1/* boost random/inversive_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_INVERSIVE_CONGRUENTIAL_HPP
17#define BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
18
19#include <iosfwd>
20#include <stdexcept>
21#include <boost/assert.hpp>
22#include <boost/config.hpp>
23#include <boost/cstdint.hpp>
24#include <boost/integer/static_log2.hpp>
25#include <boost/random/detail/config.hpp>
26#include <boost/random/detail/const_mod.hpp>
27#include <boost/random/detail/seed.hpp>
28#include <boost/random/detail/operators.hpp>
29#include <boost/random/detail/seed_impl.hpp>
30
31#include <boost/random/detail/disable_warnings.hpp>
32
33namespace boost {
34namespace random {
35
36// Eichenauer and Lehn 1986
37/**
38 * Instantiations of class template @c inversive_congruential_engine model a
39 * \pseudo_random_number_generator. It uses the inversive congruential
40 * algorithm (ICG) described in
41 *
42 * @blockquote
43 * "Inversive pseudorandom number generators: concepts, results and links",
44 * Peter Hellekalek, In: "Proceedings of the 1995 Winter Simulation
45 * Conference", C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman
46 * (editors), 1995, pp. 255-262. ftp://random.mat.sbg.ac.at/pub/data/wsc95.ps
47 * @endblockquote
48 *
49 * The output sequence is defined by x(n+1) = (a*inv(x(n)) - b) (mod p),
50 * where x(0), a, b, and the prime number p are parameters of the generator.
51 * The expression inv(k) denotes the multiplicative inverse of k in the
52 * field of integer numbers modulo p, with inv(0) := 0.
53 *
54 * The template parameter IntType shall denote a signed integral type large
55 * enough to hold p; a, b, and p are the parameters of the generators. The
56 * template parameter val is the validation value checked by validation.
57 *
58 * @xmlnote
59 * The implementation currently uses the Euclidian Algorithm to compute
60 * the multiplicative inverse. Therefore, the inversive generators are about
61 * 10-20 times slower than the others (see section"performance"). However,
62 * the paper talks of only 3x slowdown, so the Euclidian Algorithm is probably
63 * not optimal for calculating the multiplicative inverse.
64 * @endxmlnote
65 */
66template<class IntType, IntType a, IntType b, IntType p>
67class inversive_congruential_engine
68{
69public:
70 typedef IntType result_type;
71 BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
72
73 BOOST_STATIC_CONSTANT(result_type, multiplier = a);
74 BOOST_STATIC_CONSTANT(result_type, increment = b);
75 BOOST_STATIC_CONSTANT(result_type, modulus = p);
76 BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
77
78 static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return b == 0 ? 1 : 0; }
79 static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () { return p-1; }
80
81 /**
82 * Constructs an @c inversive_congruential_engine, seeding it with
83 * the default seed.
84 */
85 inversive_congruential_engine() { seed(); }
86
87 /**
88 * Constructs an @c inversive_congruential_engine, seeding it with @c x0.
89 */
90 BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(inversive_congruential_engine,
91 IntType, x0)
92 { seed(x0); }
93
94 /**
95 * Constructs an @c inversive_congruential_engine, seeding it with values
96 * produced by a call to @c seq.generate().
97 */
98 BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(inversive_congruential_engine,
99 SeedSeq, seq)
100 { seed(seq); }
101
102 /**
103 * Constructs an @c inversive_congruential_engine, seeds it
104 * with values taken from the itrator range [first, last),
105 * and adjusts first to point to the element after the last one
106 * used. If there are not enough elements, throws @c std::invalid_argument.
107 *
108 * first and last must be input iterators.
109 */
110 template<class It> inversive_congruential_engine(It& first, It last)
111 { seed(first, last); }
112
113 /**
114 * Calls seed(default_seed)
115 */
116 void seed() { seed(default_seed); }
117
118 /**
119 * If c mod m is zero and x0 mod m is zero, changes the current value of
120 * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero,
121 * distinct seeds in the range [1,m) will leave the generator in distinct
122 * states. If c is not zero, the range is [0,m).
123 */
124 BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(inversive_congruential_engine, IntType, x0)
125 {
126 // wrap _x if it doesn't fit in the destination
127 if(modulus == 0) {
128 _value = x0;
129 } else {
130 _value = x0 % modulus;
131 }
132 // handle negative seeds
133 if(_value <= 0 && _value != 0) {
134 _value += modulus;
135 }
136 // adjust to the correct range
137 if(increment == 0 && _value == 0) {
138 _value = 1;
139 }
140 BOOST_ASSERT(_value >= (min)());
141 BOOST_ASSERT(_value <= (max)());
142 }
143
144 /**
145 * Seeds an @c inversive_congruential_engine using values from a SeedSeq.
146 */
147 BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(inversive_congruential_engine, SeedSeq, seq)
148 { seed(detail::seed_one_int<IntType, modulus>(seq)); }
149
150 /**
151 * seeds an @c inversive_congruential_engine with values taken
152 * from the itrator range [first, last) and adjusts @c first to
153 * point to the element after the last one used. If there are
154 * not enough elements, throws @c std::invalid_argument.
155 *
156 * @c first and @c last must be input iterators.
157 */
158 template<class It> void seed(It& first, It last)
159 { seed(detail::get_one_int<IntType, modulus>(first, last)); }
160
161 /** Returns the next output of the generator. */
162 IntType operator()()
163 {
164 typedef const_mod<IntType, p> do_mod;
165 _value = do_mod::mult_add(a, do_mod::invert(_value), b);
166 return _value;
167 }
168
169 /** Fills a range with random values */
170 template<class Iter>
171 void generate(Iter first, Iter last)
172 { detail::generate_from_int(*this, first, last); }
173
174 /** Advances the state of the generator by @c z. */
175 void discard(boost::uintmax_t z)
176 {
177 for(boost::uintmax_t j = 0; j < z; ++j) {
178 (*this)();
179 }
180 }
181
182 /**
183 * Writes the textual representation of the generator to a @c std::ostream.
184 */
185 BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, inversive_congruential_engine, x)
186 {
187 os << x._value;
188 return os;
189 }
190
191 /**
192 * Reads the textual representation of the generator from a @c std::istream.
193 */
194 BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, inversive_congruential_engine, x)
195 {
196 is >> x._value;
197 return is;
198 }
199
200 /**
201 * Returns true if the two generators will produce identical
202 * sequences of outputs.
203 */
204 BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(inversive_congruential_engine, x, y)
205 { return x._value == y._value; }
206
207 /**
208 * Returns true if the two generators will produce different
209 * sequences of outputs.
210 */
211 BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(inversive_congruential_engine)
212
213private:
214 IntType _value;
215};
216
217#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
218// A definition is required even for integral static constants
219template<class IntType, IntType a, IntType b, IntType p>
220const bool inversive_congruential_engine<IntType, a, b, p>::has_fixed_range;
221template<class IntType, IntType a, IntType b, IntType p>
222const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::multiplier;
223template<class IntType, IntType a, IntType b, IntType p>
224const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::increment;
225template<class IntType, IntType a, IntType b, IntType p>
226const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::modulus;
227template<class IntType, IntType a, IntType b, IntType p>
228const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::default_seed;
229#endif
230
231/// \cond show_deprecated
232
233// provided for backwards compatibility
234template<class IntType, IntType a, IntType b, IntType p, IntType val = 0>
235class inversive_congruential : public inversive_congruential_engine<IntType, a, b, p>
236{
237 typedef inversive_congruential_engine<IntType, a, b, p> base_type;
238public:
239 inversive_congruential(IntType x0 = 1) : base_type(x0) {}
240 template<class It>
241 inversive_congruential(It& first, It last) : base_type(first, last) {}
242};
243
244/// \endcond
245
246/**
247 * The specialization hellekalek1995 was suggested in
248 *
249 * @blockquote
250 * "Inversive pseudorandom number generators: concepts, results and links",
251 * Peter Hellekalek, In: "Proceedings of the 1995 Winter Simulation
252 * Conference", C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman
253 * (editors), 1995, pp. 255-262. ftp://random.mat.sbg.ac.at/pub/data/wsc95.ps
254 * @endblockquote
255 */
256typedef inversive_congruential_engine<uint32_t, 9102, 2147483647-36884165,
257 2147483647> hellekalek1995;
258
259} // namespace random
260
261using random::hellekalek1995;
262
263} // namespace boost
264
265#include <boost/random/detail/enable_warnings.hpp>
266
267#endif // BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
268