```/* <![CDATA[ */
function get_sym_list(){return [["Macro","xm",[["EIGEN_NUMTRAITS_H",11]]],["Namespace","xn",[["Eigen",13]]],["Struct","xs",[["GenericNumTraits",51]]],["Typedef","xt",[["Real",63]]]];} /* ]]> */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
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
51template<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,
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
71  static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); }
72  static inline Real dummy_precision()
73  {
74    // make sure to override this for floating-point types
75    return Real(0);
76  }
77  static inline T highest() { return (std::numeric_limits<T>::max)(); }
78  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
88template<typename T> struct NumTraits : GenericNumTraits<T>
89{};
90
91template<> struct NumTraits<float>
92  : GenericNumTraits<float>
93{
94  static inline float dummy_precision() { return 1e-5f; }
95};
96
97template<> struct NumTraits<double> : GenericNumTraits<double>
98{
99  static inline double dummy_precision() { return 1e-12; }
100};
101
102template<> struct NumTraits<long double>
103  : GenericNumTraits<long double>
104{
105  static inline long double dummy_precision() { return 1e-15l; }
106};
107
108template<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,
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
124template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
125struct 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,