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/Src/Dependencies/Boost/boost/random/inversive_congruential.hpp

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  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: inversive_congruential.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
 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