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 |
316 | |