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/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 | */ |
125 | BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0_) |
126 | { |
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_; |
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 |
138 | if(_x < 0) { |
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 | */ |
171 | static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () |
172 | { return c == 0 ? 1 : 0; } |
173 | /** |
174 | * Returns the largest value that the @c linear_congruential_engine |
175 | * can produce. |
176 | */ |
177 | static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () |
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 | */ |
358 | static BOOST_CONSTEXPR uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } |
359 | /** |
360 | * Returns the largest value that the generator can produce |
361 | */ |
362 | static BOOST_CONSTEXPR uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION () |
363 | { return 0x7FFFFFFF; } |
364 | |
365 | /** Seeds the generator with the default seed. */ |
366 | rand48() : lcf(cnv(x: 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(x0: 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(x0_: cnv(x: 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 |
469 | |