// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 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(__CUDA_ARCH__)
#include <math_constants.h>
#endif

namespace Eigen {

/**
 * \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.
  */

struct true_type {  enum { value = 1 }; };
struct false_type { enum { value = 0 }; };

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, typename U> struct is_same { enum { value = 0 }; };
template<typename T> struct is_same<T,T> { enum { value = 1 }; };

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> 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; };

/** \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(__CUDA_ARCH__)
 
namespace device {

template<typename T> struct numeric_limits
{
  EIGEN_DEVICE_FUNC
  static T epsilon() { return 0; }
  static T max() { assert(false && "Max not suppoted for this type"); }
  static T lowest() { assert(false && "Lowest not suppoted for this type"); }
  static T infinity() { assert(false && "Infinity not supported for this type"); }
  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() { return CUDART_MAX_NORMAL_F; }
  EIGEN_DEVICE_FUNC
  static float lowest() { return -CUDART_MAX_NORMAL_F; }
  EIGEN_DEVICE_FUNC
  static float infinity() { return CUDART_INF_F; }
  EIGEN_DEVICE_FUNC
  static float quiet_NaN() { return CUDART_NAN_F; }
};
template<> struct numeric_limits<double>
{
  EIGEN_DEVICE_FUNC
  static double epsilon() { return __DBL_EPSILON__; }
  EIGEN_DEVICE_FUNC
  static double max() { return CUDART_INF; }
  EIGEN_DEVICE_FUNC
  static double lowest() { return -CUDART_INF; }
  EIGEN_DEVICE_FUNC
  static double infinity() { return CUDART_INF; }
  EIGEN_DEVICE_FUNC
  static double quiet_NaN() { return CUDART_NAN; }
};
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 lowest() { return INT_MIN; }
};
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 lowest() { return LONG_MIN; }
};
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 lowest() { return LLONG_MIN; }
};

}

#endif

/** \internal
  * A base class do disable default copy ctor and copy assignement operator.
  */
class noncopyable
{
  noncopyable(const noncopyable&);
  const noncopyable& operator=(const noncopyable&);
protected:
  noncopyable() {}
  ~noncopyable() {}
};


/** \internal
  * Convenient struct to get the result type of a unary or binary functor.
  *
  * It supports both the current STL mechanism (using the result_type member) as well as
  * upcoming next STL generation (using a templated result member).
  * If none of these members is provided, then the type of the first argument is returned. FIXME, that behavior is a pretty bad hack.
  */
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, typename ArgType, int SizeOf=sizeof(has_none)>
struct unary_result_of_select {typedef ArgType 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 ArgType0 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;
};

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(typename C::ReturnType const *);
  template <typename C> static meta_no testFunctor(...);

  enum { value = sizeof(testFunctor<T>(0)) == sizeof(meta_yes) };
};

template<typename T> const T& return_ref();

template <typename T>
struct has_nullary_operator
{
  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ref<C>().operator()())>0)>::type * = 0);
  static meta_no testFunctor(...);

  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
};

template <typename T>
struct has_unary_operator
{
  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ref<C>().operator()(Index(0)))>0)>::type * = 0);
  static meta_no testFunctor(...);

  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
};

template <typename T>
struct has_binary_operator
{
  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ref<C>().operator()(Index(0),Index(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 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 };
};

template<typename T> struct scalar_product_traits<T,T>
{
  enum {
    // Cost = NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef T ReturnType;
};

template<typename T> struct scalar_product_traits<T, const T>
{
  enum {
    // Cost = NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef T ReturnType;
};

template<typename T> struct scalar_product_traits<const T, T>
{
  enum {
    // Cost = NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef T ReturnType;
};

template<typename T> struct scalar_product_traits<T,std::complex<T> >
{
  enum {
    // Cost = 2*NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef std::complex<T> ReturnType;
};

template<typename T> struct scalar_product_traits<std::complex<T>, T>
{
  enum {
    // Cost = 2*NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef std::complex<T> ReturnType;
};

// 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;
// };

template<typename T> struct is_diagonal
{ enum { ret = false }; };

template<typename T> struct is_diagonal<DiagonalBase<T> >
{ enum { ret = true }; };

template<typename T> struct is_diagonal<DiagonalWrapper<T> >
{ enum { ret = true }; };

template<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >
{ enum { ret = true }; };

/** \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 };
};

} // end namespace internal

namespace numext {
  
#if defined(__CUDA_ARCH__)
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

} // end namespace numext

} // end namespace Eigen

#endif // EIGEN_META_H