by seed, since the state transform preserves * this relationship. */ void normalize_state() { const UIntType upper_mask = (~static_cast<UIntType>(0)) << r; const UIntType lower_mask = ~upper_mask; UIntType y0 = x[m-1] ^ x[n-1]; if(y0 & (static_cast<UIntType>(1) << (w-1))) { y0 = ((y0 ^ a) << 1) | 1; } else { y0 = y0 << 1; } x[0] = (x[0] & upper_mask) | (y0 & lower_mask); // fix up the state if it's all zeroes. for(std::size_t j = 0; j < n; ++j) { if(x[j] != 0) return; } x[0] = static_cast<UIntType>(1) << (w-1); } /** * Given a pointer to the last element of the rewind array, * and the current size of the rewind array, finds an element * relative to the next available slot in the rewind array. */ UIntType rewind_find(UIntType* last, std::size_t size, std::size_t j) const { std::size_t index = (j + n - size + n - 1) % n; if(index < n - size) { return x[index]; } else { return *(last - (n - 1 - index)); } } /** * Optimized algorithm for large jumps. * * Hiroshi Haramoto, Makoto Matsumoto, and Pierre L'Ecuyer. 2008. * A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial * Space. In Proceedings of the 5th international conference on * Sequences and Their Applications (SETA '08). * DOI=10.1007/978-3-540-85912-3_26 */ void discard_many(boost::uintmax_t z) { // Compute the minimal polynomial, phi(t) // This depends only on the transition function, // which is constant. The characteristic // polynomial is the same as the minimal // polynomial for a maximum period generator // (which should be all specializations of // mersenne_twister.) Even if it weren't, // the characteristic polynomial is guaranteed // to be a multiple of the minimal polynomial, // which is good enough. detail::polynomial phi = get_characteristic_polynomial(); // calculate g(t) = t^z % phi(t) detail::polynomial g = mod_pow_x(z, phi); // h(s_0, t) = \sum_{i=0}^{2k-1}o(s_i)t^{2k-i-1} detail::polynomial h; const std::size_t num_bits = w*n - r; for(std::size_t j = 0; j < num_bits * 2; ++j) { // Yes, we're advancing the generator state // here, but it doesn't matter because // we're going to overwrite it completely // in reconstruct_state. if(i >= n) twist(); h[2*num_bits - j - 1] = x[i++] & UIntType(1); } // g(t)h(s_0, t) detail::polynomial gh = g * h; detail::polynomial result; for(std::size_t j = 0; j <= num_bits; ++j) { result[j] = gh[2*num_bits - j - 1]; } reconstruct_state(result); } static detail::polynomial get_characteristic_polynomial() { const std::size_t num_bits = w*n - r; detail::polynomial helper; helper[num_bits - 1] = 1; mersenne_twister_engine tmp; tmp.reconstruct_state(helper); // Skip the first num_bits elements, since we // already know what they are. for(std::size_t j = 0; j < num_bits; ++j) { if(tmp.i >= n) tmp.twist(); if(j == num_bits - 1) assert((tmp.x[tmp.i] & 1) == 1); else assert((tmp.x[tmp.i] & 1) == 0); ++tmp.i; } detail::polynomial phi; phi[num_bits] = 1; detail::polynomial next_bits = tmp.as_polynomial(num_bits); for(std::size_t j = 0; j < num_bits; ++j) { int val = next_bits[j] ^ phi[num_bits-j-1]; phi[num_bits-j-1] = val; if(val) { for(std::size_t k = j + 1; k < num_bits; ++k) { phi[num_bits-k-1] ^= next_bits[k-j-1]; } } } return phi; } detail::polynomial as_polynomial(std::size_t size) { detail::polynomial result; for(std::size_t j = 0; j < size; ++j) { if(i >= n) twist(); result[j] = x[i++] & UIntType(1); } return result; } void reconstruct_state(const detail::polynomial& p) { const UIntType upper_mask = (~static_cast<UIntType>(0)) << r; const UIntType lower_mask = ~upper_mask; const std::size_t num_bits = w*n - r; for(std::size_t j = num_bits - n + 1; j <= num_bits; ++j) x[j % n] = p[j]; UIntType y0 = 0; for(std::size_t j = num_bits + 1; j >= n - 1; --j) { UIntType y1 = x[j % n] ^ x[(j + m) % n]; if(p[j - n + 1]) y1 = (y1 ^ a) << UIntType(1) | UIntType(1); else y1 = y1 << UIntType(1); x[(j + 1) % n] = (y0 & upper_mask) | (y1 & lower_mask); y0 = y1; } i = 0; } /// \endcond // state representation: next output is o(x(i)) // x[0] ... x[k] x[k+1] ... x[n-1] represents // x(i-k) ... x(i) x(i+1) ... x(i-k+n-1) UIntType x[n]; std::size_t i; }; /// \cond show_private #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION // A definition is required even for integral static constants #define BOOST_RANDOM_MT_DEFINE_CONSTANT(type, name) \ template<class UIntType, std::size_t w, std::size_t n, std::size_t m, \ std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s, \ UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f> \ const type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::name BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, word_size); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, state_size); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, shift_size); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, mask_bits); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, xor_mask); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_u); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_d); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_s); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_b); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_t); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_c); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_l); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, initialization_multiplier); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, default_seed); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, parameter_a); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_u ); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_s); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_b); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_t); BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_c); BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_l); BOOST_RANDOM_MT_DEFINE_CONSTANT(bool, has_fixed_range); #undef BOOST_RANDOM_MT_DEFINE_CONSTANT #endif template<class UIntType, std::size_t w, std::size_t n, std::size_t m, std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s, UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f> void mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::twist() { const UIntType upper_mask = (~static_cast<UIntType>(0)) << r; const UIntType lower_mask = ~upper_mask; const std::size_t unroll_factor = 6; const std::size_t unroll_extra1 = (n-m) % unroll_factor; const std::size_t unroll_extra2 = (m-1) % unroll_factor; // split loop to avoid costly modulo operations { // extra scope for MSVC brokenness w.r.t. for scope for(std::size_t j = 0; j < n-m-unroll_extra1; j++) { UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask); x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a); } } { for(std::size_t j = n-m-unroll_extra1; j < n-m; j++) { UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask); x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a); } } { for(std::size_t j = n-m; j < n-1-unroll_extra2; j++) { UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask); x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a); } } { for(std::size_t j = n-1-unroll_extra2; j < n-1; j++) { UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask); x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a); } } // last iteration UIntType y = (x[n-1] & upper_mask) | (x[0] & lower_mask); x[n-1] = x[m-1] ^ (y >> 1) ^ ((x[0]&1) * a); i = 0; } /// \endcond template<class UIntType, std::size_t w, std::size_t n, std::size_t m, std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s, UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f> inline typename mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::result_type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::operator()() { if(i == n) twist(); // Step 4 UIntType z = x[i]; ++i; z ^= ((z >> u) & d); z ^= ((z << s) & b); z ^= ((z << t) & c); z ^= (z >> l); return z; } /** * 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 mersenne_twister_engine<uint32_t,32,351,175,19,0xccab8ee7, 11,0xffffffff,7,0x31b6ab00,15,0xffe50000,17,1812433253> 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 mersenne_twister_engine<uint32_t,32,624,397,31,0x9908b0df, 11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253> mt19937; #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T) typedef mersenne_twister_engine<uint64_t,64,312,156,31, UINT64_C(0xb5026f5aa96619e9),29,UINT64_C(0x5555555555555555),17, UINT64_C(0x71d67fffeda60000),37,UINT64_C(0xfff7eee000000000),43, UINT64_C(6364136223846793005)> mt19937_64; #endif /// \cond show_deprecated template<class UIntType, int w, int n, int m, int r, UIntType a, int u, std::size_t s, UIntType b, int t, UIntType c, int l, UIntType v> class mersenne_twister : public mersenne_twister_engine<UIntType, w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> { typedef mersenne_twister_engine<UIntType, w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> base_type; public: mersenne_twister() {} BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen) { seed(gen); } BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val) { seed(val); } template<class It> mersenne_twister(It& first, It last) : base_type(first, last) {} void seed() { base_type::seed(); } BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Gen, gen) { detail::generator_seed_seq<Gen> seq(gen); base_type::seed(seq); } BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val) { base_type::seed(val); } template<class It> void seed(It& first, It last) { base_type::seed(first, last); } }; /// \endcond } // namespace random using random::mt11213b; using random::mt19937; using random::mt19937_64; } // namespace boost BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt11213b) BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937) BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937_64) #include <boost/random/detail/enable_warnings.hpp> #endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP