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
37namespace boost {
38namespace 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 */
62template<class IntType, IntType a, IntType c, IntType m>
63class linear_congruential_engine
64{
65public:
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
256private:
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
279template<class IntType, IntType a, IntType c, IntType m>
280const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range;
281template<class IntType, IntType a, IntType c, IntType m>
282const IntType linear_congruential_engine<IntType,a,c,m>::multiplier;
283template<class IntType, IntType a, IntType c, IntType m>
284const IntType linear_congruential_engine<IntType,a,c,m>::increment;
285template<class IntType, IntType a, IntType c, IntType m>
286const IntType linear_congruential_engine<IntType,a,c,m>::modulus;
287template<class IntType, IntType a, IntType c, IntType m>
288const IntType linear_congruential_engine<IntType,a,c,m>::default_seed;
289#endif
290
291/// \cond show_deprecated
292
293// provided for backwards compatibility
294template<class IntType, IntType a, IntType c, IntType m, IntType val = 0>
295class linear_congruential : public linear_congruential_engine<IntType, a, c, m>
296{
297 typedef linear_congruential_engine<IntType, a, c, m> base_type;
298public:
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 */
323typedef 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 */
333typedef 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 */
347class rand48
348{
349public:
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); }
442private:
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
458using random::minstd_rand0;
459using random::minstd_rand;
460using random::rand48;
461
462} // namespace boost
463
464#include <boost/random/detail/enable_warnings.hpp>
465
466#endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
467