1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_NUMTRAITS_H
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11 | #define EIGEN_NUMTRAITS_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /** \class NumTraits
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16 | * \ingroup Core_Module
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17 | *
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18 | * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
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19 | *
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20 | * \param T the numeric type at hand
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21 | *
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22 | * This class stores enums, typedefs and static methods giving information about a numeric type.
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23 | *
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24 | * The provided data consists of:
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25 | * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
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26 | * then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
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27 | * is a typedef to \a U.
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28 | * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
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29 | * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
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30 | * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
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31 | * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
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32 | * only intended as a helper for code that needs to explicitly promote types.
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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
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34 | * this means, just use \a T here.
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35 | * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
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36 | * type, and to 0 otherwise.
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37 | * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
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38 | * and to \c 0 otherwise.
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39 | * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
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40 | * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
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41 | * Stay vague here. No need to do architecture-specific stuff.
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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.
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43 | * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
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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.
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45 | * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T.
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46 | * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
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47 | * value by the fuzzy comparison operators.
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48 | * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
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49 | */
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50 |
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51 | template<typename T> struct GenericNumTraits
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52 | {
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53 | enum {
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54 | IsInteger = std::numeric_limits<T>::is_integer,
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55 | IsSigned = std::numeric_limits<T>::is_signed,
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56 | IsComplex = 0,
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57 | RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
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58 | ReadCost = 1,
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59 | AddCost = 1,
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60 | MulCost = 1
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61 | };
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62 |
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63 | typedef T Real;
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64 | typedef typename internal::conditional<
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65 | IsInteger,
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66 | typename internal::conditional<sizeof(T)<=2, float, double>::type,
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67 | T
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68 | >::type NonInteger;
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69 | typedef T Nested;
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70 |
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71 | static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); }
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72 | static inline Real dummy_precision()
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73 | {
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74 | // make sure to override this for floating-point types
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75 | return Real(0);
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76 | }
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77 | static inline T highest() { return (std::numeric_limits<T>::max)(); }
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78 | static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); }
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79 |
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80 | #ifdef EIGEN2_SUPPORT
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81 | enum {
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82 | HasFloatingPoint = !IsInteger
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83 | };
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84 | typedef NonInteger FloatingPoint;
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85 | #endif
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86 | };
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87 |
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88 | template<typename T> struct NumTraits : GenericNumTraits<T>
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89 | {};
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90 |
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91 | template<> struct NumTraits<float>
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92 | : GenericNumTraits<float>
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93 | {
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94 | static inline float dummy_precision() { return 1e-5f; }
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95 | };
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96 |
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97 | template<> struct NumTraits<double> : GenericNumTraits<double>
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98 | {
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99 | static inline double dummy_precision() { return 1e-12; }
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100 | };
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101 |
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102 | template<> struct NumTraits<long double>
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103 | : GenericNumTraits<long double>
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104 | {
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105 | static inline long double dummy_precision() { return 1e-15l; }
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106 | };
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107 |
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108 | template<typename _Real> struct NumTraits<std::complex<_Real> >
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109 | : GenericNumTraits<std::complex<_Real> >
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110 | {
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111 | typedef _Real Real;
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112 | enum {
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113 | IsComplex = 1,
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114 | RequireInitialization = NumTraits<_Real>::RequireInitialization,
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115 | ReadCost = 2 * NumTraits<_Real>::ReadCost,
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116 | AddCost = 2 * NumTraits<Real>::AddCost,
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117 | MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
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118 | };
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119 |
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120 | static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
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121 | static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
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122 | };
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123 |
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124 | template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
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125 | struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
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126 | {
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127 | typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
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128 | typedef typename NumTraits<Scalar>::Real RealScalar;
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129 | typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
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130 | typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
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131 | typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
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132 | typedef ArrayType & Nested;
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133 |
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134 | enum {
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135 | IsComplex = NumTraits<Scalar>::IsComplex,
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136 | IsInteger = NumTraits<Scalar>::IsInteger,
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137 | IsSigned = NumTraits<Scalar>::IsSigned,
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138 | RequireInitialization = 1,
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139 | ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
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140 | AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
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141 | MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
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142 | };
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143 |
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144 | static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
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145 | static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
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146 | };
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147 |
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148 | } // end namespace Eigen
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149 |
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150 | #endif // EIGEN_NUMTRAITS_H
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