// Copyright (c) 2019 PaddlePaddle Authors. All Rights Reserved. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #include "paddle/fluid/inference/api/mkldnn_quantizer.h" #include #include #include #include #include #include #include "paddle/fluid/framework/eigen.h" #include "paddle/fluid/framework/ir/fuse_pass_base.h" #include "paddle/fluid/framework/ir/graph.h" #include "paddle/fluid/framework/ir/pass.h" #include "paddle/fluid/framework/operator.h" #include "paddle/fluid/framework/type_defs.h" #include "paddle/fluid/inference/analysis/analyzer.h" #include "paddle/fluid/inference/api/analysis_predictor.h" #include "paddle/fluid/platform/mkldnn_helper.h" #include "paddle/fluid/platform/place.h" #include "paddle/fluid/string/pretty_log.h" namespace paddle { using framework::LoDTensor; using framework::Variable; using framework::ir::Graph; using platform::CPUPlace; using ConstEigenVectorArrayMap = Eigen::Map>; using EigenMatrixDoubleArray = Eigen::Array; using EigenMatrixArray = Eigen::Array; using ConstEigenMatrixArrayMap = Eigen::Map; using string::PrettyLogH1; using VariableNameMap = std::map>; static LoDTensor CreateScaleTensor(int64_t channels_num = 1); static void check_var(const Variable* var, const std::string& var_name) { PADDLE_ENFORCE_NOT_NULL( var, platform::errors::PreconditionNotMet("%s is not in the scope", var_name)); PADDLE_ENFORCE_EQ( var->IsType(), true, platform::errors::PreconditionNotMet("Only support lod tensor now.")); } static void check_tensor(const LoDTensor& tensor) { PADDLE_ENFORCE_GT( tensor.dims().size(), 0, platform::errors::InvalidArgument("Tensor dimension is empty.")); } void AnalysisPredictor::MkldnnQuantizer::CalculateScalesForRNNWeights( const paddle::framework::OpDesc* op, bool gru) { const auto& wx_names = op->Input("WeightX"); const auto& wh_names = op->Input("WeightH"); for (size_t i = 0; i < wx_names.size(); ++i) { const auto& wx_name = wx_names[i]; const auto& wh_name = wh_names[i]; auto* wx_var = predictor_.sub_scope_->FindVar(wx_name); auto* wh_var = predictor_.sub_scope_->FindVar(wh_name); check_var(wx_var, wx_name); check_var(wh_var, wh_name); LoDTensor* wx_tensor = wx_var->GetMutable(); LoDTensor* wh_tensor = wh_var->GetMutable(); if (gru) { scales_[wx_name] = GetMaxChGRUScalingFactor(*wx_tensor, *wh_tensor); } else { scales_[wx_name] = GetMaxChLSTMScalingFactor(*wx_tensor, *wh_tensor); } } } void AnalysisPredictor::MkldnnQuantizer::CalculateScalesForOpInputs( const paddle::framework::OpDesc* op) { if (op->Type() == "fusion_gru" || op->Type() == "multi_gru") { CalculateScalesForRNNWeights(op, true); } else if (op->Type() == "fusion_lstm") { CalculateScalesForRNNWeights(op, false); } for (auto const& input : op->Inputs()) { for (const auto& var_name : input.second) { // skip if scale already computed if (scales_.find(var_name) != scales_.end()) continue; auto* var = predictor_.sub_scope_->FindVar(var_name); check_var(var, var_name); LoDTensor* var_tensor = var->GetMutable(); // force unsigned type if already know it bool is_unsigned = false; CalculateSingleScale( op->Type(), input.first, var_name, *var_tensor, is_unsigned); } } } void AnalysisPredictor::MkldnnQuantizer::CalculateScalesForOpOutputs( const paddle::framework::OpDesc* op) { for (auto const& output : op->Outputs()) { for (const auto& var_name : output.second) { // skip if scale already computed if (scales_.find(var_name) != scales_.end()) continue; auto* var = predictor_.sub_scope_->FindVar(var_name); check_var(var, var_name); LoDTensor* var_tensor = var->GetMutable(); // force unsigned type if already know it bool is_unsigned = false; bool compute_scale = true; if (op->Type() == "conv2d" || op->Type() == "fc") { // output of conv2d with relu must be unsigned std::string fuse_activation = op->GetAttrIfExists("fuse_activation"); is_unsigned = (fuse_activation == "relu" || fuse_activation == "relu6"); } else if (op->Type() == "relu") { is_unsigned = true; } else if (op->Type() == "transpose2" || op->Type() == "reshape2" || op->Type() == "pool2d" || op->Type() == "nearest_interp" || op->Type() == "nearest_interp_v2") { auto input_var_name = op->Input("X")[0]; PADDLE_ENFORCE_NE(scales_.find(input_var_name), scales_.end(), platform::errors::PreconditionNotMet( "Input scales must be calculated before the " "output scales to infer if output is unsigned.")); if (scales_.find(input_var_name) != scales_.end()) { scales_[var_name] = scales_[input_var_name]; } compute_scale = false; } else if (op->Type() == "slice" || op->Type() == "shape") { auto input_var_name = op->Input("Input")[0]; PADDLE_ENFORCE_NE(scales_.find(input_var_name), scales_.end(), platform::errors::PreconditionNotMet( "Input scales must be calculated before the " "output scales to infer if output is unsigned.")); if (scales_.find(input_var_name) != scales_.end()) { scales_[var_name] = scales_[input_var_name]; } compute_scale = false; } else if (op->Type() == "concat") { // output of ops with unsigned input must be unsigned is_unsigned = true; double min_scale = std::numeric_limits::max(); for (auto input_var_name : op->Input("X")) { PADDLE_ENFORCE_NE( scales_.find(input_var_name), scales_.end(), platform::errors::PreconditionNotMet( "Input scales must be calculated before the " "output scales to infer if output is unsigned.")); is_unsigned = is_unsigned && scales_[input_var_name].first; min_scale = std::min( min_scale, scales_[input_var_name].second.data()[0]); } auto scale_tensor = CreateScaleTensor(); scale_tensor.data()[0] = min_scale; scales_[var_name] = {is_unsigned, scale_tensor}; compute_scale = false; } if (compute_scale) { CalculateSingleScale( op->Type(), output.first, var_name, *var_tensor, is_unsigned); } } } } bool AnalysisPredictor::MkldnnQuantizer::CalculateScales() { PrettyLogH1("--- Calculating scales for quantization"); std::map> gathered_data; for (const auto* op : predictor_.inference_program_->Block(0).AllOps()) { if (platform::HasOpINT8DataType(op)) { // handle inputs first to let is_unsigned be inferred for the outputs CalculateScalesForOpInputs(op); CalculateScalesForOpOutputs(op); } } return true; } void AnalysisPredictor::MkldnnQuantizer::CalculateSingleScale( const std::string& op_type_name, const std::string& conn_name, const std::string& var_name, const LoDTensor& var_tensor, bool is_unsigned) { auto rule = qconfig_->scale_algo(op_type_name, conn_name); if (rule == ScaleAlgo::NONE) return; PADDLE_ENFORCE_GT( var_tensor.numel(), 0, platform::errors::InvalidArgument( "MkldnnQuantizer: LoDTensor of variable %s for quantization of op " "%s of connection %s should not be empty.", var_name, op_type_name, conn_name)); switch (rule) { case ScaleAlgo::MAX: scales_[var_name] = GetMaxScalingFactor(var_tensor, is_unsigned); break; case ScaleAlgo::MAX_CH: scales_[var_name] = GetMaxChScalingFactor(var_tensor, is_unsigned, /*is_transposed*/ false); break; case ScaleAlgo::MAX_CH_T: scales_[var_name] = GetMaxChScalingFactor(var_tensor, is_unsigned, /*is_transposed*/ true); break; case ScaleAlgo::KL: scales_[var_name] = GetKLScalingFactor(var_tensor, is_unsigned); break; default: throw std::runtime_error( "MkldnnQuantizer: Unexpected ScaleAlgo specified."); } } static LoDTensor CreateScaleTensor(int64_t channels_num) { LoDTensor scale_tensor; scale_tensor.Resize({channels_num}); scale_tensor.mutable_data(CPUPlace()); return scale_tensor; } std::vector AnalysisPredictor::MkldnnQuantizer::ExpandQuantizedBins( std::vector quantized_bins, std::vector reference_bins) const { std::vector expanded_quantized_bins(reference_bins.size(), 0); int num_merged_bins = reference_bins.size() / quantized_bins.size(); int j_start = 0; int j_end = num_merged_bins; for (size_t idx = 0; idx < quantized_bins.size(); idx++) { int zero_count = std::count(&reference_bins[j_start], &reference_bins[j_end], 0); num_merged_bins = j_end - j_start; int avg_bin_ele; if (zero_count == num_merged_bins) { avg_bin_ele = 0; } else { avg_bin_ele = quantized_bins[idx] / (num_merged_bins - zero_count + 0.0); } for (int idx1 = j_start; idx1 < j_end; idx1++) { expanded_quantized_bins[idx1] = (reference_bins[idx1] == 0) ? 0 : avg_bin_ele; } j_start += num_merged_bins; j_end += num_merged_bins; if ((idx + 1) == quantized_bins.size() - 1) { j_end = reference_bins.size(); } } return expanded_quantized_bins; } std::pair AnalysisPredictor::MkldnnQuantizer::GetKLScalingFactor( const LoDTensor& var_tensor, bool is_unsigned) const { ConstEigenVectorArrayMap eigen_tensor{ var_tensor.data(), var_tensor.numel(), 1}; int precision_hist_num_bins = 2048; float max_val = eigen_tensor.maxCoeff(); float min_val = eigen_tensor.minCoeff(); bool is_positive = min_val >= 0.0f; if (is_unsigned) PADDLE_ENFORCE_EQ( is_positive, true, platform::errors::InvalidArgument( "Tensor is claimed to be unsigned, but its min value (%f) is < 0.0", min_val)); int num_quantized_bins = 255; std::vector hist; float bin_width; int starting_iter; int ending_iter = precision_hist_num_bins - 1; if (is_positive) { std::tie(hist, bin_width) = Histogram(var_tensor, min_val, max_val, precision_hist_num_bins); starting_iter = static_cast(ending_iter * 0.7); } else { float th = std::max(std::abs(max_val), std::abs(min_val)); std::tie(hist, bin_width) = Histogram(var_tensor, -th, th, precision_hist_num_bins); starting_iter = 0; if (std::abs(max_val) > std::abs(min_val)) { while (starting_iter < ending_iter) { if (hist[starting_iter] == 0) { ++starting_iter; continue; } else { break; } } starting_iter += static_cast((ending_iter - starting_iter) * 0.6); } else { while (ending_iter > 0) { if (hist[ending_iter] == 0) { --ending_iter; continue; } else { break; } } starting_iter = static_cast(0.6 * ending_iter); } } auto P_sum = eigen_tensor.size(); int min_kl_divergence = 0; int min_kl_index = 0; bool kl_inited = false; for (int i = starting_iter; i <= ending_iter; i++) { std::vector reference_distr_P(&hist[0], &hist[i]); auto outliers_count = std::accumulate(&hist[i], &hist[precision_hist_num_bins], 0); if (i <= 0 || reference_distr_P[i - 1] == 0) { continue; } reference_distr_P[i - 1] += outliers_count; auto reference_distr_bins = reference_distr_P; std::vector candidate_distr_Q(&hist[0], &hist[i]); int num_merged_bins = i / num_quantized_bins; std::vector candidate_distr_Q_quantized(num_quantized_bins, 0); int j_start = 0; int j_end = num_merged_bins; for (int idx = 0; idx < num_quantized_bins; idx++) { candidate_distr_Q_quantized[idx] = std::accumulate( &candidate_distr_Q[j_start], &candidate_distr_Q[j_end], 0); j_start += num_merged_bins; j_end += num_merged_bins; if ((idx + 1) == num_quantized_bins - 1) { j_end = i; } } candidate_distr_Q = ExpandQuantizedBins(candidate_distr_Q_quantized, reference_distr_bins); int Q_sum = std::accumulate(candidate_distr_Q.begin(), candidate_distr_Q.end(), 0); auto kl_divergence = SafeEntropy(reference_distr_P, P_sum, candidate_distr_Q, Q_sum); if (!kl_inited) { min_kl_divergence = kl_divergence; min_kl_index = i; kl_inited = true; } else if (kl_divergence < min_kl_divergence) { min_kl_divergence = kl_divergence; min_kl_index = i; } else { } } if (min_kl_index == 0) { while (starting_iter > 0) { if (hist[starting_iter] == 0) { starting_iter -= 1; continue; } else { break; } } min_kl_index = starting_iter; } LoDTensor scale_tensor = CreateScaleTensor(); scale_tensor.data()[0] = 1.0 / ((min_kl_index + 0.5) * bin_width); return std::make_pair(is_unsigned, scale_tensor); } std::pair AnalysisPredictor::MkldnnQuantizer::GetMaxScalingFactor( const LoDTensor& var_tensor, bool is_unsigned) const { ConstEigenVectorArrayMap eigen_tensor{ var_tensor.data(), var_tensor.numel(), 1}; float max_abs = eigen_tensor.abs().maxCoeff(); float min_val = eigen_tensor.minCoeff(); if (is_unsigned) PADDLE_ENFORCE_GE( min_val, 0.0f, platform::errors::InvalidArgument( "Tensor is claimed to be unsigned, but its min value (%f) is < 0.0", min_val)); LoDTensor scale_tensor = CreateScaleTensor(); scale_tensor.data()[0] = 1.0 / max_abs; return std::make_pair(is_unsigned, scale_tensor); } std::pair AnalysisPredictor::MkldnnQuantizer::GetMaxChScalingFactor( const LoDTensor& var_tensor, bool is_unsigned, bool is_transposed) const { check_tensor(var_tensor); ConstEigenVectorArrayMap eigen_tensor{ var_tensor.data(), var_tensor.numel(), 1}; float min_val = eigen_tensor.minCoeff(); if (is_unsigned) PADDLE_ENFORCE_GE( min_val, 0.0f, platform::errors::InvalidArgument( "Tensor is claimed to be unsigned, but its min value (%f) is < 0.0", min_val)); auto dims = var_tensor.dims(); constexpr int num_col_dims = 1; auto flattened_dims = phi::flatten_to_2d(dims, num_col_dims); ConstEigenMatrixArrayMap eigen_tensor_mat{ var_tensor.data(), flattened_dims[0], flattened_dims[1]}; EigenMatrixDoubleArray scales; if (is_transposed) { scales = 1.0 / eigen_tensor_mat.cast().abs().colwise().maxCoeff(); } else { scales = 1.0 / eigen_tensor_mat.cast().abs().rowwise().maxCoeff(); } int output_channel_axis = is_transposed; int channels = dims[output_channel_axis]; LoDTensor scale_tensor = CreateScaleTensor(channels); auto* scale_ptr = scale_tensor.mutable_data(CPUPlace()); std::copy(scales.data(), scales.data() + scales.size(), scale_ptr); return std::make_pair(is_unsigned, scale_tensor); } std::pair AnalysisPredictor::MkldnnQuantizer::GetMaxChGRUScalingFactor( const LoDTensor& wx_tensor, const LoDTensor& wh_tensor) const { check_tensor(wx_tensor); check_tensor(wh_tensor); int OC = wh_tensor.dims()[0]; std::vector scale_ur(2 * OC); std::vector scale_o(OC); for (int row_id = 0; row_id < wx_tensor.dims()[0]; row_id++) { for (int col_id = 0; col_id < 2 * OC; col_id++) { int idx = (row_id * wx_tensor.dims()[1]) + col_id; auto abs_value = std::abs(wx_tensor.data()[idx]); if (row_id == 0) { scale_ur[col_id] = abs_value; } else { if (abs_value > scale_ur[col_id]) scale_ur[col_id] = abs_value; } } } for (int i = 0; i < 2 * OC * OC; i++) { int col_id = i % (2 * OC); auto abs_value = std::abs(wh_tensor.data()[i]); if (abs_value > scale_ur[col_id]) scale_ur[col_id] = abs_value; } for (int row_id = 0; row_id < wx_tensor.dims()[0]; row_id++) { for (int col_id = 2 * OC; col_id < wx_tensor.dims()[1]; col_id++) { int idx = (row_id * wx_tensor.dims()[1]) + col_id; auto abs_value = std::abs(wx_tensor.data()[idx]); if (row_id == 0) { scale_o[col_id % OC] = abs_value; } else { if (abs_value > scale_o[col_id]) scale_o[col_id % OC] = abs_value; } } } for (int i = 2 * OC * OC; i < OC * wh_tensor.dims()[1]; i++) { int col_id = i % OC; auto abs_value = std::abs(wh_tensor.data()[i]); if (abs_value > scale_o[col_id]) scale_o[col_id] = abs_value; } scale_ur.insert(scale_ur.end(), scale_o.begin(), scale_o.end()); transform(scale_ur.begin(), scale_ur.end(), scale_ur.begin(), [](float& c) { return 1 / c; }); LoDTensor scale_tensor = CreateScaleTensor(scale_ur.size()); auto* scale_ptr = scale_tensor.mutable_data(CPUPlace()); std::copy(scale_ur.begin(), scale_ur.end(), scale_ptr); bool is_unsigned = false; return std::make_pair(is_unsigned, scale_tensor); } std::pair AnalysisPredictor::MkldnnQuantizer::GetMaxChLSTMScalingFactor( const LoDTensor& wx_tensor, const LoDTensor& wh_tensor) const { check_tensor(wx_tensor); check_tensor(wh_tensor); std::vector scale(wx_tensor.dims()[1]); for (int row_id = 0; row_id < wx_tensor.dims()[0]; row_id++) { for (int col_id = 0; col_id < wx_tensor.dims()[1]; col_id++) { int idx = (row_id * wx_tensor.dims()[1]) + col_id; auto abs_value = std::abs(wx_tensor.data()[idx]); if (row_id == 0) { scale[col_id] = abs_value; } else { if (abs_value > scale[col_id]) scale[col_id] = abs_value; } } } for (int row_id = 0; row_id < wh_tensor.dims()[0]; row_id++) { for (int col_id = 0; col_id < wh_tensor.dims()[1]; col_id++) { int idx = (row_id * wh_tensor.dims()[1]) + col_id; auto abs_value = std::abs(wh_tensor.data()[idx]); if (abs_value > scale[col_id]) scale[col_id] = abs_value; } } transform(scale.begin(), scale.end(), scale.begin(), [](float& c) { return 1 / c; }); LoDTensor scale_tensor = CreateScaleTensor(scale.size()); auto* scale_ptr = scale_tensor.mutable_data(CPUPlace()); std::copy(scale.begin(), scale.end(), scale_ptr); bool is_unsigned = false; return std::make_pair(is_unsigned, scale_tensor); } std::pair, float> AnalysisPredictor::MkldnnQuantizer::Histogram( const framework::LoDTensor& var_tensor, float min_val, float max_val, size_t num_bins) const { PADDLE_ENFORCE_GT(num_bins, 0, platform::errors::InvalidArgument( "MkldnnQuantizer: To calculate Histogram, num_bins (" + std::to_string(num_bins) + ") must be positive.")); PADDLE_ENFORCE_GT(var_tensor.numel(), 0, platform::errors::InvalidArgument( "MkldnnQuantizer: To calculate Histogram, the tensor " "must not be empty.")); PADDLE_ENFORCE_GE(max_val, min_val, platform::errors::InvalidArgument( "MkldnnQuantizer: To calculate Histogram, max_val (" + std::to_string(max_val) + ") must be greater or equal" "to min_val (" + std::to_string(min_val) + ").")); ConstEigenVectorArrayMap eigen_tensor{ var_tensor.data(), var_tensor.numel(), 1}; auto bin_width = std::abs(max_val - min_val) / num_bins; std::vector hist(num_bins); for (int i = 0; i < eigen_tensor.size(); i++) { int bin = std::min( num_bins - 1, static_cast(floor((eigen_tensor[i] - min_val) / bin_width))); ++hist[bin]; } return std::make_pair(std::move(hist), std::move(bin_width)); } void AnalysisPredictor::MkldnnQuantizer::ClearDeviceContext() const { platform::DeviceContextPool& pool = platform::DeviceContextPool::Instance(); platform::MKLDNNDeviceContext* dev_ctx = (platform::MKLDNNDeviceContext*)pool.Get(predictor_.place_); dev_ctx->ResetBlobMap( paddle::platform::MKLDNNDeviceContext::tls().get_curr_exec()); } void AnalysisPredictor::MkldnnQuantizer::PrepareArgument() const { auto& arg = predictor_.argument_; if (!arg.scope_valid()) arg.SetScope(new framework::Scope); arg.SetMainProgramNotOwned(predictor_.inference_program_.get()); auto graph = std::unique_ptr(new Graph(arg.main_program())); arg.SetMainGraph(graph.release()); auto* scope_ptr = arg.scope_ptr(); PADDLE_ENFORCE_NOT_NULL( scope_ptr, platform::errors::PreconditionNotMet("The scope should not be nullptr.")); arg.main_graph().SetNotOwned(framework::ir::kParamScopeAttr, scope_ptr); auto* builder = predictor_.config_.pass_builder(); builder->SetPasses({"cpu_quantize_pass", "cpu_quantize_squash_pass", "int8_scale_calculation_mkldnn_pass", "params_quantization_mkldnn_pass"}); if (predictor_.config_.ir_debug_) builder->TurnOnDebug(); auto passes = builder->AllPasses(); predictor_.argument_.SetIrAnalysisPasses(passes); predictor_.argument_.SetAnalysisPasses({"ir_graph_clean_pass", "ir_analysis_pass", "memory_optimize_pass", "ir_graph_to_program_pass"}); predictor_.argument_.SetQuantVarScales(scales_); } bool AnalysisPredictor::MkldnnQuantizer::Quantize() { if (!RunWarmup()) return false; if (!CalculateScales()) return false; ClearDeviceContext(); predictor_.PrepareScope(predictor_.scope_); predictor_.CreateExecutor(); if (!RunQuantizePasses()) return false; predictor_.PrepareExecutor(); predictor_.PrepareFeedFetch(); return true; } bool AnalysisPredictor::MkldnnQuantizer::RunQuantizePasses() const { predictor_.executor_->CreateVariables( *predictor_.inference_program_, 0, true, predictor_.sub_scope_); PrepareArgument(); auto& arg = predictor_.argument_; Analyzer().Run(&arg); PADDLE_ENFORCE_EQ( arg.scope_valid(), true, platform::errors::PreconditionNotMet("The scope should be valid.")); VLOG(5) << "to prepare executor"; ARGUMENT_CHECK_FIELD((&arg), ir_analyzed_program); predictor_.inference_program_.reset( new framework::ProgramDesc(arg.ir_analyzed_program())); LOG(INFO) << "== optimize 2 end =="; predictor_.executor_->CreateVariables( *predictor_.inference_program_, 0, false, predictor_.sub_scope_); return true; } bool AnalysisPredictor::MkldnnQuantizer::RunWarmup() const { VLOG(3) << "Predictor: run a quantization warmup iteration"; auto warmup_data = qconfig_->warmup_data(); PADDLE_ENFORCE_NOT_NULL(warmup_data, platform::errors::PreconditionNotMet( "Warmup data cannot be NULL in the config.")); PrettyLogH1("--- Running warmup iteration for quantization"); // Run the inference program std::vector output_slots; predictor_.Run(*warmup_data, &output_slots, qconfig_->warmup_batch_size()); return true; } float AnalysisPredictor::MkldnnQuantizer::SafeEntropy( std::vector reference_distr_P, int P_sum, std::vector candidate_distr_Q, int Q_sum) const { PADDLE_ENFORCE_EQ(reference_distr_P.size(), candidate_distr_Q.size(), platform::errors::InvalidArgument( "The P size %d should be equal to Q size %d", reference_distr_P.size(), candidate_distr_Q.size())); float tmp_sum1 = 0; float tmp_sum2 = 0; for (size_t idx = 0; idx < reference_distr_P.size(); idx++) { int p_idx = reference_distr_P[idx]; int q_idx = candidate_distr_Q[idx]; if (p_idx == 0) { tmp_sum1 += 0; tmp_sum2 += 0; } else { PADDLE_ENFORCE_NE( q_idx, 0, platform::errors::PreconditionNotMet( "MkldnnQuantizer: Fatal error!, idx = " + std::to_string(idx) + " qindex = 0! p_idx = " + std::to_string(p_idx))); } tmp_sum1 += p_idx * (log(Q_sum * p_idx)); tmp_sum2 += p_idx * (log(P_sum * q_idx)); } return (tmp_sum1 - tmp_sum2) / P_sum; } } // namespace paddle