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 /** \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 
epsilonGenericNumTraits71   static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); }
dummy_precisionGenericNumTraits72   static inline Real dummy_precision()
73   {
74     // make sure to override this for floating-point types
75     return Real(0);
76   }
highestGenericNumTraits77   static inline T highest() { return (std::numeric_limits<T>::max)(); }
lowestGenericNumTraits78   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