| // 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 |
| |
| // IWYU pragma: private |
| #include "./InternalHeaderCheck.h" |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| // default implementation of digits(), based on numeric_limits if specialized, |
| // 0 for integer types, and log2(epsilon()) otherwise. |
| template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized, |
| bool is_integer = NumTraits<T>::IsInteger> |
| struct default_digits_impl { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits; } |
| }; |
| |
| template <typename T> |
| struct default_digits_impl<T, false, false> // Floating point |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { |
| using std::ceil; |
| using std::log2; |
| typedef typename NumTraits<T>::Real Real; |
| return int(ceil(-log2(NumTraits<Real>::epsilon()))); |
| } |
| }; |
| |
| template <typename T> |
| struct default_digits_impl<T, false, true> // Integer |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; } |
| }; |
| |
| // default implementation of digits10(), based on numeric_limits if specialized, |
| // 0 for integer types, and floor((digits()-1)*log10(2)) otherwise. |
| template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized, |
| bool is_integer = NumTraits<T>::IsInteger> |
| struct default_digits10_impl { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits10; } |
| }; |
| |
| template <typename T> |
| struct default_digits10_impl<T, false, false> // Floating point |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { |
| using std::floor; |
| using std::log10; |
| typedef typename NumTraits<T>::Real Real; |
| return int(floor((internal::default_digits_impl<Real>::run() - 1) * log10(2))); |
| } |
| }; |
| |
| template <typename T> |
| struct default_digits10_impl<T, false, true> // Integer |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; } |
| }; |
| |
| // default implementation of max_digits10(), based on numeric_limits if specialized, |
| // 0 for integer types, and log10(2) * digits() + 1 otherwise. |
| template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized, |
| bool is_integer = NumTraits<T>::IsInteger> |
| struct default_max_digits10_impl { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::max_digits10; } |
| }; |
| |
| template <typename T> |
| struct default_max_digits10_impl<T, false, false> // Floating point |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { |
| using std::ceil; |
| using std::log10; |
| typedef typename NumTraits<T>::Real Real; |
| return int(ceil(internal::default_digits_impl<Real>::run() * log10(2) + 1)); |
| } |
| }; |
| |
| template <typename T> |
| struct default_max_digits10_impl<T, false, true> // Integer |
| { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; } |
| }; |
| |
| } // end namespace internal |
| |
| namespace numext { |
| /** \internal bit-wise cast without changing the underlying bit representation. */ |
| |
| // TODO: Replace by std::bit_cast (available in C++20) |
| template <typename Tgt, typename Src> |
| EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) { |
| // The behaviour of memcpy is not specified for non-trivially copyable types |
| EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED); |
| EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value, |
| THIS_TYPE_IS_NOT_SUPPORTED); |
| EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED); |
| |
| Tgt tgt; |
| // Load src into registers first. This allows the memcpy to be elided by CUDA. |
| const Src staged = src; |
| EIGEN_USING_STD(memcpy) |
| memcpy(static_cast<void*>(&tgt), static_cast<const void*>(&staged), sizeof(Tgt)); |
| return tgt; |
| } |
| } // namespace numext |
| |
| /** \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. If you don't know what this means, just |
| * use \c Eigen::HugeCost. \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 digits() function returning the number of radix digits (non-sign digits for |
| * integers, mantissa for floating-point). This is the analogue of <a |
| * href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a> which is used |
| * as the default implementation if specialized. \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. \li max_digits10() function returning the number of decimal digits |
| * required to uniquely represent all distinct values of the type. This is the analogue of <a |
| * href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_digits10">std::numeric_limits<T>::max_digits10</a> |
| * which is used as the default implementation if specialized. |
| * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively, |
| * such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent |
| * to <a |
| * href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/ |
| * <a |
| * href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>. |
| * \li infinity() function returning a representation of positive infinity, if available. |
| * \li quiet_NaN function returning a non-signaling "not-a-number", if available. |
| */ |
| |
| 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 std::conditional_t<IsInteger, std::conditional_t<sizeof(T) <= 2, float, double>, T> NonInteger; |
| typedef T Nested; |
| typedef T Literal; |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return numext::numeric_limits<T>::epsilon(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return internal::default_digits10_impl<T>::run(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() { |
| return internal::default_max_digits10_impl<T>::run(); |
| } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits() { return internal::default_digits_impl<T>::run(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int min_exponent() { return numext::numeric_limits<T>::min_exponent; } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_exponent() { return numext::numeric_limits<T>::max_exponent; } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() { |
| // make sure to override this for floating-point types |
| return Real(0); |
| } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T highest() { return (numext::numeric_limits<T>::max)(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T lowest() { return (numext::numeric_limits<T>::lowest)(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T infinity() { return numext::numeric_limits<T>::infinity(); } |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR 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 EIGEN_CONSTEXPR static inline float dummy_precision() { return 1e-5f; } |
| }; |
| |
| template <> |
| struct NumTraits<double> : GenericNumTraits<double> { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline double dummy_precision() { return 1e-12; } |
| }; |
| |
| // GPU devices treat `long double` as `double`. |
| #ifndef EIGEN_GPU_COMPILE_PHASE |
| template <> |
| struct NumTraits<long double> : GenericNumTraits<long double> { |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double dummy_precision() { |
| return static_cast<long double>(1e-15l); |
| } |
| |
| #if defined(EIGEN_ARCH_PPC) && (__LDBL_MANT_DIG__ == 106) |
| // PowerPC double double causes issues with some values |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double epsilon() { |
| // 2^(-(__LDBL_MANT_DIG__)+1) |
| return static_cast<long double>(2.4651903288156618919116517665087e-32l); |
| } |
| #endif |
| }; |
| #endif |
| |
| 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 EIGEN_CONSTEXPR static inline Real epsilon() { return NumTraits<Real>::epsilon(); } |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return NumTraits<Real>::digits10(); } |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() { return NumTraits<Real>::max_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 * int(NumTraits<Scalar>::ReadCost), |
| AddCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost |
| : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost), |
| MulCost = ArrayType::SizeAtCompileTime == Dynamic ? HugeCost |
| : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost) |
| }; |
| |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); } |
| EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar dummy_precision() { |
| return NumTraits<RealScalar>::dummy_precision(); |
| } |
| |
| EIGEN_CONSTEXPR |
| static inline int digits10() { return NumTraits<Scalar>::digits10(); } |
| EIGEN_CONSTEXPR |
| static inline int max_digits10() { return NumTraits<Scalar>::max_digits10(); } |
| }; |
| |
| template <> |
| struct NumTraits<std::string> : GenericNumTraits<std::string> { |
| enum { RequireInitialization = 1, ReadCost = HugeCost, AddCost = HugeCost, MulCost = HugeCost }; |
| |
| EIGEN_CONSTEXPR |
| static inline int digits10() { return 0; } |
| EIGEN_CONSTEXPR |
| static inline int max_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> {}; |
| |
| template <> |
| struct NumTraits<bool> : GenericNumTraits<bool> {}; |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_NUMTRAITS_H |