text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@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_CXX11_TENSOR_TENSOR_PADDING_H
  #define EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
  
  namespace Eigen {
  
  /** \class TensorPadding
    * \ingroup CXX11_Tensor_Module
    *
    * \brief Tensor padding class.
    * At the moment only padding with a constant value is supported.
    *
    */
  namespace internal {
  template<typename PaddingDimensions, typename XprType>
  struct traits<TensorPaddingOp<PaddingDimensions, XprType> > : public traits<XprType>
  {
    typedef typename XprType::Scalar Scalar;
    typedef traits<XprType> XprTraits;
    typedef typename packet_traits<Scalar>::type Packet;
    typedef typename XprTraits::StorageKind StorageKind;
    typedef typename XprTraits::Index Index;
    typedef typename XprType::Nested Nested;
    typedef typename remove_reference<Nested>::type _Nested;
    static const int NumDimensions = XprTraits::NumDimensions;
    static const int Layout = XprTraits::Layout;
  };
  
  template<typename PaddingDimensions, typename XprType>
  struct eval<TensorPaddingOp<PaddingDimensions, XprType>, Eigen::Dense>
  {
    typedef const TensorPaddingOp<PaddingDimensions, XprType>& type;
  };
  
  template<typename PaddingDimensions, typename XprType>
  struct nested<TensorPaddingOp<PaddingDimensions, XprType>, 1, typename eval<TensorPaddingOp<PaddingDimensions, XprType> >::type>
  {
    typedef TensorPaddingOp<PaddingDimensions, XprType> type;
  };
  
  }  // end namespace internal
  
  
  
  template<typename PaddingDimensions, typename XprType>
  class TensorPaddingOp : public TensorBase<TensorPaddingOp<PaddingDimensions, XprType>, ReadOnlyAccessors>
  {
    public:
    typedef typename Eigen::internal::traits<TensorPaddingOp>::Scalar Scalar;
    typedef typename Eigen::internal::traits<TensorPaddingOp>::Packet Packet;
    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
    typedef typename XprType::CoeffReturnType CoeffReturnType;
    typedef typename XprType::PacketReturnType PacketReturnType;
    typedef typename Eigen::internal::nested<TensorPaddingOp>::type Nested;
    typedef typename Eigen::internal::traits<TensorPaddingOp>::StorageKind StorageKind;
    typedef typename Eigen::internal::traits<TensorPaddingOp>::Index Index;
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPaddingOp(const XprType& expr, const PaddingDimensions& padding_dims,
                                                          const Scalar padding_value)
        : m_xpr(expr), m_padding_dims(padding_dims), m_padding_value(padding_value) {}
  
      EIGEN_DEVICE_FUNC
      const PaddingDimensions& padding() const { return m_padding_dims; }
      EIGEN_DEVICE_FUNC
      Scalar padding_value() const { return m_padding_value; }
  
      EIGEN_DEVICE_FUNC
      const typename internal::remove_all<typename XprType::Nested>::type&
      expression() const { return m_xpr; }
  
    protected:
      typename XprType::Nested m_xpr;
      const PaddingDimensions m_padding_dims;
      const Scalar m_padding_value;
  };
  
  
  // Eval as rvalue
  template<typename PaddingDimensions, typename ArgType, typename Device>
  struct TensorEvaluator<const TensorPaddingOp<PaddingDimensions, ArgType>, Device>
  {
    typedef TensorPaddingOp<PaddingDimensions, ArgType> XprType;
    typedef typename XprType::Index Index;
    static const int NumDims = internal::array_size<PaddingDimensions>::value;
    typedef DSizes<Index, NumDims> Dimensions;
  
    enum {
      IsAligned = false,
      PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
      BlockAccess = false,
      Layout = TensorEvaluator<ArgType, Device>::Layout,
      CoordAccess = true,
    };
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
        : m_impl(op.expression(), device), m_padding(op.padding()), m_paddingValue(op.padding_value())
    {
      // Compute dimensions
      m_dimensions = m_impl.dimensions();
      for (int i = 0; i < NumDims; ++i) {
        m_dimensions[i] += m_padding[i].first + m_padding[i].second;
      }
      const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        m_outputStrides[0] = 1;
        if (NumDims > 0) {
          m_inputStrides[0] = 1;
          for (int i = 1; i < NumDims; ++i) {
            m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
            m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
          }
          m_outputStrides[NumDims] = m_outputStrides[NumDims-1] * m_dimensions[NumDims-1];
        }
      } else {
        m_outputStrides[NumDims] = 1;
        if (NumDims > 0) {
          m_inputStrides[NumDims - 1] = 1;
          for (int i = NumDims - 2; i >= 0; --i) {
            m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
            m_outputStrides[i+1] = m_outputStrides[i+2] * m_dimensions[i+1];
          }
          m_outputStrides[0] = m_outputStrides[1] * m_dimensions[0];
        }
      }
    }
  
    typedef typename XprType::Scalar Scalar;
    typedef typename XprType::CoeffReturnType CoeffReturnType;
    typedef typename XprType::PacketReturnType PacketReturnType;
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {
      m_impl.evalSubExprsIfNeeded(NULL);
      return true;
    }
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
      m_impl.cleanup();
    }
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
    {
      eigen_assert(index < dimensions().TotalSize());
      Index inputIndex = 0;
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        for (int i = NumDims - 1; i > 0; --i) {
          const Index idx = index / m_outputStrides[i];
          if (idx < m_padding[i].first || idx >= m_dimensions[i] - m_padding[i].second) {
            return m_paddingValue;
          }
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
          index -= idx * m_outputStrides[i];
        }
        if (NumDims > 0) {
          if (index < m_padding[0].first || index >= m_dimensions[0] - m_padding[0].second) {
            return m_paddingValue;
          }
          inputIndex += (index - m_padding[0].first);
        }
      } else {
        for (int i = 0; i < NumDims - 1; ++i) {
          const Index idx = index / m_outputStrides[i+1];
          if (idx < m_padding[i].first || idx >= m_dimensions[i] - m_padding[i].second) {
            return m_paddingValue;
          }
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
          index -= idx * m_outputStrides[i+1];
        }
        if (NumDims > 0) {
          if (index < m_padding[NumDims-1].first ||
              index >= m_dimensions[NumDims-1] - m_padding[NumDims-1].second) {
            return m_paddingValue;
          }
          inputIndex += (index - m_padding[NumDims-1].first);
        }
      }
      return m_impl.coeff(inputIndex);
    }
  
    template<int LoadMode>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
    {
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        return packetColMajor(index);
      }
      return packetRowMajor(index);
    }
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(const array<Index, NumDims>& coords) const
    {
      Index inputIndex = 0;
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        if (NumDims > 0) {
          const Index idx = coords[0];
          if (idx < m_padding[0].first || idx >= m_dimensions[0] - m_padding[0].second) {
            return m_paddingValue;
          }
          inputIndex = idx - m_padding[0].first;
        }
        for (int i = 1; i < NumDims; ++i) {
          const Index idx = coords[i];
          if (idx < m_padding[i].first || idx >= m_dimensions[i] - m_padding[i].second) {
            return m_paddingValue;
          }
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
        }
      } else {
        if (NumDims > 0) {
          const Index idx = coords[NumDims-1];
          if (idx < m_padding[NumDims-1].first || idx >= m_dimensions[NumDims-1] - m_padding[NumDims-1].second) {
            return m_paddingValue;
          }
          inputIndex = idx - m_padding[NumDims-1].first;
        }
        for (int i = NumDims - 2; i >= 0; --i) {
          const Index idx = coords[i];
          if (idx < m_padding[i].first || idx >= m_dimensions[i] - m_padding[i].second) {
            return m_paddingValue;
          }
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
        }
      }
      return m_impl.coeff(inputIndex);
    }
  
    EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }
  
   protected:
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const
    {
      const int packetSize = internal::unpacket_traits<PacketReturnType>::size;
      EIGEN_STATIC_ASSERT(packetSize > 1, YOU_MADE_A_PROGRAMMING_MISTAKE)
      eigen_assert(index+packetSize-1 < dimensions().TotalSize());
  
      const Index initialIndex = index;
      Index inputIndex = 0;
      for (int i = NumDims - 1; i > 0; --i) {
        const Index first = index;
        const Index last = index + packetSize - 1;
        const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i];
        const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i];
        const Index lastPaddedRight = m_outputStrides[i+1];
  
        if (last < lastPaddedLeft) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= firstPaddedRight && last < lastPaddedRight) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= lastPaddedLeft && last < firstPaddedRight) {
          // all the coefficient are between the 2 padding zones.
          const Index idx = index / m_outputStrides[i];
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
          index -= idx * m_outputStrides[i];
        }
        else {
          // Every other case
          return packetWithPossibleZero(initialIndex);
        }
      }
  
      const Index last = index + packetSize - 1;
      const Index first = index;
  
      if (NumDims > 0) {
        const Index lastPaddedLeft = m_padding[0].first;
        const Index firstPaddedRight = (m_dimensions[0] - m_padding[0].second);
        const Index lastPaddedRight = m_outputStrides[1];
  
        if (last < lastPaddedLeft) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= firstPaddedRight && last < lastPaddedRight) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= lastPaddedLeft && last < firstPaddedRight) {
          // all the coefficient are between the 2 padding zones.
          inputIndex += (index - m_padding[0].first);
          return m_impl.template packet<Unaligned>(inputIndex);
        }
      }
  
      // Every other case
      return packetWithPossibleZero(initialIndex);
    }
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const
    {
      const int packetSize = internal::unpacket_traits<PacketReturnType>::size;
      EIGEN_STATIC_ASSERT(packetSize > 1, YOU_MADE_A_PROGRAMMING_MISTAKE)
      eigen_assert(index+packetSize-1 < dimensions().TotalSize());
  
      const Index initialIndex = index;
      Index inputIndex = 0;
  
      for (int i = 0; i < NumDims - 1; ++i) {
        const Index first = index;
        const Index last = index + packetSize - 1;
        const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i+1];
        const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i+1];
        const Index lastPaddedRight = m_outputStrides[i];
  
        if (last < lastPaddedLeft) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= firstPaddedRight && last < lastPaddedRight) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= lastPaddedLeft && last < firstPaddedRight) {
          // all the coefficient are between the 2 padding zones.
          const Index idx = index / m_outputStrides[i+1];
          inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
          index -= idx * m_outputStrides[i+1];
        }
        else {
          // Every other case
          return packetWithPossibleZero(initialIndex);
        }
      }
  
      const Index last = index + packetSize - 1;
      const Index first = index;
  
      if (NumDims > 0) {
        const Index lastPaddedLeft = m_padding[NumDims-1].first;
        const Index firstPaddedRight = (m_dimensions[NumDims-1] - m_padding[NumDims-1].second);
        const Index lastPaddedRight = m_outputStrides[NumDims-1];
  
        if (last < lastPaddedLeft) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= firstPaddedRight && last < lastPaddedRight) {
          // all the coefficient are in the padding zone.
          return internal::pset1<PacketReturnType>(m_paddingValue);
        }
        else if (first >= lastPaddedLeft && last < firstPaddedRight) {
          // all the coefficient are between the 2 padding zones.
          inputIndex += (index - m_padding[NumDims-1].first);
          return m_impl.template packet<Unaligned>(inputIndex);
        }
      }
  
      // Every other case
      return packetWithPossibleZero(initialIndex);
    }
  
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const
    {
      const int packetSize = internal::unpacket_traits<PacketReturnType>::size;
      EIGEN_ALIGN_DEFAULT typename internal::remove_const<CoeffReturnType>::type values[packetSize];
      for (int i = 0; i < packetSize; ++i) {
        values[i] = coeff(index+i);
      }
      PacketReturnType rslt = internal::pload<PacketReturnType>(values);
      return rslt;
    }
  
    Dimensions m_dimensions;
    array<Index, NumDims+1> m_outputStrides;
    array<Index, NumDims> m_inputStrides;
    TensorEvaluator<ArgType, Device> m_impl;
    PaddingDimensions m_padding;
  
    Scalar m_paddingValue;
  };
  
  
  
  
  } // end namespace Eigen
  
  #endif // EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
  