[136] | 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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