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 (at) 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 /** \class NumTraits 16 * \ingroup Core_Module 17 * 18 * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen. 19 * 20 * \param T the numeric type at hand 21 * 22 * This class stores enums, typedefs and static methods giving information about a numeric type. 23 * 24 * The provided data consists of: 25 * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real, 26 * then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real 27 * is a typedef to \a U. 28 * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values, 29 * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives 30 * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to 31 * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is 32 * only intended as a helper for code that needs to explicitly promote types. 33 * \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 34 * this means, just use \a T here. 35 * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex 36 * type, and to 0 otherwise. 37 * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, 38 * and to \c 0 otherwise. 39 * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed 40 * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers. 41 * Stay vague here. No need to do architecture-specific stuff. 42 * \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. 43 * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must 44 * 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. 45 * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T. 46 * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default 47 * value by the fuzzy comparison operators. 48 * \li highest() and lowest() functions returning the highest and lowest possible values respectively. 49 */ 50 51 template<typename T> struct GenericNumTraits 52 { 53 enum { 54 IsInteger = std::numeric_limits<T>::is_integer, 55 IsSigned = std::numeric_limits<T>::is_signed, 56 IsComplex = 0, 57 RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1, 58 ReadCost = 1, 59 AddCost = 1, 60 MulCost = 1 61 }; 62 63 typedef T Real; 64 typedef typename internal::conditional< 65 IsInteger, 66 typename internal::conditional<sizeof(T)<=2, float, double>::type, 67 T 68 >::type NonInteger; 69 typedef T Nested; 70 71 static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); } 72 static inline Real dummy_precision() 73 { 74 // make sure to override this for floating-point types 75 return Real(0); 76 } 77 static inline T highest() { return (std::numeric_limits<T>::max)(); } 78 static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); } 79 80 #ifdef EIGEN2_SUPPORT 81 enum { 82 HasFloatingPoint = !IsInteger 83 }; 84 typedef NonInteger FloatingPoint; 85 #endif 86 }; 87 88 template<typename T> struct NumTraits : GenericNumTraits<T> 89 {}; 90 91 template<> struct NumTraits<float> 92 : GenericNumTraits<float> 93 { 94 static inline float dummy_precision() { return 1e-5f; } 95 }; 96 97 template<> struct NumTraits<double> : GenericNumTraits<double> 98 { 99 static inline double dummy_precision() { return 1e-12; } 100 }; 101 102 template<> struct NumTraits<long double> 103 : GenericNumTraits<long double> 104 { 105 static inline long double dummy_precision() { return 1e-15l; } 106 }; 107 108 template<typename _Real> struct NumTraits<std::complex<_Real> > 109 : GenericNumTraits<std::complex<_Real> > 110 { 111 typedef _Real Real; 112 enum { 113 IsComplex = 1, 114 RequireInitialization = NumTraits<_Real>::RequireInitialization, 115 ReadCost = 2 * NumTraits<_Real>::ReadCost, 116 AddCost = 2 * NumTraits<Real>::AddCost, 117 MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost 118 }; 119 120 static inline Real epsilon() { return NumTraits<Real>::epsilon(); } 121 static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } 122 }; 123 124 template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> 125 struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > 126 { 127 typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType; 128 typedef typename NumTraits<Scalar>::Real RealScalar; 129 typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real; 130 typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar; 131 typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger; 132 typedef ArrayType & Nested; 133 134 enum { 135 IsComplex = NumTraits<Scalar>::IsComplex, 136 IsInteger = NumTraits<Scalar>::IsInteger, 137 IsSigned = NumTraits<Scalar>::IsSigned, 138 RequireInitialization = 1, 139 ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost, 140 AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost, 141 MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost 142 }; 143 144 static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); } 145 static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); } 146 }; 147 148 } // end namespace Eigen 149 150 #endif // EIGEN_NUMTRAITS_H 151
