| // 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_H |
| #define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H |
| |
| namespace Eigen { |
| |
| /** \class TensorContraction |
| * \ingroup CXX11_Tensor_Module |
| * |
| * \brief Tensor contraction class. |
| * |
| * |
| */ |
| namespace internal { |
| |
| template<typename Scalar, typename Index> |
| void pack_simple(Scalar * dst, const Scalar * src, Index cols, Index rows, Index lddst, Index ldsrc) { |
| size_t psize = packet_traits<Scalar>::size; // Packet size |
| typedef typename packet_traits<Scalar>::type Packet; // Packet type |
| size_t alignment = psize*sizeof(Scalar); // Needed alignment |
| if (rows % psize == 0 && (lddst*sizeof(Scalar)) % alignment == 0 && |
| (ldsrc*sizeof(Scalar)) % alignment == 0 && |
| reinterpret_cast<uintptr_t>(src) % alignment == 0 && |
| reinterpret_cast<uintptr_t>(dst) % alignment == 0) { |
| // Optimized version using packets |
| size_t num_packets = rows / psize; |
| for (Index col = 0; col < cols; ++col) { |
| EIGEN_ASM_COMMENT("begin pack_simple inner copy"); |
| // Unrolled manually 4 times. |
| for (size_t i=0; i < num_packets/4; ++i) { |
| internal::pstore(dst, internal::pload<Packet>(src)); |
| dst += psize; src += psize; |
| internal::pstore(dst, internal::pload<Packet>(src)); |
| dst += psize; src += psize; |
| internal::pstore(dst, internal::pload<Packet>(src)); |
| dst += psize; src += psize; |
| internal::pstore(dst, internal::pload<Packet>(src)); |
| dst += psize; src += psize; |
| } |
| for (size_t i=0; i < num_packets%4; ++i) { |
| internal::pstore(dst, internal::pload<Packet>(src)); |
| dst += psize; src += psize; |
| } |
| dst += lddst - num_packets*psize; |
| src += ldsrc - num_packets*psize; |
| EIGEN_ASM_COMMENT("end pack_simple inner copy"); |
| } |
| } else { |
| // Naive memcpy calls |
| for (Index col = 0; col < cols; ++col) { |
| memcpy(dst + col*lddst, src + col*ldsrc, rows*sizeof(Scalar)); |
| } |
| } |
| } |
| |
| #if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM) |
| // This is a hack needed to be able to compile contraction for Scalar |
| // unsupported by libxsmm (such as int). While we do not use xsmm in that case, |
| // the check is performed using if(std::is_same<...>), so compiler runs through |
| // both branches and then optimizes out unused one, but still would complain. |
| template<typename LhsScalar, typename RhsScalar, typename Scalar> |
| struct libxsmm_wrapper { |
| libxsmm_wrapper() {} |
| libxsmm_wrapper(int flags, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta, int prefetch) {} |
| void operator()(const LhsScalar* a, const RhsScalar* b, Scalar* c) {} |
| void operator()(const LhsScalar* a, const RhsScalar* b, Scalar* c, const LhsScalar* ap, const RhsScalar* bp, const Scalar* cp) {} |
| }; |
| |
| template<> |
| struct libxsmm_wrapper<float, float, float>: public libxsmm_mmfunction<float> { |
| libxsmm_wrapper(): libxsmm_mmfunction() {} |
| libxsmm_wrapper(int flags, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta, int prefetch) : |
| libxsmm_mmfunction(flags, m, n, k, lda, ldb, ldc, alpha, beta, prefetch) {} |
| }; |
| |
| template<> |
| struct libxsmm_wrapper<double, double, double>: public libxsmm_mmfunction<double> { |
| libxsmm_wrapper(): libxsmm_mmfunction() {} |
| libxsmm_wrapper(int flags, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta, int prefetch) : |
| libxsmm_mmfunction(flags, m, n, k, lda, ldb, ldc, alpha, beta, prefetch) {} |
| }; |
| #endif |
| |
| template<typename Dimensions, typename LhsXprType, typename RhsXprType> |
| struct traits<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> > |
| { |
| // Type promotion to handle the case where the types of the lhs and the rhs are different. |
| typedef typename scalar_product_traits<typename LhsXprType::Scalar, typename RhsXprType::Scalar>::ReturnType Scalar; |
| |
| typedef typename scalar_product_traits<typename traits<LhsXprType>::StorageKind, |
| typename traits<RhsXprType>::StorageKind>::ReturnType StorageKind; |
| typedef typename promote_index_type<typename traits<LhsXprType>::Index, |
| typename traits<RhsXprType>::Index>::type Index; |
| typedef typename LhsXprType::Nested LhsNested; |
| typedef typename RhsXprType::Nested RhsNested; |
| typedef typename remove_reference<LhsNested>::type _LhsNested; |
| typedef typename remove_reference<RhsNested>::type _RhsNested; |
| |
| // From NumDims below. |
| static const int NumDimensions = traits<RhsXprType>::NumDimensions + traits<RhsXprType>::NumDimensions - 2 * array_size<Dimensions>::value; |
| static const int Layout = traits<LhsXprType>::Layout; |
| |
| enum { |
| Flags = 0, |
| }; |
| }; |
| |
| template<typename Dimensions, typename LhsXprType, typename RhsXprType> |
| struct eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, Eigen::Dense> |
| { |
| typedef const TensorContractionOp<Dimensions, LhsXprType, RhsXprType>& type; |
| }; |
| |
| template<typename Dimensions, typename LhsXprType, typename RhsXprType> |
| struct nested<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, 1, typename eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> >::type> |
| { |
| typedef TensorContractionOp<Dimensions, LhsXprType, RhsXprType> type; |
| }; |
| |
| template<typename Indices_, typename LeftArgType_, typename RightArgType_, typename Device_> |
| struct traits<TensorEvaluator<const TensorContractionOp<Indices_, LeftArgType_, RightArgType_>, Device_> > { |
| typedef Indices_ Indices; |
| typedef LeftArgType_ LeftArgType; |
| typedef RightArgType_ RightArgType; |
| typedef Device_ Device; |
| |
| // From NumDims below. |
| static const int NumDimensions = traits<LeftArgType_>::NumDimensions + traits<RightArgType_>::NumDimensions - 2 * array_size<Indices_>::value; |
| }; |
| |
| } // end namespace internal |
| |
| template<typename Indices, typename LhsXprType, typename RhsXprType> |
| class TensorContractionOp : public TensorBase<TensorContractionOp<Indices, LhsXprType, RhsXprType> > |
| { |
| public: |
| typedef typename Eigen::internal::traits<TensorContractionOp>::Scalar Scalar; |
| typedef typename internal::scalar_product_traits<typename LhsXprType::CoeffReturnType, |
| typename RhsXprType::CoeffReturnType>::ReturnType CoeffReturnType; |
| typedef typename Eigen::internal::nested<TensorContractionOp>::type Nested; |
| typedef typename Eigen::internal::traits<TensorContractionOp>::StorageKind StorageKind; |
| typedef typename Eigen::internal::traits<TensorContractionOp>::Index Index; |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionOp( |
| const LhsXprType& lhs, const RhsXprType& rhs, const Indices& dims) |
| : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_indices(dims) {} |
| |
| EIGEN_DEVICE_FUNC const Indices& indices() const { return m_indices; } |
| |
| /** \returns the nested expressions */ |
| EIGEN_DEVICE_FUNC |
| const typename internal::remove_all<typename LhsXprType::Nested>::type& |
| lhsExpression() const { return m_lhs_xpr; } |
| |
| EIGEN_DEVICE_FUNC |
| const typename internal::remove_all<typename RhsXprType::Nested>::type& |
| rhsExpression() const { return m_rhs_xpr; } |
| |
| protected: |
| typename LhsXprType::Nested m_lhs_xpr; |
| typename RhsXprType::Nested m_rhs_xpr; |
| const Indices m_indices; |
| }; |
| |
| |
| template<typename Derived> |
| struct TensorContractionEvaluatorBase |
| { |
| typedef typename internal::traits<Derived>::Indices Indices; |
| typedef typename internal::traits<Derived>::LeftArgType LeftArgType; |
| typedef typename internal::traits<Derived>::RightArgType RightArgType; |
| typedef typename internal::traits<Derived>::Device Device; |
| |
| typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType; |
| typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar; |
| typedef typename XprType::Index Index; |
| typedef typename XprType::CoeffReturnType CoeffReturnType; |
| typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType; |
| |
| enum { |
| IsAligned = true, |
| PacketAccess = (internal::packet_traits<Scalar>::size > 1), |
| BlockAccess = false, |
| Layout = TensorEvaluator<LeftArgType, Device>::Layout, |
| CoordAccess = false, // to be implemented |
| RawAccess = true |
| }; |
| |
| // Most of the code is assuming that both input tensors are ColMajor. If the |
| // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS: |
| // If we want to compute A * B = C, where A is LHS and B is RHS, the code |
| // will pretend B is LHS and A is RHS. |
| typedef typename internal::conditional< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType; |
| typedef typename internal::conditional< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType; |
| |
| static const int LDims = |
| internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value; |
| static const int RDims = |
| internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value; |
| static const int ContractDims = internal::array_size<Indices>::value; |
| static const int NumDims = LDims + RDims - 2 * ContractDims; |
| |
| typedef array<Index, LDims> left_dim_mapper_t; |
| typedef array<Index, RDims> right_dim_mapper_t; |
| typedef array<Index, ContractDims> contract_t; |
| typedef array<Index, LDims - ContractDims> left_nocontract_t; |
| typedef array<Index, RDims - ContractDims> right_nocontract_t; |
| |
| typedef DSizes<Index, NumDims> Dimensions; |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE |
| TensorContractionEvaluatorBase(const XprType& op, const Device& device) |
| : m_leftImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(), |
| op.lhsExpression(), op.rhsExpression()), device), |
| m_rightImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(), |
| op.rhsExpression(), op.lhsExpression()), device), |
| m_device(device), |
| m_result(NULL) { |
| EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == |
| static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)), |
| YOU_MADE_A_PROGRAMMING_MISTAKE); |
| |
| DSizes<Index, LDims> eval_left_dims; |
| DSizes<Index, RDims> eval_right_dims; |
| array<IndexPair<Index>, ContractDims> eval_op_indices; |
| if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) { |
| // For ColMajor, we keep using the existing dimensions |
| for (int i = 0; i < LDims; i++) { |
| eval_left_dims[i] = m_leftImpl.dimensions()[i]; |
| } |
| for (int i = 0; i < RDims; i++) { |
| eval_right_dims[i] = m_rightImpl.dimensions()[i]; |
| } |
| // We keep the pairs of contracting indices. |
| for (int i = 0; i < ContractDims; i++) { |
| eval_op_indices[i].first = op.indices()[i].first; |
| eval_op_indices[i].second = op.indices()[i].second; |
| } |
| } else { |
| // For RowMajor, we need to reverse the existing dimensions |
| for (int i = 0; i < LDims; i++) { |
| eval_left_dims[i] = m_leftImpl.dimensions()[LDims - i - 1]; |
| } |
| for (int i = 0; i < RDims; i++) { |
| eval_right_dims[i] = m_rightImpl.dimensions()[RDims - i - 1]; |
| } |
| // We need to flip all the pairs of contracting indices as well as |
| // reversing the dimensions. |
| for (int i = 0; i < ContractDims; i++) { |
| eval_op_indices[i].first = LDims - 1 - op.indices()[ContractDims - 1 - i].second; |
| eval_op_indices[i].second = RDims - 1 - op.indices()[ContractDims - 1 - i].first; |
| } |
| } |
| |
| // Check for duplicate axes and make sure the first index in eval_op_indices |
| // is increasing. Using O(n^2) sorting is OK since ContractDims is at |
| // most 8. |
| for (int i = 0; i < ContractDims; i++) { |
| for (int j = i + 1; j < ContractDims; j++) { |
| eigen_assert(eval_op_indices[j].first != eval_op_indices[i].first && |
| eval_op_indices[j].second != eval_op_indices[i].second && |
| "contraction axes should be unique"); |
| if (eval_op_indices[j].first < eval_op_indices[i].first) { |
| using numext::swap; |
| swap(eval_op_indices[j], eval_op_indices[i]); |
| } |
| } |
| } |
| |
| array<Index, LDims> lhs_strides; |
| if (LDims > 0) { |
| lhs_strides[0] = 1; |
| for (int i = 0; i < LDims-1; ++i) { |
| lhs_strides[i+1] = lhs_strides[i] * eval_left_dims[i]; |
| } |
| } |
| |
| array<Index, RDims> rhs_strides; |
| if (RDims > 0) { |
| rhs_strides[0] = 1; |
| for (int i = 0; i < RDims-1; ++i) { |
| rhs_strides[i+1] = rhs_strides[i] * eval_right_dims[i]; |
| } |
| } |
| |
| if (m_i_strides.size() > 0) m_i_strides[0] = 1; |
| if (m_j_strides.size() > 0) m_j_strides[0] = 1; |
| if (m_k_strides.size() > 0) m_k_strides[0] = 1; |
| |
| m_i_size = 1; |
| m_j_size = 1; |
| m_k_size = 1; |
| |
| // To compute the dimension, we simply concatenate the non-contracting |
| // dimensions of the left and then the right tensor. Additionally, I also |
| // want to compute the cumulative products of the left non-contracting |
| // dimensions, right non-contracting dimensions, and the contracting |
| // dimensions (in the order of the contraction) to aid in the later |
| // computation of tensor indices for matrix indices. |
| m_lhs_inner_dim_contiguous = true; |
| int dim_idx = 0; |
| int nocontract_idx = 0; |
| |
| for (int i = 0; i < LDims; i++) { |
| // find if we are contracting on index i of left tensor |
| bool contracting = false; |
| for (int j = 0; j < ContractDims; j++) { |
| if (eval_op_indices[j].first == i) { |
| contracting = true; |
| break; |
| } |
| } |
| if (!contracting) { |
| // add dimension size to output dimensions |
| m_dimensions[dim_idx] = eval_left_dims[i]; |
| m_left_nocontract_strides[nocontract_idx] = lhs_strides[i]; |
| if (dim_idx != i) { |
| m_lhs_inner_dim_contiguous = false; |
| } |
| if (nocontract_idx+1 < internal::array_size<left_nocontract_t>::value) { |
| m_i_strides[nocontract_idx+1] = |
| m_i_strides[nocontract_idx] * eval_left_dims[i]; |
| } else { |
| m_i_size = m_i_strides[nocontract_idx] * eval_left_dims[i]; |
| } |
| dim_idx++; |
| nocontract_idx++; |
| } |
| } |
| |
| nocontract_idx = 0; |
| for (int i = 0; i < RDims; i++) { |
| bool contracting = false; |
| // find if we are contracting on index i of right tensor |
| for (int j = 0; j < ContractDims; j++) { |
| if (eval_op_indices[j].second == i) { |
| contracting = true; |
| break; |
| } |
| } |
| if (!contracting) { |
| m_dimensions[dim_idx] = eval_right_dims[i]; |
| if (nocontract_idx+1 < internal::array_size<right_nocontract_t>::value) { |
| m_j_strides[nocontract_idx+1] = |
| m_j_strides[nocontract_idx] * eval_right_dims[i]; |
| } else { |
| m_j_size = m_j_strides[nocontract_idx] * eval_right_dims[i]; |
| } |
| m_right_nocontract_strides[nocontract_idx] = rhs_strides[i]; |
| dim_idx++; |
| nocontract_idx++; |
| } |
| } |
| |
| // now build contraction cumprod. We assumed above that non-contracting axes |
| // are represented in the same order in the matrix as they are in the tensor. |
| // This is not the case for contracting axes. As the contracting axes must be |
| // of the same size in each tensor, I'll only look at the first tensor here. |
| m_rhs_inner_dim_contiguous = true; |
| m_rhs_inner_dim_reordered = false; |
| for (int i = 0; i < ContractDims; i++) { |
| Index left = eval_op_indices[i].first; |
| Index right = eval_op_indices[i].second; |
| |
| Index size = eval_left_dims[left]; |
| eigen_assert(size == eval_right_dims[right] && |
| "Contraction axes must be same size"); |
| |
| if (i+1 < internal::array_size<contract_t>::value) { |
| m_k_strides[i+1] = m_k_strides[i] * size; |
| } else { |
| m_k_size = m_k_strides[i] * size; |
| } |
| m_left_contracting_strides[i] = lhs_strides[left]; |
| m_right_contracting_strides[i] = rhs_strides[right]; |
| |
| if (i > 0 && right < eval_op_indices[i-1].second) { |
| m_rhs_inner_dim_reordered = true; |
| } |
| if (right != i) { |
| m_rhs_inner_dim_contiguous = false; |
| } |
| } |
| |
| #if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM) |
| // Check if we can use faster matmul algorithms. For contraction to be |
| // equivalent to matmul, we need both lhs and rhs contracting dims sequences |
| // to be either a prefix or suffix of all dims. Also, the order of both |
| // must be the same, so we don't have to do reordering. |
| // For example: |
| // * OK: lhs 4D, rhs 4D, contraction: [(0, 2), (1, 3)] |
| // * BAD: lhs 3D, rhs 3D, contraction: [(1,1)] |
| // * BAD: lhs 3D, rhs 3D, contraction: [(0, 0), (2, 2)] |
| // * BAD: lhs 3D, rhs 3D, contraction: [(0, 2), (1, 1)] |
| // Depending if contraction dims are prefix or suffix of all dims we need to |
| // pre-transpose matrices in matmul algorithm: |
| // lhs: prefix -> transpose, suffix -> no transpose |
| // rhs: prefix -> no transpose, suffix -> transpose |
| // For example, for lhs 2D, rhs 2D, contraction [(1, 0)] is regular, |
| // non-transposed matmul. |
| bool equivalent_to_matmul = true; |
| |
| if (ContractDims == 0) { |
| // This case is totally uninteresting, filter it out to avoid problems |
| // with iterations in further tests. |
| equivalent_to_matmul = false; |
| } |
| |
| // Check if RHS dims list is increasing. LHS already is, so if not, the |
| // order is different and we cannot do matmul. |
| for (int i = 1; i < ContractDims; i++) { |
| if (eval_op_indices[i].second < eval_op_indices[i-1].second) { |
| equivalent_to_matmul = false; |
| } |
| } |
| |
| if (equivalent_to_matmul) { |
| // Check if no holes. |
| int diff; |
| for (int i = 1; i < ContractDims; i++) { |
| // LHS contract dims are sorted to form an increasing seq. |
| diff = eval_op_indices[i].first - eval_op_indices[i-1].first; |
| if (diff != 1) { |
| equivalent_to_matmul = false; |
| } |
| // Now we may already assume RHS contract dims seq is increasing too. |
| diff = eval_op_indices[i].second - eval_op_indices[i-1].second; |
| if (diff != 1) { |
| equivalent_to_matmul = false; |
| } |
| } |
| |
| // Check if suffix or prefix. |
| if (eval_op_indices[0].first != 0 && |
| eval_op_indices[ContractDims-1].first != LDims-1) { |
| equivalent_to_matmul = false; |
| } |
| if (eval_op_indices[0].second != 0 && |
| eval_op_indices[ContractDims-1].second != RDims-1) { |
| equivalent_to_matmul = false; |
| } |
| } |
| |
| typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar; |
| typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar; |
| m_can_use_xsmm = equivalent_to_matmul && |
| std::is_same<Scalar, LhsScalar>::value && |
| std::is_same<Scalar, RhsScalar>::value && |
| (std::is_same<Scalar, float>::value || |
| std::is_same<Scalar, double>::value) && |
| m_leftImpl.data() != NULL && m_rightImpl.data() != NULL; |
| #else |
| m_can_use_xsmm = false; |
| #endif |
| |
| // If the layout is RowMajor, we need to reverse the m_dimensions |
| if (static_cast<int>(Layout) == static_cast<int>(RowMajor)) { |
| for (int i = 0, j = NumDims - 1; i < j; i++, j--) { |
| numext::swap(m_dimensions[i], m_dimensions[j]); |
| } |
| } |
| |
| eigen_assert(ContractDims == 0 || !m_lhs_inner_dim_contiguous || |
| (m_left_contracting_strides[0] == m_i_size)); |
| } |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; } |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) { |
| m_leftImpl.evalSubExprsIfNeeded(NULL); |
| m_rightImpl.evalSubExprsIfNeeded(NULL); |
| if (data) { |
| evalTo(data); |
| return false; |
| } else { |
| m_result = static_cast<Scalar *>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar))); |
| evalTo(m_result); |
| return true; |
| } |
| } |
| |
| #define TENSOR_CONTRACTION_DISPATCH(METHOD, ALIGNMENT, ARGS) \ |
| if (this->m_lhs_inner_dim_contiguous) { \ |
| if (this->m_rhs_inner_dim_contiguous) { \ |
| if (this->m_rhs_inner_dim_reordered) { \ |
| METHOD<true, true, true, ALIGNMENT>ARGS; \ |
| } \ |
| else { \ |
| METHOD<true, true, false, ALIGNMENT>ARGS; \ |
| } \ |
| } \ |
| else { \ |
| if (this->m_rhs_inner_dim_reordered) { \ |
| METHOD<true, false, true, ALIGNMENT>ARGS; \ |
| } \ |
| else { \ |
| METHOD<true, false, false, ALIGNMENT>ARGS; \ |
| } \ |
| } \ |
| } \ |
| else { \ |
| if (this->m_rhs_inner_dim_contiguous) { \ |
| if (this->m_rhs_inner_dim_reordered) { \ |
| METHOD<false, true, true, ALIGNMENT>ARGS; \ |
| } \ |
| else { \ |
| METHOD<false, true, false, ALIGNMENT>ARGS; \ |
| } \ |
| } \ |
| else { \ |
| if (this->m_rhs_inner_dim_reordered) { \ |
| METHOD<false, false, true, ALIGNMENT>ARGS; \ |
| } \ |
| else { \ |
| METHOD<false, false, false, ALIGNMENT>ARGS; \ |
| } \ |
| } \ |
| } |
| |
| EIGEN_DEVICE_FUNC void evalTo(Scalar* buffer) const { |
| static_cast<const Derived*>(this)->template evalProduct<Unaligned>(buffer); |
| } |
| |
| template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, |
| bool rhs_inner_dim_reordered, int Alignment> |
| void evalProductSequential(Scalar* buffer) const { |
| if (this->m_j_size == 1) { |
| this->template evalGemv<lhs_inner_dim_contiguous, |
| rhs_inner_dim_contiguous, rhs_inner_dim_reordered, |
| Alignment>(buffer); |
| } else { |
| this->template evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, |
| rhs_inner_dim_reordered, Alignment>(buffer); |
| } |
| } |
| |
| template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment> |
| void evalGemv(Scalar* buffer) const { |
| const Index rows = m_i_size; |
| const Index cols = m_k_size; |
| |
| internal::EigenStatsWrapper::get()->add(internal::MatmulOp{ |
| internal::MatmulOp::Algorithm::GEMV, static_cast<std::size_t>(rows), static_cast<std::size_t>(cols), 1, |
| !lhs_inner_dim_contiguous, !rhs_inner_dim_contiguous, 1}); |
| |
| typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar; |
| typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar; |
| typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator; |
| typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator; |
| const int lhs_packet_size = PacketType<LhsScalar, Device>::size; |
| const int rhs_packet_size = PacketType<RhsScalar, Device>::size; |
| const int lhs_alignment = LeftEvaluator::IsAligned ? Aligned : Unaligned; |
| const int rhs_alignment = RightEvaluator::IsAligned ? Aligned : Unaligned; |
| typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs, |
| LeftEvaluator, left_nocontract_t, |
| contract_t, lhs_packet_size, |
| lhs_inner_dim_contiguous, |
| false, lhs_alignment> LhsMapper; |
| |
| typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs, |
| RightEvaluator, right_nocontract_t, |
| contract_t, rhs_packet_size, |
| rhs_inner_dim_contiguous, |
| rhs_inner_dim_reordered, rhs_alignment> RhsMapper; |
| |
| LhsMapper lhs(m_leftImpl, m_left_nocontract_strides, m_i_strides, |
| m_left_contracting_strides, m_k_strides); |
| RhsMapper rhs(m_rightImpl, m_right_nocontract_strides, m_j_strides, |
| m_right_contracting_strides, m_k_strides); |
| |
| const RhsScalar alpha(1); |
| const Index resIncr(1); |
| |
| // zero out the result buffer (which must be of size at least rows * sizeof(Scalar) |
| m_device.memset(buffer, 0, rows * sizeof(Scalar)); |
| |
| internal::general_matrix_vector_product |
| <Index, LhsScalar, LhsMapper, ColMajor, false, |
| RhsScalar, RhsMapper, false>::run( |
| rows, cols, lhs, rhs, |
| buffer, resIncr, alpha); |
| } |
| |
| template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, |
| bool rhs_inner_dim_reordered, int Alignment> |
| EIGEN_DEVICE_FUNC void evalGemm(Scalar* buffer) const { |
| typedef |
| typename internal::remove_const<typename EvalLeftArgType::Scalar>::type |
| LhsScalar; |
| typedef |
| typename internal::remove_const<typename EvalRightArgType::Scalar>::type |
| RhsScalar; |
| |
| // rows in left side |
| const Index m = this->m_i_size; |
| |
| // columns in right side |
| const Index n = this->m_j_size; |
| |
| #if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM) |
| if (m_can_use_xsmm) { |
| evalGemmPartialXSMM(buffer, 0, this->m_k_size, 1); |
| return; |
| } |
| #endif |
| // Use more generic Gebp |
| |
| // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar) |
| this->m_device.memset(buffer, 0, m * n * sizeof(Scalar)); |
| |
| this->template evalGemmPartial<lhs_inner_dim_contiguous, |
| rhs_inner_dim_contiguous, |
| rhs_inner_dim_reordered, Alignment>( |
| buffer, 0, this->m_k_size, 1); |
| } |
| |
| template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment> |
| EIGEN_DEVICE_FUNC void evalGemmPartial(Scalar* buffer, Index k_start, Index k_end, int num_threads) const { |
| // columns in left side, rows in right side |
| const Index k = this->m_k_size; |
| |
| eigen_assert(k_end >= k_start && k_start >= 0 && k_end <= k); |
| const Index k_slice = k_end - k_start; |
| |
| // rows in left side |
| const Index m = this->m_i_size; |
| |
| // columns in right side |
| const Index n = this->m_j_size; |
| |
| internal::EigenStatsWrapper::get()->add(internal::MatmulOp{ |
| internal::MatmulOp::Algorithm::GEBP, static_cast<std::size_t>(m), static_cast<std::size_t>(k), static_cast<std::size_t>(n), |
| !lhs_inner_dim_contiguous, !rhs_inner_dim_contiguous, static_cast<std::size_t>(num_threads)}); |
| |
| // define mr, nr, and all of my data mapper types |
| typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar; |
| typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar; |
| typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits; |
| |
| const Index nr = Traits::nr; |
| const Index mr = Traits::mr; |
| |
| typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator; |
| typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator; |
| |
| const int lhs_packet_size = internal::packet_traits<LhsScalar>::size; |
| const int rhs_packet_size = internal::packet_traits<RhsScalar>::size; |
| |
| typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs, |
| LeftEvaluator, left_nocontract_t, |
| contract_t, lhs_packet_size, |
| lhs_inner_dim_contiguous, |
| false, Unaligned> LhsMapper; |
| |
| typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs, |
| RightEvaluator, right_nocontract_t, |
| contract_t, rhs_packet_size, |
| rhs_inner_dim_contiguous, |
| rhs_inner_dim_reordered, Unaligned> RhsMapper; |
| |
| typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper; |
| |
| // declare GEBP packing and kernel structs |
| // TODO: packing could be faster sometimes if we supported row major tensor mappers |
| internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, mr, Traits::LhsProgress, ColMajor> pack_lhs; |
| internal::gemm_pack_rhs<RhsScalar, Index, typename RhsMapper::SubMapper, nr, ColMajor> pack_rhs; |
| |
| // TODO: replace false, false with conjugate values? |
| internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper, mr, nr, false, false> gebp; |
| |
| // initialize data mappers |
| LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides, |
| this->m_left_contracting_strides, this->m_k_strides); |
| |
| RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides, |
| this->m_right_contracting_strides, this->m_k_strides); |
| |
| OutputMapper output(buffer, m); |
| |
| // compute block sizes (which depend on number of threads) |
| internal::TensorContractionBlocking<LhsScalar, RhsScalar, Index, |
| internal::ShardByCol> |
| blocking(k_slice, m, n, num_threads); |
| |
| const Index kc = blocking.kc(); |
| const Index mc = (std::min<Index>)(m, blocking.mc()); |
| const Index nc = (std::min<Index>)(n, blocking.nc()); |
| |
| // sizes of submatrices to live in cache. see Goto paper. |
| int sizeA = blocking.mc() * kc; |
| int sizeB = kc * blocking.nc(); |
| |
| // note: m_device.allocate should return 16 byte aligned pointers, but if blockA and blockB |
| // aren't 16 byte aligned segfaults will happen due to SIMD instructions |
| LhsScalar* blockA = static_cast<LhsScalar *>(this->m_device.allocate(sizeA * sizeof(LhsScalar))); |
| RhsScalar* blockB = static_cast<RhsScalar *>(this->m_device.allocate(sizeB * sizeof(RhsScalar))); |
| |
| for (Index i2=0; i2<m; i2+=mc) |
| { |
| const Index actual_mc = numext::mini(i2+mc,m)-i2; |
| for (Index k2 = k_start; k2 < k_end; k2 += kc) { |
| // make sure we don't overshoot right edge of left matrix, then pack vertical panel |
| const Index actual_kc = numext::mini(k2 + kc, k_end) - k2; |
| pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc, 0, 0); |
| |
| // series of horizontal blocks |
| for (Index j2 = 0; j2 < n; j2 += nc) { |
| // make sure we don't overshoot right edge of right matrix, then pack block |
| const Index actual_nc = numext::mini(j2 + nc, n) - j2; |
| pack_rhs(blockB, rhs.getSubMapper(k2, j2), actual_kc, actual_nc, 0, 0); |
| |
| // call gebp (matrix kernel) |
| // The parameters here are copied from Eigen's GEMM implementation |
| gebp(output.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, Scalar(1), -1, -1, 0, 0); |
| } |
| } |
| } |
| |
| this->m_device.deallocate(blockA); |
| this->m_device.deallocate(blockB); |
| } |
| |
| #if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM) |
| EIGEN_DEVICE_FUNC void evalGemmPartialXSMM(Scalar* buffer, Index k_start, Index k_end, int num_threads) const { |
| const Index k = this->m_k_size; |
| |
| eigen_assert(k_end >= k_start && k_start >= 0 && k_end <= k); |
| const Index k_slice = k_end - k_start; |
| |
| // rows in left side |
| const Index m = this->m_i_size; |
| |
| // columns in right side |
| const Index n = this->m_j_size; |
| |
| const bool transposeA = !m_lhs_inner_dim_contiguous; |
| const bool transposeB = !m_rhs_inner_dim_contiguous; |
| |
| internal::EigenStatsWrapper::get()->add(internal::MatmulOp{ |
| internal::MatmulOp::Algorithm::XSMM, m, k, n, transposeA, transposeB, |
| num_threads}); |
| |
| typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar; |
| typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar; |
| |
| internal::TensorXsmmContractionBlocking<LhsScalar, RhsScalar, Index> blocking( |
| k_end - k_start, m, n, num_threads, transposeA, transposeB); |
| |
| // Outer blocks sizes |
| const Index mc_outer = blocking.outer_m(); |
| const Index nc_outer = blocking.outer_n(); |
| const Index kc_outer = blocking.outer_k(); |
| // Inner blocks sizes |
| const Index mc = blocking.mc(); |
| const Index nc = blocking.nc(); |
| const Index kc = blocking.kc(); |
| // Decisions whether we should copy parts of matrices |
| const bool copyA = blocking.copyA(); |
| const bool copyB = blocking.copyB(); |
| |
| const LhsScalar * leftData = m_leftImpl.data(); |
| const RhsScalar * rightData = m_rightImpl.data(); |
| |
| libxsmm_blasint stride_A = static_cast<libxsmm_blasint>(transposeA ? k : m); |
| libxsmm_blasint stride_B = static_cast<libxsmm_blasint>(transposeB ? n : k); |
| libxsmm_blasint stride_C = static_cast<libxsmm_blasint>(m); |
| |
| libxsmm_blasint stride_blockA = static_cast<libxsmm_blasint>(mc); |
| // Use bigger stride to avoid hitting same cache line too often. |
| // This consistently gives +~0.5 Gflops. |
| libxsmm_blasint stride_panelB = static_cast<libxsmm_blasint>( |
| kc % 32 == 0 ? kc + 16 : kc |
| ); |
| |
| // Kernel for the general case (not edges) |
| internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar> kernel; |
| |
| const LhsScalar *ap; |
| const RhsScalar *bp; |
| const Scalar *cp; |
| |
| LhsScalar* blockA; |
| RhsScalar* panelB; |
| |
| if (copyA) { |
| blockA = static_cast<LhsScalar*>(this->m_device.allocate(mc * kc * sizeof(LhsScalar))); |
| } |
| if (copyB) { |
| panelB = static_cast<RhsScalar*>(this->m_device.allocate(nc_outer * stride_panelB * sizeof(RhsScalar))); |
| } |
| |
| Index kernel_stride_A = copyA ? stride_blockA : stride_A; |
| Index kernel_stride_B = copyB ? stride_panelB : stride_B; |
| kernel = internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar>(0, mc, nc, kc, kernel_stride_A, kernel_stride_B, stride_C, 1, 1, blocking.prefetch()); |
| |
| // Outer blocking |
| for (Index ki_outer = k_start; ki_outer < k_end; ki_outer += kc_outer) { |
| for (Index mi_outer = 0; mi_outer < m; mi_outer += mc_outer) { |
| for (Index ni_outer = 0; ni_outer < n; ni_outer += nc_outer) { |
| using numext::mini; |
| |
| Index actual_nc_outer = mini(ni_outer+nc_outer, n) - ni_outer; |
| |
| // Inner blocking |
| for (Index ki = ki_outer; ki < mini(ki_outer+kc_outer, k_end); ki += kc) { |
| const Index actual_kc = mini(ki_outer+kc_outer, mini(ki+kc, k_end)) - ki; |
| |
| if (copyB) { |
| if (transposeB) { |
| libxsmm_otrans(panelB, rightData + ki*stride_B + ni_outer, sizeof(RhsScalar), actual_nc_outer, actual_kc, stride_B, stride_panelB); |
| } else { |
| internal::pack_simple<RhsScalar, Index>(panelB, rightData + ni_outer*stride_B + ki, actual_nc_outer, actual_kc, stride_panelB, stride_B); |
| } |
| } |
| |
| for (Index mi = mi_outer; mi < mini(mi_outer+mc_outer, m); mi += mc) { |
| const Index actual_mc = mini(mi_outer+mc_outer, mini(mi+mc, m)) - mi; |
| |
| const LhsScalar * a = transposeA ? leftData + mi*stride_A + ki : |
| leftData + ki*stride_A + mi; |
| |
| if (copyA) { |
| if (transposeA) { |
| libxsmm_otrans(blockA, a, sizeof(LhsScalar), actual_kc, actual_mc, stride_A, stride_blockA); |
| } else { |
| internal::pack_simple<LhsScalar, Index>(blockA, a, actual_kc, actual_mc, stride_blockA, stride_A); |
| } |
| } |
| |
| for (Index ni = ni_outer; ni < mini(ni_outer+nc_outer, n); ni += nc) { |
| const Index actual_nc = mini(ni_outer+nc_outer, mini(ni+nc, n)) - ni; |
| |
| |
| const RhsScalar * b = rightData + ni*stride_B + ki; |
| Scalar * c = buffer + ni*stride_C + mi; |
| cp = c + nc*stride_C; |
| |
| const LhsScalar * actual_a = copyA ? blockA : a; |
| const Index actual_lda = copyA ? stride_blockA : stride_A; |
| ap = copyA ? blockA : a; |
| |
| const RhsScalar * actual_b = copyB ? panelB + (ni-ni_outer)*stride_panelB : b; |
| const Index actual_ldb = copyB ? stride_panelB : stride_B; |
| bp = copyB ? panelB + nc*stride_panelB : b + nc*stride_B; |
| |
| float beta = ki == 0 ? 0 : 1; |
| |
| if (actual_mc == mc && actual_kc == kc && actual_nc == nc && beta == 1) { |
| // Most used, cached kernel. |
| kernel(actual_a, actual_b, c, ap, bp, cp); |
| } else { |
| // Edges - use libxsmm kernel cache. |
| internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar>(0, actual_mc, actual_nc, actual_kc, actual_lda, actual_ldb, stride_C, 1, beta, blocking.prefetch())(actual_a, actual_b, c, ap, bp, cp); |
| } |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| if (copyA) { |
| this->m_device.deallocate(blockA); |
| } |
| if (copyB) { |
| this->m_device.deallocate(panelB); |
| } |
| } |
| #endif |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { |
| m_leftImpl.cleanup(); |
| m_rightImpl.cleanup(); |
| |
| if (m_result != NULL) { |
| m_device.deallocate(m_result); |
| m_result = NULL; |
| } |
| } |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const { |
| return m_result[index]; |
| } |
| |
| EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const { |
| return TensorOpCost(sizeof(CoeffReturnType), 0, 0); |
| } |
| |
| template<int LoadMode> |
| EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const { |
| return internal::ploadt<PacketReturnType, LoadMode>(m_result + index); |
| } |
| |
| EIGEN_DEVICE_FUNC Scalar* data() const { return m_result; } |
| |
| protected: |
| // Note: nvcc doesn't like implicit copy constructor. If this is needed anywhere, |
| // then we'll have to write an explicit copy constructor... |
| //TensorContractionEvaluatorBase(const TensorContractionEvaluatorBase&); |
| |
| TensorContractionEvaluatorBase& operator = (const TensorContractionEvaluatorBase&); |
| Dimensions m_dimensions; |
| |
| contract_t m_k_strides; |
| contract_t m_left_contracting_strides; |
| contract_t m_right_contracting_strides; |
| |
| bool m_lhs_inner_dim_contiguous; |
| bool m_rhs_inner_dim_contiguous; |
| bool m_rhs_inner_dim_reordered; |
| bool m_can_use_xsmm; |
| |
| left_nocontract_t m_i_strides; |
| right_nocontract_t m_j_strides; |
| left_nocontract_t m_left_nocontract_strides; |
| right_nocontract_t m_right_nocontract_strides; |
| |
| Index m_i_size; |
| Index m_j_size; |
| Index m_k_size; |
| |
| TensorEvaluator<EvalLeftArgType, Device> m_leftImpl; |
| TensorEvaluator<EvalRightArgType, Device> m_rightImpl; |
| const Device& m_device; |
| Scalar* m_result; |
| }; |
| |
| |
| // evaluator for default device |
| template<typename Indices, typename LeftArgType, typename RightArgType, typename Device> |
| struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> : |
| public TensorContractionEvaluatorBase< |
| TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> > { |
| typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> Self; |
| typedef TensorContractionEvaluatorBase<Self> Base; |
| |
| typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType; |
| typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar; |
| typedef typename XprType::Index Index; |
| typedef typename XprType::CoeffReturnType CoeffReturnType; |
| typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType; |
| |
| enum { |
| Layout = TensorEvaluator<LeftArgType, Device>::Layout, |
| }; |
| |
| // Most of the code is assuming that both input tensors are ColMajor. If the |
| // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS: |
| // If we want to compute A * B = C, where A is LHS and B is RHS, the code |
| // will pretend B is LHS and A is RHS. |
| typedef typename internal::conditional< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType; |
| typedef typename internal::conditional< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType; |
| |
| static const int LDims = |
| internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value; |
| static const int RDims = |
| internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value; |
| static const int ContractDims = internal::array_size<Indices>::value; |
| |
| typedef array<Index, LDims> left_dim_mapper_t; |
| typedef array<Index, RDims> right_dim_mapper_t; |
| |
| typedef array<Index, ContractDims> contract_t; |
| typedef array<Index, LDims - ContractDims> left_nocontract_t; |
| typedef array<Index, RDims - ContractDims> right_nocontract_t; |
| |
| static const int NumDims = LDims + RDims - 2 * ContractDims; |
| |
| // Could we use NumDimensions here? |
| typedef DSizes<Index, NumDims> Dimensions; |
| |
| |
| EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device) : |
| Base(op, device) { } |
| |
| template <int Alignment> |
| void evalProduct(Scalar* buffer) const { |
| TENSOR_CONTRACTION_DISPATCH(this->template evalProductSequential, Alignment, (buffer)); |
| } |
| }; |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H |
