TensorMorphing.h

// 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_MORPHING_H
#define EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H

namespace Eigen {

namespace internal {
template<typename NewDimensions, typename XprType>
struct traits<TensorReshapingOp<NewDimensions, XprType> > : public traits<XprType>
{
  typedef typename XprType::Scalar Scalar;
  typedef traits<XprType> XprTraits;
  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 = array_size<NewDimensions>::value;
  static const int Layout = XprTraits::Layout;
};

template<typename NewDimensions, typename XprType>
struct eval<TensorReshapingOp<NewDimensions, XprType>, Eigen::Dense>
{
  typedef const TensorReshapingOp<NewDimensions, XprType>& type;
};

template<typename NewDimensions, typename XprType>
struct nested<TensorReshapingOp<NewDimensions, XprType>, 1, typename eval<TensorReshapingOp<NewDimensions, XprType> >::type>
{
  typedef TensorReshapingOp<NewDimensions, XprType> type;
};

}  // end namespace internal



template<typename NewDimensions, typename XprType>
class TensorReshapingOp : public TensorBase<TensorReshapingOp<NewDimensions, XprType>, WriteAccessors>
{
  public:
  typedef typename Eigen::internal::traits<TensorReshapingOp>::Scalar Scalar;
  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;
  typedef typename Eigen::internal::nested<TensorReshapingOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorReshapingOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorReshapingOp>::Index Index;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReshapingOp(const XprType& expr, const NewDimensions& dims)
      : m_xpr(expr), m_dims(dims) {}

    EIGEN_DEVICE_FUNC
    const NewDimensions& dimensions() const { return m_dims; }

    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<typename XprType::Nested>::type&
    expression() const { return m_xpr; }

    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorReshapingOp& operator = (const TensorReshapingOp& other)
    {
      typedef TensorAssignOp<TensorReshapingOp, const TensorReshapingOp> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
      return *this;
    }

    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorReshapingOp& operator = (const OtherDerived& other)
    {
      typedef TensorAssignOp<TensorReshapingOp, const OtherDerived> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
      return *this;
    }

  protected:
    typename XprType::Nested m_xpr;
    const NewDimensions m_dims;
};


// Eval as rvalue
template<typename NewDimensions, typename ArgType, typename Device>
struct TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>
{
  typedef TensorReshapingOp<NewDimensions, ArgType> XprType;
  typedef NewDimensions Dimensions;

  enum {
    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    CoordAccess = false,  // to be implemented
    RawAccess = TensorEvaluator<ArgType, Device>::RawAccess
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
      : m_impl(op.expression(), device), m_dimensions(op.dimensions())
  {
    // The total size of the reshaped tensor must be equal to the total size
    // of the input tensor.
    eigen_assert(internal::array_prod(m_impl.dimensions()) == internal::array_prod(op.dimensions()));
  }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {
    return m_impl.evalSubExprsIfNeeded(data);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
    m_impl.cleanup();
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
  {
    return m_impl.coeff(index);
  }

  template<int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
  {
    return m_impl.template packet<LoadMode>(index);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    return m_impl.costPerCoeff(vectorized);
  }

  EIGEN_DEVICE_FUNC Scalar* data() const { return const_cast<Scalar*>(m_impl.data()); }

  EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }

 protected:
  TensorEvaluator<ArgType, Device> m_impl;
  NewDimensions m_dimensions;
};


// Eval as lvalue
template<typename NewDimensions, typename ArgType, typename Device>
  struct TensorEvaluator<TensorReshapingOp<NewDimensions, ArgType>, Device>
  : public TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>

{
  typedef TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device> Base;
  typedef TensorReshapingOp<NewDimensions, ArgType> XprType;
  typedef NewDimensions Dimensions;

  enum {
    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    CoordAccess = false,  // to be implemented
    RawAccess = TensorEvaluator<ArgType, Device>::RawAccess
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
    : Base(op, device)
  { }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
  {
    return this->m_impl.coeffRef(index);
  }
  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  void writePacket(Index index, const PacketReturnType& x)
  {
    this->m_impl.template writePacket<StoreMode>(index, x);
  }
};


namespace internal {
template<typename StartIndices, typename Sizes, typename XprType>
struct traits<TensorSlicingOp<StartIndices, Sizes, XprType> > : public traits<XprType>
{
  typedef typename XprType::Scalar Scalar;
  typedef traits<XprType> XprTraits;
  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 = array_size<StartIndices>::value;
  static const int Layout = XprTraits::Layout;
};

template<typename StartIndices, typename Sizes, typename XprType>
struct eval<TensorSlicingOp<StartIndices, Sizes, XprType>, Eigen::Dense>
{
  typedef const TensorSlicingOp<StartIndices, Sizes, XprType>& type;
};

template<typename StartIndices, typename Sizes, typename XprType>
struct nested<TensorSlicingOp<StartIndices, Sizes, XprType>, 1, typename eval<TensorSlicingOp<StartIndices, Sizes, XprType> >::type>
{
  typedef TensorSlicingOp<StartIndices, Sizes, XprType> type;
};

}  // end namespace internal



template<typename StartIndices, typename Sizes, typename XprType>
class TensorSlicingOp : public TensorBase<TensorSlicingOp<StartIndices, Sizes, XprType> >
{
  public:
  typedef typename Eigen::internal::traits<TensorSlicingOp>::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename Eigen::internal::nested<TensorSlicingOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorSlicingOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorSlicingOp>::Index Index;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorSlicingOp(const XprType& expr, const StartIndices& indices, const Sizes& sizes)
      : m_xpr(expr), m_indices(indices), m_sizes(sizes) {}

    EIGEN_DEVICE_FUNC
    const StartIndices& startIndices() const { return m_indices; }
    EIGEN_DEVICE_FUNC
    const Sizes& sizes() const { return m_sizes; }

    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<typename XprType::Nested>::type&
    expression() const { return m_xpr; }

    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorSlicingOp& operator = (const OtherDerived& other)
    {
      typedef TensorAssignOp<TensorSlicingOp, const OtherDerived> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
      return *this;
    }

    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorSlicingOp& operator = (const TensorSlicingOp& other)
    {
      typedef TensorAssignOp<TensorSlicingOp, const TensorSlicingOp> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
      return *this;
    }


  protected:
    typename XprType::Nested m_xpr;
    const StartIndices m_indices;
    const Sizes m_sizes;
};


// Fixme: figure out the exact threshold
namespace {
template <typename Index, typename Device> struct MemcpyTriggerForSlicing {
  EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const Device& device) : threshold_(2 * device.numThreads()) { }
  EIGEN_DEVICE_FUNC bool operator ()(Index val) const { return val > threshold_; }

 private:
  Index threshold_;
};

// It is very expensive to start the memcpy kernel on GPU: we therefore only
// use it for large copies.
#ifdef EIGEN_USE_GPU
template <typename Index> struct MemcpyTriggerForSlicing<Index, GpuDevice>  {
  EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const GpuDevice&) { }
  EIGEN_DEVICE_FUNC bool operator ()(Index val) const { return val > 4*1024*1024; }
};
#endif
}

// Eval as rvalue
template<typename StartIndices, typename Sizes, typename ArgType, typename Device>
struct TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
{
  typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;
  static const int NumDims = internal::array_size<Sizes>::value;

  enum {
    // Alignment can't be guaranteed at compile time since it depends on the
    // slice offsets and sizes.
    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    CoordAccess = false,
    RawAccess = false
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
      : m_impl(op.expression(), device), m_device(device), m_dimensions(op.sizes()), m_offsets(op.startIndices())
  {
    for (std::size_t i = 0; i < internal::array_size<Dimensions>::value; ++i) {
      eigen_assert(m_impl.dimensions()[i] >= op.sizes()[i] + op.startIndices()[i]);
    }

    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
    const Sizes& output_dims = op.sizes();
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_inputStrides[0] = 1;
      for (int i = 1; i < NumDims; ++i) {
        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
      }

     // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.
      m_outputStrides[0] = 1;
      for (int i = 1; i < NumDims; ++i) {
        m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];
        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
      }
    } else {
      m_inputStrides[NumDims-1] = 1;
      for (int i = NumDims - 2; i >= 0; --i) {
        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
      }

     // Don't initialize m_fastOutputStrides[NumDims-1] since it won't ever be accessed.
      m_outputStrides[NumDims-1] = 1;
      for (int i = NumDims - 2; i >= 0; --i) {
        m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];
        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
      }
    }
  }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  typedef Sizes Dimensions;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }


  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {
    m_impl.evalSubExprsIfNeeded(NULL);
    if (!NumTraits<typename internal::remove_const<Scalar>::type>::RequireInitialization && data && m_impl.data()) {
      Index contiguous_values = 1;
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        for (int i = 0; i < NumDims; ++i) {
          contiguous_values *= dimensions()[i];
          if (dimensions()[i] != m_impl.dimensions()[i]) {
            break;
          }
        }
      } else {
        for (int i = NumDims-1; i >= 0; --i) {
          contiguous_values *= dimensions()[i];
          if (dimensions()[i] != m_impl.dimensions()[i]) {
            break;
          }
        }
      }
      // Use memcpy if it's going to be faster than using the regular evaluation.
      const MemcpyTriggerForSlicing<Index, Device> trigger(m_device);
      if (trigger(contiguous_values)) {
        Scalar* src = (Scalar*)m_impl.data();
        for (int i = 0; i < internal::array_prod(dimensions()); i += contiguous_values) {
          Index offset = srcCoeff(i);
          m_device.memcpy((void*)(data+i), src+offset, contiguous_values * sizeof(Scalar));
        }
        return false;
      }
    }
    return true;
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
    m_impl.cleanup();
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
  {
    return m_impl.coeff(srcCoeff(index));
  }

  template<int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(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 < internal::array_prod(dimensions()));

    Index inputIndices[] = {0, 0};
    Index indices[] = {index, index + packetSize - 1};
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      for (int i = NumDims - 1; i > 0; --i) {
        const Index idx0 = indices[0] / m_fastOutputStrides[i];
        const Index idx1 = indices[1] / m_fastOutputStrides[i];
        inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];
        inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];
        indices[0] -= idx0 * m_outputStrides[i];
        indices[1] -= idx1 * m_outputStrides[i];
      }
      inputIndices[0] += (indices[0] + m_offsets[0]);
      inputIndices[1] += (indices[1] + m_offsets[0]);
    } else {
      for (int i = 0; i < NumDims - 1; ++i) {
        const Index idx0 = indices[0] / m_fastOutputStrides[i];
        const Index idx1 = indices[1] / m_fastOutputStrides[i];
        inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];
        inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];
        indices[0] -= idx0 * m_outputStrides[i];
        indices[1] -= idx1 * m_outputStrides[i];
      }
      inputIndices[0] += (indices[0] + m_offsets[NumDims-1]);
      inputIndices[1] += (indices[1] + m_offsets[NumDims-1]);
    }
    if (inputIndices[1] - inputIndices[0] == packetSize - 1) {
      PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);
      return rslt;
    }
    else {
      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[packetSize];
      values[0] = m_impl.coeff(inputIndices[0]);
      values[packetSize-1] = m_impl.coeff(inputIndices[1]);
      for (int i = 1; i < packetSize-1; ++i) {
        values[i] = coeff(index+i);
      }
      PacketReturnType rslt = internal::pload<PacketReturnType>(values);
      return rslt;
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, NumDims);
  }


  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar* data() const {
    Scalar* result = m_impl.data();
    if (result) {
      Index offset = 0;
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        for (int i = 0; i < NumDims; ++i) {
          if (m_dimensions[i] != m_impl.dimensions()[i]) {
            offset += m_offsets[i] * m_inputStrides[i];
            for (int j = i+1; j < NumDims; ++j) {
              if (m_dimensions[j] > 1) {
                return NULL;
              }
              offset += m_offsets[j] * m_inputStrides[j];
            }
            break;
          }
        }
      } else {
        for (int i = NumDims - 1; i >= 0; --i) {
          if (m_dimensions[i] != m_impl.dimensions()[i]) {
            offset += m_offsets[i] * m_inputStrides[i];
            for (int j = i-1; j >= 0; --j) {
              if (m_dimensions[j] > 1) {
                return NULL;
              }
              offset += m_offsets[j] * m_inputStrides[j];
            }
            break;
          }
        }
      }
      return result + offset;
    }
    return NULL;
  }

 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
  {
    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_fastOutputStrides[i];
        inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];
        index -= idx * m_outputStrides[i];
      }
      inputIndex += (index + m_offsets[0]);
    } else {
      for (int i = 0; i < NumDims - 1; ++i) {
        const Index idx = index / m_fastOutputStrides[i];
        inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];
        index -= idx * m_outputStrides[i];
      }
      inputIndex += (index + m_offsets[NumDims-1]);
    }
    return inputIndex;
  }

  array<Index, NumDims> m_outputStrides;
  array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;
  array<Index, NumDims> m_inputStrides;
  TensorEvaluator<ArgType, Device> m_impl;
  const Device& m_device;
  Dimensions m_dimensions;
  const StartIndices m_offsets;
};


// Eval as lvalue
template<typename StartIndices, typename Sizes, typename ArgType, typename Device>
struct TensorEvaluator<TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
  : public TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
{
  typedef TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device> Base;
  typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;
  static const int NumDims = internal::array_size<Sizes>::value;

  enum {
    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    CoordAccess = false,
    RawAccess = false
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
    : Base(op, device)
    { }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  typedef Sizes Dimensions;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
  {
    return this->m_impl.coeffRef(this->srcCoeff(index));
  }

  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  void writePacket(Index index, const PacketReturnType& x)
  {
    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;
    Index inputIndices[] = {0, 0};
    Index indices[] = {index, index + packetSize - 1};
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      for (int i = NumDims - 1; i > 0; --i) {
        const Index idx0 = indices[0] / this->m_fastOutputStrides[i];
        const Index idx1 = indices[1] / this->m_fastOutputStrides[i];
        inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];
        inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];
        indices[0] -= idx0 * this->m_outputStrides[i];
        indices[1] -= idx1 * this->m_outputStrides[i];
      }
      inputIndices[0] += (indices[0] + this->m_offsets[0]);
      inputIndices[1] += (indices[1] + this->m_offsets[0]);
    } else {
      for (int i = 0; i < NumDims - 1; ++i) {
        const Index idx0 = indices[0] / this->m_fastOutputStrides[i];
        const Index idx1 = indices[1] / this->m_fastOutputStrides[i];
        inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];
        inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];
        indices[0] -= idx0 * this->m_outputStrides[i];
        indices[1] -= idx1 * this->m_outputStrides[i];
      }
      inputIndices[0] += (indices[0] + this->m_offsets[NumDims-1]);
      inputIndices[1] += (indices[1] + this->m_offsets[NumDims-1]);
    }
    if (inputIndices[1] - inputIndices[0] == packetSize - 1) {
      this->m_impl.template writePacket<StoreMode>(inputIndices[0], x);
    }
    else {
      EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];
      internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
      this->m_impl.coeffRef(inputIndices[0]) = values[0];
      this->m_impl.coeffRef(inputIndices[1]) = values[packetSize-1];
      for (int i = 1; i < packetSize-1; ++i) {
        this->coeffRef(index+i) = values[i];
      }
    }
  }
};



namespace internal {
template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
struct traits<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> > : public traits<XprType>
{
  typedef typename XprType::Scalar Scalar;
  typedef traits<XprType> XprTraits;
  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 = array_size<StartIndices>::value;
  static const int Layout = XprTraits::Layout;
};

template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
struct eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, Eigen::Dense>
{
  typedef const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>& type;
};

template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
struct nested<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, 1, typename eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >::type>
{
  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> type;
};

}  // end namespace internal


template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
class TensorStridingSlicingOp : public TensorBase<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >
{
  public:
  typedef typename internal::traits<TensorStridingSlicingOp>::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename internal::nested<TensorStridingSlicingOp>::type Nested;
  typedef typename internal::traits<TensorStridingSlicingOp>::StorageKind StorageKind;
  typedef typename internal::traits<TensorStridingSlicingOp>::Index Index;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorStridingSlicingOp(
    const XprType& expr, const StartIndices& startIndices,
    const StopIndices& stopIndices, const Strides& strides)
      : m_xpr(expr), m_startIndices(startIndices), m_stopIndices(stopIndices),
        m_strides(strides) {}

    EIGEN_DEVICE_FUNC
    const StartIndices& startIndices() const { return m_startIndices; }
    EIGEN_DEVICE_FUNC
    const StartIndices& stopIndices() const { return m_stopIndices; }
    EIGEN_DEVICE_FUNC
    const StartIndices& strides() const { return m_strides; }

    EIGEN_DEVICE_FUNC
    const typename internal::remove_all<typename XprType::Nested>::type&
    expression() const { return m_xpr; }

    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorStridingSlicingOp& operator = (const TensorStridingSlicingOp& other)
    {
      typedef TensorAssignOp<TensorStridingSlicingOp, const TensorStridingSlicingOp> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(
          assign, DefaultDevice());
      return *this;
    }

    template<typename OtherDerived>
    EIGEN_DEVICE_FUNC
    EIGEN_STRONG_INLINE TensorStridingSlicingOp& operator = (const OtherDerived& other)
    {
      typedef TensorAssignOp<TensorStridingSlicingOp, const OtherDerived> Assign;
      Assign assign(*this, other);
      internal::TensorExecutor<const Assign, DefaultDevice>::run(
          assign, DefaultDevice());
      return *this;
    }

  protected:
    typename XprType::Nested m_xpr;
    const StartIndices m_startIndices;
    const StopIndices m_stopIndices;
    const Strides m_strides;
};

// Eval as rvalue
template<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>
struct TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
{
  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;
  static const int NumDims = internal::array_size<Strides>::value;

  enum {
    // Alignment can't be guaranteed at compile time since it depends on the
    // slice offsets and sizes.
    IsAligned = false,
    PacketAccess = false,
    BlockAccess = false,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    RawAccess = false
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
      : m_impl(op.expression(), device), m_device(device), m_strides(op.strides())
  {
    // Handle degenerate intervals by gracefully clamping and allowing m_dimensions to be zero
    DSizes<Index,NumDims> startIndicesClamped, stopIndicesClamped;
    for (size_t i = 0; i < internal::array_size<Dimensions>::value; ++i) {
      eigen_assert(m_strides[i] != 0 && "0 stride is invalid");
      if(m_strides[i]>0){
        startIndicesClamped[i] = clamp(op.startIndices()[i], 0, m_impl.dimensions()[i]);
        stopIndicesClamped[i] = clamp(op.stopIndices()[i], 0, m_impl.dimensions()[i]);
      }else{
        /* implies m_strides[i]<0 by assert */
        startIndicesClamped[i] = clamp(op.startIndices()[i], -1, m_impl.dimensions()[i] - 1);
        stopIndicesClamped[i] = clamp(op.stopIndices()[i], -1, m_impl.dimensions()[i] - 1);
      }
      m_startIndices[i] = startIndicesClamped[i];
    }

    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();

    // check for degenerate intervals and compute output tensor shape
    bool degenerate = false;;
    for(int i = 0; i < NumDims; i++){
      Index interval = stopIndicesClamped[i] - startIndicesClamped[i];
      if(interval == 0 || ((interval<0) != (m_strides[i]<0))){
        m_dimensions[i] = 0;
        degenerate = true;
      }else{
        m_dimensions[i] = interval / m_strides[i]
                          + (interval % m_strides[i] != 0 ? 1 : 0);
        eigen_assert(m_dimensions[i] >= 0);
      }
    }
    Strides output_dims = m_dimensions;

    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_inputStrides[0] = m_strides[0];
      m_offsets[0] = startIndicesClamped[0];
      Index previousDimProduct = 1;
      for (int i = 1; i < NumDims; ++i) {
        previousDimProduct *= input_dims[i-1];
        m_inputStrides[i] = previousDimProduct * m_strides[i];
        m_offsets[i] = startIndicesClamped[i] * previousDimProduct;
      }

      // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.
      m_outputStrides[0] = 1;
      for (int i = 1; i < NumDims; ++i) {
        m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];
        // NOTE: if tensor is degenerate, we send 1 to prevent TensorIntDivisor constructor crash
        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(degenerate ? 1 : m_outputStrides[i]);
      }
    } else {
      m_inputStrides[NumDims-1] = m_strides[NumDims-1];
      m_offsets[NumDims-1] = startIndicesClamped[NumDims-1];
      Index previousDimProduct = 1;
      for (int i = NumDims - 2; i >= 0; --i) {
        previousDimProduct *= input_dims[i+1];
        m_inputStrides[i] = previousDimProduct * m_strides[i];
        m_offsets[i] = startIndicesClamped[i] * previousDimProduct;
      }

      m_outputStrides[NumDims-1] = 1;
      for (int i = NumDims - 2; i >= 0; --i) {
        m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];
        // NOTE: if tensor is degenerate, we send 1 to prevent TensorIntDivisor constructor crash
        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(degenerate ? 1 : m_outputStrides[i]);
      }
    }
    m_block_total_size_max = numext::maxi(static_cast<std::size_t>(1),
                                          device.lastLevelCacheSize() /
                                          sizeof(Scalar));
  }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename internal::remove_const<Scalar>::type ScalarNonConst;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  typedef Strides Dimensions;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }


  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {
    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
  {
    return m_impl.coeff(srcCoeff(index));
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, NumDims);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar* data() const {
    return NULL;
  }

 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
  {
    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_fastOutputStrides[i];
        inputIndex += idx * m_inputStrides[i] + m_offsets[i];
        index -= idx * m_outputStrides[i];
      }
    } else {
      for (int i = 0; i < NumDims; ++i) {
        const Index idx = index / m_fastOutputStrides[i];
        inputIndex += idx * m_inputStrides[i] + m_offsets[i];
        index -= idx * m_outputStrides[i];
      }
    }
    return inputIndex;
  }

  static EIGEN_STRONG_INLINE Index clamp(Index value, Index min, Index max) {
    return numext::maxi(min, numext::mini(max,value));
  }

  array<Index, NumDims> m_outputStrides;
  array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;
  array<Index, NumDims> m_inputStrides;
  TensorEvaluator<ArgType, Device> m_impl;
  const Device& m_device;
  DSizes<Index, NumDims> m_startIndices; // clamped startIndices
  DSizes<Index, NumDims> m_dimensions;
  DSizes<Index, NumDims> m_offsets; // offset in a flattened shape
  const Strides m_strides;
  std::size_t m_block_total_size_max;
};

// Eval as lvalue
template<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>
struct TensorEvaluator<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
  : public TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
{
  typedef TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device> Base;
  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;
  static const int NumDims = internal::array_size<Strides>::value;

  enum {
    IsAligned = false,
    PacketAccess = false,
    BlockAccess = false,
    Layout = TensorEvaluator<ArgType, Device>::Layout,
    CoordAccess = TensorEvaluator<ArgType, Device>::CoordAccess,
    RawAccess = false
  };

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
    : Base(op, device)
    { }

  typedef typename XprType::Index Index;
  typedef typename XprType::Scalar Scalar;
  typedef typename internal::remove_const<Scalar>::type ScalarNonConst;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  typedef Strides Dimensions;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
  {
    return this->m_impl.coeffRef(this->srcCoeff(index));
  }
};


} // end namespace Eigen

#endif // EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H