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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> | |
26 | #include <boost/integer/static_log2.hpp> | |
27 | #include <boost/mpl/if.hpp> | |
28 | #include <boost/type_traits/is_arithmetic.hpp> | |
29 | #include <boost/random/detail/config.hpp> | |
30 | #include <boost/random/detail/const_mod.hpp> | |
31 | #include <boost/random/detail/seed.hpp> | |
32 | #include <boost/random/detail/seed_impl.hpp> | |
33 | #include <boost/detail/workaround.hpp> | |
34 | ||
35 | #include <boost/random/detail/disable_warnings.hpp> | |
36 | ||
37 | namespace boost { | |
38 | namespace random { | |
39 | ||
40 | /** | |
41 | * Instantiations of class template linear_congruential_engine model a | |
42 | * \pseudo_random_number_generator. Linear congruential pseudo-random | |
43 | * number generators are described in: | |
44 | * | |
45 | * @blockquote | |
46 | * "Mathematical methods in large-scale computing units", D. H. Lehmer, | |
47 | * Proc. 2nd Symposium on Large-Scale Digital Calculating Machines, | |
48 | * Harvard University Press, 1951, pp. 141-146 | |
49 | * @endblockquote | |
50 | * | |
51 | * Let x(n) denote the sequence of numbers returned by some pseudo-random | |
52 | * number generator. Then for the linear congruential generator, | |
53 | * x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are | |
54 | * x(0), a, c, m. The template parameter IntType shall denote an integral | |
55 | * type. It must be large enough to hold values a, c, and m. The template | |
56 | * parameters a and c must be smaller than m. | |
57 | * | |
58 | * Note: The quality of the generator crucially depends on the choice of | |
59 | * the parameters. User code should use one of the sensibly parameterized | |
60 | * generators such as minstd_rand instead. | |
61 | */ | |
62 | template<class IntType, IntType a, IntType c, IntType m> | |
63 | class linear_congruential_engine | |
64 | { | |
65 | public: | |
66 | typedef IntType result_type; | |
67 | ||
68 | // Required for old Boost.Random concept | |
69 | BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); | |
70 | ||
71 | BOOST_STATIC_CONSTANT(IntType, multiplier = a); | |
72 | BOOST_STATIC_CONSTANT(IntType, increment = c); | |
73 | BOOST_STATIC_CONSTANT(IntType, modulus = m); | |
74 | BOOST_STATIC_CONSTANT(IntType, default_seed = 1); | |
75 | ||
76 | BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer); | |
77 | BOOST_STATIC_ASSERT(m == 0 || a < m); | |
78 | BOOST_STATIC_ASSERT(m == 0 || c < m); | |
79 | ||
80 | /** | |
81 | * Constructs a @c linear_congruential_engine, using the default seed | |
82 | */ | |
83 | linear_congruential_engine() { seed(); } | |
84 | ||
85 | /** | |
86 | * Constructs a @c linear_congruential_engine, seeding it with @c x0. | |
87 | */ | |
88 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine, | |
89 | IntType, x0) | |
90 | { seed(x0); } | |
91 | ||
92 | /** | |
93 | * Constructs a @c linear_congruential_engine, seeding it with values | |
94 | * produced by a call to @c seq.generate(). | |
95 | */ | |
96 | BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine, | |
97 | SeedSeq, seq) | |
98 | { seed(seq); } | |
99 | ||
100 | /** | |
101 | * Constructs a @c linear_congruential_engine and seeds it | |
102 | * with values taken from the itrator range [first, last) | |
103 | * and adjusts first to point to the element after the last one | |
104 | * used. If there are not enough elements, throws @c std::invalid_argument. | |
105 | * | |
106 | * first and last must be input iterators. | |
107 | */ | |
108 | template<class It> | |
109 | linear_congruential_engine(It& first, It last) | |
110 | { | |
111 | seed(first, last); | |
112 | } | |
113 | ||
114 | // compiler-generated copy constructor and assignment operator are fine | |
115 | ||
116 | /** | |
117 | * Calls seed(default_seed) | |
118 | */ | |
119 | void seed() { seed(default_seed); } | |
120 | ||
121 | /** | |
122 | * If c mod m is zero and x0 mod m is zero, changes the current value of | |
123 | * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero, | |
124 | * distinct seeds in the range [1,m) will leave the generator in distinct | |
125 | * states. If c is not zero, the range is [0,m). | |
126 | */ | |
127 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0) | |
128 | { | |
129 | // wrap _x if it doesn't fit in the destination | |
130 | if(modulus == 0) { | |
131 | _x = x0; | |
132 | } else { | |
133 | _x = x0 % modulus; | |
134 | } | |
135 | // handle negative seeds | |
136 | if(_x <= 0 && _x != 0) { | |
137 | _x += modulus; | |
138 | } | |
139 | // adjust to the correct range | |
140 | if(increment == 0 && _x == 0) { | |
141 | _x = 1; | |
142 | } | |
143 | BOOST_ASSERT(_x >= (min)()); | |
144 | BOOST_ASSERT(_x <= (max)()); | |
145 | } | |
146 | ||
147 | /** | |
148 | * Seeds a @c linear_congruential_engine using values from a SeedSeq. | |
149 | */ | |
150 | BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq) | |
151 | { seed(detail::seed_one_int<IntType, m>(seq)); } | |
152 | ||
153 | /** | |
154 | * seeds a @c linear_congruential_engine with values taken | |
155 | * from the itrator range [first, last) and adjusts @c first to | |
156 | * point to the element after the last one used. If there are | |
157 | * not enough elements, throws @c std::invalid_argument. | |
158 | * | |
159 | * @c first and @c last must be input iterators. | |
160 | */ | |
161 | template<class It> | |
162 | void seed(It& first, It last) | |
163 | { seed(detail::get_one_int<IntType, m>(first, last)); } | |
164 | ||
165 | /** | |
166 | * Returns the smallest value that the @c linear_congruential_engine | |
167 | * can produce. | |
168 | */ | |
169 | static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () | |
170 | { return c == 0 ? 1 : 0; } | |
171 | /** | |
172 | * Returns the largest value that the @c linear_congruential_engine | |
173 | * can produce. | |
174 | */ | |
175 | static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () | |
176 | { return modulus-1; } | |
177 | ||
178 | /** Returns the next value of the @c linear_congruential_engine. */ | |
179 | IntType operator()() | |
180 | { | |
181 | _x = const_mod<IntType, m>::mult_add(a, _x, c); | |
182 | return _x; | |
183 | } | |
184 | ||
185 | /** Fills a range with random values */ | |
186 | template<class Iter> | |
187 | void generate(Iter first, Iter last) | |
188 | { detail::generate_from_int(*this, first, last); } | |
189 | ||
190 | /** Advances the state of the generator by @c z. */ | |
191 | void discard(boost::uintmax_t z) | |
192 | { | |
193 | typedef const_mod<IntType, m> mod_type; | |
194 | IntType b_inv = mod_type::invert(a-1); | |
195 | IntType b_gcd = mod_type::mult(a-1, b_inv); | |
196 | if(b_gcd == 1) { | |
197 | IntType a_z = mod_type::pow(a, z); | |
198 | _x = mod_type::mult_add(a_z, _x, | |
199 | mod_type::mult(mod_type::mult(c, b_inv), a_z - 1)); | |
200 | } else { | |
201 | // compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd) | |
202 | // we're storing the intermediate result / b_gcd | |
203 | IntType a_zm1_over_gcd = 0; | |
204 | IntType a_km1_over_gcd = (a - 1) / b_gcd; | |
205 | boost::uintmax_t exponent = z; | |
206 | while(exponent != 0) { | |
207 | if(exponent % 2 == 1) { | |
208 | a_zm1_over_gcd = | |
209 | mod_type::mult_add( | |
210 | b_gcd, | |
211 | mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd), | |
212 | mod_type::add(a_zm1_over_gcd, a_km1_over_gcd)); | |
213 | } | |
214 | a_km1_over_gcd = mod_type::mult_add( | |
215 | b_gcd, | |
216 | mod_type::mult(a_km1_over_gcd, a_km1_over_gcd), | |
217 | mod_type::add(a_km1_over_gcd, a_km1_over_gcd)); | |
218 | exponent /= 2; | |
219 | } | |
220 | ||
221 | IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1); | |
222 | IntType num = mod_type::mult(c, a_zm1_over_gcd); | |
223 | b_inv = mod_type::invert((a-1)/b_gcd); | |
224 | _x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num)); | |
225 | } | |
226 | } | |
227 | ||
228 | friend bool operator==(const linear_congruential_engine& x, | |
229 | const linear_congruential_engine& y) | |
230 | { return x._x == y._x; } | |
231 | friend bool operator!=(const linear_congruential_engine& x, | |
232 | const linear_congruential_engine& y) | |
233 | { return !(x == y); } | |
234 | ||
235 | #if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS) | |
236 | /** Writes a @c linear_congruential_engine to a @c std::ostream. */ | |
237 | template<class CharT, class Traits> | |
238 | friend std::basic_ostream<CharT,Traits>& | |
239 | operator<<(std::basic_ostream<CharT,Traits>& os, | |
240 | const linear_congruential_engine& lcg) | |
241 | { | |
242 | return os << lcg._x; | |
243 | } | |
244 | ||
245 | /** Reads a @c linear_congruential_engine from a @c std::istream. */ | |
246 | template<class CharT, class Traits> | |
247 | friend std::basic_istream<CharT,Traits>& | |
248 | operator>>(std::basic_istream<CharT,Traits>& is, | |
249 | linear_congruential_engine& lcg) | |
250 | { | |
251 | lcg.read(is); | |
252 | return is; | |
253 | } | |
254 | #endif | |
255 | ||
256 | private: | |
257 | ||
258 | /// \cond show_private | |
259 | ||
260 | template<class CharT, class Traits> | |
261 | void read(std::basic_istream<CharT, Traits>& is) { | |
262 | IntType x; | |
263 | if(is >> x) { | |
264 | if(x >= (min)() && x <= (max)()) { | |
265 | _x = x; | |
266 | } else { | |
267 | is.setstate(std::ios_base::failbit); | |
268 | } | |
269 | } | |
270 | } | |
271 | ||
272 | /// \endcond | |
273 | ||
274 | IntType _x; | |
275 | }; | |
276 | ||
277 | #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION | |
278 | // A definition is required even for integral static constants | |
279 | template<class IntType, IntType a, IntType c, IntType m> | |
280 | const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range; | |
281 | template<class IntType, IntType a, IntType c, IntType m> | |
282 | const IntType linear_congruential_engine<IntType,a,c,m>::multiplier; | |
283 | template<class IntType, IntType a, IntType c, IntType m> | |
284 | const IntType linear_congruential_engine<IntType,a,c,m>::increment; | |
285 | template<class IntType, IntType a, IntType c, IntType m> | |
286 | const IntType linear_congruential_engine<IntType,a,c,m>::modulus; | |
287 | template<class IntType, IntType a, IntType c, IntType m> | |
288 | const IntType linear_congruential_engine<IntType,a,c,m>::default_seed; | |
289 | #endif | |
290 | ||
291 | /// \cond show_deprecated | |
292 | ||
293 | // provided for backwards compatibility | |
294 | template<class IntType, IntType a, IntType c, IntType m, IntType val = 0> | |
295 | class linear_congruential : public linear_congruential_engine<IntType, a, c, m> | |
296 | { | |
297 | typedef linear_congruential_engine<IntType, a, c, m> base_type; | |
298 | public: | |
299 | linear_congruential(IntType x0 = 1) : base_type(x0) {} | |
300 | template<class It> | |
301 | linear_congruential(It& first, It last) : base_type(first, last) {} | |
302 | }; | |
303 | ||
304 | /// \endcond | |
305 | ||
306 | /** | |
307 | * The specialization \minstd_rand0 was originally suggested in | |
308 | * | |
309 | * @blockquote | |
310 | * A pseudo-random number generator for the System/360, P.A. Lewis, | |
311 | * A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2, | |
312 | * 1969, pp. 136-146 | |
313 | * @endblockquote | |
314 | * | |
315 | * It is examined more closely together with \minstd_rand in | |
316 | * | |
317 | * @blockquote | |
318 | * "Random Number Generators: Good ones are hard to find", | |
319 | * Stephen K. Park and Keith W. Miller, Communications of | |
320 | * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 | |
321 | * @endblockquote | |
322 | */ | |
323 | typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0; | |
324 | ||
325 | /** The specialization \minstd_rand was suggested in | |
326 | * | |
327 | * @blockquote | |
328 | * "Random Number Generators: Good ones are hard to find", | |
329 | * Stephen K. Park and Keith W. Miller, Communications of | |
330 | * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 | |
331 | * @endblockquote | |
332 | */ | |
333 | typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand; | |
334 | ||
335 | ||
336 | #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T) | |
337 | /** | |
338 | * Class @c rand48 models a \pseudo_random_number_generator. It uses | |
339 | * the linear congruential algorithm with the parameters a = 0x5DEECE66D, | |
340 | * c = 0xB, m = 2**48. It delivers identical results to the @c lrand48() | |
341 | * function available on some systems (assuming lcong48 has not been called). | |
342 | * | |
343 | * It is only available on systems where @c uint64_t is provided as an | |
344 | * integral type, so that for example static in-class constants and/or | |
345 | * enum definitions with large @c uint64_t numbers work. | |
346 | */ | |
347 | class rand48 | |
348 | { | |
349 | public: | |
350 | typedef boost::uint32_t result_type; | |
351 | ||
352 | BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); | |
353 | /** | |
354 | * Returns the smallest value that the generator can produce | |
355 | */ | |
356 | static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } | |
357 | /** | |
358 | * Returns the largest value that the generator can produce | |
359 | */ | |
360 | static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION () | |
361 | { return 0x7FFFFFFF; } | |
362 | ||
363 | /** Seeds the generator with the default seed. */ | |
364 | rand48() : lcf(cnv(static_cast<uint32_t>(1))) {} | |
365 | /** | |
366 | * Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e. | |
367 | */ | |
368 | BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0) | |
369 | { seed(x0); } | |
370 | /** | |
371 | * Seeds the generator with values produced by @c seq.generate(). | |
372 | */ | |
373 | BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq) | |
374 | { seed(seq); } | |
375 | /** | |
376 | * Seeds the generator using values from an iterator range, | |
377 | * and updates first to point one past the last value consumed. | |
378 | */ | |
379 | template<class It> rand48(It& first, It last) : lcf(first, last) { } | |
380 | ||
381 | // compiler-generated copy ctor and assignment operator are fine | |
382 | ||
383 | /** Seeds the generator with the default seed. */ | |
384 | void seed() { seed(static_cast<uint32_t>(1)); } | |
385 | /** | |
386 | * Changes the current value x(n) of the generator to (x0 << 16) | 0x330e. | |
387 | */ | |
388 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0) | |
389 | { lcf.seed(cnv(x0)); } | |
390 | /** | |
391 | * Seeds the generator using values from an iterator range, | |
392 | * and updates first to point one past the last value consumed. | |
393 | */ | |
394 | template<class It> void seed(It& first, It last) { lcf.seed(first,last); } | |
395 | /** | |
396 | * Seeds the generator with values produced by @c seq.generate(). | |
397 | */ | |
398 | BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq) | |
399 | { lcf.seed(seq); } | |
400 | ||
401 | /** Returns the next value of the generator. */ | |
402 | uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); } | |
403 | ||
404 | /** Advances the state of the generator by @c z. */ | |
405 | void discard(boost::uintmax_t z) { lcf.discard(z); } | |
406 | ||
407 | /** Fills a range with random values */ | |
408 | template<class Iter> | |
409 | void generate(Iter first, Iter last) | |
410 | { | |
411 | for(; first != last; ++first) { | |
412 | *first = (*this)(); | |
413 | } | |
414 | } | |
415 | ||
416 | #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS | |
417 | /** Writes a @c rand48 to a @c std::ostream. */ | |
418 | template<class CharT,class Traits> | |
419 | friend std::basic_ostream<CharT,Traits>& | |
420 | operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r) | |
421 | { os << r.lcf; return os; } | |
422 | ||
423 | /** Reads a @c rand48 from a @c std::istream. */ | |
424 | template<class CharT,class Traits> | |
425 | friend std::basic_istream<CharT,Traits>& | |
426 | operator>>(std::basic_istream<CharT,Traits>& is, rand48& r) | |
427 | { is >> r.lcf; return is; } | |
428 | #endif | |
429 | ||
430 | /** | |
431 | * Returns true if the two generators will produce identical | |
432 | * sequences of values. | |
433 | */ | |
434 | friend bool operator==(const rand48& x, const rand48& y) | |
435 | { return x.lcf == y.lcf; } | |
436 | /** | |
437 | * Returns true if the two generators will produce different | |
438 | * sequences of values. | |
439 | */ | |
440 | friend bool operator!=(const rand48& x, const rand48& y) | |
441 | { return !(x == y); } | |
442 | private: | |
443 | /// \cond show_private | |
444 | typedef random::linear_congruential_engine<uint64_t, | |
445 | // xxxxULL is not portable | |
446 | uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32), | |
447 | 0xB, uint64_t(1)<<48> lcf_t; | |
448 | lcf_t lcf; | |
449 | ||
450 | static boost::uint64_t cnv(boost::uint32_t x) | |
451 | { return (static_cast<uint64_t>(x) << 16) | 0x330e; } | |
452 | /// \endcond | |
453 | }; | |
454 | #endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */ | |
455 | ||
456 | } // namespace random | |
457 | ||
458 | using random::minstd_rand0; | |
459 | using random::minstd_rand; | |
460 | using random::rand48; | |
461 | ||
462 | } // namespace boost | |
463 | ||
464 | #include <boost/random/detail/enable_warnings.hpp> | |
465 | ||
466 | #endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP |