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Eigen  3.4.0
 
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NumTraits.h
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 {
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
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
Namespace containing all symbols from the Eigen library.
Definition: Core:141
const int HugeCost
Definition: Constants.h:44
const int Dynamic
Definition: Constants.h:22
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233