| // 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_CONTRACTION_THREAD_POOL_H |
| #define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H |
| |
| // evaluator for thread pool device |
| #ifdef EIGEN_USE_THREADS |
| |
| #include "./InternalHeaderCheck.h" |
| |
| namespace Eigen { |
| |
| template<typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType> |
| struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, ThreadPoolDevice> : |
| public TensorContractionEvaluatorBase<TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, ThreadPoolDevice> > { |
| |
| typedef ThreadPoolDevice Device; |
| |
| typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self; |
| typedef TensorContractionEvaluatorBase<Self> Base; |
| |
| typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType; |
| typedef std::remove_const_t<typename XprType::Scalar> Scalar; |
| typedef typename XprType::Index Index; |
| typedef typename XprType::CoeffReturnType CoeffReturnType; |
| typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType; |
| |
| static constexpr int 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 std::conditional_t< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType; |
| typedef std::conditional_t< |
| static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType; |
| |
| static constexpr int LDims = |
| internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value; |
| static constexpr int RDims = |
| internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value; |
| static constexpr 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 constexpr int NumDims = LDims + RDims - 2 * ContractDims; |
| |
| typedef DSizes<Index, NumDims> Dimensions; |
| |
| // typedefs needed in evalTo |
| typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar; |
| typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar; |
| typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits; |
| |
| typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator; |
| typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator; |
| |
| TensorEvaluator(const XprType& op, const Device& device) : |
| Base(op, device) {} |
| |
| template <int Alignment> |
| void evalProduct(Scalar* buffer) const { |
| evalProductImpl<NoCallback, Alignment>(buffer, NoCallback()); |
| } |
| |
| template <typename EvalToCallback, int Alignment> |
| void evalProductAsync(Scalar* buffer, EvalToCallback done) const { |
| evalProductImpl<EvalToCallback, Alignment>(buffer, std::move(done)); |
| } |
| |
| template <typename DoneCallback, int Alignment> |
| void evalProductImpl(Scalar* buffer, DoneCallback done) const { |
| // This function computes a lot of heuristics in multiple steps, and it |
| // also has multiple exit points. To keep it sane, readable and all in one |
| // place, sync/async execution decision is made at runtime at the very end. |
| // |
| // (1) In sync mode we allocate Context on the stack, submit computations |
| // to the device thread pool, and block on a barrier until it is |
| // completed. |
| // |
| // (2) In async mode we allocate Context on the heap, and after all tasks |
| // are finished, we call provided the done callback, and delete a |
| // context from the heap. |
| // |
| // (*) EvalParallelContext & EvalShardedByInnerDimContext owns all the state |
| // and temporary buffers, required for executing the tensor contraction. |
| // They are responsible for cleaning it up after contraction is done. |
| static const bool IsEvalInSyncMode = |
| std::is_same<DoneCallback, NoCallback>::value; |
| |
| const Index m = this->m_i_size; |
| const Index n = this->m_j_size; |
| const Index k = this->m_k_size; |
| if (m == 0 || n == 0 || k == 0) return; |
| |
| // Compute a set of algorithm parameters: |
| // - kernel block sizes (bm, bn, bk) |
| // - task grain sizes (number of kernels executed per task: gm, gn) |
| // - number of threads |
| // - sharding by row/column |
| // - parallel packing or first lhs then rhs |
| // and some derived parameters: |
| // - number of tasks (nm, nn, nk) |
| // - number of kernels (nm0, nn0) |
| // Unfortunately, all these parameters are tightly interdependent. |
| // So in some cases we first compute approximate values, then compute other |
| // values based on these approximations and then refine the approximations. |
| |
| // There are lots of heuristics here. There is some reasoning behind them, |
| // but ultimately they are just tuned on contraction benchmarks for |
| // different input configurations, thread counts and instruction sets. |
| // So feel free to question any of them. |
| |
| // Compute whether we want to shard by row or by column. |
| // This is a first approximation, it will be refined later. Since we don't |
| // know number of threads yet we use 2, because what's we are most |
| // interested in at this point is whether it makes sense to use |
| // parallelization at all or not. |
| bool shard_by_col = shardByCol(m, n, 2); |
| |
| // First approximation of kernel blocking sizes. |
| // Again, we don't know number of threads yet, so we use 2. |
| Index bm, bn, bk; |
| if (shard_by_col) { |
| internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index, |
| internal::ShardByCol> |
| blocking(k, m, n, 2); |
| bm = blocking.mc(); |
| bn = blocking.nc(); |
| bk = blocking.kc(); |
| } else { |
| internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index, |
| internal::ShardByRow> |
| blocking(k, m, n, 2); |
| bm = blocking.mc(); |
| bn = blocking.nc(); |
| bk = blocking.kc(); |
| } |
| |
| // Compute optimal number of threads. |
| // Note: we use bk instead of k here because we are interested in amount of |
| // _parallelizable_ computations, and computations are not parallelizable |
| // across k dimension. |
| const TensorOpCost cost = |
| contractionCost(m, n, bm, bn, bk, shard_by_col, false); |
| int num_threads = TensorCostModel<ThreadPoolDevice>::numThreads( |
| static_cast<double>(n) * m, cost, this->m_device.numThreads()); |
| int num_threads_by_k = numThreadsInnerDim(m, n, k); |
| if (shardByInnerDim(m, n, k, num_threads, num_threads_by_k)) { |
| // We are in the scenario where it is more effective to shard by the |
| // inner dimension. |
| if (IsEvalInSyncMode) { |
| EvalShardedByInnerDimContext<DoneCallback> ctx( |
| this, num_threads_by_k, buffer, m, n, k, std::move(done)); |
| ctx.template run<Alignment>(); |
| } else { |
| auto* ctx = new EvalShardedByInnerDimContext<DoneCallback>( |
| this, num_threads_by_k, buffer, m, n, k, std::move(done)); |
| ctx->template runAsync<Alignment>(); |
| } |
| |
| return; |
| } |
| |
| // TODO(dvyukov): this is a stop-gap to prevent regressions while the cost |
| // model is not tuned. Remove this when the cost model is tuned. |
| if (n == 1) num_threads = 1; |
| |
| if (num_threads == 1) { |
| TENSOR_CONTRACTION_DISPATCH(this->template evalProductSequential, |
| Unaligned, (buffer)); |
| if (!IsEvalInSyncMode) done(); |
| return; |
| } |
| |
| // Now that we know number of threads, recalculate sharding and blocking. |
| shard_by_col = shardByCol(m, n, num_threads); |
| if (shard_by_col) { |
| internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index, |
| internal::ShardByCol> |
| blocking(k, m, n, num_threads); |
| bm = blocking.mc(); |
| bn = blocking.nc(); |
| bk = blocking.kc(); |
| } else { |
| internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index, |
| internal::ShardByRow> |
| blocking(k, m, n, num_threads); |
| bm = blocking.mc(); |
| bn = blocking.nc(); |
| bk = blocking.kc(); |
| } |
| |
| // Number of kernels for each dimension. |
| Index nm0 = divup(m, bm); |
| Index nn0 = divup(n, bn); |
| Index nk = divup(k, bk); |
| |
| // Calculate task grain size (number of kernels executed per task). |
| // This task size coarsening serves two purposes: |
| // 1. It reduces per-task overheads including synchronization overheads. |
| // 2. It allows to use caches better (reuse the same packed rhs in several |
| // consecutive kernels). |
| Index gm = 1; |
| Index gn = 1; |
| // If we are sharding by column, then we prefer to reduce rows first. |
| if (shard_by_col) { |
| gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col); |
| gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col); |
| } else { |
| gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col); |
| gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col); |
| } |
| // Number of tasks in each dimension. |
| Index nm = divup(nm0, gm); |
| Index nn = divup(nn0, gn); |
| |
| // If there is enough concurrency in the sharding dimension, we choose not |
| // to paralellize by the other dimension, and execute all kernels in sync |
| // mode. This reduces parallelism from the nm x nn down to nn |
| // (shard_by_col==true) or nm (shard_by_col==false). |
| const Index sharding_dim_tasks = shard_by_col ? nn : nm; |
| const int num_worker_threads = this->m_device.numThreadsInPool(); |
| |
| // With small number of threads we want to make sure that we do not reduce |
| // parallelism too much. With large number of threads we trade maximum |
| // parallelism for better memory locality. |
| const float oversharding_factor = |
| num_worker_threads <= 4 ? 8.0 : |
| num_worker_threads <= 8 ? 4.0 : |
| num_worker_threads <= 16 ? 2.0 : |
| num_worker_threads <= 32 ? 1.0 : |
| num_worker_threads <= 64 ? 0.8 : /* num_worker_threads > 64 */ 0.6; |
| |
| const bool parallelize_by_sharding_dim_only = |
| sharding_dim_tasks >= oversharding_factor * num_worker_threads; |
| |
| // Last by not least, decide whether we want to issue both lhs and rhs |
| // packing in parallel; or issue lhs packing first, and then issue rhs |
| // packing when lhs packing completes (for !shard_by_col lhs and rhs are |
| // swapped). Parallel packing allows more parallelism (for both packing and |
| // kernels), while sequential packing provides better locality (once |
| // a thread finishes rhs packing it proceed to kernels with that rhs). |
| // First, we are interested in parallel packing if there are few tasks. |
| bool parallel_pack = num_threads >= nm * nn; |
| // Also do parallel packing if all data fits into L2$. |
| if (m * bk * Index(sizeof(LhsScalar)) + n * bk * Index(sizeof(RhsScalar)) <= |
| l2CacheSize() * num_threads) |
| parallel_pack = true; |
| // But don't do it if we will use each rhs only once. Locality seems to be |
| // more important in this case. |
| if ((shard_by_col ? nm : nn) == 1) parallel_pack = false; |
| // Also don't get in the way of parallelize_by_sharding_dim_only |
| // optimization. |
| if (parallelize_by_sharding_dim_only) parallel_pack = false; |
| |
| // TODO(ezhulnev): With if contexpr we don't need SyncEvalParallelContext. |
| if (IsEvalInSyncMode) { |
| #define CONTEXT_ARGS \ |
| (this, num_threads, buffer, m, n, k, bm, bn, bk, nm, nn, nk, gm, gn, nm0, \ |
| nn0, shard_by_col, parallel_pack, parallelize_by_sharding_dim_only, \ |
| NoCallback()) \ |
| .run() |
| TENSOR_CONTRACTION_DISPATCH(SyncEvalParallelContext, Alignment, |
| CONTEXT_ARGS); |
| #undef CONTEXT_ARGS |
| |
| } else { |
| #define CONTEXT_ARGS \ |
| (this, num_threads, buffer, m, n, k, bm, bn, bk, nm, nn, nk, gm, gn, nm0, \ |
| nn0, shard_by_col, parallel_pack, parallelize_by_sharding_dim_only, \ |
| std::move(done)) |
| TENSOR_CONTRACTION_ASYNC_DISPATCH(EvalParallelContext, DoneCallback, |
| Alignment, CONTEXT_ARGS, run()); |
| #undef CONTEXT_ARGS |
| } |
| } |
| |
| // ------------------------------------------------------------------------ // |
| |
| // Dummy struct to represent an empty DoneCallback. |
| |
| struct NoCallback { |
| void operator()() { |
| eigen_assert(false && "NoCallback should never be called"); |
| } |
| }; |
| |
| // ------------------------------------------------------------------------ // |
| |
| template <typename DoneCallback, typename Context> |
| class EvalParallelNotification; |
| |
| // Synchronous evaluation notification that blocks caller thread in Wait(). |
| template <typename Context> |
| class EvalParallelNotification<NoCallback, Context> { |
| public: |
| EvalParallelNotification(Context*, NoCallback) {} |
| void Notify() { done_.Notify(); } |
| void Wait() { done_.Wait(); } |
| private: |
| Eigen::Notification done_; |
| }; |
| |
| // Asynchronous evaluation notification that does not block in Wait(). |
| template <typename DoneCallback, typename Context> |
| class EvalParallelNotification { |
| public: |
| EvalParallelNotification(Context* ctx, DoneCallback done) |
| : ctx_(ctx), done_(std::move(done)) {} |
| |
| void Notify() { |
| // Make a copy of done callback, because it will be destructed when we |
| // will delete context in the next line (EvalParallelNotification is a |
| // data member of EvalParallelContext class). |
| DoneCallback done_copy = std::move(done_); |
| |
| // Delete parallel evaluation context. |
| delete ctx_; |
| |
| // Now safely call the done callback. |
| done_copy(); |
| } |
| |
| void Wait() {} |
| |
| private: |
| Context* ctx_; |
| DoneCallback done_; |
| }; |
| |
| // Context orchestrates sync/async parallel contraction evaluation. When it is |
| // executed in asynchronous mode, it owns all the shared state that might be |
| // accessible by block packing and kernel tasks. |
| |
| template <typename DoneCallback, bool lhs_inner_dim_contiguous, |
| bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, |
| int Alignment> |
| class EvalParallelContext { |
| public: |
| typedef internal::TensorContractionInputMapper< |
| LhsScalar, Index, internal::Lhs, LeftEvaluator, left_nocontract_t, |
| contract_t, internal::packet_traits<LhsScalar>::size, |
| lhs_inner_dim_contiguous, false, Unaligned> |
| LhsMapper; |
| typedef internal::TensorContractionInputMapper< |
| RhsScalar, Index, internal::Rhs, RightEvaluator, right_nocontract_t, |
| contract_t, internal::packet_traits<RhsScalar>::size, |
| rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Unaligned> |
| RhsMapper; |
| |
| typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper; |
| |
| typedef internal::TensorContractionKernel< |
| Scalar, LhsScalar, RhsScalar, Index, OutputMapper, LhsMapper, RhsMapper> |
| TensorContractionKernel; |
| |
| typedef typename TensorContractionKernel::LhsBlock LhsBlock; |
| typedef typename TensorContractionKernel::RhsBlock RhsBlock; |
| typedef typename TensorContractionKernel::BlockMemHandle BlockMemHandle; |
| |
| EvalParallelContext(const Self* self, int num_threads, Scalar* buffer, |
| Index tm, Index tn, Index tk, Index bm, Index bn, |
| Index bk, Index nm, Index nn, Index nk, Index gm, |
| Index gn, Index nm0, Index nn0, bool shard_by_col, |
| bool parallel_pack, |
| bool parallelize_by_sharding_dim_only, |
| DoneCallback done) |
| : created_by_thread_id_(std::this_thread::get_id()), |
| done_(this, std::move(done)), |
| device_(self->m_device), |
| lhs_(self->m_leftImpl, self->m_left_nocontract_strides, |
| self->m_i_strides, self->m_left_contracting_strides, |
| self->m_k_strides), |
| rhs_(self->m_rightImpl, self->m_right_nocontract_strides, |
| self->m_j_strides, self->m_right_contracting_strides, |
| self->m_k_strides), |
| buffer_(buffer), |
| output_(buffer, tm), |
| output_kernel_(self->m_output_kernel), |
| tensor_contraction_params_(self->m_tensor_contraction_params), |
| num_threads_(num_threads), |
| shard_by_col_(shard_by_col), |
| parallel_pack_(parallel_pack), |
| parallelize_by_sharding_dim_only_(parallelize_by_sharding_dim_only), |
| m_(tm), |
| n_(tn), |
| k_(tk), |
| bm_(bm), |
| bn_(bn), |
| bk_(bk), |
| nm_(nm), |
| nn_(nn), |
| nk_(nk), |
| gm_(gm), |
| gn_(gn), |
| nm0_(nm0), |
| nn0_(nn0), |
| kernel_(m_, k_, n_, bm_, bk_, bn_), |
| num_thread_local_allocations_(0), |
| // We reserve 2X more capacity for a thread local values, than the |
| // number of threads in the pool to efficiently handle task stealing |
| // by threads that are not managed by the pool. |
| thread_local_capacity(2 * (parallelize_by_sharding_dim_only_ |
| ? device_.numThreadsInPool() |
| : 0)), |
| // We will use only one of the Lhs/Rhs thread local storage depending |
| // on the shard_by_col value and we parallelize by sharding dim ONLY. |
| lhs_thread_local_blocks_(shard_by_col_ ? 0 : thread_local_capacity, |
| {*this}, {*this}), |
| rhs_thread_local_blocks_(shard_by_col_ ? thread_local_capacity : 0, |
| {*this}, {*this}) { |
| // These two options are mutually exclusive. |
| eigen_assert(!(parallel_pack && parallelize_by_sharding_dim_only)); |
| |
| for (Index x = 0; x < P; x++) { |
| // Normal number of notifications for k slice switch is |
| // nm_ + nn_ + nm_ * nn_. However, first P - 1 slices will receive only |
| // nm_ + nn_ notifications, because they will not receive notifications |
| // from preceding kernels. |
| state_switch_[x] = |
| x == 0 |
| ? 1 |
| : (parallel_pack_ ? nn_ + nm_ : (shard_by_col_ ? nn_ : nm_)) + |
| (x == P - 1 ? nm_ * nn_ : 0); |
| state_packing_ready_[x] = |
| parallel_pack_ ? 0 : (shard_by_col_ ? nm_ : nn_); |
| state_kernel_[x] = new std::atomic<uint8_t>*[nm_]; |
| for (Index m = 0; m < nm_; m++) { |
| state_kernel_[x][m] = new std::atomic<uint8_t>[nn_]; |
| // Kernels generally receive 3 notifications (previous kernel + 2 |
| // packing), but the first slice won't get notifications from previous |
| // kernels. |
| for (Index n = 0; n < nn_; n++) |
| state_kernel_[x][m][n].store( |
| (x == 0 ? 0 : 1) + (parallel_pack_ ? 2 : 1), |
| std::memory_order_relaxed); |
| } |
| } |
| |
| // Allocate memory for packed rhs/lhs matrices. |
| packed_mem_ = kernel_.allocateSlices( // |
| device_, // |
| /*num_lhs=*/nm0_, // |
| /*num_rhs=*/nn0_, // |
| /*num_slices=*/std::min<Index>(nk_, P - 1), // |
| packed_lhs_, packed_rhs_); |
| |
| if (parallelize_by_sharding_dim_only_) { |
| const int num_worker_threads = device_.numThreadsInPool(); |
| |
| if (shard_by_col) { |
| can_use_thread_local_packed_ = new std::atomic<bool>[nn_]; |
| for (int i = 0; i < nn_; ++i) |
| can_use_thread_local_packed_[i].store(true, |
| std::memory_order_relaxed); |
| |
| Index num_blocks = num_worker_threads * gn_; |
| thread_local_pre_alocated_mem_ = kernel_.allocateSlices( // |
| device_, // |
| /*num_lhs=*/0, // |
| /*num_rhs=*/num_blocks, // |
| /*num_slices=*/1, // |
| /*lhs_blocks=*/nullptr, &rhs_thread_local_pre_allocated_); |
| |
| } else { |
| can_use_thread_local_packed_ = new std::atomic<bool>[nm_]; |
| for (int i = 0; i < nm_; ++i) |
| can_use_thread_local_packed_[i].store(true, |
| std::memory_order_relaxed); |
| |
| Index num_blocks = num_worker_threads * gm_; |
| thread_local_pre_alocated_mem_ = kernel_.allocateSlices( // |
| device_, // |
| /*num_lhs=*/num_blocks, // |
| /*num_rhs=*/0, // |
| /*num_slices=*/1, &lhs_thread_local_pre_allocated_, // |
| /*rhs_blocks=*/nullptr); |
| } |
| } |
| } |
| |
| ~EvalParallelContext() { |
| for (Index x = 0; x < P; x++) { |
| for (Index m = 0; m < nm_; m++) delete[] state_kernel_[x][m]; |
| delete[] state_kernel_[x]; |
| } |
| kernel_.deallocate(device_, packed_mem_); |
| if (parallelize_by_sharding_dim_only_) { |
| kernel_.deallocate(device_, thread_local_pre_alocated_mem_); |
| delete[] can_use_thread_local_packed_; |
| } |
| } |
| |
| void run() { |
| // Kick off packing of the first slice. |
| signal_switch(0, 1); |
| |
| // Wait for overall completion. |
| // |
| // If parallel evaluation is executed in async mode, this is a no-op, and |
| // Wait() will return immediately. In synchronous mode it will block the |
| // caller thread until it will receive notification from last task. |
| // |
| // In async mode, last task when completed will call done callback from |
| // the same thread, and will delete this context. |
| // |
| // TODO(dvyukov): This wait can lead to deadlock if contraction is |
| // evaluated in synchronous mode. If nthreads contractions are |
| // concurrently submitted from worker threads, this wait will block all |
| // worker threads and the system will deadlock. |
| done_.Wait(); |
| } |
| |
| private: |
| std::thread::id created_by_thread_id_; |
| |
| // This notification is specialized on the type of DoneCallback and can be |
| // blocking or non-blocking. |
| EvalParallelNotification<DoneCallback, EvalParallelContext> done_; |
| |
| const Device& device_; |
| LhsMapper lhs_; |
| RhsMapper rhs_; |
| Scalar* const buffer_; |
| OutputMapper output_; |
| OutputKernelType output_kernel_; |
| TensorContractionParams tensor_contraction_params_; |
| const int num_threads_; |
| const bool shard_by_col_; |
| const bool parallel_pack_; |
| const bool parallelize_by_sharding_dim_only_; |
| // Matrix sizes. |
| const Index m_; |
| const Index n_; |
| const Index k_; |
| // Block sizes. |
| const Index bm_; |
| const Index bn_; |
| const Index bk_; |
| // Number of tasks. |
| const Index nm_; |
| const Index nn_; |
| const Index nk_; |
| // Task grain sizes (number of kernels executed per task). |
| const Index gm_; |
| const Index gn_; |
| // Number of blocks (this is different from ni_/nn_ because of task size |
| // coarsening). |
| const Index nm0_; |
| const Index nn0_; |
| // Tensor contraction kernel. |
| TensorContractionKernel kernel_; |
| |
| // Parallelization strategy. |
| // |
| // Blocks related to the same k block can run in parallel because they write |
| // to different output blocks. So we parallelize within k slices, this |
| // gives us parallelism level of m x n. Before we can start any kernels |
| // related to k-th slice, we need to issue m lhs packing tasks and n rhs |
| // packing tasks. |
| // |
| // However, there is a bottleneck when we are finishing kernels for k-th |
| // slice (at the very end there is only 1 runnable kernel). To mitigate this |
| // bottleneck we allow kernels from k-th and k+1-th slices to run in |
| // parallel. Note that (m, n, k) and (m, n, k+1) kernels write to the same |
| // output block, so they must not run in parallel. |
| // |
| // This gives us the following dependency graph. |
| // On each k slice we have m x n kernel tasks, m lhs paking tasks and n rhs |
| // packing tasks. |
| // Kernel (m, n, k) can start when: |
| // - kernel (m, n, k-1) has finished |
| // - lhs packing (m, k) has finished |
| // - rhs packing (n, k) has finished |
| // Lhs/rhs packing can start when: |
| // - all k-1 packing has finished (artificially imposed to limit amount of |
| // parallel packing) |
| // |
| // On top of that we limit runnable tasks to two consecutive k slices. |
| // This is done to limit amount of memory we need for packed lhs/rhs |
| // (for each k slice we need m*bk + n*bk memory in packed_lhs_/packed_rhs_). |
| // |
| // state_switch_ tracks when we are ready to switch to the next k slice. |
| // state_kernel_[m][n] tracks when we are ready to kick off kernel (m, n). |
| // These variable are rolling over 3 consecutive k slices: first two we are |
| // actively executing + one to track completion of kernels in the second |
| // slice. |
| static constexpr Index P = 3; |
| |
| // Handle to the allocated temporary storage for Lhs/Rhs blocks. |
| BlockMemHandle packed_mem_; |
| std::vector<LhsBlock> packed_lhs_[P - 1]; |
| std::vector<RhsBlock> packed_rhs_[P - 1]; |
| |
| // If we choose to parallelize only by the sharding dimension, each thread |
| // will have it's own "thead local" (not a c++ thread local storage) memory |
| // for packed_lhs or packed_rhs (shard_by_col = false of true). This memory |
| // can't be passed to a kernel that might execute on a different thread. |
| // |
| // In practice when we are ready to pack memory for the sharding dimension |
| // (rhs if shard_by_col==true) of the K-th slice, all kernels for K-1 slice |
| // already computed (99% of the time), and we can pack data into the thread |
| // local storage, and guarantee that all the kernels will be executed |
| // immediately in the same thread. This significantly increases L1 cache hit |
| // ratio and reduces pressure on the memory bus. |
| // |
| // It's still possible that kernel for the K-th slice will be ready before |
| // completion of the K-1 kernel, so we have to allocate "global" packed_lhs_ |
| // and packed_rhs_ to allow kernels to be executed later on a thread |
| // different from the thread that was used for packing. |
| |
| // Handle for pre-allocated thread local memory buffers. |
| BlockMemHandle thread_local_pre_alocated_mem_; |
| |
| // Only one of these will be initialized depending on shard_by_col value |
| // (the size will be `num_worker_threads * num_grains_in_the_sharding_dim`). |
| std::vector<LhsBlock> lhs_thread_local_pre_allocated_; |
| std::vector<RhsBlock> rhs_thread_local_pre_allocated_; |
| |
| // How many thread local blocks were already allocated. |
| std::atomic<int> num_thread_local_allocations_; |
| const int thread_local_capacity; |
| |
| // We will use pre-allocated Lhs/Rhs blocks defined above, if the number of |
| // unique threads in a system is below or equal to the number of threads in |
| // a thread pool. We will fallback on dynamic memory allocation after that. |
| |
| // ThreadLocalBlocks is a container for Lhs or Rhs thread local buffers. Its |
| // size is equal to the grain size in Lhs/Rhs sharding dimension. |
| template <typename BlockType> |
| class ThreadLocalBlocks { |
| public: |
| ThreadLocalBlocks() = default; |
| |
| ThreadLocalBlocks(BlockType* base, size_t grain_size) |
| : is_pre_allocated_(true), |
| thread_local_pre_allocated_base_(base), |
| grain_size_(grain_size) {} |
| |
| ThreadLocalBlocks(BlockMemHandle mem_handle, |
| std::vector<BlockType> blocks) |
| : is_pre_allocated_(false), |
| mem_handle_(std::move(mem_handle)), |
| blocks_(std::move(blocks)) {} |
| |
| BlockType& block(int grain_index) { |
| eigen_assert(grain_index >= 0); |
| eigen_assert(static_cast<size_t>(grain_index) < size()); |
| return is_pre_allocated_ ? thread_local_pre_allocated_base_[grain_index] |
| : blocks_[grain_index]; |
| } |
| |
| void Release(EvalParallelContext& ctx) const { |
| if (!is_pre_allocated_) { |
| ctx.kernel_.deallocate(ctx.device_, mem_handle_); |
| } |
| } |
| |
| size_t size() const { |
| return is_pre_allocated_ ? grain_size_ : blocks_.size(); |
| } |
| |
| private: |
| bool is_pre_allocated_; |
| |
| // Reuse pre-allocated thread local buffers. |
| BlockType* thread_local_pre_allocated_base_ = nullptr; |
| size_t grain_size_ = 0; |
| |
| // These will be initialized only if `is_pre_allocated == false`. |
| BlockMemHandle mem_handle_{}; |
| std::vector<BlockType> blocks_; |
| }; |
| |
| // ThreadLocalBlocksInitialize callable does custom thread local blocks |
| // initialization, and will reuse pre-allocated buffers if possible, or will |
| // dynamically allocate new memory. |
| // |
| // Lhs/Rhs blocks might be of the same type, so we have to pass explicitly |
| // for what side do we plan to do block allocation. |
| template <typename BlockType, bool is_rhs> |
| class ThreadLocalBlocksInitialize { |
| static constexpr bool kIsLhs = |
| !is_rhs && std::is_same<BlockType, LhsBlock>::value; |
| static const bool kIsRhs = |
| is_rhs && std::is_same<BlockType, RhsBlock>::value; |
| static_assert(kIsLhs || kIsRhs, "Unknown block type"); |
| |
| using Blocks = ThreadLocalBlocks<BlockType>; |
| |
| public: |
| ThreadLocalBlocksInitialize(EvalParallelContext& ctx) |
| : ctx_(ctx), |
| num_worker_threads_(ctx_.device_.numThreadsInPool()) {} |
| |
| void operator()(Blocks& blocks) { |
| const int n = ctx_.num_thread_local_allocations_.fetch_add( |
| 1, std::memory_order_relaxed); |
| |
| if (n >= num_worker_threads_) { |
| ThreadLocalBlocksAllocator<is_rhs>::allocate(ctx_, blocks); |
| } else { |
| ThreadLocalBlocksAllocator<is_rhs>::reuse(ctx_, n, blocks); |
| } |
| } |
| |
| private: |
| // NOTE(ezhulenev): Without 'if constexpr' we have to put calls to |
| // TensorContractionKernel::allocateSlices into template specializations. |
| // Also explicit specializations are not allowed at class scope in C++03, |
| // EvalCtx type parameter is just a workaround for that limitation. |
| template <bool pack_rhs, typename EvalCtx = EvalParallelContext> |
| struct ThreadLocalBlocksAllocator; |
| |
| template <typename EvalCtx> |
| struct ThreadLocalBlocksAllocator</*pack_rhs=*/true, EvalCtx> { |
| static void allocate(EvalCtx& ctx, Blocks& blocks) { |
| std::vector<RhsBlock> rhs_blocks; |
| BlockMemHandle mem_handle = ctx.kernel_.allocateSlices( |
| ctx.device_, |
| /*num_lhs=*/0, |
| /*num_rhs=*/ctx.gn_, |
| /*num_slices=*/1, |
| /*lhs_blocks=*/nullptr, /*rhs_blocks=*/&rhs_blocks); |
| |
| blocks = ThreadLocalBlocks<RhsBlock>(std::move(mem_handle), |
| std::move(rhs_blocks)); |
| } |
| |
| static void reuse(EvalCtx& ctx, int index, Blocks& blocks) { |
| RhsBlock* ptr = &ctx.rhs_thread_local_pre_allocated_[ctx.gn_ * index]; |
| blocks = ThreadLocalBlocks<RhsBlock>(ptr, ctx.gn_); |
| } |
| }; |
| |
| template <typename EvalCtx> |
| struct ThreadLocalBlocksAllocator</*pack_rhs=*/false, EvalCtx> { |
| static void allocate(EvalCtx& ctx, Blocks& blocks) { |
| std::vector<LhsBlock> lhs_blocks; |
| BlockMemHandle mem_handle = ctx.kernel_.allocateSlices( |
| ctx.device_, |
| /*num_lhs=*/ctx.gm_, |
| /*num_rhs=*/0, |
| /*num_slices=*/1, |
| /*lhs_blocks=*/&lhs_blocks, /*rhs_blocks=*/nullptr); |
| |
| blocks = ThreadLocalBlocks<LhsBlock>(std::move(mem_handle), |
| std::move(lhs_blocks)); |
| } |
| |
| static void reuse(EvalCtx& ctx, int index, Blocks& blocks) { |
| LhsBlock* ptr = &ctx.lhs_thread_local_pre_allocated_[ctx.gm_ * index]; |
| blocks = ThreadLocalBlocks<LhsBlock>(ptr, ctx.gm_); |
| } |
| }; |
| |
| EvalParallelContext& ctx_; |
| const int num_worker_threads_; |
| }; |
| |
| template <typename BlockType> |
| class ThreadLocalBlocksRelease { |
| public: |
| using Blocks = ThreadLocalBlocks<BlockType>; |
| ThreadLocalBlocksRelease(EvalParallelContext& ctx) : ctx_(ctx) {} |
| void operator()(Blocks& blocks) { blocks.Release(ctx_); } |
| |
| private: |
| EvalParallelContext& ctx_; |
| }; |
| |
| // ThreadLocalBlocks initialization callables. |
| using ThreadLocalLhsInit = |
| ThreadLocalBlocksInitialize<LhsBlock, /*is_rhs=*/false>; |
| using ThreadLocalRhsInit = |
| ThreadLocalBlocksInitialize<RhsBlock, /*is_rhs=*/true>; |
| |
| // ThreadLocalBlocks release callables. |
| using ThreadLocalLhsRelease = ThreadLocalBlocksRelease<LhsBlock>; |
| using ThreadLocalRhsRelease = ThreadLocalBlocksRelease<RhsBlock>; |
| |
| // Thread local containers for Lhs/Rhs block packs. In practice only one of |
| // them will be used, depending on the shard_by_col value. |
| Eigen::ThreadLocal<ThreadLocalBlocks<LhsBlock>, ThreadLocalLhsInit, |
| ThreadLocalLhsRelease> |
| lhs_thread_local_blocks_; |
| Eigen::ThreadLocal<ThreadLocalBlocks<RhsBlock>, ThreadLocalRhsInit, |
| ThreadLocalRhsRelease> |
| rhs_thread_local_blocks_; |
| |
| // After a particular shard for Kth slice missed thread local execution |
| // opportunity (K-1 slice didn't complete kernels execution), we can no |
| // longer schedule K+1 and following slices in thread local mode, because |
| // there is no more guarantee that previous kernels were executed |
| // sequentially in the same thread (size is nn_ or nm_). |
| std::atomic<bool>* can_use_thread_local_packed_; |
| |
| std::atomic<uint8_t>** state_kernel_[P]; |
| // state_switch_ is frequently modified by worker threads, while other |
| // fields are read-only after constructor. Let's move it to a separate cache |
| // line to reduce cache-coherency traffic. |
| char pad_[128]; |
| std::atomic<Index> state_packing_ready_[P]; |
| std::atomic<Index> state_switch_[P]; |
| |
| LhsBlock& packed_lhs(Index m, Index k, Index m1, bool use_thread_local) { |
| if (use_thread_local) { |
| eigen_assert(!shard_by_col_); |
| ThreadLocalBlocks<LhsBlock>& blocks = lhs_thread_local_blocks_.local(); |
| |
| Index grain_index = m1 - m * gm_; |
| return blocks.block(internal::convert_index<int>(grain_index)); // FIXME better make ThreadLocalBlocks use Eigen::Index? |
| } else { |
| return packed_lhs_[k % (P - 1)][m1]; |
| } |
| } |
| |
| RhsBlock& packed_rhs(Index n, Index k, Index n1, bool use_thread_local) { |
| if (use_thread_local) { |
| eigen_assert(shard_by_col_); |
| ThreadLocalBlocks<RhsBlock>& blocks = rhs_thread_local_blocks_.local(); |
| |
| Index grain_index = n1 - n * gn_; |
| return blocks.block(internal::convert_index<int>(grain_index)); // FIXME better make ThreadLocalBlocks use Eigen::Index? |
| } else { |
| return packed_rhs_[k % (P - 1)][n1]; |
| } |
| } |
| |
| // In following two methods (pack_lhs and pack_rhs), if we know for sure |
| // that we'll be able to immediately call a kernel with packed data, and do |
| // not submit it to the thread pool, we can use thread local memory for |
| // packed data. |
| // |
| // We can only reliably check it if we are running all kernels in sync mode |
| // (parallelize only by sharding dim). If kernel for m==0 (n==0) is ready to |
| // run, it's guaranteed that all kernels with larger values of m (n) are |
| // also ready, because we execute them in the same order for all K slices. |
| |
| void pack_lhs(Index m, Index k) { |
| bool use_thread_local = false; |
| |
| if (parallelize_by_sharding_dim_only_ && !shard_by_col_ && |
| can_use_thread_local_packed_[m].load(std::memory_order_relaxed)) { |
| if (state_kernel_[k % P][m][0].load(std::memory_order_relaxed) == 1) { |
| use_thread_local = true; |
| } else { |
| // If we can't guarantee that all kernels in `k` slice will be |
| // executed sequentially in current thread, it's no longer safe to use |
| // thread local memory in following slices along the k dimensions. |
| eigen_assert(k > 0); |
| can_use_thread_local_packed_[m].store(false, |
| std::memory_order_relaxed); |
| } |
| } |
| |
| const Index mend = m * gm_ + gm(m); |
| for (Index m1 = m * gm_; m1 < mend; m1++) |
| kernel_.packLhs(&packed_lhs(m, k, m1, use_thread_local), |
| lhs_.getSubMapper(m1 * bm_, k * bk_), bk(k), bm(m1)); |
| |
| if (!parallel_pack_ && shard_by_col_) { |
| eigen_assert(!use_thread_local); |
| signal_packing(k); |
| } else { |
| signal_switch(k + 1); |
| for (Index n = nn_ - 1; n >= 0; n--) { |
| bool sync = parallelize_by_sharding_dim_only_ || n == 0; |
| signal_kernel(m, n, k, sync, use_thread_local); |
| } |
| } |
| } |
| |
| void pack_rhs(Index n, Index k) { |
| bool use_thread_local = false; |
| |
| if (parallelize_by_sharding_dim_only_ && shard_by_col_ && |
| can_use_thread_local_packed_[n].load(std::memory_order_relaxed)) { |
| if (state_kernel_[k % P][0][n].load(std::memory_order_relaxed) == 1) { |
| use_thread_local = true; |
| } else { |
| // If we can't guarantee that all kernels in `k` slice will be |
| // executed sequentially in current thread, it's no longer safe to use |
| // thread local memory in following slices along the k dimensions. |
| eigen_assert(k > 0); |
| can_use_thread_local_packed_[n].store(false, |
| std::memory_order_relaxed); |
| } |
| } |
| |
| const Index nend = n * gn_ + gn(n); |
| for (Index n1 = n * gn_; n1 < nend; n1++) { |
| if (!TensorContractionKernel::HasBeta && k == 0) { |
| // Zero the output memory in parallel, only if contraction kernel does |
| // not support `beta`. Otherwise we will pass beta 0.0 to the first |
| // call to the `TensorContractionKernel::invoke()`. |
| // |
| // On 10000x2x10000 mm zeroing can easily take half of time. Zero (bn |
| // x m) row. Safe to do here because all kernels that will write to |
| // this memory depend on completion of this task. Note: don't call |
| // device_.fill() here. device_.fill() blocks on thread pool |
| // worker thread, which can lead to underutilization and deadlocks. |
| std::fill_n(buffer_ + n1 * bn_ * m_, bn(n1) * m_, Scalar(0)); |
| } |
| kernel_.packRhs(&packed_rhs(n, k, n1, use_thread_local), |
| rhs_.getSubMapper(k * bk_, n1 * bn_), bk(k), bn(n1)); |
| } |
| |
| if (parallel_pack_ || shard_by_col_) { |
| signal_switch(k + 1); |
| for (Index m = nm_ - 1; m >= 0; m--) { |
| bool sync = parallelize_by_sharding_dim_only_ || m == 0; |
| signal_kernel(m, n, k, sync, use_thread_local); |
| } |
| } else { |
| eigen_assert(!use_thread_local); |
| signal_packing(k); |
| } |
| } |
| |
| void kernel(Index m, Index n, Index k, bool use_thread_local) { |
| // Note: order of iteration matters here. Iteration over m is innermost |
| // because we want to reuse the same packed rhs in consecutive tasks |
| // (rhs fits into L2$ while lhs only into L3$). |
| const Index nend = n * gn_ + gn(n); |
| const Index mend = m * gm_ + gm(m); |
| |
| // NOTE: output = alpha * LHS * RHS + beta * output. |
| const Scalar alpha = Scalar(1); |
| const Scalar beta = |
| (TensorContractionKernel::HasBeta && k == 0) ? Scalar(0) : Scalar(1); |
| |
| if (shard_by_col_) { |
| for (Index n1 = n * gn_; n1 < nend; n1++) { |
| for (Index m1 = m * gm_; m1 < mend; m1++) { |
| const auto output_mapper = output_.getSubMapper(m1 * bm_, n1 * bn_); |
| kernel_.invoke( |
| output_mapper, |
| packed_lhs(m, k, m1, !shard_by_col_ && use_thread_local), |
| packed_rhs(n, k, n1, shard_by_col_ && use_thread_local), bm(m1), |
| bk(k), bn(n1), alpha, beta); |
| |
| // We are done with the last task for the [m1, n1] block. |
| if (k + 1 == nk_) { |
| output_kernel_(output_mapper, tensor_contraction_params_, |
| m1 * bm_, n1 * bn_, bm(m1), bn(n1)); |
| } |
| } |
| } |
| } else { |
| for (Index m1 = m * gm_; m1 < mend; m1++) |
| for (Index n1 = n * gn_; n1 < nend; n1++) { |
| const auto output_mapper = output_.getSubMapper(m1 * bm_, n1 * bn_); |
| kernel_.invoke( |
| output_mapper, |
| packed_lhs(m, k, m1, !shard_by_col_ && use_thread_local), |
| packed_rhs(n, k, n1, shard_by_col_ && use_thread_local), bm(m1), |
| bk(k), bn(n1), alpha, beta); |
| |
| // We are done with the last task for the [m1, n1] block. |
| if (k + 1 == nk_) { |
| output_kernel_(output_mapper, tensor_contraction_params_, |
| m1 * bm_, n1 * bn_, bm(m1), bn(n1)); |
| } |
| } |
| } |
| signal_kernel(m, n, k + 1, /*sync=*/false, /*use_thread_local=*/false); |
| signal_switch(k + 2); |
| } |
| |
| void signal_packing(Index k) { |
| eigen_assert(!parallel_pack_); |
| Index s = state_packing_ready_[k % P].fetch_sub(1); |
| eigen_assert(s > 0); |
| if (s != 1) return; |
| state_packing_ready_[k % P] = shard_by_col_ ? nm_ : nn_; |
| enqueue_packing(k, shard_by_col_); |
| } |
| |
| void signal_kernel(Index m, Index n, Index k, bool sync, |
| bool use_thread_local) { |
| std::atomic<uint8_t>* state = &state_kernel_[k % P][m][n]; |
| Index s = state->load(); |
| eigen_assert(s > 0); |
| if (s != 1 && state->fetch_sub(1) != 1) { |
| eigen_assert(!use_thread_local); |
| return; |
| } |
| state->store(parallel_pack_ ? 3 : 2, std::memory_order_relaxed); |
| if (sync) { |
| kernel(m, n, k, use_thread_local); |
| } else { |
| eigen_assert(!use_thread_local); |
| device_.enqueueNoNotification( |
| [=]() { kernel(m, n, k, use_thread_local); }); |
| } |
| } |
| |
| void signal_switch(Index k, Index v = 1) { |
| Index s = state_switch_[k % P].fetch_sub(v); |
| eigen_assert(s >= v); |
| if (s != v) return; |
| |
| // Ready to switch to the next k slice. |
| // Reset counter for the next iteration. |
| state_switch_[k % P] = |
| (parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_)) + |
| nm_ * nn_; |
| if (k < nk_) { |
| // Issue lhs/rhs packing. Their completion will in turn kick off |
| // kernels. |
| if (parallel_pack_) { |
| enqueue_packing(k, !shard_by_col_); |
| enqueue_packing(k, shard_by_col_); |
| } else if (shard_by_col_) { |
| enqueue_packing(k, false); |
| } else { |
| enqueue_packing(k, true); |
| } |
| |
| // Termination handling. |
| // Because kernel completion signals k + 2 switch, we need to finish nk |
| // + 2 slices without issuing any tasks on nk + 1 slice. So here we |
| // pretend that all nk + 1 packing tasks just finish instantly; so that |
| // nk + 2 switch only waits for completion of nk kernels. |
| } else if (k == nk_) { |
| signal_switch(k + 1, |
| parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_)); |
| } else { |
| done_.Notify(); |
| } |
| } |
| |
| // Enqueue all rhs/lhs packing for k-th slice. |
| void enqueue_packing(Index k, bool rhs) { |
| enqueue_packing_helper(0, rhs ? nn_ : nm_, k, rhs); |
| } |
| |
| void enqueue_packing_helper(Index start, Index end, Index k, bool rhs) { |
| if (end - start == 1) { |
| if (rhs) |
| pack_rhs(start, k); |
| else |
| pack_lhs(start, k); |
| } else { |
| while (end - start > 1) { |
| Index mid = (start + end) / 2; |
| device_.enqueueNoNotification( |
| [=]() { enqueue_packing_helper(mid, end, k, rhs); }); |
| end = mid; |
| } |
| |
| // Decide if we want to run first packing task (start == 0) in |
| // async mode if we parallelize only by sharding dim: |
| // (1) pack_lhs and pack_rhs call signal_switch before completing |
| // all calls to signal_kernel, which in sync mode might lead |
| // to the execution of the first kernel of the k+1 slice, before |
| // completing a call to the last kernel of the k slice. |
| // (2) all pack tasks for sharded dim must be executed in a thread |
| // pool to get pre-allocated thead local buffers. |
| bool pack_async = |
| (start == 0) && |
| (parallelize_by_sharding_dim_only_&& shard_by_col_ == rhs) && |
| (k > 0 || std::this_thread::get_id() == created_by_thread_id_); |
| |
| if (pack_async) { |
| device_.enqueueNoNotification( |
| [=]() { enqueue_packing_helper(start, end, k, rhs); }); |
| } else { |
| enqueue_packing_helper(start, end, k, rhs); |
| } |
| } |
| } |
| |
| // Block sizes with accounting for potentially incomplete last block. |
| Index bm(Index m) const { return m + 1 < nm0_ ? bm_ : m_ + bm_ - bm_ * nm0_; } |
| Index bn(Index n) const { return n + 1 < nn0_ ? bn_ : n_ + bn_ - bn_ * nn0_; } |
| Index bk(Index k) const { return k + 1 < nk_ ? bk_ : k_ + bk_ - bk_ * nk_; } |
| // Task grain sizes accounting for potentially incomplete last task. |
| Index gm(Index m) const { return m + 1 < nm_ ? gm_ : nm0_ + gm_ - gm_ * nm_; } |
| Index gn(Index n) const { return n + 1 < nn_ ? gn_ : nn0_ + gn_ - gn_ * nn_; } |
| |
| EvalParallelContext(const EvalParallelContext&) = delete; |
| void operator=(const EvalParallelContext&) = delete; |
| }; |
| |
| template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, |
| bool rhs_inner_dim_reordered, int Alignment> |
| using SyncEvalParallelContext = |
| EvalParallelContext<NoCallback, lhs_inner_dim_contiguous, |
| rhs_inner_dim_contiguous, rhs_inner_dim_reordered, |
| Alignment>; |
| |
| // ------------------------------------------------------------------------ // |
| |
| // EvalShardedByInnerDimContext orchestrates sync/async contraction |
| // evaluation, when we shard by inner dimension. When it is executed in |
| // asynchronous mode, it owns all the shared state that might be accessible by |
| // block processing tasks. |
| |
| template <typename DoneCallback> |
| struct EvalShardedByInnerDimContext { |
| EvalShardedByInnerDimContext(const Self* self, int num_threads, |
| Scalar* result_buffer, |
| Index m_size, Index n_size, Index k_size, |
| DoneCallback done_callback) |
| : evaluator(self), |
| m_lhs_inner_dim_contiguous(evaluator->m_lhs_inner_dim_contiguous), |
| m_rhs_inner_dim_contiguous(evaluator->m_rhs_inner_dim_contiguous), |
| m_rhs_inner_dim_reordered(evaluator->m_rhs_inner_dim_reordered), |
| result(result_buffer), |
| m(m_size), |
| n(n_size), |
| k(k_size), |
| done(std::move(done_callback)), |
| buffer_size_bytes(m * n * sizeof(Scalar)), |
| block_size(blockSize(k, num_threads)), |
| num_blocks(divup<Index>(k, block_size)), |
| num_pending_blocks(internal::convert_index<int>(num_blocks)), |
| l0_ranges(divup<Index>(num_blocks, l0_size)), |
| l0_state(l0_ranges), |
| block_buffers(num_blocks) { |
| // Keep count of pending gemm tasks for each l0 range. |
| for (int i = 0; i < l0_ranges; ++i) { |
| const Index num_pending_tasks = actualRangeSize(l0_ranges, l0_size, i); |
| l0_state.emplace_back(internal::convert_index<int>(num_pending_tasks)); |
| } |
| |
| // Allocate temporary buffers for each block. |
| for (Index block_idx = 0; block_idx < num_blocks; ++block_idx) { |
| Scalar* buf = block_idx == 0 |
| ? result |
| : static_cast<Scalar*>(evaluator->m_device.allocate( |
| buffer_size_bytes)); |
| block_buffers.emplace_back(buf); |
| } |
| } |
| |
| ~EvalShardedByInnerDimContext() { |
| for (Index i = 1; i < num_blocks; ++i) { |
| evaluator->m_device.deallocate(block_buffers[i]); |
| } |
| } |
| |
| template <int Alignment> |
| void run() { |
| Barrier barrier(internal::convert_index<int>(num_blocks)); |
| eval<Alignment>(barrier, 0, num_blocks); |
| barrier.Wait(); |
| |
| // Aggregate partial sums from l0 ranges. |
| aggregateL0Blocks<Alignment>(); |
| |
| // Apply output kernel. |
| applyOutputKernel(); |
| } |
| |
| template <int Alignment> |
| void runAsync() { |
| evalAsync<Alignment>(0, num_blocks); |
| } |
| |
| private: |
| // The underlying GEMM kernel assumes that k is a multiple of |
| // the packet size and subtle breakage occurs if this is violated. |
| static const Index packet_size = internal::packet_traits<RhsScalar>::size; |
| |
| const Self* evaluator; // TensorContraction evaluator |
| |
| // These fields required fromTENSOR_CONTRACTION_DISPATCH macro. |
| bool m_lhs_inner_dim_contiguous; |
| bool m_rhs_inner_dim_contiguous; |
| bool m_rhs_inner_dim_reordered; |
| |
| Scalar* result; |
| |
| Index m; |
| Index n; |
| Index k; |
| |
| DoneCallback done; |
| |
| // ----------------------------------------------------------------------// |
| // Algorithm parameters. |
| |
| // We will compute partial results into the buffers of this size. |
| Index buffer_size_bytes; |
| |
| Index block_size; |
| Index num_blocks; |
| |
| // Keep track of pending tasks when evaluate in async mode. |
| std::atomic<int> num_pending_blocks; |
| |
| // We compute partial gemm results in parallel, and to get the final result |
| // we need to add them all together. For the large number of threads (>= 48) |
| // this adds a very expensive sequential step at the end. |
| // |
| // We split the [0, num_blocks) into small ranges, and when a task for the |
| // block finishes its partial gemm computation, it checks if it was the last |
| // gemm in the range, and if so, it will add all blocks of the range. |
| // |
| // After all tasks done, we need to add only these pre-aggregated blocks. |
| |
| // For now we use just a single level of ranges to compute pre-aggregated |
| // partial sums, but in general we can use more layers to compute tree |
| // aggregation in parallel and reduce the size of the sequential step. |
| // |
| // TODO(ezhulenev): Add multilevel tree aggregation? Probably will make |
| // sense only if number of threads >= ~128? |
| static const Index l0_size = 4; |
| Index l0_ranges; |
| |
| // Keep count of pending gemm tasks for each l0 range. |
| MaxSizeVector<std::atomic<int>> l0_state; // [0, l0_ranges) |
| |
| // Buffers allocated for each temporary block computation. |
| MaxSizeVector<Scalar*> block_buffers; // [0, num_blocks) |
| |
| template <int Alignment> |
| void processBlock(Index block_idx, Index begin, Index end) { |
| Scalar* buf = block_buffers[block_idx]; |
| |
| TENSOR_CONTRACTION_DISPATCH( |
| evaluator->template evalGemmPartialWithoutOutputKernel, Alignment, |
| (buf, begin, end, |
| /*num_threads=*/internal::convert_index<int>(num_blocks))); |
| |
| // Check if it was the last task in l0 range. |
| const Index l0_index = block_idx / l0_size; |
| const int v = l0_state[l0_index].fetch_sub(1); |
| eigen_assert(v >= 1); |
| |
| // If we processed the last block of the range, we can aggregate all |
| // partial results into the first block of the range. |
| if (v == 1) { |
| const Index rng_size = actualRangeSize(l0_ranges, l0_size, l0_index); |
| const Index dst_block_idx = l0_index * l0_size; |
| |
| if (rng_size == l0_size) { |
| addAllToBuffer<Alignment>( |
| m * n, |
| /*src_buf0=*/block_buffers[dst_block_idx + 1], |
| /*src_buf1=*/block_buffers[dst_block_idx + 2], |
| /*src_buf2=*/block_buffers[dst_block_idx + 3], |
| /*dst_buf= */ block_buffers[dst_block_idx]); |
| } else { |
| // Aggregate blocks of potentially incomplete last range. |
| for (int i = 1; i < rng_size; ++i) { |
| addToBuffer<Alignment>(m * n, |
| /*src_buf=*/block_buffers[dst_block_idx + i], |
| /*dst_buf=*/block_buffers[dst_block_idx]); |
| } |
| } |
| } |
| } |
| |
| // Aggregate partial sums from l0 ranges. |
| template <int Alignment> |
| void aggregateL0Blocks() const { |
| Index l0_index = 1; |
| |
| for (; l0_index + 2 < l0_ranges; l0_index += 3) { |
| addAllToBuffer<Alignment>( |
| m * n, |
| /*src_buf0=*/block_buffers[(l0_index + 0) * l0_size], |
| /*src_buf1=*/block_buffers[(l0_index + 1) * l0_size], |
| /*src_buf2=*/block_buffers[(l0_index + 2) * l0_size], |
| /*dst_buf= */ block_buffers[0]); |
| } |
| |
| for (; l0_index < l0_ranges; ++l0_index) { |
| addToBuffer<Alignment>(m * n, block_buffers[l0_index * l0_size], |
| block_buffers[0]); |
| } |
| } |
| |
| void applyOutputKernel() const { |
| typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper; |
| evaluator->m_output_kernel( |
| OutputMapper(result, m), evaluator->m_tensor_contraction_params, |
| static_cast<Eigen::Index>(0), static_cast<Eigen::Index>(0), m, n); |
| } |
| |
| // Compute block size with accounting for potentially incomplete last block. |
| Index actualBlockSize(Index block_idx) const { |
| return block_idx + 1 < num_blocks |
| ? block_size |
| : k + block_size - block_size * num_blocks; |
| }; |
| |
| // Compute range size with accounting for potentially incomplete last range. |
| Index actualRangeSize(Index num_ranges, Index range_size, |
| Index range_idx) const { |
| eigen_assert(range_idx < num_ranges); |
| return range_idx + 1 < num_ranges |
| ? range_size |
| : num_blocks + range_size - range_size * num_ranges; |
| }; |
| |
| template <int Alignment> |
| EIGEN_STRONG_INLINE static void addToBuffer(size_t n, const Scalar* src_buf, |
| Scalar* tgt_buf) { |
| const int output_packet_size = |
| internal::unpacket_traits<PacketReturnType>::size; |
| size_t i = 0; |
| const size_t num_packets = n / output_packet_size; |
| for (; i < output_packet_size * num_packets; i += output_packet_size) { |
| const PacketReturnType src_val = |
| internal::pload<PacketReturnType>(src_buf + i); |
| const PacketReturnType tgt_val = |
| internal::ploadt<PacketReturnType, Alignment>(tgt_buf + i); |
| const PacketReturnType sum = internal::padd(src_val, tgt_val); |
| internal::pstoret<Scalar, PacketReturnType, Alignment>(tgt_buf + i, |
| sum); |
| } |
| for (; i < n; ++i) { |
| tgt_buf[i] += src_buf[i]; |
| } |
| } |
| |
| template <int Alignment> |
| EIGEN_STRONG_INLINE static void addAllToBuffer(size_t n, |
| const Scalar* src_buf0, |
| const Scalar* src_buf1, |
| const Scalar* src_buf2, |
| Scalar* dst_buf) { |
| using ::Eigen::internal::padd; |
| using ::Eigen::internal::pload; |
| using ::Eigen::internal::ploadt; |
| using ::Eigen::internal::pstoret; |
| |
| const int output_packet_size = |
| internal::unpacket_traits<PacketReturnType>::size; |
| |
| size_t i = 0; |
| const size_t num_packets = n / output_packet_size; |
| for (; i < output_packet_size * num_packets; i += output_packet_size) { |
| const auto src_val0 = pload<PacketReturnType>(src_buf0 + i); |
| const auto src_val1 = pload<PacketReturnType>(src_buf1 + i); |
| const auto src_val2 = pload<PacketReturnType>(src_buf2 + i); |
| |
| const auto dst_val = ploadt<PacketReturnType, Alignment>(dst_buf + i); |
| const auto sum = |
| padd(padd(dst_val, src_val0), padd(src_val1, src_val2)); |
| |
| pstoret<Scalar, PacketReturnType, Alignment>(dst_buf + i, sum); |
| } |
| for (; i < n; ++i) { |
| dst_buf[i] += src_buf0[i] + src_buf1[i] + src_buf2[i]; |
| } |
| } |
| |
| template <int Alignment> |
| void eval(Barrier& barrier, Index start_block_idx, Index end_block_idx) { |
| while (end_block_idx - start_block_idx > 1) { |
| Index mid_block_idx = (start_block_idx + end_block_idx) / 2; |
| evaluator->m_device.enqueueNoNotification( |
| [this, &barrier, mid_block_idx, end_block_idx]() { |
| eval<Alignment>(barrier, mid_block_idx, end_block_idx); |
| }); |
| end_block_idx = mid_block_idx; |
| } |
| |
| Index block_idx = start_block_idx; |
| Index block_start = block_idx * block_size; |
| Index block_end = block_start + actualBlockSize(block_idx); |
| |
| processBlock<Alignment>(block_idx, block_start, block_end); |
| barrier.Notify(); |
| } |
| |
| template <int Alignment> |
| void evalAsync(Index start_block_idx, Index end_block_idx) { |
| while (end_block_idx - start_block_idx > 1) { |
| Index mid_block_idx = (start_block_idx + end_block_idx) / 2; |
| evaluator->m_device.enqueueNoNotification( |
| [this, mid_block_idx, end_block_idx]() { |
| evalAsync<Alignment>(mid_block_idx, end_block_idx); |
| }); |
| end_block_idx = mid_block_idx; |
| } |
| |
| Index block_idx = start_block_idx; |
| |
| Index block_start = block_idx * block_size; |
| Index block_end = block_start + actualBlockSize(block_idx); |
| |
| processBlock<Alignment>(block_idx, block_start, block_end); |
| |
| int v = num_pending_blocks.fetch_sub(1); |
| eigen_assert(v >= 1); |
| |
| if (v == 1) { |
| // Aggregate partial sums from l0 ranges. |
| aggregateL0Blocks<Alignment>(); |
| |
| // Apply output kernel. |
| applyOutputKernel(); |
| |
| // NOTE: If we call `done` callback before deleting this (context), |
| // it might deallocate Self* pointer captured by context, and we'll |
| // fail in destructor trying to deallocate temporary buffers. |
| |
| // Move done call back from context before it will be destructed. |
| DoneCallback done_copy = std::move(done); |
| |
| // We are confident that we are the last one who touches context. |
| delete this; |
| |
| // Now safely call the done callback. |
| done_copy(); |
| } |
| } |
| |
| // Cost model doesn't capture well the cost associated with constructing |
| // tensor contraction mappers and computing loop bounds in gemm_pack_lhs |
| // and gemm_pack_rhs, so we specify minimum desired block size. |
| static Index blockSize(Index k, int num_threads) { |
| const auto round_up = [=](Index index) -> Index { |
| const Index kmultiple = packet_size <= 8 ? 8 : packet_size; |
| return divup<Index>(index, kmultiple) * kmultiple; |
| }; |
| |
| const Index target_block_size = round_up(divup<Index>(k, num_threads)); |
| const Index desired_min_block_size = 12 * packet_size; |
| |
| return numext::mini<Index>( |
| k, numext::maxi<Index>(desired_min_block_size, target_block_size)); |
| } |
| |
| EvalShardedByInnerDimContext(const EvalShardedByInnerDimContext&) = delete; |
| void operator=(const EvalShardedByInnerDimContext&) = delete; |
| }; |
| |
| // ------------------------------------------------------------------------ // |
| |
| // Below are the function used by evalProductImpl heuristics, trying to select |
| // optimcal parameters for parallelization algorithm. |
| |
| // Decide whether we want to shard m x n contraction by columns or by rows. |
| static bool shardByCol(Index m, Index n, Index num_threads) { |
| // Note: we are comparing both n and m against Traits::nr, it is not |
| // a mistake. We are trying to figure out how both n and m will fit into |
| // the main sharding dimension. |
| |
| // Sharding by column is the default |
| // ... unless there is enough data for vectorization over rows |
| if (m / num_threads >= Traits::nr && |
| // and not enough data for vectorization over columns |
| (n / num_threads < Traits::nr || |
| // ... or barely enough data for vectorization over columns, |
| // but it is not evenly dividable across threads |
| (n / num_threads < 4 * Traits::nr && |
| (n % (num_threads * Traits::nr)) != 0 && |
| // ... and it is evenly dividable across threads for rows |
| ((m % (num_threads * Traits::nr)) == 0 || |
| // .. or it is not evenly dividable for both dimensions but |
| // there is much more data over rows so that corner effects are |
| // mitigated. |
| (m / n >= 6))))) |
| return false; |
| // Wait, or if matrices are just substantially prolonged over the other |
| // dimension. |
| if (n / num_threads < 16 * Traits::nr && m > n * 32) return false; |
| return true; |
| } |
| |
| Index coarsenM(Index m, Index n, Index bm, Index bn, Index bk, Index gn, |
| int num_threads, bool shard_by_col) const { |
| Index gm = 1; |
| Index gm1 = 1; |
| Index nm0 = divup(m, bm); |
| Index nm1 = nm0; |
| for (;;) { |
| // Find the next candidate for m grain size. It needs to result in |
| // different number of blocks. E.g. if we have 10 kernels, we want to try |
| // 5 and 10, but not 6, 7, 8 and 9. |
| while (gm1 <= nm0 && nm1 == divup(nm0, gm1)) gm1++; |
| if (gm1 > nm0) break; |
| // Check the candidate. |
| int res = checkGrain(m, n, bm, bn, bk, gm1, gn, gm, gn, num_threads, |
| shard_by_col); |
| if (res < 0) break; |
| nm1 = divup(nm0, gm1); |
| if (res == 0) continue; |
| // Commit new grain size. |
| gm = gm1; |
| } |
| return gm; |
| } |
| |
| Index coarsenN(Index m, Index n, Index bm, Index bn, Index bk, Index gm, |
| int num_threads, bool shard_by_col) const { |
| Index gn = 1; |
| Index gn1 = 1; |
| Index nn0 = divup(n, bn); |
| Index nn1 = nn0; |
| for (;;) { |
| while (gn1 <= nn0 && nn1 == divup(nn0, gn1)) gn1++; |
| if (gn1 > nn0) break; |
| int res = checkGrain(m, n, bm, bn, bk, gm, gn1, gm, gn, num_threads, |
| shard_by_col); |
| if (res < 0) break; |
| nn1 = divup(nn0, gn1); |
| if (res == 0) continue; |
| gn = gn1; |
| } |
| return gn; |
| } |
| |
| // checkGrain checks whether grain (gm, gn) is suitable and is better than |
| // (oldgm, oldgn). |
| int checkGrain(Index m, Index n, Index bm, Index bn, Index bk, Index gm, |
| Index gn, Index oldgm, Index oldgn, int num_threads, |
| bool shard_by_col) const { |
| const TensorOpCost cost = |
| contractionCost(bm * gm, bn * gn, bm, bn, bk, shard_by_col, true); |
| double taskSize = TensorCostModel<ThreadPoolDevice>::taskSize( |
| static_cast<double>(bm) * gm * bn * gn, cost); |
| // If the task is too small, then we agree on it regardless of anything |
| // else. Otherwise synchronization overheads will dominate. |
| if (taskSize < 1) return 1; |
| // If it is too large, then we reject it and all larger tasks. |
| if (taskSize > 2) return -1; |
| // Now we are in presumably good task size range. |
| // The main deciding factor here is parallelism. Consider that we have 12 |
| // kernels and 4 threads. Grains of 2, 3 and 4 all yield good task sizes. |
| // But 2/4 yield 6/3 tasks, which gives us parallelism of 0.75 (at most 3/4 |
| // of cores will be busy). While grain size 3 gives us 4 tasks, which gives |
| // us parallelism of 1 (we can load all cores). |
| Index nm0 = divup(m, bm); |
| Index nn0 = divup(n, bn); |
| Index new_tasks = divup(nm0, gm) * divup(nn0, gn); |
| double new_parallelism = static_cast<double>(new_tasks) / |
| (divup<int>(new_tasks, num_threads) * num_threads); |
| Index old_tasks = divup(nm0, oldgm) * divup(nn0, oldgn); |
| double old_parallelism = static_cast<double>(old_tasks) / |
| (divup<int>(old_tasks, num_threads) * num_threads); |
| if (new_parallelism > old_parallelism || new_parallelism == 1) return 1; |
| return 0; |
| } |
| |
| TensorOpCost contractionCost(Index m, Index n, Index bm, Index bn, Index bk, |
| bool shard_by_col, bool prepacked) const { |
| const int packed_size = std::min<int>(PacketType<LhsScalar, Device>::size, |
| PacketType<RhsScalar, Device>::size); |
| const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size; |
| const double kd = static_cast<double>(bk); |
| double compute_bandwidth = computeBandwidth(false, bm, bn, bk); |
| // Computations. |
| TensorOpCost cost = TensorOpCost(0, 0, kd * compute_bandwidth, true, packed_size); |
| // Output stores. |
| cost += TensorOpCost(0, sizeof(CoeffReturnType), 0, true, output_packet_size); |
| if (prepacked) { |
| // Packing and kernels are executed in different tasks. When we calculate |
| // task grain size we look only at kernel cost assuming that kernel |
| // is more expensive than packing. |
| return cost; |
| } |
| // Lhs/rhs loads + computations. |
| TensorOpCost lhsCost = this->m_leftImpl.costPerCoeff(true) * (kd / n); |
| TensorOpCost rhsCost = this->m_rightImpl.costPerCoeff(true) * (kd / m); |
| // Lhs packing memory cost does not contribute considerably to overall |
| // execution time because lhs is prefetched early and accessed sequentially. |
| if (shard_by_col) |
| lhsCost.dropMemoryCost(); |
| else |
| rhsCost.dropMemoryCost(); |
| return cost + lhsCost + rhsCost; |
| } |
| |
| // Decide whether we want to shard m x k x n contraction over the inner |
| // (contraction) dimension (k). |
| static bool shardByInnerDim(Index m, Index n, Index k, int num_threads, |
| int num_threads_by_k) { |
| std::ptrdiff_t bufsize = m * n * sizeof(Scalar); |
| bool shard_by_k = false; |
| if (n == 1 || // If mat*vec or... |
| num_threads_by_k < 2 || // running single threaded or... |
| num_threads_by_k < |
| num_threads || // sharding by k gives less parallelism or... |
| bufsize > l3CacheSize() / num_threads_by_k || // need more buffer space |
| // than L3 cache or... |
| k / num_threads_by_k < 2 * Traits::nr) { // k per thread is tiny. |
| shard_by_k = false; |
| } else if (numext::maxi(m, n) / num_threads < |
| Traits::nr || // both other dimensions are tiny or... |
| // k per thread is not small and... |
| (k / num_threads_by_k > 8 * Traits::nr && |
| // one of the outer dimensions is tiny or sharding by k offers |
| // more parallelism. |
| (numext::mini(m, n) < 2 * Traits::nr || |
| num_threads_by_k > num_threads))) { |
| shard_by_k = true; |
| } |
| return shard_by_k; |
| } |
| |
| TensorOpCost contractionCostPerInnerDim(Index m, Index n, Index k) const { |
| // Compute cost. |
| const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size; |
| TensorOpCost cost(0, 0, (computeBandwidth(true, m, n, k) * m) * n, true, output_packet_size); |
| // Output stores. |
| cost += TensorOpCost(0, sizeof(CoeffReturnType), 0, true, output_packet_size); |
| TensorOpCost lhsCost = this->m_leftImpl.costPerCoeff(true) * m; |
| TensorOpCost rhsCost = this->m_rightImpl.costPerCoeff(true) * n; |
| // Since the inner gemm kernel is always sharded by column, the lhs |
| // load cost is negligible. |
| lhsCost.dropMemoryCost(); |
| return cost + lhsCost + rhsCost; |
| } |
| |
| int numThreadsInnerDim(Index m, Index n, Index k) const { |
| const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size; |
| TensorOpCost cost = contractionCostPerInnerDim(m, n, k); |
| double total_parallel_cost = |
| TensorCostModel<ThreadPoolDevice>::totalCost(k, cost); |
| // Cost of reduction step accumulating the m*n per-thread buffers into the |
| // result. |
| double reduction_cost = TensorCostModel<ThreadPoolDevice>::totalCost( |
| m * n, TensorOpCost(2, 1, 1, true, output_packet_size)); |
| int num_threads = 1; |
| double min_cost = total_parallel_cost; |
| double kPerThreadOverHead = 3000; |
| double kFixedOverHead = 100000; |
| for (int nt = 2; nt <= this->m_device.numThreads(); nt += 2) { |
| double sequential_cost = |
| kFixedOverHead + nt * (reduction_cost + kPerThreadOverHead); |
| double parallel_cost = total_parallel_cost / nt + sequential_cost; |
| if (parallel_cost < min_cost) { |
| num_threads = nt; |
| min_cost = parallel_cost; |
| } |
| } |
| return num_threads; |
| } |
| |
| double computeBandwidth(bool shard_by_col, Index bm, Index bn, |
| Index bk) const { |
| // Peak VFMA bandwidth is 0.5. However if we have not enough data for |
| // vectorization bandwidth drops. The 4.0 and 2.0 bandwidth is determined |
| // experimentally. |
| double computeBandwidth = |
| bk == 1 ? 4.0 |
| : (shard_by_col ? bn : bm) < Traits::nr || |
| (shard_by_col ? bm : bn) < Traits::mr |
| ? 2.0 |
| : 0.5; |
| #ifndef EIGEN_VECTORIZE_FMA |
| // Bandwidth of all of VFMA/MULPS/ADDPS is 0.5 on latest Intel processors. |
| // However for MULPS/ADDPS we have dependent sequence of 2 such |
| // instructions, |
| // so overall bandwidth is 1.0. |
| if (computeBandwidth == 0.5) computeBandwidth = 1.0; |
| #endif |
| return computeBandwidth; |
| } |
| |
| }; |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_USE_THREADS |
| #endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H |
