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 |
467 | |