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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.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_COST_MODEL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H
+
+namespace Eigen {
+
+/** \class TensorEvaluator
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief A cost model used to limit the number of threads used for evaluating
+ * tensor expression.
+ *
+ */
+
+// Class storing the cost of evaluating a tensor expression in terms of the
+// estimated number of operand bytes loads, bytes stored, and compute cycles.
+class TensorOpCost {
+ public:
+ // TODO(rmlarsen): Fix the scalar op costs in Eigen proper. Even a simple
+ // model based on minimal reciprocal throughput numbers from Intel or
+ // Agner Fog's tables would be better than what is there now.
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int MulCost() {
+ return internal::functor_traits<
+ internal::scalar_product_op<ArgType, ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int AddCost() {
+ return internal::functor_traits<internal::scalar_sum_op<ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int DivCost() {
+ return internal::functor_traits<
+ internal::scalar_quotient_op<ArgType, ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int ModCost() {
+ return internal::functor_traits<internal::scalar_mod_op<ArgType> >::Cost;
+ }
+ template <typename SrcType, typename TargetType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int CastCost() {
+ return internal::functor_traits<
+ internal::scalar_cast_op<SrcType, TargetType> >::Cost;
+ }
+
+ EIGEN_DEVICE_FUNC
+ TensorOpCost() : bytes_loaded_(0), bytes_stored_(0), compute_cycles_(0) {}
+ EIGEN_DEVICE_FUNC
+ TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles)
+ : bytes_loaded_(bytes_loaded),
+ bytes_stored_(bytes_stored),
+ compute_cycles_(compute_cycles) {}
+
+ EIGEN_DEVICE_FUNC
+ TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles,
+ bool vectorized, double packet_size)
+ : bytes_loaded_(bytes_loaded),
+ bytes_stored_(bytes_stored),
+ compute_cycles_(vectorized ? compute_cycles / packet_size
+ : compute_cycles) {
+ eigen_assert(bytes_loaded >= 0 && (numext::isfinite)(bytes_loaded));
+ eigen_assert(bytes_stored >= 0 && (numext::isfinite)(bytes_stored));
+ eigen_assert(compute_cycles >= 0 && (numext::isfinite)(compute_cycles));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_loaded() const {
+ return bytes_loaded_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_stored() const {
+ return bytes_stored_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double compute_cycles() const {
+ return compute_cycles_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double total_cost(
+ double load_cost, double store_cost, double compute_cost) const {
+ return load_cost * bytes_loaded_ + store_cost * bytes_stored_ +
+ compute_cost * compute_cycles_;
+ }
+
+ // Drop memory access component. Intended for cases when memory accesses are
+ // sequential or are completely masked by computations.
+ EIGEN_DEVICE_FUNC void dropMemoryCost() {
+ bytes_loaded_ = 0;
+ bytes_stored_ = 0;
+ }
+
+ // TODO(rmlarsen): Define min in terms of total cost, not elementwise.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMin(
+ const TensorOpCost& rhs) const {
+ double bytes_loaded = numext::mini(bytes_loaded_, rhs.bytes_loaded());
+ double bytes_stored = numext::mini(bytes_stored_, rhs.bytes_stored());
+ double compute_cycles = numext::mini(compute_cycles_, rhs.compute_cycles());
+ return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);
+ }
+
+ // TODO(rmlarsen): Define max in terms of total cost, not elementwise.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMax(
+ const TensorOpCost& rhs) const {
+ double bytes_loaded = numext::maxi(bytes_loaded_, rhs.bytes_loaded());
+ double bytes_stored = numext::maxi(bytes_stored_, rhs.bytes_stored());
+ double compute_cycles = numext::maxi(compute_cycles_, rhs.compute_cycles());
+ return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator+=(
+ const TensorOpCost& rhs) {
+ bytes_loaded_ += rhs.bytes_loaded();
+ bytes_stored_ += rhs.bytes_stored();
+ compute_cycles_ += rhs.compute_cycles();
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator*=(double rhs) {
+ bytes_loaded_ *= rhs;
+ bytes_stored_ *= rhs;
+ compute_cycles_ *= rhs;
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator+(
+ TensorOpCost lhs, const TensorOpCost& rhs) {
+ lhs += rhs;
+ return lhs;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(
+ TensorOpCost lhs, double rhs) {
+ lhs *= rhs;
+ return lhs;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(
+ double lhs, TensorOpCost rhs) {
+ rhs *= lhs;
+ return rhs;
+ }
+
+ friend std::ostream& operator<<(std::ostream& os, const TensorOpCost& tc) {
+ return os << "[bytes_loaded = " << tc.bytes_loaded()
+ << ", bytes_stored = " << tc.bytes_stored()
+ << ", compute_cycles = " << tc.compute_cycles() << "]";
+ }
+
+ private:
+ double bytes_loaded_;
+ double bytes_stored_;
+ double compute_cycles_;
+};
+
+// TODO(rmlarsen): Implement a policy that chooses an "optimal" number of theads
+// in [1:max_threads] instead of just switching multi-threading off for small
+// work units.
+template <typename Device>
+class TensorCostModel {
+ public:
+ // Scaling from Eigen compute cost to device cycles.
+ static const int kDeviceCyclesPerComputeCycle = 1;
+
+ // Costs in device cycles.
+ static const int kStartupCycles = 100000;
+ static const int kPerThreadCycles = 100000;
+ static const int kTaskSize = 40000;
+
+ // Returns the number of threads in [1:max_threads] to use for
+ // evaluating an expression with the given output size and cost per
+ // coefficient.
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int numThreads(
+ double output_size, const TensorOpCost& cost_per_coeff, int max_threads) {
+ double cost = totalCost(output_size, cost_per_coeff);
+ int threads = (cost - kStartupCycles) / kPerThreadCycles + 0.9;
+ return numext::mini(max_threads, numext::maxi(1, threads));
+ }
+
+ // taskSize assesses parallel task size.
+ // Value of 1.0 means ideal parallel task size. Values < 1.0 mean that task
+ // granularity needs to be increased to mitigate parallelization overheads.
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double taskSize(
+ double output_size, const TensorOpCost& cost_per_coeff) {
+ return totalCost(output_size, cost_per_coeff) / kTaskSize;
+ }
+
+ private:
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double totalCost(
+ double output_size, const TensorOpCost& cost_per_coeff) {
+ // Cost of memory fetches from L2 cache. 64 is typical cache line size.
+ // 11 is L2 cache latency on Haswell.
+ // We don't know whether data is in L1, L2 or L3. But we are most interested
+ // in single-threaded computational time around 100us-10ms (smaller time
+ // is too small for parallelization, larger time is not intersting
+ // either because we are probably using all available threads already).
+ // And for the target time range, L2 seems to be what matters. Data set
+ // fitting into L1 is too small to take noticeable time. Data set fitting
+ // only into L3 presumably will take more than 10ms to load and process.
+ const double kLoadCycles = 1.0 / 64 * 11;
+ const double kStoreCycles = 1.0 / 64 * 11;
+ // Scaling from Eigen compute cost to device cycles.
+ return output_size *
+ cost_per_coeff.total_cost(kLoadCycles, kStoreCycles,
+ kDeviceCyclesPerComputeCycle);
+ }
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H