TensorPadding.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_PADDING_H
#define EIGEN_CXX11_TENSOR_TENSOR_PADDING_H

namespace Eigen {

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 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::NumTraits<Scalar>::Real RealScalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  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;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;

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

  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())
  {
    // The padding op doesn't change the rank of the tensor. Directly padding a scalar would lead
    // to a vector, which doesn't make sense. Instead one should reshape the scalar into a vector
    // of 1 element first and then pad.
    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);

    // 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_inputStrides[0] = 1;
      m_outputStrides[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_inputStrides[NumDims - 1] = 1;
      m_outputStrides[NumDims] = 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];
    }
  }

  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 (isPaddingAtIndexForDim(idx, i)) {
          return m_paddingValue;
        }
        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
        index -= idx * m_outputStrides[i];
      }
      if (isPaddingAtIndexForDim(index, 0)) {
        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 (isPaddingAtIndexForDim(idx, i)) {
          return m_paddingValue;
        }
        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
        index -= idx * m_outputStrides[i+1];
      }
      if (isPaddingAtIndexForDim(index, NumDims-1)) {
        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 TensorOpCost costPerCoeff(bool vectorized) const {
    TensorOpCost cost = m_impl.costPerCoeff(vectorized);
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      for (int i = 0; i < NumDims; ++i)
        updateCostPerDimension(cost, i, i == 0);
    } else {
      for (int i = NumDims - 1; i >= 0; --i)
        updateCostPerDimension(cost, i, i == NumDims - 1);
    }
    return cost;
  }

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

 private:
  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isPaddingAtIndexForDim(
      Index index, int dim_index) const {
#if defined(EIGEN_HAS_INDEX_LIST)
    return (!internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0) &&
            index < m_padding[dim_index].first) ||
        (!internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0) &&
         index >= m_dimensions[dim_index] - m_padding[dim_index].second);
#else
    return (index < m_padding[dim_index].first) ||
           (index >= m_dimensions[dim_index] - m_padding[dim_index].second);
#endif
  }

  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isLeftPaddingCompileTimeZero(
      int dim_index) const {
#if defined(EIGEN_HAS_INDEX_LIST)
    return internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0);
#else
    EIGEN_UNUSED_VARIABLE(dim_index);
    return false;
#endif
  }

  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isRightPaddingCompileTimeZero(
      int dim_index) const {
#if defined(EIGEN_HAS_INDEX_LIST)
    return internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0);
#else
    EIGEN_UNUSED_VARIABLE(dim_index);
    return false;
#endif
  }


  void updateCostPerDimension(TensorOpCost& cost, int i, bool first) const {
    const double in = static_cast<double>(m_impl.dimensions()[i]);
    const double out = in + m_padding[i].first + m_padding[i].second;
    if (out == 0)
      return;
    const double reduction = in / out;
    cost *= reduction;
    if (first) {
      cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +
                    reduction * (1 * TensorOpCost::AddCost<Index>()));
    } else {
      cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +
                                 2 * TensorOpCost::MulCost<Index>() +
                    reduction * (2 * TensorOpCost::MulCost<Index>() +
                                 1 * TensorOpCost::DivCost<Index>()));
    }
  }

 protected:

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const
  {
    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 (!isLeftPaddingCompileTimeZero(i) && last < lastPaddedLeft) {
        // all the coefficient are in the padding zone.
        return internal::pset1<PacketReturnType>(m_paddingValue);
      }
      else if (!isRightPaddingCompileTimeZero(i) && first >= firstPaddedRight && last < lastPaddedRight) {
        // all the coefficient are in the padding zone.
        return internal::pset1<PacketReturnType>(m_paddingValue);
      }
      else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (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;
    const Index lastPaddedLeft = m_padding[0].first;
    const Index firstPaddedRight = (m_dimensions[0] - m_padding[0].second);
    const Index lastPaddedRight = m_outputStrides[1];

    if (!isLeftPaddingCompileTimeZero(0) && last < lastPaddedLeft) {
      // all the coefficient are in the padding zone.
      return internal::pset1<PacketReturnType>(m_paddingValue);
    }
    else if (!isRightPaddingCompileTimeZero(0) && first >= firstPaddedRight && last < lastPaddedRight) {
      // all the coefficient are in the padding zone.
      return internal::pset1<PacketReturnType>(m_paddingValue);
    }
    else if ((isLeftPaddingCompileTimeZero(0) && isRightPaddingCompileTimeZero(0)) || (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
  {
    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 (!isLeftPaddingCompileTimeZero(i) && last < lastPaddedLeft) {
        // all the coefficient are in the padding zone.
        return internal::pset1<PacketReturnType>(m_paddingValue);
      }
      else if (!isRightPaddingCompileTimeZero(i) && first >= firstPaddedRight && last < lastPaddedRight) {
        // all the coefficient are in the padding zone.
        return internal::pset1<PacketReturnType>(m_paddingValue);
      }
      else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (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;
    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 (!isLeftPaddingCompileTimeZero(NumDims-1) && last < lastPaddedLeft) {
      // all the coefficient are in the padding zone.
      return internal::pset1<PacketReturnType>(m_paddingValue);
    }
    else if (!isRightPaddingCompileTimeZero(NumDims-1) && first >= firstPaddedRight && last < lastPaddedRight) {
      // all the coefficient are in the padding zone.
      return internal::pset1<PacketReturnType>(m_paddingValue);
    }
    else if ((isLeftPaddingCompileTimeZero(NumDims-1) && isRightPaddingCompileTimeZero(NumDims-1)) || (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
  {
    EIGEN_ALIGN_MAX 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