text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
  // Copyright (C) 2006-2008 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_META_H
  #define EIGEN_META_H
  
  #if defined(EIGEN_GPU_COMPILE_PHASE)
  
   #include <cfloat>
  
   #if defined(EIGEN_CUDA_ARCH)
    #include <math_constants.h>
   #endif
  
   #if defined(EIGEN_HIP_DEVICE_COMPILE)
    #include "Eigen/src/Core/arch/HIP/hcc/math_constants.h"
    #endif
  
  #endif
  
  // Recent versions of ICC require <cstdint> for pointer types below.
  #define EIGEN_ICC_NEEDS_CSTDINT (EIGEN_COMP_ICC>=1600 && EIGEN_COMP_CXXVER >= 11)
  
  // Define portable (u)int{32,64} types
  #if EIGEN_HAS_CXX11 || EIGEN_ICC_NEEDS_CSTDINT
  #include <cstdint>
  namespace Eigen {
  namespace numext {
  typedef std::uint8_t  uint8_t;
  typedef std::int8_t   int8_t;
  typedef std::uint16_t uint16_t;
  typedef std::int16_t  int16_t;
  typedef std::uint32_t uint32_t;
  typedef std::int32_t  int32_t;
  typedef std::uint64_t uint64_t;
  typedef std::int64_t  int64_t;
  }
  }
  #else
  // Without c++11, all compilers able to compile Eigen also
  // provide the C99 stdint.h header file.
  #include <stdint.h>
  namespace Eigen {
  namespace numext {
  typedef ::uint8_t  uint8_t;
  typedef ::int8_t   int8_t;
  typedef ::uint16_t uint16_t;
  typedef ::int16_t  int16_t;
  typedef ::uint32_t uint32_t;
  typedef ::int32_t  int32_t;
  typedef ::uint64_t uint64_t;
  typedef ::int64_t  int64_t;
  }
  }
  #endif
  
  namespace Eigen {
  
  typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
  
  /**
   * \brief The Index type as used for the API.
   * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
   * \sa \blank \ref TopicPreprocessorDirectives, StorageIndex.
   */
  
  typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Index;
  
  namespace internal {
  
  /** \internal
    * \file Meta.h
    * This file contains generic metaprogramming classes which are not specifically related to Eigen.
    * \note In case you wonder, yes we're aware that Boost already provides all these features,
    * we however don't want to add a dependency to Boost.
    */
  
  // Only recent versions of ICC complain about using ptrdiff_t to hold pointers,
  // and older versions do not provide *intptr_t types.
  #if EIGEN_ICC_NEEDS_CSTDINT
  typedef std::intptr_t  IntPtr;
  typedef std::uintptr_t UIntPtr;
  #else
  typedef std::ptrdiff_t IntPtr;
  typedef std::size_t UIntPtr;
  #endif
  #undef EIGEN_ICC_NEEDS_CSTDINT
  
  struct true_type {  enum { value = 1 }; };
  struct false_type { enum { value = 0 }; };
  
  template<bool Condition>
  struct bool_constant;
  
  template<>
  struct bool_constant<true> : true_type {};
  
  template<>
  struct bool_constant<false> : false_type {};
  
  template<bool Condition, typename Then, typename Else>
  struct conditional { typedef Then type; };
  
  template<typename Then, typename Else>
  struct conditional <false, Then, Else> { typedef Else type; };
  
  template<typename T> struct remove_reference { typedef T type; };
  template<typename T> struct remove_reference<T&> { typedef T type; };
  
  template<typename T> struct remove_pointer { typedef T type; };
  template<typename T> struct remove_pointer<T*> { typedef T type; };
  template<typename T> struct remove_pointer<T*const> { typedef T type; };
  
  template <class T> struct remove_const { typedef T type; };
  template <class T> struct remove_const<const T> { typedef T type; };
  template <class T> struct remove_const<const T[]> { typedef T type[]; };
  template <class T, unsigned int Size> struct remove_const<const T[Size]> { typedef T type[Size]; };
  
  template<typename T> struct remove_all { typedef T type; };
  template<typename T> struct remove_all<const T>   { typedef typename remove_all<T>::type type; };
  template<typename T> struct remove_all<T const&>  { typedef typename remove_all<T>::type type; };
  template<typename T> struct remove_all<T&>        { typedef typename remove_all<T>::type type; };
  template<typename T> struct remove_all<T const*>  { typedef typename remove_all<T>::type type; };
  template<typename T> struct remove_all<T*>        { typedef typename remove_all<T>::type type; };
  
  template<typename T> struct is_arithmetic      { enum { value = false }; };
  template<> struct is_arithmetic<float>         { enum { value = true }; };
  template<> struct is_arithmetic<double>        { enum { value = true }; };
  template<> struct is_arithmetic<long double>   { enum { value = true }; };
  template<> struct is_arithmetic<bool>          { enum { value = true }; };
  template<> struct is_arithmetic<char>          { enum { value = true }; };
  template<> struct is_arithmetic<signed char>   { enum { value = true }; };
  template<> struct is_arithmetic<unsigned char> { enum { value = true }; };
  template<> struct is_arithmetic<signed short>  { enum { value = true }; };
  template<> struct is_arithmetic<unsigned short>{ enum { value = true }; };
  template<> struct is_arithmetic<signed int>    { enum { value = true }; };
  template<> struct is_arithmetic<unsigned int>  { enum { value = true }; };
  template<> struct is_arithmetic<signed long>   { enum { value = true }; };
  template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
  
  template<typename T, typename U> struct is_same { enum { value = 0 }; };
  template<typename T> struct is_same<T,T> { enum { value = 1 }; };
  
  template< class T >
  struct is_void : is_same<void, typename remove_const<T>::type> {};
  
  #if EIGEN_HAS_CXX11
  template<> struct is_arithmetic<signed long long>   { enum { value = true }; };
  template<> struct is_arithmetic<unsigned long long> { enum { value = true }; };
  using std::is_integral;
  #else
  template<typename T> struct is_integral               { enum { value = false }; };
  template<> struct is_integral<bool>                   { enum { value = true }; };
  template<> struct is_integral<char>                   { enum { value = true }; };
  template<> struct is_integral<signed char>            { enum { value = true }; };
  template<> struct is_integral<unsigned char>          { enum { value = true }; };
  template<> struct is_integral<signed short>           { enum { value = true }; };
  template<> struct is_integral<unsigned short>         { enum { value = true }; };
  template<> struct is_integral<signed int>             { enum { value = true }; };
  template<> struct is_integral<unsigned int>           { enum { value = true }; };
  template<> struct is_integral<signed long>            { enum { value = true }; };
  template<> struct is_integral<unsigned long>          { enum { value = true }; };
  #if EIGEN_COMP_MSVC
  template<> struct is_integral<signed __int64>         { enum { value = true }; };
  template<> struct is_integral<unsigned __int64>       { enum { value = true }; };
  #endif
  #endif
  
  #if EIGEN_HAS_CXX11
  using std::make_unsigned;
  #else
  // TODO: Possibly improve this implementation of make_unsigned.
  // It is currently used only by
  // template<typename Scalar> struct random_default_impl<Scalar, false, true>.
  template<typename> struct make_unsigned;
  template<> struct make_unsigned<char>             { typedef unsigned char type; };
  template<> struct make_unsigned<signed char>      { typedef unsigned char type; };
  template<> struct make_unsigned<unsigned char>    { typedef unsigned char type; };
  template<> struct make_unsigned<signed short>     { typedef unsigned short type; };
  template<> struct make_unsigned<unsigned short>   { typedef unsigned short type; };
  template<> struct make_unsigned<signed int>       { typedef unsigned int type; };
  template<> struct make_unsigned<unsigned int>     { typedef unsigned int type; };
  template<> struct make_unsigned<signed long>      { typedef unsigned long type; };
  template<> struct make_unsigned<unsigned long>    { typedef unsigned long type; };
  #if EIGEN_COMP_MSVC
  template<> struct make_unsigned<signed __int64>   { typedef unsigned __int64 type; };
  template<> struct make_unsigned<unsigned __int64> { typedef unsigned __int64 type; };
  #endif
  
  // Some platforms define int64_t as long long even for C++03. In this case we
  // are missing the definition for make_unsigned. If we just define it, we get
  // duplicated definitions for platforms defining int64_t as signed long for
  // C++03. We therefore add the specialization for C++03 long long for these
  // platforms only.
  #if EIGEN_OS_MAC
  template<> struct make_unsigned<unsigned long long> { typedef unsigned long long type; };
  template<> struct make_unsigned<long long>          { typedef unsigned long long type; };
  #endif
  #endif
  
  template <typename T> struct add_const { typedef const T type; };
  template <typename T> struct add_const<T&> { typedef T& type; };
  
  template <typename T> struct is_const { enum { value = 0 }; };
  template <typename T> struct is_const<T const> { enum { value = 1 }; };
  
  template<typename T> struct add_const_on_value_type            { typedef const T type;  };
  template<typename T> struct add_const_on_value_type<T&>        { typedef T const& type; };
  template<typename T> struct add_const_on_value_type<T*>        { typedef T const* type; };
  template<typename T> struct add_const_on_value_type<T* const>  { typedef T const* const type; };
  template<typename T> struct add_const_on_value_type<T const* const>  { typedef T const* const type; };
  
  #if EIGEN_HAS_CXX11
  
  using std::is_convertible;
  
  #else
  
  template<typename From, typename To>
  struct is_convertible_impl
  {
  private:
    struct any_conversion
    {
      template <typename T> any_conversion(const volatile T&);
      template <typename T> any_conversion(T&);
    };
    struct yes {int a[1];};
    struct no  {int a[2];};
  
    template<typename T>
    static yes test(T, int);
  
    template<typename T>
    static no  test(any_conversion, ...);
  
  public:
    static typename internal::remove_reference<From>::type* ms_from;
  #ifdef __INTEL_COMPILER
    #pragma warning push
    #pragma warning ( disable : 2259 )
  #endif
    enum { value = sizeof(test<To>(*ms_from, 0))==sizeof(yes) };
  #ifdef __INTEL_COMPILER
    #pragma warning pop
  #endif
  };
  
  template<typename From, typename To>
  struct is_convertible
  {
    enum { value = is_convertible_impl<From,To>::value };
  };
  
  template<typename T>
  struct is_convertible<T,T&> { enum { value = false }; };
  
  template<typename T>
  struct is_convertible<const T,const T&> { enum { value = true }; };
  
  #endif
  
  /** \internal Allows to enable/disable an overload
    * according to a compile time condition.
    */
  template<bool Condition, typename T=void> struct enable_if;
  
  template<typename T> struct enable_if<true,T>
  { typedef T type; };
  
  #if defined(EIGEN_GPU_COMPILE_PHASE)
  #if !defined(__FLT_EPSILON__)
  #define __FLT_EPSILON__ FLT_EPSILON
  #define __DBL_EPSILON__ DBL_EPSILON
  #endif
  
  namespace device {
  
  template<typename T> struct numeric_limits
  {
    EIGEN_DEVICE_FUNC static T epsilon() { return 0; }
    EIGEN_DEVICE_FUNC static T (max)() { assert(false && "Highest not supported for this type"); }
    EIGEN_DEVICE_FUNC static T (min)() { assert(false && "Lowest not supported for this type"); }
    EIGEN_DEVICE_FUNC static T infinity() { assert(false && "Infinity not supported for this type"); }
    EIGEN_DEVICE_FUNC static T quiet_NaN() { assert(false && "quiet_NaN not supported for this type"); }
  };
  template<> struct numeric_limits<float>
  {
    EIGEN_DEVICE_FUNC
    static float epsilon() { return __FLT_EPSILON__; }
    EIGEN_DEVICE_FUNC
    static float (max)() {
    #if defined(EIGEN_CUDA_ARCH)
      return CUDART_MAX_NORMAL_F;
    #else
      return HIPRT_MAX_NORMAL_F;
    #endif
    }
    EIGEN_DEVICE_FUNC
    static float (min)() { return FLT_MIN; }
    EIGEN_DEVICE_FUNC
    static float infinity() {
    #if defined(EIGEN_CUDA_ARCH)
      return CUDART_INF_F;
    #else
      return HIPRT_INF_F;
    #endif
    }
    EIGEN_DEVICE_FUNC
    static float quiet_NaN() {
    #if defined(EIGEN_CUDA_ARCH)
      return CUDART_NAN_F;
    #else
      return HIPRT_NAN_F;
    #endif
    }
  };
  template<> struct numeric_limits<double>
  {
    EIGEN_DEVICE_FUNC
    static double epsilon() { return __DBL_EPSILON__; }
    EIGEN_DEVICE_FUNC
    static double (max)() { return DBL_MAX; }
    EIGEN_DEVICE_FUNC
    static double (min)() { return DBL_MIN; }
    EIGEN_DEVICE_FUNC
    static double infinity() {
    #if defined(EIGEN_CUDA_ARCH)
      return CUDART_INF;
    #else
      return HIPRT_INF;
    #endif
    }
    EIGEN_DEVICE_FUNC
    static double quiet_NaN() {
    #if defined(EIGEN_CUDA_ARCH)
      return CUDART_NAN;
    #else
      return HIPRT_NAN;
    #endif
    }
  };
  template<> struct numeric_limits<int>
  {
    EIGEN_DEVICE_FUNC
    static int epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static int (max)() { return INT_MAX; }
    EIGEN_DEVICE_FUNC
    static int (min)() { return INT_MIN; }
  };
  template<> struct numeric_limits<unsigned int>
  {
    EIGEN_DEVICE_FUNC
    static unsigned int epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static unsigned int (max)() { return UINT_MAX; }
    EIGEN_DEVICE_FUNC
    static unsigned int (min)() { return 0; }
  };
  template<> struct numeric_limits<long>
  {
    EIGEN_DEVICE_FUNC
    static long epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static long (max)() { return LONG_MAX; }
    EIGEN_DEVICE_FUNC
    static long (min)() { return LONG_MIN; }
  };
  template<> struct numeric_limits<unsigned long>
  {
    EIGEN_DEVICE_FUNC
    static unsigned long epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static unsigned long (max)() { return ULONG_MAX; }
    EIGEN_DEVICE_FUNC
    static unsigned long (min)() { return 0; }
  };
  template<> struct numeric_limits<long long>
  {
    EIGEN_DEVICE_FUNC
    static long long epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static long long (max)() { return LLONG_MAX; }
    EIGEN_DEVICE_FUNC
    static long long (min)() { return LLONG_MIN; }
  };
  template<> struct numeric_limits<unsigned long long>
  {
    EIGEN_DEVICE_FUNC
    static unsigned long long epsilon() { return 0; }
    EIGEN_DEVICE_FUNC
    static unsigned long long (max)() { return ULLONG_MAX; }
    EIGEN_DEVICE_FUNC
    static unsigned long long (min)() { return 0; }
  };
  template<> struct numeric_limits<bool>
  {
    EIGEN_DEVICE_FUNC
    static bool epsilon() { return false; }
    EIGEN_DEVICE_FUNC
    static bool (max)() { return true; }
    EIGEN_DEVICE_FUNC
    static bool (min)() { return false; }
  };
  
  }
  
  #endif
  
  /** \internal
    * A base class do disable default copy ctor and copy assignment operator.
    */
  class noncopyable
  {
    EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);
    EIGEN_DEVICE_FUNC const noncopyable& operator=(const noncopyable&);
  protected:
    EIGEN_DEVICE_FUNC noncopyable() {}
    EIGEN_DEVICE_FUNC ~noncopyable() {}
  };
  
  /** \internal
    * Provides access to the number of elements in the object of as a compile-time constant expression.
    * It "returns" Eigen::Dynamic if the size cannot be resolved at compile-time (default).
    *
    * Similar to std::tuple_size, but more general.
    *
    * It currently supports:
    *  - any types T defining T::SizeAtCompileTime
    *  - plain C arrays as T[N]
    *  - std::array (c++11)
    *  - some internal types such as SingleRange and AllRange
    *
    * The second template parameter eases SFINAE-based specializations.
    */
  template<typename T, typename EnableIf = void> struct array_size {
    enum { value = Dynamic };
  };
  
  template<typename T> struct array_size<T,typename internal::enable_if<((T::SizeAtCompileTime&0)==0)>::type> {
    enum { value = T::SizeAtCompileTime };
  };
  
  template<typename T, int N> struct array_size<const T (&)[N]> {
    enum { value = N };
  };
  template<typename T, int N> struct array_size<T (&)[N]> {
    enum { value = N };
  };
  
  #if EIGEN_HAS_CXX11
  template<typename T, std::size_t N> struct array_size<const std::array<T,N> > {
    enum { value = N };
  };
  template<typename T, std::size_t N> struct array_size<std::array<T,N> > {
    enum { value = N };
  };
  #endif
  
  /** \internal
    * Analogue of the std::size free function.
    * It returns the size of the container or view \a x of type \c T
    *
    * It currently supports:
    *  - any types T defining a member T::size() const
    *  - plain C arrays as T[N]
    *
    */
  template<typename T>
  Index size(const T& x) { return x.size(); }
  
  template<typename T,std::size_t N>
  Index size(const T (&) [N]) { return N; }
  
  /** \internal
    * Convenient struct to get the result type of a nullary, unary, binary, or
    * ternary functor.
    * 
    * Pre C++11:
    * Supports both a Func::result_type member and templated
    * Func::result<Func(ArgTypes...)>::type member.
    * 
    * If none of these members is provided, then the type of the first
    * argument is returned.
    * 
    * Post C++11:
    * This uses std::result_of. However, note the `type` member removes
    * const and converts references/pointers to their corresponding value type.
    */
  #if EIGEN_HAS_STD_INVOKE_RESULT
  template<typename T> struct result_of;
  
  template<typename F, typename... ArgTypes>
  struct result_of<F(ArgTypes...)> {
    typedef typename std::invoke_result<F, ArgTypes...>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  #elif EIGEN_HAS_STD_RESULT_OF
  template<typename T> struct result_of {
    typedef typename std::result_of<T>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  #else
  template<typename T> struct result_of { };
  
  struct has_none {int a[1];};
  struct has_std_result_type {int a[2];};
  struct has_tr1_result {int a[3];};
  
  template<typename Func, int SizeOf>
  struct nullary_result_of_select {};
  
  template<typename Func>
  struct nullary_result_of_select<Func, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
  
  template<typename Func>
  struct nullary_result_of_select<Func, sizeof(has_tr1_result)> {typedef typename Func::template result<Func()>::type type;};
  
  template<typename Func>
  struct result_of<Func()> {
      template<typename T>
      static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
      template<typename T>
      static has_tr1_result         testFunctor(T const *, typename T::template result<T()>::type const * = 0);
      static has_none               testFunctor(...);
  
      // note that the following indirection is needed for gcc-3.3
      enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
      typedef typename nullary_result_of_select<Func, FunctorType>::type type;
  };
  
  template<typename Func, typename ArgType, int SizeOf=sizeof(has_none)>
  struct unary_result_of_select {typedef typename internal::remove_all<ArgType>::type type;};
  
  template<typename Func, typename ArgType>
  struct unary_result_of_select<Func, ArgType, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
  
  template<typename Func, typename ArgType>
  struct unary_result_of_select<Func, ArgType, sizeof(has_tr1_result)> {typedef typename Func::template result<Func(ArgType)>::type type;};
  
  template<typename Func, typename ArgType>
  struct result_of<Func(ArgType)> {
      template<typename T>
      static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
      template<typename T>
      static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
      static has_none               testFunctor(...);
  
      // note that the following indirection is needed for gcc-3.3
      enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
      typedef typename unary_result_of_select<Func, ArgType, FunctorType>::type type;
  };
  
  template<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(has_none)>
  struct binary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1>
  struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_std_result_type)>
  {typedef typename Func::result_type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1>
  struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_tr1_result)>
  {typedef typename Func::template result<Func(ArgType0,ArgType1)>::type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1>
  struct result_of<Func(ArgType0,ArgType1)> {
      template<typename T>
      static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
      template<typename T>
      static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
      static has_none               testFunctor(...);
  
      // note that the following indirection is needed for gcc-3.3
      enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
      typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
  };
  
  template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>
  struct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
  struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>
  {typedef typename Func::result_type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
  struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>
  {typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};
  
  template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
  struct result_of<Func(ArgType0,ArgType1,ArgType2)> {
      template<typename T>
      static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
      template<typename T>
      static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);
      static has_none               testFunctor(...);
  
      // note that the following indirection is needed for gcc-3.3
      enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
      typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;
  };
  
  #endif
  
  #if EIGEN_HAS_STD_INVOKE_RESULT
  template<typename F, typename... ArgTypes>
  struct invoke_result {
    typedef typename std::invoke_result<F, ArgTypes...>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  #elif EIGEN_HAS_CXX11
  template<typename F, typename... ArgTypes>
  struct invoke_result {
    typedef typename result_of<F(ArgTypes...)>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  #else
  template<typename F, typename ArgType0 = void, typename ArgType1 = void, typename ArgType2 = void>
  struct invoke_result {
    typedef typename result_of<F(ArgType0, ArgType1, ArgType2)>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  
  template<typename F>
  struct invoke_result<F, void, void, void> {
    typedef typename result_of<F()>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  
  template<typename F, typename ArgType0>
  struct invoke_result<F, ArgType0, void, void> {
    typedef typename result_of<F(ArgType0)>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  
  template<typename F, typename ArgType0, typename ArgType1>
  struct invoke_result<F, ArgType0, ArgType1, void> {
    typedef typename result_of<F(ArgType0, ArgType1)>::type type1;
    typedef typename remove_all<type1>::type type;
  };
  #endif
  
  struct meta_yes { char a[1]; };
  struct meta_no  { char a[2]; };
  
  // Check whether T::ReturnType does exist
  template <typename T>
  struct has_ReturnType
  {
    template <typename C> static meta_yes testFunctor(C const *, typename C::ReturnType const * = 0);
    template <typename C> static meta_no  testFunctor(...);
  
    enum { value = sizeof(testFunctor<T>(static_cast<T*>(0))) == sizeof(meta_yes) };
  };
  
  template<typename T> const T* return_ptr();
  
  template <typename T, typename IndexType=Index>
  struct has_nullary_operator
  {
    template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()())>0)>::type * = 0);
    static meta_no testFunctor(...);
  
    enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
  };
  
  template <typename T, typename IndexType=Index>
  struct has_unary_operator
  {
    template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0)))>0)>::type * = 0);
    static meta_no testFunctor(...);
  
    enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
  };
  
  template <typename T, typename IndexType=Index>
  struct has_binary_operator
  {
    template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0),IndexType(0)))>0)>::type * = 0);
    static meta_no testFunctor(...);
  
    enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
  };
  
  /** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
    * Usage example: \code meta_sqrt<1023>::ret \endcode
    */
  template<int Y,
           int InfX = 0,
           int SupX = ((Y==1) ? 1 : Y/2),
           bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >
                                  // use ?: instead of || just to shut up a stupid gcc 4.3 warning
  class meta_sqrt
  {
      enum {
        MidX = (InfX+SupX)/2,
        TakeInf = MidX*MidX > Y ? 1 : 0,
        NewInf = int(TakeInf) ? InfX : int(MidX),
        NewSup = int(TakeInf) ? int(MidX) : SupX
      };
    public:
      enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };
  };
  
  template<int Y, int InfX, int SupX>
  class meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
  
  
  /** \internal Computes the least common multiple of two positive integer A and B
    * at compile-time. It implements a naive algorithm testing all multiples of A.
    * It thus works better if A>=B.
    */
  template<int A, int B, int K=1, bool Done = ((A*K)%B)==0>
  struct meta_least_common_multiple
  {
    enum { ret = meta_least_common_multiple<A,B,K+1>::ret };
  };
  template<int A, int B, int K>
  struct meta_least_common_multiple<A,B,K,true>
  {
    enum { ret = A*K };
  };
  
  /** \internal determines whether the product of two numeric types is allowed and what the return type is */
  template<typename T, typename U> struct scalar_product_traits
  {
    enum { Defined = 0 };
  };
  
  // FIXME quick workaround around current limitation of result_of
  // template<typename Scalar, typename ArgType0, typename ArgType1>
  // struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
  // typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
  // };
  
  /** \internal Obtains a POD type suitable to use as storage for an object of a size
    * of at most Len bytes, aligned as specified by \c Align.
    */
  template<unsigned Len, unsigned Align>
  struct aligned_storage {
    struct type {
      EIGEN_ALIGN_TO_BOUNDARY(Align) unsigned char data[Len];
    };
  };
  
  } // end namespace internal
  
  namespace numext {
  
  #if defined(EIGEN_GPU_COMPILE_PHASE)
  template<typename T> EIGEN_DEVICE_FUNC   void swap(T &a, T &b) { T tmp = b; b = a; a = tmp; }
  #else
  template<typename T> EIGEN_STRONG_INLINE void swap(T &a, T &b) { std::swap(a,b); }
  #endif
  
  #if defined(EIGEN_GPU_COMPILE_PHASE)
  using internal::device::numeric_limits;
  #else
  using std::numeric_limits;
  #endif
  
  // Integer division with rounding up.
  // T is assumed to be an integer type with a>=0, and b>0
  template<typename T>
  EIGEN_DEVICE_FUNC
  T div_ceil(const T &a, const T &b)
  {
    return (a+b-1) / b;
  }
  
  // The aim of the following functions is to bypass -Wfloat-equal warnings
  // when we really want a strict equality comparison on floating points.
  template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool equal_strict(const X& x,const Y& y) { return x == y; }
  
  #if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
  template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool equal_strict(const float& x,const float& y) { return std::equal_to<float>()(x,y); }
  
  template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool equal_strict(const double& x,const double& y) { return std::equal_to<double>()(x,y); }
  #endif
  
  template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool not_equal_strict(const X& x,const Y& y) { return x != y; }
  
  #if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
  template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool not_equal_strict(const float& x,const float& y) { return std::not_equal_to<float>()(x,y); }
  
  template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
  bool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }
  #endif
  
  } // end namespace numext
  
  } // end namespace Eigen
  
  #endif // EIGEN_META_H
  