contrib/Eigen/src/Tensor/TensorChipping.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/.
// SPDX-License-Identifier: MPL-2.0

#ifndef EIGEN_TENSOR_TENSOR_CHIPPING_H
#define EIGEN_TENSOR_TENSOR_CHIPPING_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {
template <DenseIndex DimId, typename XprType>
struct traits<TensorChippingOp<DimId, XprType> > : public traits<XprType> {
  typedef typename XprType::Scalar Scalar;
  typedef traits<XprType> XprTraits;
  typedef typename XprTraits::StorageKind StorageKind;
  typedef typename XprTraits::Index Index;
  static constexpr int NumDimensions = XprTraits::NumDimensions - 1;
  static constexpr int Layout = XprTraits::Layout;
  typedef typename XprTraits::PointerType PointerType;
};

template <DenseIndex DimId, typename XprType>
struct eval<TensorChippingOp<DimId, XprType>, Eigen::Dense> {
  typedef const TensorChippingOp<DimId, XprType> EIGEN_DEVICE_REF type;
};

template <DenseIndex DimId>
struct DimensionId {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) {
    EIGEN_UNUSED_VARIABLE(dim);
    eigen_assert(dim == DimId);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const { return DimId; }
};
template <>
struct DimensionId<Dynamic> {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) : actual_dim(dim) { eigen_assert(dim >= 0); }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const { return actual_dim; }

 private:
  const DenseIndex actual_dim;
};

template <typename EvalT, typename PacketT, typename IndexType, typename = void>
struct chipping_has_partial_packet : bool_constant<false> {};

template <typename EvalT, typename PacketT, typename IndexType>
struct chipping_has_partial_packet<
    EvalT, PacketT, IndexType,
    void_t<decltype(std::declval<const EvalT>().template partialPacket<PacketT>(
        std::declval<IndexType>(), std::declval<typename unpacket_traits<PacketT>::mask_t>()))>>
    : bool_constant<unpacket_traits<PacketT>::masked_load_available &&
                    std::is_same<PacketT, decltype(std::declval<const EvalT>().template partialPacket<PacketT>(
                                              std::declval<IndexType>(),
                                              std::declval<typename unpacket_traits<PacketT>::mask_t>()))>::value> {};

template <typename EvalT, typename PacketT, typename IndexType,
          bool HasPartial = chipping_has_partial_packet<EvalT, PacketT, IndexType>::value>
struct chipping_forward_partial_packet {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const EvalT& impl, IndexType index,
                                                           typename unpacket_traits<PacketT>::mask_t umask) {
    return impl.template partialPacket<PacketT>(index, umask);
  }
};

template <typename EvalT, typename PacketT, typename IndexType>
struct chipping_forward_partial_packet<EvalT, PacketT, IndexType, false> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const EvalT&, IndexType,
                                                           typename unpacket_traits<PacketT>::mask_t) {
    eigen_assert(false && "unreachable");
    return pset1<PacketT>(typename unpacket_traits<PacketT>::type(0));
  }
};

template <typename EvalT, int LoadMode, typename PacketT, typename IndexType, typename = void>
struct chipping_has_packet_t : bool_constant<false> {};

template <typename EvalT, int LoadMode, typename PacketT, typename IndexType>
struct chipping_has_packet_t<
    EvalT, LoadMode, PacketT, IndexType,
    void_t<decltype(std::declval<const EvalT>().template packet<LoadMode, PacketT>(std::declval<IndexType>()))>>
    : bool_constant<std::is_same<PacketT, decltype(std::declval<const EvalT>().template packet<LoadMode, PacketT>(
                                              std::declval<IndexType>()))>::value> {};

template <int LoadMode, typename PacketT, typename ArgEvaluator,
          bool SamePacket = std::is_same<PacketT, typename ArgEvaluator::PacketReturnType>::value,
          bool HasPacketT = chipping_has_packet_t<ArgEvaluator, LoadMode, PacketT, typename ArgEvaluator::Index>::value,
          bool IsRawPointer = std::is_convertible<
              typename ArgEvaluator::EvaluatorPointerType,
              const std::remove_const_t<std::remove_reference_t<typename ArgEvaluator::CoeffReturnType>>*>::value>
struct chipping_packet_load {
  using Index = typename ArgEvaluator::Index;
  using Scalar = std::remove_const_t<std::remove_reference_t<typename ArgEvaluator::CoeffReturnType>>;
  static constexpr int kSize = unpacket_traits<PacketT>::size;

  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const ArgEvaluator& impl, Index index) {
    EIGEN_ALIGN_TO_BOUNDARY(unpacket_traits<PacketT>::alignment) Scalar values[kSize];
    EIGEN_UNROLL_LOOP
    for (int i = 0; i < kSize; ++i) {
      values[i] = impl.coeff(index + i);
    }
    return pload<PacketT>(values);
  }
};

template <int LoadMode, typename PacketT, typename ArgEvaluator, bool HasPacketT, bool IsRawPointer>
struct chipping_packet_load<LoadMode, PacketT, ArgEvaluator, true, HasPacketT, IsRawPointer> {
  using Index = typename ArgEvaluator::Index;

  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const ArgEvaluator& impl, Index index) {
    return impl.template packet<LoadMode>(index);
  }
};

template <int LoadMode, typename PacketT, typename ArgEvaluator, bool IsRawPointer>
struct chipping_packet_load<LoadMode, PacketT, ArgEvaluator, false, true, IsRawPointer> {
  using Index = typename ArgEvaluator::Index;

  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const ArgEvaluator& impl, Index index) {
    return impl.template packet<LoadMode, PacketT>(index);
  }
};

template <int LoadMode, typename PacketT, typename ArgEvaluator>
struct chipping_packet_load<LoadMode, PacketT, ArgEvaluator, false, false, true> {
  using Index = typename ArgEvaluator::Index;
  using Scalar = std::remove_const_t<std::remove_reference_t<typename ArgEvaluator::CoeffReturnType>>;

  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketT run(const ArgEvaluator& impl, Index index) {
    const Scalar* src_ptr = impl.data();
    EIGEN_IF_CONSTEXPR (!static_cast<bool>(ArgEvaluator::RawAccess)) {
      if (src_ptr == nullptr) {
        return chipping_packet_load<LoadMode, PacketT, ArgEvaluator, false, false, false>::run(impl, index);
      }
    }
    return ploadt_ro<PacketT, Unaligned>(src_ptr + index);
  }
};

}  // end namespace internal

/** A chip is a thin slice, corresponding to a column or a row in a 2-d tensor.
 * \ingroup Tensor_Module
 */
template <DenseIndex DimId, typename XprType>
class TensorChippingOp : public TensorBase<TensorChippingOp<DimId, XprType> > {
 public:
  typedef TensorBase<TensorChippingOp<DimId, XprType> > Base;
  typedef typename Eigen::internal::traits<TensorChippingOp>::Scalar Scalar;
  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename Eigen::internal::ref_selector<TensorChippingOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorChippingOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorChippingOp>::Index Index;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorChippingOp(const XprType& expr, const Index offset, const Index dim)
      : m_xpr(expr), m_offset(offset), m_dim(dim) {
    eigen_assert(dim < XprType::NumDimensions && dim >= 0 && "Chip_Dim_out_of_range");
  }

  EIGEN_DEVICE_FUNC const Index offset() const { return m_offset; }
  EIGEN_DEVICE_FUNC const Index dim() const { return m_dim.actualDim(); }

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

  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TensorChippingOp)

 protected:
  typename XprType::Nested m_xpr;
  const Index m_offset;
  const internal::DimensionId<DimId> m_dim;
};

// Eval as rvalue
template <DenseIndex DimId, typename ArgType, typename Device>
struct TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device> {
  typedef TensorChippingOp<DimId, ArgType> XprType;
  static constexpr int NumInputDims =
      internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
  static constexpr int NumDims = NumInputDims - 1;
  typedef typename XprType::Index Index;
  typedef DSizes<Index, NumDims> Dimensions;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
  typedef StorageMemory<CoeffReturnType, Device> Storage;
  typedef typename Storage::Type EvaluatorPointerType;
  static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;

  enum {
    // Alignment can't be guaranteed at compile time since it depends on the
    // slice offsets.
    IsAligned = false,
    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
    BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
    // Chipping of outer-most dimension is a trivial operation, because we can
    // read and write directly from the underlying tensor using a single offset.
    IsOuterChipping = (Layout == ColMajor && DimId == NumInputDims - 1) || (Layout == RowMajor && DimId == 0),
    // Chipping inner-most dimension.
    IsInnerChipping = (Layout == ColMajor && DimId == 0) || (Layout == RowMajor && DimId == NumInputDims - 1),
    // Prefer block access if the underlying expression prefers it, otherwise
    // only if chipping is not trivial.
    PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess || !IsOuterChipping,
    CoordAccess = false,  // to be implemented
    RawAccess = false
  };

  typedef std::remove_const_t<Scalar> ScalarNoConst;

  //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
  typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
  typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;

  typedef internal::TensorBlockDescriptor<NumInputDims, Index> ArgTensorBlockDesc;
  typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock ArgTensorBlock;

  typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims, Layout, Index> TensorBlock;
  //===--------------------------------------------------------------------===//

  EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
      : m_impl(op.expression(), device), m_dim(op.dim()), m_device(device) {
    EIGEN_STATIC_ASSERT((NumInputDims >= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);

    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
    eigen_assert(NumInputDims > m_dim.actualDim() && op.offset() < input_dims[m_dim.actualDim()]);

    int j = 0;
    for (int i = 0; i < NumInputDims; ++i) {
      if (i != m_dim.actualDim()) {
        m_dimensions[j] = input_dims[i];
        ++j;
      }
    }

    m_stride = 1;
    m_inputStride = 1;
    EIGEN_IF_CONSTEXPR (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      for (int i = 0; i < m_dim.actualDim(); ++i) {
        m_stride *= input_dims[i];
        m_inputStride *= input_dims[i];
      }
    } else {
      for (int i = NumInputDims - 1; i > m_dim.actualDim(); --i) {
        m_stride *= input_dims[i];
        m_inputStride *= input_dims[i];
      }
    }
    m_inputStride *= input_dims[m_dim.actualDim()];
    m_inputOffset = m_stride * op.offset();

    // Check if chipping is effectively inner or outer: product of dimensions
    // before or after the chipped dimension is `1`, or the chipped dimension itself has size `1`.
    Index after_chipped_dim_product = 1;
    for (int i = static_cast<int>(m_dim.actualDim()) + 1; i < NumInputDims; ++i) {
      after_chipped_dim_product *= input_dims[i];
    }

    Index before_chipped_dim_product = 1;
    for (int i = 0; i < m_dim.actualDim(); ++i) {
      before_chipped_dim_product *= input_dims[i];
    }

    const bool is_trivial_chip_dim = input_dims[m_dim.actualDim()] == 1;
    EIGEN_IF_CONSTEXPR (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      m_isEffectivelyInnerChipping = (before_chipped_dim_product == 1) && !is_trivial_chip_dim;
      m_isEffectivelyOuterChipping = (after_chipped_dim_product == 1) || is_trivial_chip_dim;
    } else {
      m_isEffectivelyInnerChipping = (after_chipped_dim_product == 1) && !is_trivial_chip_dim;
      m_isEffectivelyOuterChipping = (before_chipped_dim_product == 1) || is_trivial_chip_dim;
    }
  }

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

  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
    m_impl.evalSubExprsIfNeeded(nullptr);
    return true;
  }

#ifdef EIGEN_USE_THREADS
  template <typename EvalSubExprsCallback>
  EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(EvaluatorPointerType /*data*/, EvalSubExprsCallback done) {
    m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
  }
#endif  // EIGEN_USE_THREADS

  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, typename PacketReturnTypeT = PacketReturnType>
  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnTypeT packet(Index index) const {
    constexpr int RequestedPacketSize = internal::unpacket_traits<PacketReturnTypeT>::size;
    EIGEN_STATIC_ASSERT((RequestedPacketSize <= PacketSize), YOU_MADE_A_PROGRAMMING_MISTAKE);
    eigen_assert(index >= 0 && index + RequestedPacketSize - 1 < dimensions().TotalSize());

    EIGEN_IF_CONSTEXPR (IsInnerChipping) {
      return packetInnerChipping<LoadMode, PacketReturnTypeT>(index);
    } else EIGEN_IF_CONSTEXPR (IsOuterChipping) {
      return packetOuterChipping<LoadMode, PacketReturnTypeT>(index);
    } else if (m_isEffectivelyInnerChipping) {
      // index * m_inputStride is linear in the caller's loop index; keep clang-19+ LSR
      // from hoisting per-lane induction variables across this runtime branch.
      Index opaqueIndex = index;
#if EIGEN_COMP_CLANG >= 1900 && !defined(__apple_build_version__) && !defined(EIGEN_GPU_COMPILE_PHASE) && \
    !defined(EIGEN_SYCL_DEVICE_ONLY)
      __asm__("" : "+r"(opaqueIndex));
#endif
      return packetInnerChipping<LoadMode, PacketReturnTypeT>(opaqueIndex);
    } else if (m_isEffectivelyOuterChipping) {
      return packetOuterChipping<LoadMode, PacketReturnTypeT>(index);
    } else {
      const Index idx = index / m_stride;
      const Index rem = index - idx * m_stride;
      Index inputIndex = idx * m_inputStride + m_inputOffset + rem;
      if (EIGEN_PREDICT_TRUE(rem + RequestedPacketSize <= m_stride)) {
        return internal::chipping_packet_load<LoadMode, PacketReturnTypeT, TensorEvaluator<ArgType, Device>>::run(
            m_impl, inputIndex);
      } else {
        EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnTypeT>::alignment)
        std::remove_const_t<CoeffReturnType> values[RequestedPacketSize];
        const Index strideDelta = m_inputStride - m_stride;
        Index lane_in_slice = rem;
        EIGEN_UNROLL_LOOP
        for (int i = 0; i < RequestedPacketSize; ++i) {
          values[i] = m_impl.coeff(inputIndex);
          ++inputIndex;
          if (++lane_in_slice == m_stride) {
            lane_in_slice = 0;
            inputIndex += strideDelta;
          }
        }
        return internal::pload<PacketReturnTypeT>(values);
      }
    }
  }

  template <
      typename PacketReturnTypeT,
      std::enable_if_t<PacketAccess && internal::unpacket_traits<PacketReturnTypeT>::masked_load_available, int> = 0>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnTypeT
  partialPacket(Index index, typename internal::unpacket_traits<PacketReturnTypeT>::mask_t umask) const {
    using MaskT = typename internal::unpacket_traits<PacketReturnTypeT>::mask_t;
    using RawCoeffType = std::remove_const_t<CoeffReturnType>;
    using ArgEval = TensorEvaluator<ArgType, Device>;
    constexpr int RequestedPacketSize = internal::unpacket_traits<PacketReturnTypeT>::size;
    constexpr int kMaskBits = static_cast<int>(CHAR_BIT * sizeof(MaskT));
    constexpr bool kHasImplPartial = internal::chipping_has_partial_packet<ArgEval, PacketReturnTypeT, Index>::value;

    EIGEN_IF_CONSTEXPR (RequestedPacketSize < kMaskBits) {
      umask &= static_cast<MaskT>((MaskT(1) << (RequestedPacketSize < kMaskBits ? RequestedPacketSize : 0)) - 1);
    }
    if (umask == 0) {
      return internal::pset1<PacketReturnTypeT>(CoeffReturnType(0));
    }

    const Index first_lane = static_cast<Index>(internal::ctz(umask));
    const Index last_lane = static_cast<Index>(kMaskBits - 1 - internal::clz(umask));
    const Index active_start = index + first_lane;
    const Index active_count = last_lane - first_lane + 1;
    eigen_assert(active_start >= 0 && active_start + active_count - 1 < dimensions().TotalSize());

    if (isOuterChipping()) {
      const Index target_index = index + m_inputOffset;
      if (kHasImplPartial && EIGEN_PREDICT_TRUE(target_index >= 0)) {
        return internal::chipping_forward_partial_packet<ArgEval, PacketReturnTypeT, Index>::run(m_impl, target_index,
                                                                                                 umask);
      }
      EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnTypeT>::alignment)
      RawCoeffType values[RequestedPacketSize];
      EIGEN_UNROLL_LOOP
      for (int i = 0; i < RequestedPacketSize; ++i) {
        values[i] = RawCoeffType(0);
      }
      const Index srcOffset = srcCoeffOuterChipping(active_start);
      for (Index lane = first_lane; lane <= last_lane; ++lane) {
        if ((umask >> lane) & MaskT(1)) {
          values[lane] = m_impl.coeff(srcOffset + (lane - first_lane));
        }
      }
      return internal::pload<PacketReturnTypeT>(values);
    }

    if (isInnerChipping()) {
      EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnTypeT>::alignment)
      RawCoeffType values[RequestedPacketSize];
      EIGEN_UNROLL_LOOP
      for (int i = 0; i < RequestedPacketSize; ++i) {
        values[i] = RawCoeffType(0);
      }
      Index inputIndex = srcCoeffInnerChipping(active_start);
      for (Index lane = first_lane; lane <= last_lane; ++lane) {
        if ((umask >> lane) & MaskT(1)) {
          values[lane] = m_impl.coeff(inputIndex);
        }
        inputIndex += m_inputStride;
      }
      return internal::pload<PacketReturnTypeT>(values);
    }

    const Index idx = active_start / m_stride;
    const Index rem = active_start - idx * m_stride;
    const Index sliceBase = idx * m_inputStride + m_inputOffset;
    if (EIGEN_PREDICT_TRUE(rem + active_count <= m_stride)) {
      const Index target_index = sliceBase + rem - first_lane;
      if (kHasImplPartial && EIGEN_PREDICT_TRUE(target_index >= 0)) {
        return internal::chipping_forward_partial_packet<ArgEval, PacketReturnTypeT, Index>::run(m_impl, target_index,
                                                                                                 umask);
      }
    }

    EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnTypeT>::alignment)
    RawCoeffType values[RequestedPacketSize];
    EIGEN_UNROLL_LOOP
    for (int i = 0; i < RequestedPacketSize; ++i) {
      values[i] = RawCoeffType(0);
    }
    const Index strideDelta = m_inputStride - m_stride;
    Index inputIndex = sliceBase + rem;
    Index lane_in_slice = rem;
    for (Index lane = first_lane; lane <= last_lane; ++lane) {
      if ((umask >> lane) & MaskT(1)) {
        values[lane] = m_impl.coeff(inputIndex);
      }
      ++inputIndex;
      if (++lane_in_slice == m_stride) {
        lane_in_slice = 0;
        inputIndex += strideDelta;
      }
    }
    return internal::pload<PacketReturnTypeT>(values);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    double cost = 0;
    if (isOuterChipping()) {
      cost += TensorOpCost::AddCost<Index>();
    } else if (isInnerChipping()) {
      cost += TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();
    } else {
      cost += 3 * TensorOpCost::MulCost<Index>() + TensorOpCost::DivCost<Index>() + 3 * TensorOpCost::AddCost<Index>();
    }

    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, cost, vectorized, PacketSize);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::TensorBlockResourceRequirements getResourceRequirements() const {
    const size_t target_size = m_device.lastLevelCacheSize();
    return internal::TensorBlockResourceRequirements::merge(
        internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size), m_impl.getResourceRequirements());
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
                                                          bool root_of_expr_ast = false) const {
    const Index chip_dim = m_dim.actualDim();

    DSizes<Index, NumInputDims> input_block_dims;
    input_block_dims[chip_dim] = 1;
    for (int i = 0; i < NumDims; ++i) {
      input_block_dims[i < chip_dim ? i : i + 1] = desc.dimension(i);
    }

    ArgTensorBlockDesc arg_desc(srcCoeff(desc.offset()), input_block_dims);

    // Try to reuse destination buffer for materializing argument block.
    if (desc.HasDestinationBuffer()) {
      DSizes<Index, NumInputDims> arg_destination_strides;
      arg_destination_strides[chip_dim] = 0;  // The size-one chipped dimension does not use its stride.
      for (int i = 0; i < NumDims; ++i) {
        arg_destination_strides[i < chip_dim ? i : i + 1] = desc.destination().strides()[i];
      }

      arg_desc.template AddDestinationBuffer<Layout>(desc.destination().template data<ScalarNoConst>(),
                                                     arg_destination_strides);
    }

    ArgTensorBlock arg_block = m_impl.block(arg_desc, scratch, root_of_expr_ast);
    if (!arg_desc.HasDestinationBuffer()) desc.DropDestinationBuffer();

    if (arg_block.data() != nullptr) {
      // Forward argument block buffer if possible.
      return TensorBlock(arg_block.kind(), arg_block.data(), desc.dimensions());

    } else {
      // Assign argument block expression to a buffer.

      // Prepare storage for the materialized chipping result.
      const typename TensorBlock::Storage block_storage = TensorBlock::prepareStorage(desc, scratch);

      typedef internal::TensorBlockAssignment<ScalarNoConst, NumInputDims, typename ArgTensorBlock::XprType, Index>
          TensorBlockAssignment;

      TensorBlockAssignment::Run(
          TensorBlockAssignment::target(arg_desc.dimensions(), internal::strides<Layout>(arg_desc.dimensions()),
                                        block_storage.data()),
          arg_block.expr());

      return block_storage.AsTensorMaterializedBlock();
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Storage::Type data() const {
    typename Storage::Type result = constCast(m_impl.data());
    if (isOuterChipping() && result) {
      return result + m_inputOffset;
    } else {
      return nullptr;
    }
  }

 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const {
    EIGEN_IF_CONSTEXPR (IsInnerChipping) {
      return srcCoeffInnerChipping(index);
    } else EIGEN_IF_CONSTEXPR (IsOuterChipping) {
      return srcCoeffOuterChipping(index);
    } else if (m_isEffectivelyInnerChipping) {
      return srcCoeffInnerChipping(index);
    } else if (m_isEffectivelyOuterChipping) {
      return srcCoeffOuterChipping(index);
    } else {
      const Index idx = index / m_stride;
      Index inputIndex = idx * m_inputStride + m_inputOffset;
      index -= idx * m_stride;
      inputIndex += index;
      return inputIndex;
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeffInnerChipping(Index index) const {
    // m_stride is equal to 1, so let's avoid the integer division.
    eigen_assert(m_stride == 1);
    return index * m_inputStride + m_inputOffset;
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeffOuterChipping(Index index) const {
    // m_stride > index (or m_stride == m_inputStride when chipped dim has size 1).
    eigen_assert(m_stride > index || m_stride == m_inputStride);
    return index + m_inputOffset;
  }

  template <int LoadMode, typename PacketReturnTypeT = PacketReturnType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnTypeT packetInnerChipping(Index index) const {
    constexpr int RequestedPacketSize = internal::unpacket_traits<PacketReturnTypeT>::size;
    EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnTypeT>::alignment)
    std::remove_const_t<CoeffReturnType> values[RequestedPacketSize];
    Index inputIndex = srcCoeffInnerChipping(index);
    EIGEN_UNROLL_LOOP
    for (int i = 0; i < RequestedPacketSize; ++i) {
      values[i] = m_impl.coeff(inputIndex);
      inputIndex += m_inputStride;
    }
    return internal::pload<PacketReturnTypeT>(values);
  }

  template <int LoadMode, typename PacketReturnTypeT = PacketReturnType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnTypeT packetOuterChipping(Index index) const {
    return internal::chipping_packet_load<LoadMode, PacketReturnTypeT, TensorEvaluator<ArgType, Device>>::run(
        m_impl, srcCoeffOuterChipping(index));
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool isInnerChipping() const {
    return IsInnerChipping || m_isEffectivelyInnerChipping;
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool isOuterChipping() const {
    return IsOuterChipping || m_isEffectivelyOuterChipping;
  }

  Dimensions m_dimensions;
  Index m_stride;
  Index m_inputOffset;
  Index m_inputStride;
  TensorEvaluator<ArgType, Device> m_impl;
  const internal::DimensionId<DimId> m_dim;
  const Device EIGEN_DEVICE_REF m_device;

  // If product of all dimensions after or before the chipped dimension is `1`,
  // or the chipped dimension itself has size `1`, it is effectively the same
  // as chipping innermost or outermost dimension.
  bool m_isEffectivelyInnerChipping;
  bool m_isEffectivelyOuterChipping;
};

// Eval as lvalue
template <DenseIndex DimId, typename ArgType, typename Device>
struct TensorEvaluator<TensorChippingOp<DimId, ArgType>, Device>
    : public TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device> {
  typedef TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device> Base;
  typedef TensorChippingOp<DimId, ArgType> XprType;
  static constexpr int NumInputDims =
      internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
  static constexpr int NumDims = NumInputDims - 1;
  typedef typename XprType::Index Index;
  typedef DSizes<Index, NumDims> Dimensions;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;

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

  //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
  typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
  //===--------------------------------------------------------------------===//

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

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index) const {
    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 {
    EIGEN_IF_CONSTEXPR (Base::IsInnerChipping) {
      writePacketInnerChipping<StoreMode>(index, x);
    } else EIGEN_IF_CONSTEXPR (Base::IsOuterChipping) {
      writePacketOuterChipping<StoreMode>(index, x);
    } else if (this->m_isEffectivelyInnerChipping) {
      writePacketInnerChipping<StoreMode>(index, x);
    } else if (this->m_isEffectivelyOuterChipping) {
      writePacketOuterChipping<StoreMode>(index, x);
    } else {
      const Index idx = index / this->m_stride;
      const Index rem = index - idx * this->m_stride;
      Index inputIndex = idx * this->m_inputStride + this->m_inputOffset + rem;
      if (EIGEN_PREDICT_TRUE(rem + PacketSize <= this->m_stride)) {
        this->m_impl.template writePacket<StoreMode>(inputIndex, x);
      } else {
        EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnType>::alignment)
        std::remove_const_t<CoeffReturnType> values[PacketSize];
        internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
        const Index strideDelta = this->m_inputStride - this->m_stride;
        Index lane_in_slice = rem;
        EIGEN_UNROLL_LOOP
        for (int i = 0; i < PacketSize; ++i) {
          this->m_impl.coeffRef(inputIndex) = values[i];
          ++inputIndex;
          if (++lane_in_slice == this->m_stride) {
            lane_in_slice = 0;
            inputIndex += strideDelta;
          }
        }
      }
    }
  }

  template <typename TensorBlock>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(const TensorBlockDesc& desc, const TensorBlock& block) {
    eigen_assert(this->m_impl.data() != nullptr);

    const Index chip_dim = this->m_dim.actualDim();

    DSizes<Index, NumInputDims> input_block_dims;
    input_block_dims[chip_dim] = 1;
    for (int i = 0; i < NumDims; ++i) {
      input_block_dims[i < chip_dim ? i : i + 1] = desc.dimension(i);
    }

    typedef TensorReshapingOp<const DSizes<Index, NumInputDims>, const typename TensorBlock::XprType> TensorBlockExpr;

    typedef internal::TensorBlockAssignment<Scalar, NumInputDims, TensorBlockExpr, Index> TensorBlockAssign;

    TensorBlockAssign::Run(
        TensorBlockAssign::target(input_block_dims, internal::strides<Layout>(this->m_impl.dimensions()),
                                  this->m_impl.data(), this->srcCoeff(desc.offset())),
        block.expr().reshape(input_block_dims));
  }

 private:
  template <int StoreMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacketInnerChipping(Index index, const PacketReturnType& x) const {
    EIGEN_ALIGN_TO_BOUNDARY(internal::unpacket_traits<PacketReturnType>::alignment)
    std::remove_const_t<CoeffReturnType> values[PacketSize];
    internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
    Index inputIndex = this->srcCoeffInnerChipping(index);
    EIGEN_UNROLL_LOOP
    for (int i = 0; i < PacketSize; ++i) {
      this->m_impl.coeffRef(inputIndex) = values[i];
      inputIndex += this->m_inputStride;
    }
  }

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

}  // end namespace Eigen

#endif  // EIGEN_TENSOR_TENSOR_CHIPPING_H