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 {
rundefault_digits10_impl24   static int run() { return std::numeric_limits<T>::digits10; }
25 };
26 
27 template<typename T>
28 struct default_digits10_impl<T,false,false> // Floating point
29 {
30   static int run() {
31     using std::log10;
32     using std::ceil;
33     typedef typename NumTraits<T>::Real Real;
34     return int(ceil(-log10(NumTraits<Real>::epsilon())));
35   }
36 };
37 
38 template<typename T>
39 struct default_digits10_impl<T,false,true> // Integer
40 {
41   static int run() { return 0; }
42 };
43 
44 } // end namespace internal
45 
46 /** \class NumTraits
47   * \ingroup Core_Module
48   *
49   * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
50   *
51   * \tparam T the numeric type at hand
52   *
53   * This class stores enums, typedefs and static methods giving information about a numeric type.
54   *
55   * The provided data consists of:
56   * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
57   *     then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
58   *     is a typedef to \a U.
59   * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
60   *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
61   *     \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
62   *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
63   *     only intended as a helper for code that needs to explicitly promote types.
64   * \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.
65   *     Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
66   * \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
67   *     this means, just use \a T here.
68   * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
69   *     type, and to 0 otherwise.
70   * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
71   *     and to \c 0 otherwise.
72   * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
73   *     to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
74   *     Stay vague here. No need to do architecture-specific stuff.
75   * \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.
76   * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
77   *     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.
78   * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>,
79   *     it returns a \a Real instead of a \a T.
80   * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
81   *     value by the fuzzy comparison operators.
82   * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
83   * \li digits10() function returning the number of decimal digits that can be represented without change. This is
84   *     the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
85   *     which is used as the default implementation if specialized.
86   */
87 
88 template<typename T> struct GenericNumTraits
89 {
90   enum {
91     IsInteger = std::numeric_limits<T>::is_integer,
92     IsSigned = std::numeric_limits<T>::is_signed,
93     IsComplex = 0,
94     RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
95     ReadCost = 1,
96     AddCost = 1,
97     MulCost = 1
98   };
99 
100   typedef T Real;
101   typedef typename internal::conditional<
102                      IsInteger,
103                      typename internal::conditional<sizeof(T)<=2, float, double>::type,
104                      T
105                    >::type NonInteger;
106   typedef T Nested;
107   typedef T Literal;
108 
109   EIGEN_DEVICE_FUNC
110   static inline Real epsilon()
111   {
112     return numext::numeric_limits<T>::epsilon();
113   }
114 
115   EIGEN_DEVICE_FUNC
116   static inline int digits10()
117   {
118     return internal::default_digits10_impl<T>::run();
119   }
120 
121   EIGEN_DEVICE_FUNC
122   static inline Real dummy_precision()
123   {
124     // make sure to override this for floating-point types
125     return Real(0);
126   }
127 
128 
129   EIGEN_DEVICE_FUNC
130   static inline T highest() {
131     return (numext::numeric_limits<T>::max)();
132   }
133 
134   EIGEN_DEVICE_FUNC
135   static inline T lowest()  {
136     return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());
137   }
138 
139   EIGEN_DEVICE_FUNC
140   static inline T infinity() {
141     return numext::numeric_limits<T>::infinity();
142   }
143 
144   EIGEN_DEVICE_FUNC
145   static inline T quiet_NaN() {
146     return numext::numeric_limits<T>::quiet_NaN();
147   }
148 };
149 
150 template<typename T> struct NumTraits : GenericNumTraits<T>
151 {};
152 
153 template<> struct NumTraits<float>
154   : GenericNumTraits<float>
155 {
156   EIGEN_DEVICE_FUNC
157   static inline float dummy_precision() { return 1e-5f; }
158 };
159 
160 template<> struct NumTraits<double> : GenericNumTraits<double>
161 {
162   EIGEN_DEVICE_FUNC
163   static inline double dummy_precision() { return 1e-12; }
164 };
165 
166 template<> struct NumTraits<long double>
167   : GenericNumTraits<long double>
168 {
169   static inline long double dummy_precision() { return 1e-15l; }
170 };
171 
172 template<typename _Real> struct NumTraits<std::complex<_Real> >
173   : GenericNumTraits<std::complex<_Real> >
174 {
175   typedef _Real Real;
176   typedef typename NumTraits<_Real>::Literal Literal;
177   enum {
178     IsComplex = 1,
179     RequireInitialization = NumTraits<_Real>::RequireInitialization,
180     ReadCost = 2 * NumTraits<_Real>::ReadCost,
181     AddCost = 2 * NumTraits<Real>::AddCost,
182     MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
183   };
184 
185   EIGEN_DEVICE_FUNC
186   static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
187   EIGEN_DEVICE_FUNC
188   static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
189   EIGEN_DEVICE_FUNC
190   static inline int digits10() { return NumTraits<Real>::digits10(); }
191 };
192 
193 template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
194 struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
195 {
196   typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
197   typedef typename NumTraits<Scalar>::Real RealScalar;
198   typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
199   typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
200   typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
201   typedef ArrayType & Nested;
202   typedef typename NumTraits<Scalar>::Literal Literal;
203 
204   enum {
205     IsComplex = NumTraits<Scalar>::IsComplex,
206     IsInteger = NumTraits<Scalar>::IsInteger,
207     IsSigned  = NumTraits<Scalar>::IsSigned,
208     RequireInitialization = 1,
209     ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
210     AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
211     MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
212   };
213 
214   EIGEN_DEVICE_FUNC
215   static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
216   EIGEN_DEVICE_FUNC
217   static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
218 
219   static inline int digits10() { return NumTraits<Scalar>::digits10(); }
220 };
221 
222 template<> struct NumTraits<std::string>
223   : GenericNumTraits<std::string>
224 {
225   enum {
226     RequireInitialization = 1,
227     ReadCost = HugeCost,
228     AddCost  = HugeCost,
229     MulCost  = HugeCost
230   };
231 
232   static inline int digits10() { return 0; }
233 
234 private:
235   static inline std::string epsilon();
236   static inline std::string dummy_precision();
237   static inline std::string lowest();
238   static inline std::string highest();
239   static inline std::string infinity();
240   static inline std::string quiet_NaN();
241 };
242 
243 // Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
244 template<> struct NumTraits<void> {};
245 
246 } // end namespace Eigen
247 
248 #endif // EIGEN_NUMTRAITS_H
249