NumTraits.h revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba
1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef EIGEN_NUMTRAITS_H 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN_NUMTRAITS_H 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen { 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \class NumTraits 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \ingroup Core_Module 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen. 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param T the numeric type at hand 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This class stores enums, typedefs and static methods giving information about a numeric type. 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * The provided data consists of: 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real, 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * is a typedef to \a U. 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values, 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * only intended as a helper for code that needs to explicitly promote types. 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \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 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * this means, just use \a T here. 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * type, and to 0 otherwise. 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * and to \c 0 otherwise. 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers. 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Stay vague here. No need to do architecture-specific stuff. 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \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. 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 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. 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T. 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * value by the fuzzy comparison operators. 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li highest() and lowest() functions returning the highest and lowest possible values respectively. 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename T> struct GenericNumTraits 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsInteger = std::numeric_limits<T>::is_integer, 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsSigned = std::numeric_limits<T>::is_signed, 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsComplex = 0, 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1, 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ReadCost = 1, 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AddCost = 1, 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MulCost = 1 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef T Real; 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename internal::conditional< 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsInteger, 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename internal::conditional<sizeof(T)<=2, float, double>::type, 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath T 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath >::type NonInteger; 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef T Nested; 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); } 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline Real dummy_precision() 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // make sure to override this for floating-point types 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Real(0); 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline T highest() { return (std::numeric_limits<T>::max)(); } 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); } 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifdef EIGEN2_SUPPORT 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HasFloatingPoint = !IsInteger 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef NonInteger FloatingPoint; 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename T> struct NumTraits : GenericNumTraits<T> 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{}; 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<> struct NumTraits<float> 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : GenericNumTraits<float> 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline float dummy_precision() { return 1e-5f; } 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<> struct NumTraits<double> : GenericNumTraits<double> 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline double dummy_precision() { return 1e-12; } 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<> struct NumTraits<long double> 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : GenericNumTraits<long double> 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline long double dummy_precision() { return 1e-15l; } 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _Real> struct NumTraits<std::complex<_Real> > 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath : GenericNumTraits<std::complex<_Real> > 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef _Real Real; 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsComplex = 1, 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RequireInitialization = NumTraits<_Real>::RequireInitialization, 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ReadCost = 2 * NumTraits<_Real>::ReadCost, 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AddCost = 2 * NumTraits<Real>::AddCost, 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline Real epsilon() { return NumTraits<Real>::epsilon(); } 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType; 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real; 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar; 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger; 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef ArrayType & Nested; 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsComplex = NumTraits<Scalar>::IsComplex, 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsInteger = NumTraits<Scalar>::IsInteger, 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath IsSigned = NumTraits<Scalar>::IsSigned, 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RequireInitialization = 1, 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost, 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost, 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 1437faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1447faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); } 1457faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); } 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace Eigen 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif // EIGEN_NUMTRAITS_H 151