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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Eric Martin <eric@ericmart.in>
+//
+// 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_CONTRACTION_MAPPERS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPERS_H
+
+// NOTE: The file has strong column major bias/assumptions, which is pointed out
+// in comments. As of right now, this code will only work the column major packing
+// routines.
+
+/*
+ * A tensor contraction can be represented by a matrix multiplication. We don't
+ * want to actually reshape the tensor into a matrix (because this involves a
+ * full copy of the tensor), so the reshaping operation is implicit in a sense.
+ * This means we need a collection of methods take a matrix index and return
+ * the element of the tensor that would be at that index if we were to actually
+ * reshape the matrix. This file consists of these methods.
+ */
+
+namespace Eigen {
+namespace internal {
+
+enum {
+ Rhs = 0,
+ Lhs = 1,
+};
+
+/*
+ * Used to lookup the tensor index when working with the left and right
+ * arguments to a tensor contraction.
+ */
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ size_t packet_size, bool inner_dim_contiguous>
+class SimpleTensorContractionMapper {
+ public:
+ EIGEN_DEVICE_FUNC
+ SimpleTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ m_tensor(tensor),
+ m_nocontract_strides(nocontract_strides),
+ m_ij_strides(ij_strides),
+ m_contract_strides(contract_strides),
+ m_k_strides(k_strides) { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void prefetch(int i) { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar operator()(Index row) const {
+ // column major assumption
+ return operator()(row, 0);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar operator()(Index row, Index col) const {
+ return m_tensor.coeff(computeIndex(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index computeIndex(Index row, Index col) const {
+ const bool left = (side == Lhs);
+ Index nocontract_val = left ? row : col;
+ Index linidx = 0;
+ for (int i = array_size<nocontract_t>::value - 1; i > 0; i--) {
+ const Index idx = nocontract_val / m_ij_strides[i];
+ linidx += idx * m_nocontract_strides[i];
+ nocontract_val -= idx * m_ij_strides[i];
+ }
+ if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {
+ if (side == Lhs && inner_dim_contiguous) {
+ eigen_assert(m_nocontract_strides[0] == 1);
+ linidx += nocontract_val;
+ } else {
+ linidx += nocontract_val * m_nocontract_strides[0];
+ }
+ }
+
+ Index contract_val = left ? col : row;
+ for (int i = array_size<contract_t>::value - 1; i > 0; i--) {
+ const Index idx = contract_val / m_k_strides[i];
+ linidx += idx * m_contract_strides[i];
+ contract_val -= idx * m_k_strides[i];
+ }
+ EIGEN_STATIC_ASSERT(array_size<contract_t>::value > 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ if (side == Rhs && inner_dim_contiguous) {
+ eigen_assert(m_contract_strides[0] == 1);
+ linidx += contract_val;
+ } else {
+ linidx += contract_val * m_contract_strides[0];
+ }
+
+ return linidx;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE IndexPair<Index> computeIndexPair(Index row, Index col, const Index distance) const {
+ const bool left = (side == Lhs);
+ Index nocontract_val[2] = {left ? row : col, left ? row + distance : col};
+ Index linidx[2] = {0, 0};
+ for (int i = array_size<nocontract_t>::value - 1; i > 0; i--) {
+ const Index idx0 = nocontract_val[0] / m_ij_strides[i];
+ const Index idx1 = nocontract_val[1] / m_ij_strides[i];
+ linidx[0] += idx0 * m_nocontract_strides[i];
+ linidx[1] += idx1 * m_nocontract_strides[i];
+ nocontract_val[0] -= idx0 * m_ij_strides[i];
+ nocontract_val[1] -= idx1 * m_ij_strides[i];
+ }
+ if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {
+ if (side == Lhs && inner_dim_contiguous) {
+ eigen_assert(m_nocontract_strides[0] == 1);
+ linidx[0] += nocontract_val[0];
+ linidx[1] += nocontract_val[1];
+ } else {
+ linidx[0] += nocontract_val[0] * m_nocontract_strides[0];
+ linidx[1] += nocontract_val[1] * m_nocontract_strides[0];
+ }
+ }
+
+ Index contract_val[2] = {left ? col : row, left ? col : row + distance};
+ for (int i = array_size<contract_t>::value - 1; i > 0; i--) {
+ const Index idx0 = contract_val[0] / m_k_strides[i];
+ const Index idx1 = contract_val[1] / m_k_strides[i];
+ linidx[0] += idx0 * m_contract_strides[i];
+ linidx[1] += idx1 * m_contract_strides[i];
+ contract_val[0] -= idx0 * m_k_strides[i];
+ contract_val[1] -= idx1 * m_k_strides[i];
+ }
+ EIGEN_STATIC_ASSERT(array_size<contract_t>::value > 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ if (side == Rhs && inner_dim_contiguous) {
+ eigen_assert(m_contract_strides[0] == 1);
+ linidx[0] += contract_val[0];
+ linidx[1] += contract_val[1];
+ } else {
+ linidx[0] += contract_val[0] * m_contract_strides[0];
+ linidx[1] += contract_val[1] * m_contract_strides[0];
+ }
+ return IndexPair<Index>(linidx[0], linidx[1]);
+ }
+
+ Index firstAligned(Index size) const {
+ return size;
+ }
+ Index stride() const {
+ return 1;
+ }
+
+ protected:
+ const Tensor m_tensor;
+ const nocontract_t m_nocontract_strides;
+ const nocontract_t m_ij_strides;
+ const contract_t m_contract_strides;
+ const contract_t m_k_strides;
+};
+
+
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ size_t packet_size, bool inner_dim_contiguous,
+ bool inner_dim_reordered, int Alignment>
+ class BaseTensorContractionMapper : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous>
+{
+ public:
+ typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous> ParentMapper;
+
+ EIGEN_DEVICE_FUNC
+ BaseTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename packet_traits<Scalar>::half HalfPacket;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Packet loadPacket(Index i, Index j) const {
+ // whole method makes column major assumption
+
+ // don't need to add offsets for now (because operator handles that)
+ // current code assumes packet size must be a multiple of 2
+ EIGEN_STATIC_ASSERT(packet_size % 2 == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ if (Tensor::PacketAccess && inner_dim_contiguous && !inner_dim_reordered) {
+ const Index index = this->computeIndex(i, j);
+ eigen_assert(this->computeIndex(i+packet_size-1, j) == index + packet_size-1);
+ return this->m_tensor.template packet<Alignment>(index);
+ }
+
+ const IndexPair<Index> indexPair = this->computeIndexPair(i, j, packet_size - 1);
+ const Index first = indexPair.first;
+ const Index last = indexPair.second;
+
+ // We can always do optimized packet reads from left hand side right now, because
+ // the vertical matrix dimension on the left hand side is never contracting.
+ // On the right hand side we need to check if the contracting dimensions may have
+ // been shuffled first.
+ if (Tensor::PacketAccess &&
+ (side == Lhs || internal::array_size<contract_t>::value <= 1 || !inner_dim_reordered) &&
+ (last - first) == (packet_size - 1)) {
+
+ return this->m_tensor.template packet<Alignment>(first);
+ }
+
+ EIGEN_ALIGN_DEFAULT Scalar data[packet_size];
+
+ data[0] = this->m_tensor.coeff(first);
+ for (Index k = 1; k < packet_size - 1; k += 2) {
+ const IndexPair<Index> internal_pair = this->computeIndexPair(i + k, j, 1);
+ data[k] = this->m_tensor.coeff(internal_pair.first);
+ data[k + 1] = this->m_tensor.coeff(internal_pair.second);
+ }
+ data[packet_size - 1] = this->m_tensor.coeff(last);
+
+ return pload<Packet>(data);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {
+ // whole method makes column major assumption
+
+ // don't need to add offsets for now (because operator handles that)
+ const Index half_packet_size = unpacket_traits<HalfPacket>::size;
+ if (half_packet_size == packet_size) {
+ return loadPacket(i, j);
+ }
+ EIGEN_ALIGN_DEFAULT Scalar data[half_packet_size];
+ for (Index k = 0; k < half_packet_size; k++) {
+ data[k] = operator()(i + k, j);
+ }
+ return pload<HalfPacket>(data);
+ }
+};
+
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ bool inner_dim_contiguous,
+ bool inner_dim_reordered, int Alignment>
+class BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, inner_dim_reordered, Alignment> : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous>
+{
+ public:
+ typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous> ParentMapper;
+
+ EIGEN_DEVICE_FUNC
+ BaseTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Packet loadPacket(Index i, Index j) const {
+ EIGEN_ALIGN_DEFAULT Scalar data[1];
+ data[0] = this->m_tensor.coeff(this->computeIndex(i, j));
+ return pload<typename packet_traits<Scalar>::type>(data);
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Packet loadHalfPacket(Index i, Index j) const {
+ return loadPacket(i, j);
+ }
+};
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ size_t packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment>
+class TensorContractionInputMapper;
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ size_t packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment>
+class TensorContractionSubMapper {
+ public:
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename packet_traits<Scalar>::half HalfPacket;
+
+ typedef TensorContractionInputMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> ParentMapper;
+ typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> Self;
+ typedef Self LinearMapper;
+
+ EIGEN_DEVICE_FUNC TensorContractionSubMapper(const ParentMapper& base_mapper, Index vert_offset, Index horiz_offset)
+ : m_base_mapper(base_mapper), m_vert_offset(vert_offset), m_horiz_offset(horiz_offset) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
+ return m_base_mapper(i + m_vert_offset, m_horiz_offset);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i, Index j) const {
+ return m_base_mapper(i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {
+ return m_base_mapper.loadPacket(i + m_vert_offset, m_horiz_offset);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {
+ return m_base_mapper.loadPacket(i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {
+ return m_base_mapper.loadHalfPacket(i + m_vert_offset, m_horiz_offset);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, Packet p) const {
+ m_base_mapper.storePacket(i + m_vert_offset, m_horiz_offset, p);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+ return LinearMapper(m_base_mapper, i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ template <typename PacketT, int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i) const {
+ EIGEN_STATIC_ASSERT((internal::is_same<PacketT, Packet>::value), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((AlignmentType == Aligned || Alignment == Unaligned), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return loadPacket(i);
+ }
+
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC bool aligned(Index i) const {
+ return false;
+ }
+
+ private:
+ const ParentMapper& m_base_mapper;
+ const Index m_vert_offset;
+ const Index m_horiz_offset;
+};
+
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ size_t packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment>
+class TensorContractionInputMapper
+ : public BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> {
+
+ public:
+ typedef BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> Base;
+ typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> SubMapper;
+ typedef SubMapper VectorMapper;
+
+ EIGEN_DEVICE_FUNC TensorContractionInputMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides)
+ : Base(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE SubMapper getSubMapper(Index i, Index j) const {
+ return SubMapper(*this, i, j);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
+ return VectorMapper(*this, i, j);
+ }
+};
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPERS_H