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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
- //
- // This Source Code Form is subject to the terms of the Mozilla
- // Public License v. 2.0. If a copy of the MPL was not distributed
- // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
- #ifndef EIGEN_NUMTRAITS_H
- #define EIGEN_NUMTRAITS_H
- namespace Eigen {
- namespace internal {
- // default implementation of digits10(), based on numeric_limits if specialized,
- // 0 for integer types, and log10(epsilon()) otherwise.
- template< typename T,
- bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
- bool is_integer = NumTraits<T>::IsInteger>
- struct default_digits10_impl
- {
- static int run() { return std::numeric_limits<T>::digits10; }
- };
- template<typename T>
- struct default_digits10_impl<T,false,false> // Floating point
- {
- static int run() {
- using std::log10;
- using std::ceil;
- typedef typename NumTraits<T>::Real Real;
- return int(ceil(-log10(NumTraits<Real>::epsilon())));
- }
- };
- template<typename T>
- struct default_digits10_impl<T,false,true> // Integer
- {
- static int run() { return 0; }
- };
- } // end namespace internal
- /** \class NumTraits
- * \ingroup Core_Module
- *
- * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
- *
- * \tparam T the numeric type at hand
- *
- * This class stores enums, typedefs and static methods giving information about a numeric type.
- *
- * The provided data consists of:
- * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
- * then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
- * is a typedef to \a U.
- * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
- * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
- * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
- * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
- * only intended as a helper for code that needs to explicitly promote types.
- * \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.
- * Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
- * \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
- * this means, just use \a T here.
- * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
- * type, and to 0 otherwise.
- * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
- * and to \c 0 otherwise.
- * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
- * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
- * Stay vague here. No need to do architecture-specific stuff.
- * \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.
- * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
- * 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.
- * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>,
- * it returns a \a Real instead of a \a T.
- * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
- * value by the fuzzy comparison operators.
- * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
- * \li digits10() function returning the number of decimal digits that can be represented without change. This is
- * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
- * which is used as the default implementation if specialized.
- */
- template<typename T> struct GenericNumTraits
- {
- enum {
- IsInteger = std::numeric_limits<T>::is_integer,
- IsSigned = std::numeric_limits<T>::is_signed,
- IsComplex = 0,
- RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
- ReadCost = 1,
- AddCost = 1,
- MulCost = 1
- };
- typedef T Real;
- typedef typename internal::conditional<
- IsInteger,
- typename internal::conditional<sizeof(T)<=2, float, double>::type,
- T
- >::type NonInteger;
- typedef T Nested;
- typedef T Literal;
- EIGEN_DEVICE_FUNC
- static inline Real epsilon()
- {
- return numext::numeric_limits<T>::epsilon();
- }
- EIGEN_DEVICE_FUNC
- static inline int digits10()
- {
- return internal::default_digits10_impl<T>::run();
- }
- EIGEN_DEVICE_FUNC
- static inline Real dummy_precision()
- {
- // make sure to override this for floating-point types
- return Real(0);
- }
- EIGEN_DEVICE_FUNC
- static inline T highest() {
- return (numext::numeric_limits<T>::max)();
- }
- EIGEN_DEVICE_FUNC
- static inline T lowest() {
- return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());
- }
- EIGEN_DEVICE_FUNC
- static inline T infinity() {
- return numext::numeric_limits<T>::infinity();
- }
- EIGEN_DEVICE_FUNC
- static inline T quiet_NaN() {
- return numext::numeric_limits<T>::quiet_NaN();
- }
- };
- template<typename T> struct NumTraits : GenericNumTraits<T>
- {};
- template<> struct NumTraits<float>
- : GenericNumTraits<float>
- {
- EIGEN_DEVICE_FUNC
- static inline float dummy_precision() { return 1e-5f; }
- };
- template<> struct NumTraits<double> : GenericNumTraits<double>
- {
- EIGEN_DEVICE_FUNC
- static inline double dummy_precision() { return 1e-12; }
- };
- template<> struct NumTraits<long double>
- : GenericNumTraits<long double>
- {
- static inline long double dummy_precision() { return 1e-15l; }
- };
- template<typename _Real> struct NumTraits<std::complex<_Real> >
- : GenericNumTraits<std::complex<_Real> >
- {
- typedef _Real Real;
- typedef typename NumTraits<_Real>::Literal Literal;
- enum {
- IsComplex = 1,
- RequireInitialization = NumTraits<_Real>::RequireInitialization,
- ReadCost = 2 * NumTraits<_Real>::ReadCost,
- AddCost = 2 * NumTraits<Real>::AddCost,
- MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
- };
- EIGEN_DEVICE_FUNC
- static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
- EIGEN_DEVICE_FUNC
- static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
- EIGEN_DEVICE_FUNC
- static inline int digits10() { return NumTraits<Real>::digits10(); }
- };
- template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
- struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
- {
- typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
- typedef typename NumTraits<Scalar>::Real RealScalar;
- typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
- typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
- typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
- typedef ArrayType & Nested;
- typedef typename NumTraits<Scalar>::Literal Literal;
- enum {
- IsComplex = NumTraits<Scalar>::IsComplex,
- IsInteger = NumTraits<Scalar>::IsInteger,
- IsSigned = NumTraits<Scalar>::IsSigned,
- RequireInitialization = 1,
- ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
- AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
- MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
- };
- EIGEN_DEVICE_FUNC
- static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
- EIGEN_DEVICE_FUNC
- static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
- static inline int digits10() { return NumTraits<Scalar>::digits10(); }
- };
- template<> struct NumTraits<std::string>
- : GenericNumTraits<std::string>
- {
- enum {
- RequireInitialization = 1,
- ReadCost = HugeCost,
- AddCost = HugeCost,
- MulCost = HugeCost
- };
- static inline int digits10() { return 0; }
- private:
- static inline std::string epsilon();
- static inline std::string dummy_precision();
- static inline std::string lowest();
- static inline std::string highest();
- static inline std::string infinity();
- static inline std::string quiet_NaN();
- };
- // Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
- template<> struct NumTraits<void> {};
- } // end namespace Eigen
- #endif // EIGEN_NUMTRAITS_H
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