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1 /* boost random/mersenne_twister.hpp header file
2  *
3  * Copyright Jens Maurer 2000-2001
4  * Copyright Steven Watanabe 2010
5  * Distributed under the Boost Software License, Version 1.0. (See
6  * accompanying file LICENSE_1_0.txt or copy at
7  * http://www.boost.org/LICENSE_1_0.txt)
8  *
9  * See http://www.boost.org for most recent version including documentation.
10  *
11  * $Id$
12  *
13  * Revision history
14  *  2013-10-14  fixed some warnings with Wshadow (mgaunard)
15  *  2001-02-18  moved to individual header files
16  */
17 
18 #ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
19 #define BOOST_RANDOM_MERSENNE_TWISTER_HPP
20 
21 #include <iosfwd>
22 #include <istream>
23 #include <stdexcept>
24 #include <boost/config.hpp>
25 #include <boost/cstdint.hpp>
26 #include <boost/integer/integer_mask.hpp>
27 #include <boost/random/detail/config.hpp>
28 #include <boost/random/detail/ptr_helper.hpp>
29 #include <boost/random/detail/seed.hpp>
30 #include <boost/random/detail/seed_impl.hpp>
31 #include <boost/random/detail/generator_seed_seq.hpp>
32 #include <boost/random/detail/polynomial.hpp>
33 
34 #include <boost/random/detail/disable_warnings.hpp>
35 
36 namespace boost {
37 namespace random {
38 
39 /**
40  * Instantiations of class template mersenne_twister_engine model a
41  * \pseudo_random_number_generator. It uses the algorithm described in
42  *
43  *  @blockquote
44  *  "Mersenne Twister: A 623-dimensionally equidistributed uniform
45  *  pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura,
46  *  ACM Transactions on Modeling and Computer Simulation: Special Issue on
47  *  Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
48  *  @endblockquote
49  *
50  * @xmlnote
51  * The boost variant has been implemented from scratch and does not
52  * derive from or use mt19937.c provided on the above WWW site. However, it
53  * was verified that both produce identical output.
54  * @endxmlnote
55  *
56  * The seeding from an integer was changed in April 2005 to address a
57  * <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
58  *
59  * The quality of the generator crucially depends on the choice of the
60  * parameters.  User code should employ one of the sensibly parameterized
61  * generators such as \mt19937 instead.
62  *
63  * The generator requires considerable amounts of memory for the storage of
64  * its state array. For example, \mt11213b requires about 1408 bytes and
65  * \mt19937 requires about 2496 bytes.
66  */
67 template<class UIntType,
68          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
69          UIntType a, std::size_t u, UIntType d, std::size_t s,
70          UIntType b, std::size_t t,
71          UIntType c, std::size_t l, UIntType f>
72 class mersenne_twister_engine
73 {
74 public:
75     typedef UIntType result_type;
76     BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
77     BOOST_STATIC_CONSTANT(std::size_t, state_size = n);
78     BOOST_STATIC_CONSTANT(std::size_t, shift_size = m);
79     BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r);
80     BOOST_STATIC_CONSTANT(UIntType, xor_mask = a);
81     BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u);
82     BOOST_STATIC_CONSTANT(UIntType, tempering_d = d);
83     BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s);
84     BOOST_STATIC_CONSTANT(UIntType, tempering_b = b);
85     BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t);
86     BOOST_STATIC_CONSTANT(UIntType, tempering_c = c);
87     BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l);
88     BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f);
89     BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u);
90 
91     // backwards compatibility
92     BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
93     BOOST_STATIC_CONSTANT(std::size_t, output_u = u);
94     BOOST_STATIC_CONSTANT(std::size_t, output_s = s);
95     BOOST_STATIC_CONSTANT(UIntType, output_b = b);
96     BOOST_STATIC_CONSTANT(std::size_t, output_t = t);
97     BOOST_STATIC_CONSTANT(UIntType, output_c = c);
98     BOOST_STATIC_CONSTANT(std::size_t, output_l = l);
99 
100     // old Boost.Random concept requirements
101     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
102 
103 
104     /**
105      * Constructs a @c mersenne_twister_engine and calls @c seed().
106      */
mersenne_twister_engine()107     mersenne_twister_engine() { seed(); }
108 
109     /**
110      * Constructs a @c mersenne_twister_engine and calls @c seed(value).
111      */
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,UIntType,value)112     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,
113                                                UIntType, value)
114     { seed(value); }
mersenne_twister_engine(It & first,It last)115     template<class It> mersenne_twister_engine(It& first, It last)
116     { seed(first,last); }
117 
118     /**
119      * Constructs a mersenne_twister_engine and calls @c seed(gen).
120      *
121      * @xmlnote
122      * The copy constructor will always be preferred over
123      * the templated constructor.
124      * @endxmlnote
125      */
BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,SeedSeq,seq)126     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,
127                                              SeedSeq, seq)
128     { seed(seq); }
129 
130     // compiler-generated copy ctor and assignment operator are fine
131 
132     /** Calls @c seed(default_seed). */
seed()133     void seed() { seed(default_seed); }
134 
135     /**
136      * Sets the state x(0) to v mod 2w. Then, iteratively,
137      * sets x(i) to
138      * (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
139      * for i = 1 .. n-1. x(n) is the first value to be returned by operator().
140      */
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine,UIntType,value)141     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, UIntType, value)
142     {
143         // New seeding algorithm from
144         // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
145         // In the previous versions, MSBs of the seed affected only MSBs of the
146         // state x[].
147         const UIntType mask = (max)();
148         x[0] = value & mask;
149         for (i = 1; i < n; i++) {
150             // See Knuth "The Art of Computer Programming"
151             // Vol. 2, 3rd ed., page 106
152             x[i] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
153         }
154 
155         normalize_state();
156     }
157 
158     /**
159      * Seeds a mersenne_twister_engine using values produced by seq.generate().
160      */
BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine,SeeqSeq,seq)161     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq)
162     {
163         detail::seed_array_int<w>(seq, x);
164         i = n;
165 
166         normalize_state();
167     }
168 
169     /** Sets the state of the generator using values from an iterator range. */
170     template<class It>
seed(It & first,It last)171     void seed(It& first, It last)
172     {
173         detail::fill_array_int<w>(first, last, x);
174         i = n;
175 
176         normalize_state();
177     }
178 
179     /** Returns the smallest value that the generator can produce. */
BOOST_PREVENT_MACRO_SUBSTITUTION()180     static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
181     { return 0; }
182     /** Returns the largest value that the generator can produce. */
BOOST_PREVENT_MACRO_SUBSTITUTION()183     static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
184     { return boost::low_bits_mask_t<w>::sig_bits; }
185 
186     /** Produces the next value of the generator. */
187     result_type operator()();
188 
189     /** Fills a range with random values */
190     template<class Iter>
generate(Iter first,Iter last)191     void generate(Iter first, Iter last)
192     { detail::generate_from_int(*this, first, last); }
193 
194     /**
195      * Advances the state of the generator by @c z steps.  Equivalent to
196      *
197      * @code
198      * for(unsigned long long i = 0; i < z; ++i) {
199      *     gen();
200      * }
201      * @endcode
202      */
discard(boost::uintmax_t z)203     void discard(boost::uintmax_t z)
204     {
205 #ifndef BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD
206 #define BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD 10000000
207 #endif
208         if(z > BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD) {
209             discard_many(z);
210         } else {
211             for(boost::uintmax_t j = 0; j < z; ++j) {
212                 (*this)();
213             }
214         }
215     }
216 
217 #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
218     /** Writes a mersenne_twister_engine to a @c std::ostream */
219     template<class CharT, class Traits>
220     friend std::basic_ostream<CharT,Traits>&
operator <<(std::basic_ostream<CharT,Traits> & os,const mersenne_twister_engine & mt)221     operator<<(std::basic_ostream<CharT,Traits>& os,
222                const mersenne_twister_engine& mt)
223     {
224         mt.print(os);
225         return os;
226     }
227 
228     /** Reads a mersenne_twister_engine from a @c std::istream */
229     template<class CharT, class Traits>
230     friend std::basic_istream<CharT,Traits>&
operator >>(std::basic_istream<CharT,Traits> & is,mersenne_twister_engine & mt)231     operator>>(std::basic_istream<CharT,Traits>& is,
232                mersenne_twister_engine& mt)
233     {
234         for(std::size_t j = 0; j < mt.state_size; ++j)
235             is >> mt.x[j] >> std::ws;
236         // MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
237         // value parameter "n" available from the class template scope, so use
238         // the static constant with the same value
239         mt.i = mt.state_size;
240         return is;
241     }
242 #endif
243 
244     /**
245      * Returns true if the two generators are in the same state,
246      * and will thus produce identical sequences.
247      */
operator ==(const mersenne_twister_engine & x_,const mersenne_twister_engine & y_)248     friend bool operator==(const mersenne_twister_engine& x_,
249                            const mersenne_twister_engine& y_)
250     {
251         if(x_.i < y_.i) return x_.equal_imp(y_);
252         else return y_.equal_imp(x_);
253     }
254 
255     /**
256      * Returns true if the two generators are in different states.
257      */
operator !=(const mersenne_twister_engine & x_,const mersenne_twister_engine & y_)258     friend bool operator!=(const mersenne_twister_engine& x_,
259                            const mersenne_twister_engine& y_)
260     { return !(x_ == y_); }
261 
262 private:
263     /// \cond show_private
264 
265     void twist();
266 
267     /**
268      * Does the work of operator==.  This is in a member function
269      * for portability.  Some compilers, such as msvc 7.1 and
270      * Sun CC 5.10 can't access template parameters or static
271      * members of the class from inline friend functions.
272      *
273      * requires i <= other.i
274      */
equal_imp(const mersenne_twister_engine & other) const275     bool equal_imp(const mersenne_twister_engine& other) const
276     {
277         UIntType back[n];
278         std::size_t offset = other.i - i;
279         for(std::size_t j = 0; j + offset < n; ++j)
280             if(x[j] != other.x[j+offset])
281                 return false;
282         rewind(&back[n-1], offset);
283         for(std::size_t j = 0; j < offset; ++j)
284             if(back[j + n - offset] != other.x[j])
285                 return false;
286         return true;
287     }
288 
289     /**
290      * Does the work of operator<<.  This is in a member function
291      * for portability.
292      */
293     template<class CharT, class Traits>
print(std::basic_ostream<CharT,Traits> & os) const294     void print(std::basic_ostream<CharT, Traits>& os) const
295     {
296         UIntType data[n];
297         for(std::size_t j = 0; j < i; ++j) {
298             data[j + n - i] = x[j];
299         }
300         if(i != n) {
301             rewind(&data[n - i - 1], n - i);
302         }
303         os << data[0];
304         for(std::size_t j = 1; j < n; ++j) {
305             os << ' ' << data[j];
306         }
307     }
308 
309     /**
310      * Copies z elements of the state preceding x[0] into
311      * the array whose last element is last.
312      */
rewind(UIntType * last,std::size_t z) const313     void rewind(UIntType* last, std::size_t z) const
314     {
315         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
316         const UIntType lower_mask = ~upper_mask;
317         UIntType y0 = x[m-1] ^ x[n-1];
318         if(y0 & (static_cast<UIntType>(1) << (w-1))) {
319             y0 = ((y0 ^ a) << 1) | 1;
320         } else {
321             y0 = y0 << 1;
322         }
323         for(std::size_t sz = 0; sz < z; ++sz) {
324             UIntType y1 =
325                 rewind_find(last, sz, m-1) ^ rewind_find(last, sz, n-1);
326             if(y1 & (static_cast<UIntType>(1) << (w-1))) {
327                 y1 = ((y1 ^ a) << 1) | 1;
328             } else {
329                 y1 = y1 << 1;
330             }
331             *(last - sz) = (y0 & upper_mask) | (y1 & lower_mask);
332             y0 = y1;
333         }
334     }
335 
336     /**
337      * Converts an arbitrary array into a valid generator state.
338      * First we normalize x[0], so that it contains the same
339      * value we would get by running the generator forwards
340      * and then in reverse.  (The low order r bits are redundant).
341      * Then, if the state consists of all zeros, we set the
342      * high order bit of x[0] to 1.  This function only needs to
343      * be called by seed, since the state transform preserves
344      * this relationship.
345      */
normalize_state()346     void normalize_state()
347     {
348         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
349         const UIntType lower_mask = ~upper_mask;
350         UIntType y0 = x[m-1] ^ x[n-1];
351         if(y0 & (static_cast<UIntType>(1) << (w-1))) {
352             y0 = ((y0 ^ a) << 1) | 1;
353         } else {
354             y0 = y0 << 1;
355         }
356         x[0] = (x[0] & upper_mask) | (y0 & lower_mask);
357 
358         // fix up the state if it's all zeroes.
359         for(std::size_t j = 0; j < n; ++j) {
360             if(x[j] != 0) return;
361         }
362         x[0] = static_cast<UIntType>(1) << (w-1);
363     }
364 
365     /**
366      * Given a pointer to the last element of the rewind array,
367      * and the current size of the rewind array, finds an element
368      * relative to the next available slot in the rewind array.
369      */
370     UIntType
rewind_find(UIntType * last,std::size_t size,std::size_t j) const371     rewind_find(UIntType* last, std::size_t size, std::size_t j) const
372     {
373         std::size_t index = (j + n - size + n - 1) % n;
374         if(index < n - size) {
375             return x[index];
376         } else {
377             return *(last - (n - 1 - index));
378         }
379     }
380 
381     /**
382      * Optimized algorithm for large jumps.
383      *
384      * Hiroshi Haramoto, Makoto Matsumoto, and Pierre L'Ecuyer. 2008.
385      * A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial
386      * Space. In Proceedings of the 5th international conference on
387      * Sequences and Their Applications (SETA '08).
388      * DOI=10.1007/978-3-540-85912-3_26
389      */
discard_many(boost::uintmax_t z)390     void discard_many(boost::uintmax_t z)
391     {
392         // Compute the minimal polynomial, phi(t)
393         // This depends only on the transition function,
394         // which is constant.  The characteristic
395         // polynomial is the same as the minimal
396         // polynomial for a maximum period generator
397         // (which should be all specializations of
398         // mersenne_twister.)  Even if it weren't,
399         // the characteristic polynomial is guaranteed
400         // to be a multiple of the minimal polynomial,
401         // which is good enough.
402         detail::polynomial phi = get_characteristic_polynomial();
403 
404         // calculate g(t) = t^z % phi(t)
405         detail::polynomial g = mod_pow_x(z, phi);
406 
407         // h(s_0, t) = \sum_{i=0}^{2k-1}o(s_i)t^{2k-i-1}
408         detail::polynomial h;
409         const std::size_t num_bits = w*n - r;
410         for(std::size_t j = 0; j < num_bits * 2; ++j) {
411             // Yes, we're advancing the generator state
412             // here, but it doesn't matter because
413             // we're going to overwrite it completely
414             // in reconstruct_state.
415             if(i >= n) twist();
416             h[2*num_bits - j - 1] = x[i++] & UIntType(1);
417         }
418         // g(t)h(s_0, t)
419         detail::polynomial gh = g * h;
420         detail::polynomial result;
421         for(std::size_t j = 0; j <= num_bits; ++j) {
422             result[j] = gh[2*num_bits - j - 1];
423         }
424         reconstruct_state(result);
425     }
get_characteristic_polynomial()426     static detail::polynomial get_characteristic_polynomial()
427     {
428         const std::size_t num_bits = w*n - r;
429         detail::polynomial helper;
430         helper[num_bits - 1] = 1;
431         mersenne_twister_engine tmp;
432         tmp.reconstruct_state(helper);
433         // Skip the first num_bits elements, since we
434         // already know what they are.
435         for(std::size_t j = 0; j < num_bits; ++j) {
436             if(tmp.i >= n) tmp.twist();
437             if(j == num_bits - 1)
438                 assert((tmp.x[tmp.i] & 1) == 1);
439             else
440                 assert((tmp.x[tmp.i] & 1) == 0);
441             ++tmp.i;
442         }
443         detail::polynomial phi;
444         phi[num_bits] = 1;
445         detail::polynomial next_bits = tmp.as_polynomial(num_bits);
446         for(std::size_t j = 0; j < num_bits; ++j) {
447             int val = next_bits[j] ^ phi[num_bits-j-1];
448             phi[num_bits-j-1] = val;
449             if(val) {
450                 for(std::size_t k = j + 1; k < num_bits; ++k) {
451                     phi[num_bits-k-1] ^= next_bits[k-j-1];
452                 }
453             }
454         }
455         return phi;
456     }
as_polynomial(std::size_t size)457     detail::polynomial as_polynomial(std::size_t size) {
458         detail::polynomial result;
459         for(std::size_t j = 0; j < size; ++j) {
460             if(i >= n) twist();
461             result[j] = x[i++] & UIntType(1);
462         }
463         return result;
464     }
reconstruct_state(const detail::polynomial & p)465     void reconstruct_state(const detail::polynomial& p)
466     {
467         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
468         const UIntType lower_mask = ~upper_mask;
469         const std::size_t num_bits = w*n - r;
470         for(std::size_t j = num_bits - n + 1; j <= num_bits; ++j)
471             x[j % n] = p[j];
472 
473         UIntType y0 = 0;
474         for(std::size_t j = num_bits + 1; j >= n - 1; --j) {
475             UIntType y1 = x[j % n] ^ x[(j + m) % n];
476             if(p[j - n + 1])
477                 y1 = (y1 ^ a) << UIntType(1) | UIntType(1);
478             else
479                 y1 = y1 << UIntType(1);
480             x[(j + 1) % n] = (y0 & upper_mask) | (y1 & lower_mask);
481             y0 = y1;
482         }
483         i = 0;
484     }
485 
486     /// \endcond
487 
488     // state representation: next output is o(x(i))
489     //   x[0]  ... x[k] x[k+1] ... x[n-1]   represents
490     //  x(i-k) ... x(i) x(i+1) ... x(i-k+n-1)
491 
492     UIntType x[n];
493     std::size_t i;
494 };
495 
496 /// \cond show_private
497 
498 #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
499 //  A definition is required even for integral static constants
500 #define BOOST_RANDOM_MT_DEFINE_CONSTANT(type, name)                         \
501 template<class UIntType, std::size_t w, std::size_t n, std::size_t m,       \
502     std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s,    \
503     UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f>       \
504 const type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::name
505 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, word_size);
506 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, state_size);
507 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, shift_size);
508 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, mask_bits);
509 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, xor_mask);
510 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_u);
511 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_d);
512 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_s);
513 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_b);
514 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_t);
515 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_c);
516 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_l);
517 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, initialization_multiplier);
518 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, default_seed);
519 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, parameter_a);
520 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_u );
521 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_s);
522 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_b);
523 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_t);
524 BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_c);
525 BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_l);
526 BOOST_RANDOM_MT_DEFINE_CONSTANT(bool, has_fixed_range);
527 #undef BOOST_RANDOM_MT_DEFINE_CONSTANT
528 #endif
529 
530 template<class UIntType,
531          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
532          UIntType a, std::size_t u, UIntType d, std::size_t s,
533          UIntType b, std::size_t t,
534          UIntType c, std::size_t l, UIntType f>
535 void
twist()536 mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::twist()
537 {
538     const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
539     const UIntType lower_mask = ~upper_mask;
540 
541     const std::size_t unroll_factor = 6;
542     const std::size_t unroll_extra1 = (n-m) % unroll_factor;
543     const std::size_t unroll_extra2 = (m-1) % unroll_factor;
544 
545     // split loop to avoid costly modulo operations
546     {  // extra scope for MSVC brokenness w.r.t. for scope
547         for(std::size_t j = 0; j < n-m-unroll_extra1; j++) {
548             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
549             x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
550         }
551     }
552     {
553         for(std::size_t j = n-m-unroll_extra1; j < n-m; j++) {
554             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
555             x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
556         }
557     }
558     {
559         for(std::size_t j = n-m; j < n-1-unroll_extra2; j++) {
560             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
561             x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
562         }
563     }
564     {
565         for(std::size_t j = n-1-unroll_extra2; j < n-1; j++) {
566             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
567             x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
568         }
569     }
570     // last iteration
571     UIntType y = (x[n-1] & upper_mask) | (x[0] & lower_mask);
572     x[n-1] = x[m-1] ^ (y >> 1) ^ ((x[0]&1) * a);
573     i = 0;
574 }
575 /// \endcond
576 
577 template<class UIntType,
578          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
579          UIntType a, std::size_t u, UIntType d, std::size_t s,
580          UIntType b, std::size_t t,
581          UIntType c, std::size_t l, UIntType f>
582 inline typename
583 mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::result_type
operator ()()584 mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::operator()()
585 {
586     if(i == n)
587         twist();
588     // Step 4
589     UIntType z = x[i];
590     ++i;
591     z ^= ((z >> u) & d);
592     z ^= ((z << s) & b);
593     z ^= ((z << t) & c);
594     z ^= (z >> l);
595     return z;
596 }
597 
598 /**
599  * The specializations \mt11213b and \mt19937 are from
600  *
601  *  @blockquote
602  *  "Mersenne Twister: A 623-dimensionally equidistributed
603  *  uniform pseudo-random number generator", Makoto Matsumoto
604  *  and Takuji Nishimura, ACM Transactions on Modeling and
605  *  Computer Simulation: Special Issue on Uniform Random Number
606  *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
607  *  @endblockquote
608  */
609 typedef mersenne_twister_engine<uint32_t,32,351,175,19,0xccab8ee7,
610     11,0xffffffff,7,0x31b6ab00,15,0xffe50000,17,1812433253> mt11213b;
611 
612 /**
613  * The specializations \mt11213b and \mt19937 are from
614  *
615  *  @blockquote
616  *  "Mersenne Twister: A 623-dimensionally equidistributed
617  *  uniform pseudo-random number generator", Makoto Matsumoto
618  *  and Takuji Nishimura, ACM Transactions on Modeling and
619  *  Computer Simulation: Special Issue on Uniform Random Number
620  *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
621  *  @endblockquote
622  */
623 typedef mersenne_twister_engine<uint32_t,32,624,397,31,0x9908b0df,
624     11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253> mt19937;
625 
626 #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
627 typedef mersenne_twister_engine<uint64_t,64,312,156,31,
628     UINT64_C(0xb5026f5aa96619e9),29,UINT64_C(0x5555555555555555),17,
629     UINT64_C(0x71d67fffeda60000),37,UINT64_C(0xfff7eee000000000),43,
630     UINT64_C(6364136223846793005)> mt19937_64;
631 #endif
632 
633 /// \cond show_deprecated
634 
635 template<class UIntType,
636          int w, int n, int m, int r,
637          UIntType a, int u, std::size_t s,
638          UIntType b, int t,
639          UIntType c, int l, UIntType v>
640 class mersenne_twister :
641     public mersenne_twister_engine<UIntType,
642         w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253>
643 {
644     typedef mersenne_twister_engine<UIntType,
645         w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> base_type;
646 public:
mersenne_twister()647     mersenne_twister() {}
BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister,Gen,gen)648     BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen)
649     { seed(gen); }
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister,UIntType,val)650     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val)
651     { seed(val); }
652     template<class It>
mersenne_twister(It & first,It last)653     mersenne_twister(It& first, It last) : base_type(first, last) {}
seed()654     void seed() { base_type::seed(); }
BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister,Gen,gen)655     BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Gen, gen)
656     {
657         detail::generator_seed_seq<Gen> seq(gen);
658         base_type::seed(seq);
659     }
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister,UIntType,val)660     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val)
661     { base_type::seed(val); }
662     template<class It>
seed(It & first,It last)663     void seed(It& first, It last) { base_type::seed(first, last); }
664 };
665 
666 /// \endcond
667 
668 } // namespace random
669 
670 using random::mt11213b;
671 using random::mt19937;
672 using random::mt19937_64;
673 
674 } // namespace boost
675 
676 BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt11213b)
677 BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
678 BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937_64)
679 
680 #include <boost/random/detail/enable_warnings.hpp>
681 
682 #endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP
683