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 | */ |
107 | mersenne_twister_engine() { seed(); } |
108 | |
109 | /** |
110 | * Constructs a @c mersenne_twister_engine and calls @c seed(value). |
111 | */ |
112 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine, |
113 | UIntType, value) |
114 | { seed(value); } |
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 | */ |
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). */ |
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 | */ |
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 | */ |
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> |
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. */ |
180 | static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () |
181 | { return 0; } |
182 | /** Returns the largest value that the generator can produce. */ |
183 | static BOOST_CONSTEXPR 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> |
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 | */ |
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>& |
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>& |
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 | */ |
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 | */ |
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 | */ |
275 | 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(last: &back[n-1], z: 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> |
294 | 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(last: &data[n - i - 1], z: 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 | */ |
313 | 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, size: sz, j: m-1) ^ rewind_find(last, size: sz, j: 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 | */ |
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 |
371 | 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 | */ |
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(exponent: z, mod: 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(p: result); |
425 | } |
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 | } |
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 | } |
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 |
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 = (n-m) % unroll_factor; |
543 | const std::size_t = (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 |
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: |
647 | mersenne_twister() {} |
648 | BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen) |
649 | { seed(gen); } |
650 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val) |
651 | { seed(val); } |
652 | template<class It> |
653 | mersenne_twister(It& first, It last) : base_type(first, last) {} |
654 | void seed() { base_type::seed(); } |
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 | } |
660 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val) |
661 | { base_type::seed(val); } |
662 | template<class It> |
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 | |