NumTraits.h (12884B)
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 13 namespace Eigen { 14 15 namespace internal { 16 17 // default implementation of digits10(), based on numeric_limits if specialized, 18 // 0 for integer types, and log10(epsilon()) otherwise. 19 template< typename T, 20 bool use_numeric_limits = std::numeric_limits<T>::is_specialized, 21 bool is_integer = NumTraits<T>::IsInteger> 22 struct default_digits10_impl 23 { 24 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 25 static int run() { return std::numeric_limits<T>::digits10; } 26 }; 27 28 template<typename T> 29 struct 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 40 template<typename T> 41 struct 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. 50 template< typename T, 51 bool use_numeric_limits = std::numeric_limits<T>::is_specialized, 52 bool is_integer = NumTraits<T>::IsInteger> 53 struct default_digits_impl 54 { 55 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 56 static int run() { return std::numeric_limits<T>::digits; } 57 }; 58 59 template<typename T> 60 struct 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 71 template<typename T> 72 struct 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 80 namespace numext { 81 /** \internal bit-wise cast without changing the underlying bit representation. */ 82 83 // TODO: Replace by std::bit_cast (available in C++20) 84 template <typename Tgt, typename Src> 85 EIGEN_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 */ 151 152 template<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 }; 231 232 template<typename T> struct NumTraits : GenericNumTraits<T> 233 {}; 234 235 template<> struct NumTraits<float> 236 : GenericNumTraits<float> 237 { 238 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 239 static inline float dummy_precision() { return 1e-5f; } 240 }; 241 242 template<> struct NumTraits<double> : GenericNumTraits<double> 243 { 244 EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 245 static inline double dummy_precision() { return 1e-12; } 246 }; 247 248 template<> struct NumTraits<long double> 249 : GenericNumTraits<long double> 250 { 251 EIGEN_CONSTEXPR 252 static inline long double dummy_precision() { return 1e-15l; } 253 }; 254 255 template<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 }; 275 276 template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> 277 struct 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 }; 305 306 template<> 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; } 318 319 private: 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. 329 template<> struct NumTraits<void> {}; 330 331 template<> struct NumTraits<bool> : GenericNumTraits<bool> {}; 332 333 } // end namespace Eigen 334 335 #endif // EIGEN_NUMTRAITS_H