1 // (C) Copyright John Maddock 2005-2006.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6 #ifndef BOOST_MATH_TOOLS_FRACTION_INCLUDED
7 #define BOOST_MATH_TOOLS_FRACTION_INCLUDED
8
9 #ifdef _MSC_VER
10 #pragma once
11 #endif
12
13 #include <boost/config/no_tr1/cmath.hpp>
14 #include <boost/cstdint.hpp>
15 #include <boost/type_traits/integral_constant.hpp>
16 #include <boost/mpl/if.hpp>
17 #include <boost/math/tools/precision.hpp>
18
19 namespace boost{ namespace math{ namespace tools{
20
21 namespace detail
22 {
23
24 template <class T>
25 struct is_pair : public boost::false_type{};
26
27 template <class T, class U>
28 struct is_pair<std::pair<T,U> > : public boost::true_type{};
29
30 template <class Gen>
31 struct fraction_traits_simple
32 {
33 typedef typename Gen::result_type result_type;
34 typedef typename Gen::result_type value_type;
35
aboost::math::tools::detail::fraction_traits_simple36 static result_type a(const value_type&) BOOST_MATH_NOEXCEPT(value_type)
37 {
38 return 1;
39 }
bboost::math::tools::detail::fraction_traits_simple40 static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
41 {
42 return v;
43 }
44 };
45
46 template <class Gen>
47 struct fraction_traits_pair
48 {
49 typedef typename Gen::result_type value_type;
50 typedef typename value_type::first_type result_type;
51
aboost::math::tools::detail::fraction_traits_pair52 static result_type a(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
53 {
54 return v.first;
55 }
bboost::math::tools::detail::fraction_traits_pair56 static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
57 {
58 return v.second;
59 }
60 };
61
62 template <class Gen>
63 struct fraction_traits
64 : public boost::mpl::if_c<
65 is_pair<typename Gen::result_type>::value,
66 fraction_traits_pair<Gen>,
67 fraction_traits_simple<Gen> >::type
68 {
69 };
70
71 } // namespace detail
72
73 //
74 // continued_fraction_b
75 // Evaluates:
76 //
77 // b0 + a1
78 // ---------------
79 // b1 + a2
80 // ----------
81 // b2 + a3
82 // -----
83 // b3 + ...
84 //
85 // Note that the first a0 returned by generator Gen is disarded.
86 //
87 template <class Gen, class U>
continued_fraction_b(Gen & g,const U & factor,boost::uintmax_t & max_terms)88 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::uintmax_t& max_terms)
89 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
90 {
91 BOOST_MATH_STD_USING // ADL of std names
92
93 typedef detail::fraction_traits<Gen> traits;
94 typedef typename traits::result_type result_type;
95 typedef typename traits::value_type value_type;
96
97 result_type tiny = tools::min_value<result_type>();
98
99 value_type v = g();
100
101 result_type f, C, D, delta;
102 f = traits::b(v);
103 if(f == 0)
104 f = tiny;
105 C = f;
106 D = 0;
107
108 boost::uintmax_t counter(max_terms);
109
110 do{
111 v = g();
112 D = traits::b(v) + traits::a(v) * D;
113 if(D == 0)
114 D = tiny;
115 C = traits::b(v) + traits::a(v) / C;
116 if(C == 0)
117 C = tiny;
118 D = 1/D;
119 delta = C*D;
120 f = f * delta;
121 }while((fabs(delta - 1) > factor) && --counter);
122
123 max_terms = max_terms - counter;
124
125 return f;
126 }
127
128 template <class Gen, class U>
continued_fraction_b(Gen & g,const U & factor)129 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor)
130 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
131 {
132 boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
133 return continued_fraction_b(g, factor, max_terms);
134 }
135
136 template <class Gen>
continued_fraction_b(Gen & g,int bits)137 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits)
138 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
139 {
140 BOOST_MATH_STD_USING // ADL of std names
141
142 typedef detail::fraction_traits<Gen> traits;
143 typedef typename traits::result_type result_type;
144
145 result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
146 boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
147 return continued_fraction_b(g, factor, max_terms);
148 }
149
150 template <class Gen>
continued_fraction_b(Gen & g,int bits,boost::uintmax_t & max_terms)151 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits, boost::uintmax_t& max_terms)
152 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
153 {
154 BOOST_MATH_STD_USING // ADL of std names
155
156 typedef detail::fraction_traits<Gen> traits;
157 typedef typename traits::result_type result_type;
158
159 result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
160 return continued_fraction_b(g, factor, max_terms);
161 }
162
163 //
164 // continued_fraction_a
165 // Evaluates:
166 //
167 // a1
168 // ---------------
169 // b1 + a2
170 // ----------
171 // b2 + a3
172 // -----
173 // b3 + ...
174 //
175 // Note that the first a1 and b1 returned by generator Gen are both used.
176 //
177 template <class Gen, class U>
continued_fraction_a(Gen & g,const U & factor,boost::uintmax_t & max_terms)178 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor, boost::uintmax_t& max_terms)
179 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
180 {
181 BOOST_MATH_STD_USING // ADL of std names
182
183 typedef detail::fraction_traits<Gen> traits;
184 typedef typename traits::result_type result_type;
185 typedef typename traits::value_type value_type;
186
187 result_type tiny = tools::min_value<result_type>();
188
189 value_type v = g();
190
191 result_type f, C, D, delta, a0;
192 f = traits::b(v);
193 a0 = traits::a(v);
194 if(f == 0)
195 f = tiny;
196 C = f;
197 D = 0;
198
199 boost::uintmax_t counter(max_terms);
200
201 do{
202 v = g();
203 D = traits::b(v) + traits::a(v) * D;
204 if(D == 0)
205 D = tiny;
206 C = traits::b(v) + traits::a(v) / C;
207 if(C == 0)
208 C = tiny;
209 D = 1/D;
210 delta = C*D;
211 f = f * delta;
212 }while((fabs(delta - 1) > factor) && --counter);
213
214 max_terms = max_terms - counter;
215
216 return a0/f;
217 }
218
219 template <class Gen, class U>
continued_fraction_a(Gen & g,const U & factor)220 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor)
221 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
222 {
223 boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
224 return continued_fraction_a(g, factor, max_iter);
225 }
226
227 template <class Gen>
continued_fraction_a(Gen & g,int bits)228 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits)
229 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
230 {
231 BOOST_MATH_STD_USING // ADL of std names
232
233 typedef detail::fraction_traits<Gen> traits;
234 typedef typename traits::result_type result_type;
235
236 result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
237 boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
238
239 return continued_fraction_a(g, factor, max_iter);
240 }
241
242 template <class Gen>
continued_fraction_a(Gen & g,int bits,boost::uintmax_t & max_terms)243 inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits, boost::uintmax_t& max_terms)
244 BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
245 {
246 BOOST_MATH_STD_USING // ADL of std names
247
248 typedef detail::fraction_traits<Gen> traits;
249 typedef typename traits::result_type result_type;
250
251 result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
252 return continued_fraction_a(g, factor, max_terms);
253 }
254
255 } // namespace tools
256 } // namespace math
257 } // namespace boost
258
259 #endif // BOOST_MATH_TOOLS_FRACTION_INCLUDED
260
261