text: // 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 {
  
  /** \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 \a Real, giving the "real part" type of \a T. If \a T is already real,
    *     then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
    *     is a typedef to \a U.
    * \li A typedef \a 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 \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 std::numeric_limits::epsilon(), 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.
    */
  
  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;
  
    EIGEN_DEVICE_FUNC
    static inline Real epsilon()
    {
      #if defined(__CUDA_ARCH__)
      return internal::device::numeric_limits<T>::epsilon();
      #else
      return std::numeric_limits<T>::epsilon();
      #endif
    }
    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() {
  #if defined(__CUDA_ARCH__)
      return (internal::device::numeric_limits<T>::max)();
  #else
      return (std::numeric_limits<T>::max)();
  #endif
    }
  
    EIGEN_DEVICE_FUNC
    static inline T lowest()  {
  #if defined(__CUDA_ARCH__)
      return IsInteger ? (internal::device::numeric_limits<T>::min)() : (-(internal::device::numeric_limits<T>::max)());
  #else
      return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)());
  #endif
    }
  };
  
  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;
    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
    };
  
    static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
    static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
  };
  
  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;
    
    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
    };
    
    static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
    static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
  };
  
  } // end namespace Eigen
  
  #endif // EIGEN_NUMTRAITS_H
  