1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
|
// (C) Copyright John Maddock 2005-2006.
// (C) Copyright Matt Borland 2024.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_TOOLS_FRACTION_INCLUDED
#define BOOST_MATH_TOOLS_FRACTION_INCLUDED
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/type_traits.hpp>
#include <boost/math/tools/numeric_limits.hpp>
#include <boost/math/tools/tuple.hpp>
#include <boost/math/tools/precision.hpp>
#include <boost/math/tools/complex.hpp>
#include <boost/math/tools/cstdint.hpp>
namespace boost{ namespace math{ namespace tools{
namespace detail
{
template <typename T>
struct is_pair : public boost::math::false_type{};
template <typename T, typename U>
struct is_pair<boost::math::pair<T,U>> : public boost::math::true_type{};
template <typename Gen>
struct fraction_traits_simple
{
using result_type = typename Gen::result_type;
using value_type = typename Gen::result_type;
BOOST_MATH_GPU_ENABLED static result_type a(const value_type&) BOOST_MATH_NOEXCEPT(value_type)
{
return 1;
}
BOOST_MATH_GPU_ENABLED static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
{
return v;
}
};
template <typename Gen>
struct fraction_traits_pair
{
using value_type = typename Gen::result_type;
using result_type = typename value_type::first_type;
BOOST_MATH_GPU_ENABLED static result_type a(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
{
return v.first;
}
BOOST_MATH_GPU_ENABLED static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
{
return v.second;
}
};
template <typename Gen>
struct fraction_traits
: public boost::math::conditional<
is_pair<typename Gen::result_type>::value,
fraction_traits_pair<Gen>,
fraction_traits_simple<Gen>>::type
{
};
template <typename T, bool = is_complex_type<T>::value>
struct tiny_value
{
// For float, double, and long double, 1/min_value<T>() is finite.
// But for mpfr_float and cpp_bin_float, 1/min_value<T>() is inf.
// Multiply the min by 16 so that the reciprocal doesn't overflow.
BOOST_MATH_GPU_ENABLED static T get() {
return 16*tools::min_value<T>();
}
};
template <typename T>
struct tiny_value<T, true>
{
using value_type = typename T::value_type;
BOOST_MATH_GPU_ENABLED static T get() {
return 16*tools::min_value<value_type>();
}
};
} // namespace detail
namespace detail {
//
// continued_fraction_b
// Evaluates:
//
// b0 + a1
// ---------------
// b1 + a2
// ----------
// b2 + a3
// -----
// b3 + ...
//
// Note that the first a0 returned by generator Gen is discarded.
//
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b_impl(Gen& g, const U& factor, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
// SYCL can not handle this condition so we only check float on that platform
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
using traits = detail::fraction_traits<Gen>;
using result_type = typename traits::result_type;
using value_type = typename traits::value_type;
using integer_type = typename integer_scalar_type<result_type>::type;
using scalar_type = typename scalar_type<result_type>::type;
integer_type const zero(0), one(1);
result_type tiny = detail::tiny_value<result_type>::get();
scalar_type terminator = abs(factor);
value_type v = g();
result_type f, C, D, delta;
f = traits::b(v);
if(f == zero)
f = tiny;
C = f;
D = 0;
boost::math::uintmax_t counter(max_terms);
do{
v = g();
D = traits::b(v) + traits::a(v) * D;
if(D == result_type(0))
D = tiny;
C = traits::b(v) + traits::a(v) / C;
if(C == zero)
C = tiny;
D = one/D;
delta = C*D;
f = f * delta;
}while((abs(delta - one) > terminator) && --counter);
max_terms = max_terms - counter;
return f;
}
} // namespace detail
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
return detail::continued_fraction_b_impl(g, factor, max_terms);
}
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
boost::math::uintmax_t max_terms = (boost::math::numeric_limits<boost::math::uintmax_t>::max)();
return detail::continued_fraction_b_impl(g, factor, max_terms);
}
template <typename Gen>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
using traits = detail::fraction_traits<Gen>;
using result_type = typename traits::result_type;
result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
boost::math::uintmax_t max_terms = (boost::math::numeric_limits<boost::math::uintmax_t>::max)();
return detail::continued_fraction_b_impl(g, factor, max_terms);
}
template <typename Gen>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
using traits = detail::fraction_traits<Gen>;
using result_type = typename traits::result_type;
result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
return detail::continued_fraction_b_impl(g, factor, max_terms);
}
namespace detail {
//
// continued_fraction_a
// Evaluates:
//
// a1
// ---------------
// b1 + a2
// ----------
// b2 + a3
// -----
// b3 + ...
//
// Note that the first a1 and b1 returned by generator Gen are both used.
//
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a_impl(Gen& g, const U& factor, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
using traits = detail::fraction_traits<Gen>;
using result_type = typename traits::result_type;
using value_type = typename traits::value_type;
using integer_type = typename integer_scalar_type<result_type>::type;
using scalar_type = typename scalar_type<result_type>::type;
integer_type const zero(0), one(1);
result_type tiny = detail::tiny_value<result_type>::get();
scalar_type terminator = abs(factor);
value_type v = g();
result_type f, C, D, delta, a0;
f = traits::b(v);
a0 = traits::a(v);
if(f == zero)
f = tiny;
C = f;
D = 0;
boost::math::uintmax_t counter(max_terms);
do{
v = g();
D = traits::b(v) + traits::a(v) * D;
if(D == zero)
D = tiny;
C = traits::b(v) + traits::a(v) / C;
if(C == zero)
C = tiny;
D = one/D;
delta = C*D;
f = f * delta;
}while((abs(delta - one) > terminator) && --counter);
max_terms = max_terms - counter;
return a0/f;
}
} // namespace detail
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
return detail::continued_fraction_a_impl(g, factor, max_terms);
}
template <typename Gen, typename U>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
boost::math::uintmax_t max_iter = (boost::math::numeric_limits<boost::math::uintmax_t>::max)();
return detail::continued_fraction_a_impl(g, factor, max_iter);
}
template <typename Gen>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
boost::math::uintmax_t max_iter = (boost::math::numeric_limits<boost::math::uintmax_t>::max)();
return detail::continued_fraction_a_impl(g, factor, max_iter);
}
template <typename Gen>
BOOST_MATH_GPU_ENABLED inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits, boost::math::uintmax_t& max_terms)
noexcept(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type)
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
&& noexcept(std::declval<Gen>()())
#endif
)
{
BOOST_MATH_STD_USING // ADL of std names
using traits = detail::fraction_traits<Gen>;
using result_type = typename traits::result_type;
result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
return detail::continued_fraction_a_impl(g, factor, max_terms);
}
} // namespace tools
} // namespace math
} // namespace boost
#endif // BOOST_MATH_TOOLS_FRACTION_INCLUDED
|
