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
13namespace Eigen {
14
15namespace internal {
16
17// default implementation of digits10(), based on numeric_limits if specialized,
18// 0 for integer types, and log10(epsilon()) otherwise.
19template< typename T,
20          bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
21          bool is_integer = NumTraits<T>::IsInteger>
22struct default_digits10_impl
23{
24  static int run() { return std::numeric_limits<T>::digits10; }
25};
26
27template<typename T>
28struct 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
38template<typename T>
39struct 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
88template<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
150template<typename T> struct NumTraits : GenericNumTraits<T>
151{};
152
153template<> struct NumTraits<float>
154  : GenericNumTraits<float>
155{
156  EIGEN_DEVICE_FUNC
157  static inline float dummy_precision() { return 1e-5f; }
158};
159
160template<> struct NumTraits<double> : GenericNumTraits<double>
161{
162  EIGEN_DEVICE_FUNC
163  static inline double dummy_precision() { return 1e-12; }
164};
165
166template<> struct NumTraits<long double>
167  : GenericNumTraits<long double>
168{
169  static inline long double dummy_precision() { return 1e-15l; }
170};
171
172template<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
193template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
194struct 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
222template<> 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
234private:
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.
244template<> struct NumTraits<void> {};
245
246} // end namespace Eigen
247
248#endif // EIGEN_NUMTRAITS_H
249