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1 | /* boost random/linear_congruential.hpp header file |
2 | * | |
3 | * Copyright Jens Maurer 2000-2001 | |
4 | * Distributed under the Boost Software License, Version 1.0. (See | |
5 | * accompanying file LICENSE_1_0.txt or copy at | |
6 | * http://www.boost.org/LICENSE_1_0.txt) | |
7 | * | |
8 | * See http://www.boost.org for most recent version including documentation. | |
9 | * | |
10 | * $Id$ | |
11 | * | |
12 | * Revision history | |
13 | * 2001-02-18 moved to individual header files | |
14 | */ | |
15 | ||
16 | #ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP | |
17 | #define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP | |
18 | ||
19 | #include <iostream> | |
20 | #include <stdexcept> | |
21 | #include <boost/assert.hpp> | |
22 | #include <boost/config.hpp> | |
23 | #include <boost/cstdint.hpp> | |
24 | #include <boost/limits.hpp> | |
25 | #include <boost/static_assert.hpp> | |
7c673cae FG |
26 | #include <boost/type_traits/is_arithmetic.hpp> |
27 | #include <boost/random/detail/config.hpp> | |
28 | #include <boost/random/detail/const_mod.hpp> | |
29 | #include <boost/random/detail/seed.hpp> | |
30 | #include <boost/random/detail/seed_impl.hpp> | |
31 | #include <boost/detail/workaround.hpp> | |
32 | ||
33 | #include <boost/random/detail/disable_warnings.hpp> | |
34 | ||
35 | namespace boost { | |
36 | namespace random { | |
37 | ||
38 | /** | |
39 | * Instantiations of class template linear_congruential_engine model a | |
40 | * \pseudo_random_number_generator. Linear congruential pseudo-random | |
41 | * number generators are described in: | |
42 | * | |
43 | * @blockquote | |
44 | * "Mathematical methods in large-scale computing units", D. H. Lehmer, | |
45 | * Proc. 2nd Symposium on Large-Scale Digital Calculating Machines, | |
46 | * Harvard University Press, 1951, pp. 141-146 | |
47 | * @endblockquote | |
48 | * | |
49 | * Let x(n) denote the sequence of numbers returned by some pseudo-random | |
50 | * number generator. Then for the linear congruential generator, | |
51 | * x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are | |
52 | * x(0), a, c, m. The template parameter IntType shall denote an integral | |
53 | * type. It must be large enough to hold values a, c, and m. The template | |
54 | * parameters a and c must be smaller than m. | |
55 | * | |
56 | * Note: The quality of the generator crucially depends on the choice of | |
57 | * the parameters. User code should use one of the sensibly parameterized | |
58 | * generators such as minstd_rand instead. | |
59 | */ | |
60 | template<class IntType, IntType a, IntType c, IntType m> | |
61 | class linear_congruential_engine | |
62 | { | |
63 | public: | |
64 | typedef IntType result_type; | |
65 | ||
66 | // Required for old Boost.Random concept | |
67 | BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); | |
68 | ||
69 | BOOST_STATIC_CONSTANT(IntType, multiplier = a); | |
70 | BOOST_STATIC_CONSTANT(IntType, increment = c); | |
71 | BOOST_STATIC_CONSTANT(IntType, modulus = m); | |
72 | BOOST_STATIC_CONSTANT(IntType, default_seed = 1); | |
73 | ||
74 | BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer); | |
75 | BOOST_STATIC_ASSERT(m == 0 || a < m); | |
76 | BOOST_STATIC_ASSERT(m == 0 || c < m); | |
77 | ||
78 | /** | |
79 | * Constructs a @c linear_congruential_engine, using the default seed | |
80 | */ | |
81 | linear_congruential_engine() { seed(); } | |
82 | ||
83 | /** | |
84 | * Constructs a @c linear_congruential_engine, seeding it with @c x0. | |
85 | */ | |
86 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine, | |
87 | IntType, x0) | |
88 | { seed(x0); } | |
89 | ||
90 | /** | |
91 | * Constructs a @c linear_congruential_engine, seeding it with values | |
92 | * produced by a call to @c seq.generate(). | |
93 | */ | |
94 | BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine, | |
95 | SeedSeq, seq) | |
96 | { seed(seq); } | |
97 | ||
98 | /** | |
99 | * Constructs a @c linear_congruential_engine and seeds it | |
100 | * with values taken from the itrator range [first, last) | |
101 | * and adjusts first to point to the element after the last one | |
102 | * used. If there are not enough elements, throws @c std::invalid_argument. | |
103 | * | |
104 | * first and last must be input iterators. | |
105 | */ | |
106 | template<class It> | |
107 | linear_congruential_engine(It& first, It last) | |
108 | { | |
109 | seed(first, last); | |
110 | } | |
111 | ||
112 | // compiler-generated copy constructor and assignment operator are fine | |
113 | ||
114 | /** | |
115 | * Calls seed(default_seed) | |
116 | */ | |
117 | void seed() { seed(default_seed); } | |
118 | ||
119 | /** | |
120 | * If c mod m is zero and x0 mod m is zero, changes the current value of | |
121 | * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero, | |
122 | * distinct seeds in the range [1,m) will leave the generator in distinct | |
123 | * states. If c is not zero, the range is [0,m). | |
124 | */ | |
11fdf7f2 | 125 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0_) |
7c673cae | 126 | { |
11fdf7f2 TL |
127 | // Work around a msvc 12/14 optimizer bug, which causes |
128 | // the line _x = 1 to run unconditionally sometimes. | |
129 | // Creating a local copy seems to make it work. | |
130 | IntType x0 = x0_; | |
7c673cae FG |
131 | // wrap _x if it doesn't fit in the destination |
132 | if(modulus == 0) { | |
133 | _x = x0; | |
134 | } else { | |
135 | _x = x0 % modulus; | |
136 | } | |
137 | // handle negative seeds | |
20effc67 | 138 | if(_x < 0) { |
7c673cae FG |
139 | _x += modulus; |
140 | } | |
141 | // adjust to the correct range | |
142 | if(increment == 0 && _x == 0) { | |
143 | _x = 1; | |
144 | } | |
145 | BOOST_ASSERT(_x >= (min)()); | |
146 | BOOST_ASSERT(_x <= (max)()); | |
147 | } | |
148 | ||
149 | /** | |
150 | * Seeds a @c linear_congruential_engine using values from a SeedSeq. | |
151 | */ | |
152 | BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq) | |
153 | { seed(detail::seed_one_int<IntType, m>(seq)); } | |
154 | ||
155 | /** | |
156 | * seeds a @c linear_congruential_engine with values taken | |
157 | * from the itrator range [first, last) and adjusts @c first to | |
158 | * point to the element after the last one used. If there are | |
159 | * not enough elements, throws @c std::invalid_argument. | |
160 | * | |
161 | * @c first and @c last must be input iterators. | |
162 | */ | |
163 | template<class It> | |
164 | void seed(It& first, It last) | |
165 | { seed(detail::get_one_int<IntType, m>(first, last)); } | |
166 | ||
167 | /** | |
168 | * Returns the smallest value that the @c linear_congruential_engine | |
169 | * can produce. | |
170 | */ | |
20effc67 | 171 | static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () |
7c673cae FG |
172 | { return c == 0 ? 1 : 0; } |
173 | /** | |
174 | * Returns the largest value that the @c linear_congruential_engine | |
175 | * can produce. | |
176 | */ | |
20effc67 | 177 | static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () |
7c673cae FG |
178 | { return modulus-1; } |
179 | ||
180 | /** Returns the next value of the @c linear_congruential_engine. */ | |
181 | IntType operator()() | |
182 | { | |
183 | _x = const_mod<IntType, m>::mult_add(a, _x, c); | |
184 | return _x; | |
185 | } | |
186 | ||
187 | /** Fills a range with random values */ | |
188 | template<class Iter> | |
189 | void generate(Iter first, Iter last) | |
190 | { detail::generate_from_int(*this, first, last); } | |
191 | ||
192 | /** Advances the state of the generator by @c z. */ | |
193 | void discard(boost::uintmax_t z) | |
194 | { | |
195 | typedef const_mod<IntType, m> mod_type; | |
196 | IntType b_inv = mod_type::invert(a-1); | |
197 | IntType b_gcd = mod_type::mult(a-1, b_inv); | |
198 | if(b_gcd == 1) { | |
199 | IntType a_z = mod_type::pow(a, z); | |
200 | _x = mod_type::mult_add(a_z, _x, | |
201 | mod_type::mult(mod_type::mult(c, b_inv), a_z - 1)); | |
202 | } else { | |
203 | // compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd) | |
204 | // we're storing the intermediate result / b_gcd | |
205 | IntType a_zm1_over_gcd = 0; | |
206 | IntType a_km1_over_gcd = (a - 1) / b_gcd; | |
207 | boost::uintmax_t exponent = z; | |
208 | while(exponent != 0) { | |
209 | if(exponent % 2 == 1) { | |
210 | a_zm1_over_gcd = | |
211 | mod_type::mult_add( | |
212 | b_gcd, | |
213 | mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd), | |
214 | mod_type::add(a_zm1_over_gcd, a_km1_over_gcd)); | |
215 | } | |
216 | a_km1_over_gcd = mod_type::mult_add( | |
217 | b_gcd, | |
218 | mod_type::mult(a_km1_over_gcd, a_km1_over_gcd), | |
219 | mod_type::add(a_km1_over_gcd, a_km1_over_gcd)); | |
220 | exponent /= 2; | |
221 | } | |
222 | ||
223 | IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1); | |
224 | IntType num = mod_type::mult(c, a_zm1_over_gcd); | |
225 | b_inv = mod_type::invert((a-1)/b_gcd); | |
226 | _x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num)); | |
227 | } | |
228 | } | |
229 | ||
230 | friend bool operator==(const linear_congruential_engine& x, | |
231 | const linear_congruential_engine& y) | |
232 | { return x._x == y._x; } | |
233 | friend bool operator!=(const linear_congruential_engine& x, | |
234 | const linear_congruential_engine& y) | |
235 | { return !(x == y); } | |
236 | ||
237 | #if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS) | |
238 | /** Writes a @c linear_congruential_engine to a @c std::ostream. */ | |
239 | template<class CharT, class Traits> | |
240 | friend std::basic_ostream<CharT,Traits>& | |
241 | operator<<(std::basic_ostream<CharT,Traits>& os, | |
242 | const linear_congruential_engine& lcg) | |
243 | { | |
244 | return os << lcg._x; | |
245 | } | |
246 | ||
247 | /** Reads a @c linear_congruential_engine from a @c std::istream. */ | |
248 | template<class CharT, class Traits> | |
249 | friend std::basic_istream<CharT,Traits>& | |
250 | operator>>(std::basic_istream<CharT,Traits>& is, | |
251 | linear_congruential_engine& lcg) | |
252 | { | |
253 | lcg.read(is); | |
254 | return is; | |
255 | } | |
256 | #endif | |
257 | ||
258 | private: | |
259 | ||
260 | /// \cond show_private | |
261 | ||
262 | template<class CharT, class Traits> | |
263 | void read(std::basic_istream<CharT, Traits>& is) { | |
264 | IntType x; | |
265 | if(is >> x) { | |
266 | if(x >= (min)() && x <= (max)()) { | |
267 | _x = x; | |
268 | } else { | |
269 | is.setstate(std::ios_base::failbit); | |
270 | } | |
271 | } | |
272 | } | |
273 | ||
274 | /// \endcond | |
275 | ||
276 | IntType _x; | |
277 | }; | |
278 | ||
279 | #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION | |
280 | // A definition is required even for integral static constants | |
281 | template<class IntType, IntType a, IntType c, IntType m> | |
282 | const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range; | |
283 | template<class IntType, IntType a, IntType c, IntType m> | |
284 | const IntType linear_congruential_engine<IntType,a,c,m>::multiplier; | |
285 | template<class IntType, IntType a, IntType c, IntType m> | |
286 | const IntType linear_congruential_engine<IntType,a,c,m>::increment; | |
287 | template<class IntType, IntType a, IntType c, IntType m> | |
288 | const IntType linear_congruential_engine<IntType,a,c,m>::modulus; | |
289 | template<class IntType, IntType a, IntType c, IntType m> | |
290 | const IntType linear_congruential_engine<IntType,a,c,m>::default_seed; | |
291 | #endif | |
292 | ||
293 | /// \cond show_deprecated | |
294 | ||
295 | // provided for backwards compatibility | |
296 | template<class IntType, IntType a, IntType c, IntType m, IntType val = 0> | |
297 | class linear_congruential : public linear_congruential_engine<IntType, a, c, m> | |
298 | { | |
299 | typedef linear_congruential_engine<IntType, a, c, m> base_type; | |
300 | public: | |
301 | linear_congruential(IntType x0 = 1) : base_type(x0) {} | |
302 | template<class It> | |
303 | linear_congruential(It& first, It last) : base_type(first, last) {} | |
304 | }; | |
305 | ||
306 | /// \endcond | |
307 | ||
308 | /** | |
309 | * The specialization \minstd_rand0 was originally suggested in | |
310 | * | |
311 | * @blockquote | |
312 | * A pseudo-random number generator for the System/360, P.A. Lewis, | |
313 | * A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2, | |
314 | * 1969, pp. 136-146 | |
315 | * @endblockquote | |
316 | * | |
317 | * It is examined more closely together with \minstd_rand in | |
318 | * | |
319 | * @blockquote | |
320 | * "Random Number Generators: Good ones are hard to find", | |
321 | * Stephen K. Park and Keith W. Miller, Communications of | |
322 | * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 | |
323 | * @endblockquote | |
324 | */ | |
325 | typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0; | |
326 | ||
327 | /** The specialization \minstd_rand was suggested in | |
328 | * | |
329 | * @blockquote | |
330 | * "Random Number Generators: Good ones are hard to find", | |
331 | * Stephen K. Park and Keith W. Miller, Communications of | |
332 | * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 | |
333 | * @endblockquote | |
334 | */ | |
335 | typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand; | |
336 | ||
337 | ||
338 | #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T) | |
339 | /** | |
340 | * Class @c rand48 models a \pseudo_random_number_generator. It uses | |
341 | * the linear congruential algorithm with the parameters a = 0x5DEECE66D, | |
342 | * c = 0xB, m = 2**48. It delivers identical results to the @c lrand48() | |
343 | * function available on some systems (assuming lcong48 has not been called). | |
344 | * | |
345 | * It is only available on systems where @c uint64_t is provided as an | |
346 | * integral type, so that for example static in-class constants and/or | |
347 | * enum definitions with large @c uint64_t numbers work. | |
348 | */ | |
349 | class rand48 | |
350 | { | |
351 | public: | |
352 | typedef boost::uint32_t result_type; | |
353 | ||
354 | BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); | |
355 | /** | |
356 | * Returns the smallest value that the generator can produce | |
357 | */ | |
20effc67 | 358 | static BOOST_CONSTEXPR uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } |
7c673cae FG |
359 | /** |
360 | * Returns the largest value that the generator can produce | |
361 | */ | |
20effc67 | 362 | static BOOST_CONSTEXPR uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION () |
7c673cae FG |
363 | { return 0x7FFFFFFF; } |
364 | ||
365 | /** Seeds the generator with the default seed. */ | |
366 | rand48() : lcf(cnv(static_cast<uint32_t>(1))) {} | |
367 | /** | |
368 | * Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e. | |
369 | */ | |
370 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0) | |
371 | { seed(x0); } | |
372 | /** | |
373 | * Seeds the generator with values produced by @c seq.generate(). | |
374 | */ | |
375 | BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq) | |
376 | { seed(seq); } | |
377 | /** | |
378 | * Seeds the generator using values from an iterator range, | |
379 | * and updates first to point one past the last value consumed. | |
380 | */ | |
381 | template<class It> rand48(It& first, It last) : lcf(first, last) { } | |
382 | ||
383 | // compiler-generated copy ctor and assignment operator are fine | |
384 | ||
385 | /** Seeds the generator with the default seed. */ | |
386 | void seed() { seed(static_cast<uint32_t>(1)); } | |
387 | /** | |
388 | * Changes the current value x(n) of the generator to (x0 << 16) | 0x330e. | |
389 | */ | |
390 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0) | |
391 | { lcf.seed(cnv(x0)); } | |
392 | /** | |
393 | * Seeds the generator using values from an iterator range, | |
394 | * and updates first to point one past the last value consumed. | |
395 | */ | |
396 | template<class It> void seed(It& first, It last) { lcf.seed(first,last); } | |
397 | /** | |
398 | * Seeds the generator with values produced by @c seq.generate(). | |
399 | */ | |
400 | BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq) | |
401 | { lcf.seed(seq); } | |
402 | ||
403 | /** Returns the next value of the generator. */ | |
404 | uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); } | |
405 | ||
406 | /** Advances the state of the generator by @c z. */ | |
407 | void discard(boost::uintmax_t z) { lcf.discard(z); } | |
408 | ||
409 | /** Fills a range with random values */ | |
410 | template<class Iter> | |
411 | void generate(Iter first, Iter last) | |
412 | { | |
413 | for(; first != last; ++first) { | |
414 | *first = (*this)(); | |
415 | } | |
416 | } | |
417 | ||
418 | #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS | |
419 | /** Writes a @c rand48 to a @c std::ostream. */ | |
420 | template<class CharT,class Traits> | |
421 | friend std::basic_ostream<CharT,Traits>& | |
422 | operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r) | |
423 | { os << r.lcf; return os; } | |
424 | ||
425 | /** Reads a @c rand48 from a @c std::istream. */ | |
426 | template<class CharT,class Traits> | |
427 | friend std::basic_istream<CharT,Traits>& | |
428 | operator>>(std::basic_istream<CharT,Traits>& is, rand48& r) | |
429 | { is >> r.lcf; return is; } | |
430 | #endif | |
431 | ||
432 | /** | |
433 | * Returns true if the two generators will produce identical | |
434 | * sequences of values. | |
435 | */ | |
436 | friend bool operator==(const rand48& x, const rand48& y) | |
437 | { return x.lcf == y.lcf; } | |
438 | /** | |
439 | * Returns true if the two generators will produce different | |
440 | * sequences of values. | |
441 | */ | |
442 | friend bool operator!=(const rand48& x, const rand48& y) | |
443 | { return !(x == y); } | |
444 | private: | |
445 | /// \cond show_private | |
446 | typedef random::linear_congruential_engine<uint64_t, | |
447 | // xxxxULL is not portable | |
448 | uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32), | |
449 | 0xB, uint64_t(1)<<48> lcf_t; | |
450 | lcf_t lcf; | |
451 | ||
452 | static boost::uint64_t cnv(boost::uint32_t x) | |
453 | { return (static_cast<uint64_t>(x) << 16) | 0x330e; } | |
454 | /// \endcond | |
455 | }; | |
456 | #endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */ | |
457 | ||
458 | } // namespace random | |
459 | ||
460 | using random::minstd_rand0; | |
461 | using random::minstd_rand; | |
462 | using random::rand48; | |
463 | ||
464 | } // namespace boost | |
465 | ||
466 | #include <boost/random/detail/enable_warnings.hpp> | |
467 | ||
468 | #endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP |