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1 | // (C) Copyright Gennadiy Rozental 2001. |
2 | // Distributed under the Boost Software License, Version 1.0. | |
3 | // (See accompanying file LICENSE_1_0.txt or copy at | |
4 | // http://www.boost.org/LICENSE_1_0.txt) | |
5 | ||
6 | // See http://www.boost.org/libs/test for the library home page. | |
7 | // | |
8 | //!@file | |
9 | //!@brief algorithms for comparing floating point values | |
10 | // *************************************************************************** | |
11 | ||
12 | #ifndef BOOST_TEST_FLOATING_POINT_COMPARISON_HPP_071894GER | |
13 | #define BOOST_TEST_FLOATING_POINT_COMPARISON_HPP_071894GER | |
14 | ||
15 | // Boost.Test | |
16 | #include <boost/test/detail/global_typedef.hpp> | |
17 | #include <boost/test/tools/assertion_result.hpp> | |
18 | ||
19 | // Boost | |
20 | #include <boost/limits.hpp> // for std::numeric_limits | |
21 | #include <boost/static_assert.hpp> | |
22 | #include <boost/assert.hpp> | |
23 | #include <boost/mpl/bool.hpp> | |
24 | #include <boost/type_traits/is_floating_point.hpp> | |
25 | #include <boost/type_traits/is_array.hpp> | |
26 | #include <boost/type_traits/conditional.hpp> | |
27 | #include <boost/utility/enable_if.hpp> | |
28 | ||
29 | // STL | |
30 | #include <iosfwd> | |
31 | ||
32 | #include <boost/test/detail/suppress_warnings.hpp> | |
33 | ||
34 | //____________________________________________________________________________// | |
35 | ||
36 | namespace boost { | |
37 | namespace math { | |
38 | namespace fpc { | |
39 | ||
40 | // ************************************************************************** // | |
41 | // ************** fpc::tolerance_based ************** // | |
42 | // ************************************************************************** // | |
43 | ||
44 | ||
45 | //! @internal | |
46 | //! Protects the instanciation of std::numeric_limits from non-supported types (eg. T=array) | |
47 | template <typename T, bool enabled> | |
48 | struct tolerance_based_delegate; | |
49 | ||
50 | template <typename T> | |
51 | struct tolerance_based_delegate<T, false> : mpl::false_ {}; | |
52 | ||
53 | template <typename T> | |
54 | struct tolerance_based_delegate<T, true> | |
55 | : mpl::bool_< | |
56 | is_floating_point<T>::value || | |
57 | (!std::numeric_limits<T>::is_integer && std::numeric_limits<T>::is_specialized && !std::numeric_limits<T>::is_exact)> | |
58 | {}; | |
59 | ||
60 | ||
61 | /*!@brief Indicates if a type can be compared using a tolerance scheme | |
62 | * | |
63 | * This is a metafunction that should evaluate to @c mpl::true_ if the type | |
64 | * @c T can be compared using a tolerance based method, typically for floating point | |
65 | * types. | |
66 | * | |
67 | * This metafunction can be specialized further to declare user types that are | |
68 | * floating point (eg. boost.multiprecision). | |
69 | */ | |
70 | template <typename T> | |
71 | struct tolerance_based : tolerance_based_delegate<T, !is_array<T>::value >::type {}; | |
72 | ||
73 | // ************************************************************************** // | |
74 | // ************** fpc::strength ************** // | |
75 | // ************************************************************************** // | |
76 | ||
77 | //! Method for comparing floating point numbers | |
78 | enum strength { | |
79 | FPC_STRONG, //!< "Very close" - equation 2' in docs, the default | |
80 | FPC_WEAK //!< "Close enough" - equation 3' in docs. | |
81 | }; | |
82 | ||
83 | ||
84 | // ************************************************************************** // | |
85 | // ************** tolerance presentation types ************** // | |
86 | // ************************************************************************** // | |
87 | ||
88 | template<typename FPT> | |
89 | struct percent_tolerance_t { | |
90 | explicit percent_tolerance_t( FPT v ) : m_value( v ) {} | |
91 | ||
92 | FPT m_value; | |
93 | }; | |
94 | ||
95 | //____________________________________________________________________________// | |
96 | ||
97 | template<typename FPT> | |
98 | inline std::ostream& operator<<( std::ostream& out, percent_tolerance_t<FPT> t ) | |
99 | { | |
100 | return out << t.m_value; | |
101 | } | |
102 | ||
103 | //____________________________________________________________________________// | |
104 | ||
105 | template<typename FPT> | |
106 | inline percent_tolerance_t<FPT> | |
107 | percent_tolerance( FPT v ) | |
108 | { | |
109 | return percent_tolerance_t<FPT>( v ); | |
110 | } | |
111 | ||
112 | //____________________________________________________________________________// | |
113 | ||
114 | // ************************************************************************** // | |
115 | // ************** details ************** // | |
116 | // ************************************************************************** // | |
117 | ||
118 | namespace fpc_detail { | |
119 | ||
120 | // FPT is Floating-Point Type: float, double, long double or User-Defined. | |
121 | template<typename FPT> | |
122 | inline FPT | |
123 | fpt_abs( FPT fpv ) | |
124 | { | |
125 | return fpv < static_cast<FPT>(0) ? -fpv : fpv; | |
126 | } | |
127 | ||
128 | //____________________________________________________________________________// | |
129 | ||
130 | template<typename FPT> | |
131 | struct fpt_specialized_limits | |
132 | { | |
133 | static FPT min_value() { return (std::numeric_limits<FPT>::min)(); } | |
134 | static FPT max_value() { return (std::numeric_limits<FPT>::max)(); } | |
135 | }; | |
136 | ||
137 | template<typename FPT> | |
138 | struct fpt_non_specialized_limits | |
139 | { | |
140 | static FPT min_value() { return static_cast<FPT>(0); } | |
141 | static FPT max_value() { return static_cast<FPT>(1000000); } // for our purposes it doesn't really matter what value is returned here | |
142 | }; | |
143 | ||
144 | template<typename FPT> | |
145 | struct fpt_limits : boost::conditional<std::numeric_limits<FPT>::is_specialized, | |
146 | fpt_specialized_limits<FPT>, | |
147 | fpt_non_specialized_limits<FPT> | |
148 | >::type | |
149 | {}; | |
150 | ||
151 | //____________________________________________________________________________// | |
152 | ||
153 | // both f1 and f2 are unsigned here | |
154 | template<typename FPT> | |
155 | inline FPT | |
156 | safe_fpt_division( FPT f1, FPT f2 ) | |
157 | { | |
158 | // Avoid overflow. | |
159 | if( (f2 < static_cast<FPT>(1)) && (f1 > f2*fpt_limits<FPT>::max_value()) ) | |
160 | return fpt_limits<FPT>::max_value(); | |
161 | ||
162 | // Avoid underflow. | |
163 | if( (f1 == static_cast<FPT>(0)) || | |
164 | ((f2 > static_cast<FPT>(1)) && (f1 < f2*fpt_limits<FPT>::min_value())) ) | |
165 | return static_cast<FPT>(0); | |
166 | ||
167 | return f1/f2; | |
168 | } | |
169 | ||
170 | //____________________________________________________________________________// | |
171 | ||
172 | template<typename FPT, typename ToleranceType> | |
173 | inline FPT | |
174 | fraction_tolerance( ToleranceType tolerance ) | |
175 | { | |
176 | return static_cast<FPT>(tolerance); | |
177 | } | |
178 | ||
179 | //____________________________________________________________________________// | |
180 | ||
181 | template<typename FPT2, typename FPT> | |
182 | inline FPT2 | |
183 | fraction_tolerance( percent_tolerance_t<FPT> tolerance ) | |
184 | { | |
185 | return FPT2(tolerance.m_value)*FPT2(0.01); | |
186 | } | |
187 | ||
188 | //____________________________________________________________________________// | |
189 | ||
190 | } // namespace fpc_detail | |
191 | ||
192 | // ************************************************************************** // | |
193 | // ************** close_at_tolerance ************** // | |
194 | // ************************************************************************** // | |
195 | ||
196 | ||
197 | /*!@brief Predicate for comparing floating point numbers | |
198 | * | |
199 | * This predicate is used to compare floating point numbers. In addition the comparison produces maximum | |
200 | * related differnce, which can be used to generate detailed error message | |
201 | * The methods for comparing floating points are detailed in the documentation. The method is chosen | |
202 | * by the @ref boost::math::fpc::strength given at construction. | |
203 | */ | |
204 | template<typename FPT> | |
205 | class close_at_tolerance { | |
206 | public: | |
207 | // Public typedefs | |
208 | typedef bool result_type; | |
209 | ||
210 | // Constructor | |
211 | template<typename ToleranceType> | |
212 | explicit close_at_tolerance( ToleranceType tolerance, fpc::strength fpc_strength = FPC_STRONG ) | |
213 | : m_fraction_tolerance( fpc_detail::fraction_tolerance<FPT>( tolerance ) ) | |
214 | , m_strength( fpc_strength ) | |
215 | , m_tested_rel_diff( 0 ) | |
216 | { | |
217 | BOOST_ASSERT_MSG( m_fraction_tolerance >= FPT(0), "tolerance must not be negative!" ); // no reason for tolerance to be negative | |
218 | } | |
219 | ||
220 | // Access methods | |
221 | //! Returns the tolerance | |
222 | FPT fraction_tolerance() const { return m_fraction_tolerance; } | |
223 | ||
224 | //! Returns the comparison method | |
225 | fpc::strength strength() const { return m_strength; } | |
226 | ||
227 | //! Returns the failing fraction | |
228 | FPT tested_rel_diff() const { return m_tested_rel_diff; } | |
229 | ||
230 | /*! Compares two floating point numbers a and b such that their "left" relative difference |a-b|/a and/or | |
231 | * "right" relative difference |a-b|/b does not exceed specified relative (fraction) tolerance. | |
232 | * | |
233 | * @param[in] left first floating point number to be compared | |
234 | * @param[in] right second floating point number to be compared | |
235 | * | |
236 | * What is reported by @c tested_rel_diff in case of failure depends on the comparison method: | |
237 | * - for @c FPC_STRONG: the max of the two fractions | |
238 | * - for @c FPC_WEAK: the min of the two fractions | |
239 | * The rationale behind is to report the tolerance to set in order to make a test pass. | |
240 | */ | |
241 | bool operator()( FPT left, FPT right ) const | |
242 | { | |
243 | FPT diff = fpc_detail::fpt_abs<FPT>( left - right ); | |
244 | FPT fraction_of_right = fpc_detail::safe_fpt_division( diff, fpc_detail::fpt_abs( right ) ); | |
245 | FPT fraction_of_left = fpc_detail::safe_fpt_division( diff, fpc_detail::fpt_abs( left ) ); | |
246 | ||
247 | FPT max_rel_diff = (std::max)( fraction_of_left, fraction_of_right ); | |
248 | FPT min_rel_diff = (std::min)( fraction_of_left, fraction_of_right ); | |
249 | ||
250 | m_tested_rel_diff = m_strength == FPC_STRONG ? max_rel_diff : min_rel_diff; | |
251 | ||
252 | return m_tested_rel_diff <= m_fraction_tolerance; | |
253 | } | |
254 | ||
255 | private: | |
256 | // Data members | |
257 | FPT m_fraction_tolerance; | |
258 | fpc::strength m_strength; | |
259 | mutable FPT m_tested_rel_diff; | |
260 | }; | |
261 | ||
262 | // ************************************************************************** // | |
263 | // ************** small_with_tolerance ************** // | |
264 | // ************************************************************************** // | |
265 | ||
266 | ||
267 | /*!@brief Predicate for comparing floating point numbers against 0 | |
268 | * | |
269 | * Serves the same purpose as boost::math::fpc::close_at_tolerance, but used when one | |
270 | * of the operand is null. | |
271 | */ | |
272 | template<typename FPT> | |
273 | class small_with_tolerance { | |
274 | public: | |
275 | // Public typedefs | |
276 | typedef bool result_type; | |
277 | ||
278 | // Constructor | |
279 | explicit small_with_tolerance( FPT tolerance ) // <= absolute tolerance | |
280 | : m_tolerance( tolerance ) | |
281 | { | |
282 | BOOST_ASSERT( m_tolerance >= FPT(0) ); // no reason for the tolerance to be negative | |
283 | } | |
284 | ||
285 | // Action method | |
286 | bool operator()( FPT fpv ) const | |
287 | { | |
288 | return fpc::fpc_detail::fpt_abs( fpv ) <= m_tolerance; | |
289 | } | |
290 | ||
291 | private: | |
292 | // Data members | |
293 | FPT m_tolerance; | |
294 | }; | |
295 | ||
296 | // ************************************************************************** // | |
297 | // ************** is_small ************** // | |
298 | // ************************************************************************** // | |
299 | ||
300 | template<typename FPT> | |
301 | inline bool | |
302 | is_small( FPT fpv, FPT tolerance ) | |
303 | { | |
304 | return small_with_tolerance<FPT>( tolerance )( fpv ); | |
305 | } | |
306 | ||
307 | //____________________________________________________________________________// | |
308 | ||
309 | } // namespace fpc | |
310 | } // namespace math | |
311 | } // namespace boost | |
312 | ||
313 | #include <boost/test/detail/enable_warnings.hpp> | |
314 | ||
315 | #endif // BOOST_FLOATING_POINT_COMAPARISON_HPP_071894GER |