1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_NUMTRAITS_H
11#define EIGEN_NUMTRAITS_H
12
13namespace Eigen {
14
15namespace internal {
16
17// default implementation of digits10(), based on numeric_limits if specialized,
18// 0 for integer types, and log10(epsilon()) otherwise.
19template< typename T,
20 bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
21 bool is_integer = NumTraits<T>::IsInteger>
22struct default_digits10_impl
23{
24 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
25 static int run() { return std::numeric_limits<T>::digits10; }
26};
27
28template<typename T>
29struct default_digits10_impl<T,false,false> // Floating point
30{
31 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
32 static int run() {
33 using std::log10;
34 using std::ceil;
35 typedef typename NumTraits<T>::Real Real;
36 return int(ceil(-log10(NumTraits<Real>::epsilon())));
37 }
38};
39
40template<typename T>
41struct default_digits10_impl<T,false,true> // Integer
42{
43 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
44 static int run() { return 0; }
45};
46
47
48// default implementation of digits(), based on numeric_limits if specialized,
49// 0 for integer types, and log2(epsilon()) otherwise.
50template< typename T,
51 bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
52 bool is_integer = NumTraits<T>::IsInteger>
53struct default_digits_impl
54{
55 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
56 static int run() { return std::numeric_limits<T>::digits; }
57};
58
59template<typename T>
60struct default_digits_impl<T,false,false> // Floating point
61{
62 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
63 static int run() {
64 using std::log;
65 using std::ceil;
66 typedef typename NumTraits<T>::Real Real;
67 return int(ceil(-log(NumTraits<Real>::epsilon())/log(static_cast<Real>(2))));
68 }
69};
70
71template<typename T>
72struct default_digits_impl<T,false,true> // Integer
73{
74 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
75 static int run() { return 0; }
76};
77
78} // end namespace internal
79
80namespace numext {
81/** \internal bit-wise cast without changing the underlying bit representation. */
82
83// TODO: Replace by std::bit_cast (available in C++20)
84template <typename Tgt, typename Src>
85EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
86#if EIGEN_HAS_TYPE_TRAITS
87 // The behaviour of memcpy is not specified for non-trivially copyable types
88 EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED);
89 EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
90 THIS_TYPE_IS_NOT_SUPPORTED);
91#endif
92
93 EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED);
94 Tgt tgt;
95 EIGEN_USING_STD(memcpy)
96 memcpy(&tgt, &src, sizeof(Tgt));
97 return tgt;
98}
99} // namespace numext
100
101/** \class NumTraits
102 * \ingroup Core_Module
103 *
104 * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
105 *
106 * \tparam T the numeric type at hand
107 *
108 * This class stores enums, typedefs and static methods giving information about a numeric type.
109 *
110 * The provided data consists of:
111 * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
112 * then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
113 * is a typedef to \a U.
114 * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
115 * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
116 * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
117 * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
118 * only intended as a helper for code that needs to explicitly promote types.
119 * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex<U>, Literal is defined as \c U.
120 * Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
121 * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
122 * this means, just use \a T here.
123 * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
124 * type, and to 0 otherwise.
125 * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
126 * and to \c 0 otherwise.
127 * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
128 * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
129 * Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost.
130 * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
131 * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
132 * be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
133 * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>,
134 * it returns a \a Real instead of a \a T.
135 * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
136 * value by the fuzzy comparison operators.
137 * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
138 * \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point). This is
139 * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a>
140 * which is used as the default implementation if specialized.
141 * \li digits10() function returning the number of decimal digits that can be represented without change. This is
142 * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
143 * which is used as the default implementation if specialized.
144 * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
145 * such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent to
146 * <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
147 * <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
148 * \li infinity() function returning a representation of positive infinity, if available.
149 * \li quiet_NaN function returning a non-signaling "not-a-number", if available.
150 */
151
152template<typename T> struct GenericNumTraits
153{
154 enum {
155 IsInteger = std::numeric_limits<T>::is_integer,
156 IsSigned = std::numeric_limits<T>::is_signed,
157 IsComplex = 0,
158 RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
159 ReadCost = 1,
160 AddCost = 1,
161 MulCost = 1
162 };
163
164 typedef T Real;
165 typedef typename internal::conditional<
166 IsInteger,
167 typename internal::conditional<sizeof(T)<=2, float, double>::type,
168 T
169 >::type NonInteger;
170 typedef T Nested;
171 typedef T Literal;
172
173 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
174 static inline Real epsilon()
175 {
176 return numext::numeric_limits<T>::epsilon();
177 }
178
179 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
180 static inline int digits10()
181 {
182 return internal::default_digits10_impl<T>::run();
183 }
184
185 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
186 static inline int digits()
187 {
188 return internal::default_digits_impl<T>::run();
189 }
190
191 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
192 static inline int min_exponent()
193 {
194 return numext::numeric_limits<T>::min_exponent;
195 }
196
197 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
198 static inline int max_exponent()
199 {
200 return numext::numeric_limits<T>::max_exponent;
201 }
202
203 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
204 static inline Real dummy_precision()
205 {
206 // make sure to override this for floating-point types
207 return Real(0);
208 }
209
210 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
211 static inline T highest() {
212 return (numext::numeric_limits<T>::max)();
213 }
214
215 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
216 static inline T lowest() {
217 return IsInteger ? (numext::numeric_limits<T>::min)()
218 : static_cast<T>(-(numext::numeric_limits<T>::max)());
219 }
220
221 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
222 static inline T infinity() {
223 return numext::numeric_limits<T>::infinity();
224 }
225
226 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
227 static inline T quiet_NaN() {
228 return numext::numeric_limits<T>::quiet_NaN();
229 }
230};
231
232template<typename T> struct NumTraits : GenericNumTraits<T>
233{};
234
235template<> struct NumTraits<float>
236 : GenericNumTraits<float>
237{
238 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
239 static inline float dummy_precision() { return 1e-5f; }
240};
241
242template<> struct NumTraits<double> : GenericNumTraits<double>
243{
244 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
245 static inline double dummy_precision() { return 1e-12; }
246};
247
248template<> struct NumTraits<long double>
249 : GenericNumTraits<long double>
250{
251 EIGEN_CONSTEXPR
252 static inline long double dummy_precision() { return 1e-15l; }
253};
254
255template<typename _Real> struct NumTraits<std::complex<_Real> >
256 : GenericNumTraits<std::complex<_Real> >
257{
258 typedef _Real Real;
259 typedef typename NumTraits<_Real>::Literal Literal;
260 enum {
261 IsComplex = 1,
262 RequireInitialization = NumTraits<_Real>::RequireInitialization,
263 ReadCost = 2 * NumTraits<_Real>::ReadCost,
264 AddCost = 2 * NumTraits<Real>::AddCost,
265 MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
266 };
267
268 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
269 static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
270 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
271 static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
272 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
273 static inline int digits10() { return NumTraits<Real>::digits10(); }
274};
275
276template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
277struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
278{
279 typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
280 typedef typename NumTraits<Scalar>::Real RealScalar;
281 typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
282 typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
283 typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
284 typedef ArrayType & Nested;
285 typedef typename NumTraits<Scalar>::Literal Literal;
286
287 enum {
288 IsComplex = NumTraits<Scalar>::IsComplex,
289 IsInteger = NumTraits<Scalar>::IsInteger,
290 IsSigned = NumTraits<Scalar>::IsSigned,
291 RequireInitialization = 1,
292 ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
293 AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
294 MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
295 };
296
297 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
298 static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
299 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
300 static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
301
302 EIGEN_CONSTEXPR
303 static inline int digits10() { return NumTraits<Scalar>::digits10(); }
304};
305
306template<> struct NumTraits<std::string>
307 : GenericNumTraits<std::string>
308{
309 enum {
310 RequireInitialization = 1,
311 ReadCost = HugeCost,
312 AddCost = HugeCost,
313 MulCost = HugeCost
314 };
315
316 EIGEN_CONSTEXPR
317 static inline int digits10() { return 0; }
318
319private:
320 static inline std::string epsilon();
321 static inline std::string dummy_precision();
322 static inline std::string lowest();
323 static inline std::string highest();
324 static inline std::string infinity();
325 static inline std::string quiet_NaN();
326};
327
328// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
329template<> struct NumTraits<void> {};
330
331template<> struct NumTraits<bool> : GenericNumTraits<bool> {};
332
333} // end namespace Eigen
334
335#endif // EIGEN_NUMTRAITS_H
336

source code of qtmultimedia/src/3rdparty/eigen/Eigen/src/Core/NumTraits.h