diff --git a/cmake/external/python.cmake b/cmake/external/python.cmake
index a3599dd798c07f57ed82e3f25b6bb9fc4f8bdc3a..623c53f4f75bbd217c157bcdda0cb12c510269ee 100644
--- a/cmake/external/python.cmake
+++ b/cmake/external/python.cmake
@@ -18,8 +18,8 @@ ENDIF()
 
 INCLUDE(python_module)
 
-FIND_PACKAGE(PythonInterp ${PY_VERSION})
-FIND_PACKAGE(PythonLibs ${PY_VERSION})
+FIND_PACKAGE(PythonInterp ${PY_VERSION} REQUIRED)
+FIND_PACKAGE(PythonLibs ${PY_VERSION} REQUIRED)
 
 if(WIN32)
     execute_process(COMMAND "${PYTHON_EXECUTABLE}" "-c"
@@ -79,6 +79,5 @@ IF(PYTHONINTERP_FOUND)
         "please use pip to upgrade protobuf. pip install -U protobuf")
     ENDIF()
 ENDIF(PYTHONINTERP_FOUND)
-
 INCLUDE_DIRECTORIES(${PYTHON_INCLUDE_DIR})
 INCLUDE_DIRECTORIES(${PYTHON_NUMPY_INCLUDE_DIR})
diff --git a/paddle/fluid/operators/hierarchical_sigmoid_op.h b/paddle/fluid/operators/hierarchical_sigmoid_op.h
index b73a32af89e882ac02623dd1d312f400a78fc47a..d212e6f8437e69e71c010b6af27a33ff5e39e1e1 100644
--- a/paddle/fluid/operators/hierarchical_sigmoid_op.h
+++ b/paddle/fluid/operators/hierarchical_sigmoid_op.h
@@ -150,19 +150,27 @@ class HierarchicalSigmoidGradOpKernel : public framework::OpKernel<T> {
                                                        label.data<int64_t>()));
     }
 
-    auto& place = *ctx.template device_context<DeviceContext>().eigen_device();
-    auto pre_out_mat = EigenMatrix<T>::From(pre_out);
-    auto pre_out_grad_mat = EigenMatrix<T>::From(pre_out_grad);
-    auto out_grad_mat = EigenMatrix<T>::From(out_grad);
+    // softrelu derivative
 
-    Eigen::array<int, 2> bcast{1, static_cast<int>(pre_out_grad.dims()[1])};
+    auto blas = math::GetBlas<DeviceContext, T>(ctx);
 
-    // softrelu derivative
-    pre_out_grad_mat.device(place) =
-        static_cast<T>(1.0) - static_cast<T>(1.0) / pre_out_mat.exp();
+    auto* pre_out_grad_data = pre_out_grad.data<T>();
+    auto* pre_out_data = pre_out.data<T>();
+    auto n = pre_out.numel();
+    blas.VEXP(n, pre_out_data, pre_out_grad_data);
+    blas.VINV(n, pre_out_grad_data, pre_out_grad_data);
+    for (int64_t i = 0; i < n; ++i) {
+      pre_out_grad_data[i] = 1.0 - pre_out_grad_data[i];
+    }
     bit_code->Sub(&pre_out_grad);  // the gradient of clip(w * x + b)
-    pre_out_grad_mat.device(place) =
-        pre_out_grad_mat * out_grad_mat.broadcast(bcast);
+    auto* out_grad_data = out_grad.data<T>();
+
+    int64_t dim0 = pre_out_grad.dims()[0];
+    int64_t dim1 = pre_out_grad.dims()[1];
+    for (int64_t i = 0; i < dim0; ++i) {
+      T tmp = out_grad_data[i];
+      blas.SCAL(dim1, tmp, pre_out_grad_data + i * dim1);
+    }
     // TODO(guosheng): multiply pre_out_grad with subgradient of clipping to
     // be consistent with the clipping in forward.
 
diff --git a/paddle/fluid/operators/math/blas.h b/paddle/fluid/operators/math/blas.h
index 9f3a81f22cc52bef719f472e43f91bc81dfe2af6..f67f57827bc03e134bf87edd5bf033adb5098916 100644
--- a/paddle/fluid/operators/math/blas.h
+++ b/paddle/fluid/operators/math/blas.h
@@ -181,6 +181,9 @@ class Blas {
               const framework::Tensor& mat_b, const MatDescriptor& dim_b,
               T alpha, framework::Tensor* mat_out, T beta) const;
 
+  template <typename T>
+  void VINV(int n, const T* a, T* y) const;
+
  private:
   const DeviceContext& context_;
 };
@@ -282,6 +285,11 @@ class BlasT : private Blas<DeviceContext> {
     Base()->template BatchedGEMM<T>(args...);
   }
 
+  template <typename... ARGS>
+  void VINV(ARGS... args) const {
+    Base()->template VINV<T>(args...);
+  }
+
  private:
   const Blas<DeviceContext>* Base() const {
     return static_cast<const Blas<DeviceContext>*>(this);
diff --git a/paddle/fluid/operators/math/blas_impl.h b/paddle/fluid/operators/math/blas_impl.h
index c84087bb1e4849b27d53e05f046c93f631150f6f..972366bc093f4b7f0a090cf31213f75ccd89fd82 100644
--- a/paddle/fluid/operators/math/blas_impl.h
+++ b/paddle/fluid/operators/math/blas_impl.h
@@ -118,6 +118,11 @@ struct CBlas<float> {
   static void VPOW(ARGS... args) {
     platform::dynload::vsPowx(args...);
   }
+
+  template <typename... ARGS>
+  static void VINV(ARGS... args) {
+    platform::dynload::vsInv(args...);
+  }
 };
 
 template <>
@@ -213,6 +218,11 @@ struct CBlas<double> {
   static void VPOW(ARGS... args) {
     platform::dynload::vdPowx(args...);
   }
+
+  template <typename... ARGS>
+  static void VINV(ARGS... args) {
+    platform::dynload::vdInv(args...);
+  }
 };
 
 #else
@@ -603,6 +613,17 @@ void Blas<DeviceContext>::MatMul(const framework::Tensor &mat_a,
         dim_a.stride_, dim_b.stride_);
   }
 }
+template <typename DeviceContext>
+template <typename T>
+void Blas<DeviceContext>::VINV(int n, const T *a, T *y) const {
+#ifdef PADDLE_WITH_MKLML
+  CBlas<T>::VINV(n, a, y);
+#else
+  for (int i = 0; i < n; ++i) {
+    y[i] = 1.0 / a[i];
+  }
+#endif
+}
 
 }  // namespace math
 }  // namespace operators
diff --git a/paddle/fluid/operators/math/matrix_bit_code.cc b/paddle/fluid/operators/math/matrix_bit_code.cc
index 5a6e64b6f87d33249f0153e5f391deaf78e53de5..d55e832cc2d9a4a5e2cb7fe5cf451a1205601951 100644
--- a/paddle/fluid/operators/math/matrix_bit_code.cc
+++ b/paddle/fluid/operators/math/matrix_bit_code.cc
@@ -14,218 +14,380 @@ limitations under the License. */
 
 #include "paddle/fluid/operators/math/matrix_bit_code.h"
 #include <iostream>
+#include <map>
+
 namespace paddle {
 namespace operators {
 namespace math {
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::Add(const framework::Tensor& vec,
-                                  framework::Tensor* tmat) {
-  size_t batch_size = tmat->dims()[0];
-  size_t width = tmat->dims()[1];
-  for (size_t i = 0; i < batch_size; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      size_t index = code->calc_index(j);
-      tmat->data<T>()[i * width + j] += vec.data<T>()[index];
+struct MatrixBitCodeFunctorAdd : public boost::static_visitor<void> {
+  const framework::Tensor &vec_;
+  framework::Tensor *tmat_;
+
+  MatrixBitCodeFunctorAdd(const framework::Tensor &vec, framework::Tensor *tmat)
+      : vec_(vec), tmat_(tmat) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    size_t batch_size = tmat_->dims()[0];
+    size_t width = tmat_->dims()[1];
+    auto *tmat_data = tmat_->data<T>();
+    auto *vec_data = vec_.data<T>();
+    for (size_t i = 0; i < batch_size; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        size_t index = code.calc_index(j);
+        tmat_data[i * width + j] += vec_data[index];
+      }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::Add(const framework::Tensor &vec,
+                                  framework::Tensor *tmat) {
+  MatrixBitCodeFunctorAdd<T> func(vec, tmat);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::AddGrad(const framework::Tensor& tmat,
-                                      framework::Tensor* vec) {
-  size_t batch_size = tmat.dims()[0];
-  size_t width = tmat.dims()[1];
-  for (size_t i = 0; i < batch_size; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      size_t index = code->calc_index(j);
-      vec->data<T>()[index] += tmat.data<T>()[i * width + j];
+struct MatrixBitCodeFunctorAddGrad : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  framework::Tensor *vec_;
+  MatrixBitCodeFunctorAddGrad(const framework::Tensor &tmat,
+                              framework::Tensor *vec)
+      : tmat_(tmat), vec_(vec) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &table) {
+    size_t batch_size = tmat_.dims()[0];
+    size_t width = tmat_.dims()[1];
+    auto *vec_data = vec_->data<T>();
+    auto *tmat_data = tmat_.data<T>();
+    for (size_t i = 0; i < batch_size; ++i) {
+      auto code = table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        size_t index = code.calc_index(j);
+        vec_data[index] += tmat_data[i * width + j];
+      }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::AddGrad(const framework::Tensor &tmat,
+                                      framework::Tensor *vec) {
+  MatrixBitCodeFunctorAddGrad<T> func(tmat, vec);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::AddGrad(const framework::Tensor& tmat,
-                                      framework::SelectedRows* vec) {
-  size_t batch_size = tmat.dims()[0];
-  size_t width = tmat.dims()[1];
-  for (size_t i = 0; i < batch_size; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      size_t index = code->calc_index(j);
-      int64_t row_index = vec->GetIndexFromId(static_cast<int64_t>(index));
-      vec->mutable_value()->data<T>()[row_index] +=
-          tmat.data<T>()[i * width + j];
+struct MatrixBitCodeFunctorSelectedRowsAddGrad
+    : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  framework::SelectedRows *vec_;
+
+  MatrixBitCodeFunctorSelectedRowsAddGrad(const framework::Tensor &tmat,
+                                          framework::SelectedRows *vec)
+      : tmat_(tmat), vec_(vec) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    size_t batch_size = tmat_.dims()[0];
+    size_t width = tmat_.dims()[1];
+    auto *vec_data = vec_->mutable_value()->template data<T>();
+    auto *tmat_data = tmat_.data<T>();
+    for (size_t i = 0; i < batch_size; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        size_t index = code.calc_index(j);
+        int64_t row_index = vec_->GetIndexFromId(static_cast<int64_t>(index));
+        vec_data[row_index] += tmat_data[i * width + j];
+      }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::AddGrad(const framework::Tensor &tmat,
+                                      framework::SelectedRows *vec) {
+  MatrixBitCodeFunctorSelectedRowsAddGrad<T> func(tmat, vec);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::Sum(const framework::Tensor& tmat,
-                                  framework::Tensor* sum, T scale_sum) {
-  size_t num_samples = tmat.dims()[0];
-  size_t o_width = tmat.dims()[1];
-  for (size_t i = 0; i < num_samples; ++i) {
-    T sm = static_cast<T>(0.0);
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      if (code->calc_bit(j)) {
-        // calc_bit starts from right most bit, while data in tmat[i] is in the
-        // reverse order.
-        sm += tmat.data<T>()[i * o_width + j];
+struct MatrixBitCodeFunctorSum : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  framework::Tensor *sum_;
+  T scale_sum_;
+
+  MatrixBitCodeFunctorSum(const framework::Tensor &tmat, framework::Tensor *sum,
+                          T scale_sum)
+      : tmat_(tmat), sum_(sum), scale_sum_(scale_sum) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    size_t num_samples = tmat_.dims()[0];
+    size_t o_width = tmat_.dims()[1];
+    auto *tmat_data = tmat_.data<T>();
+    auto *sum_data = sum_->data<T>();
+    for (size_t i = 0; i < num_samples; ++i) {
+      T sm = static_cast<T>(0.0);
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        if (code.calc_bit(j)) {
+          // calc_bit starts from right most bit, while data in tmat[i] is in
+          // the
+          // reverse order.
+          sm += tmat_data[i * o_width + j];
+        }
       }
+      sum_data[i] = scale_sum_ * sm;
     }
-    sum->data<T>()[i] = scale_sum * sm;
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::Sum(const framework::Tensor &tmat,
+                                  framework::Tensor *sum, T scale_sum) {
+  MatrixBitCodeFunctorSum<T> func(tmat, sum, scale_sum);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::Mul(framework::Tensor* tmat,
-                                  const framework::Tensor& weight,
-                                  const framework::Tensor& input) {
-  auto blas =
-      GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
-  size_t num_samples = tmat->dims()[0];
-  size_t tmat_width = tmat->dims()[1];
-  size_t input_width = input.dims()[1];
-  size_t weight_width = weight.dims()[1];
-  auto tmat_value = tmat->data<T>();
-  auto weight_value = weight.data<T>();
-  auto input_value = input.data<T>();
-  for (size_t i = 0; i < num_samples; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    const T* input_row = input_value + input_width * i;
-    for (int j = 0; j < code_length; ++j) {
-      size_t index = code->calc_index(j);
-      const T* weight_row = weight_value + weight_width * index;
-      T sum = static_cast<T>(0.0);
-      sum = blas.DOT(input_width, weight_row, input_row);
-      tmat_value[i * tmat_width + j] += sum;
+struct MatrixBitCodeFunctorMul : public boost::static_visitor<void> {
+  framework::Tensor *tmat_;
+  const framework::Tensor &weight_;
+  const framework::Tensor &input_;
+
+  MatrixBitCodeFunctorMul(framework::Tensor *tmat,
+                          const framework::Tensor &weight,
+                          const framework::Tensor &input)
+      : tmat_(tmat), weight_(weight), input_(input) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    auto blas =
+        GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
+    size_t num_samples = tmat_->dims()[0];
+    size_t tmat_width = tmat_->dims()[1];
+    size_t input_width = input_.dims()[1];
+    size_t weight_width = weight_.dims()[1];
+    auto tmat_value = tmat_->data<T>();
+    auto weight_value = weight_.data<T>();
+    auto input_value = input_.data<T>();
+    for (size_t i = 0; i < num_samples; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      const T *input_row = input_value + input_width * i;
+      for (int j = 0; j < code_length; ++j) {
+        size_t index = code.calc_index(j);
+        const T *weight_row = weight_value + weight_width * index;
+        T sum = blas.DOT(input_width, weight_row, input_row);
+        tmat_value[i * tmat_width + j] += sum;
+      }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::Mul(framework::Tensor *tmat,
+                                  const framework::Tensor &weight,
+                                  const framework::Tensor &input) {
+  MatrixBitCodeFunctorMul<T> func(tmat, weight, input);
+  code_table_.apply_visitor(func);
 }
 
+template <typename T, size_t N>
+class ReservedVector : public std::vector<T> {
+ public:
+  ReservedVector() { this->reserve(N); }
+};
+
 template <typename T>
-void MatrixBitCodeFunctor<T>::MulGradWeight(const framework::Tensor& tmat,
-                                            framework::Tensor* weight,
-                                            const framework::Tensor& input) {
-  auto blas =
-      GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
-  size_t num_samples = tmat.dims()[0];
-  size_t input_width = input.dims()[1];
-  size_t tmat_width = tmat.dims()[1];
-  size_t weight_width = weight->dims()[1];
-  auto tmat_value = tmat.data<T>();
-  auto weight_value = weight->data<T>();
-  auto input_value = input.data<T>();
-
-  std::unordered_map<int, std::vector<std::pair<T, const T*>>> ops;
-
-  for (size_t i = 0; i < num_samples; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    const T* input_value_row = input_value + input_width * i;
-    const T* tmat_row = tmat_value + i * tmat_width;
-    for (int j = 0; j < code_length; ++j) {
-      ops[code->calc_index(j)].emplace_back(tmat_row[j], input_value_row);
+struct MatrixBitCodeFunctorMulGradWeight : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  framework::Tensor *weight_;
+  const framework::Tensor &input_;
+  MatrixBitCodeFunctorMulGradWeight(const framework::Tensor &tmat,
+                                    framework::Tensor *weight,
+                                    const framework::Tensor &input)
+      : tmat_(tmat), weight_(weight), input_(input) {}
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    auto blas =
+        GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
+    size_t num_samples = tmat_.dims()[0];
+    size_t input_width = input_.dims()[1];
+    size_t tmat_width = tmat_.dims()[1];
+    size_t weight_width = weight_->dims()[1];
+    auto tmat_value = tmat_.data<T>();
+    auto weight_value = weight_->data<T>();
+    auto input_value = input_.data<T>();
+
+    std::map<int, ReservedVector<std::pair<T, const T *>, 8u>> ops;
+    for (size_t i = 0; i < num_samples; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      const T *input_value_row = input_value + input_width * i;
+      const T *tmat_row = tmat_value + i * tmat_width;
+      for (int j = 0; j < code_length; ++j) {
+        ops[code.calc_index(j)].emplace_back(tmat_row[j], input_value_row);
+      }
     }
-  }
-  for (auto& op : ops) {
-    auto& op_in_row = op.second;
-    for (auto& pair : op_in_row) {
-      auto& scale = pair.first;
-      auto* input_row = pair.second;
-      T* weight_row = weight_value + op.first * weight_width;
-      blas.AXPY(input_width, scale, input_row, weight_row);
+    for (auto &op : ops) {
+      auto &op_in_row = op.second;
+      for (auto &pair : op_in_row) {
+        auto &scale = pair.first;
+        auto *input_row = pair.second;
+        T *weight_row = weight_value + op.first * weight_width;
+        blas.AXPY(input_width, scale, input_row, weight_row);
+      }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::MulGradWeight(const framework::Tensor &tmat,
+                                            framework::Tensor *weight,
+                                            const framework::Tensor &input) {
+  MatrixBitCodeFunctorMulGradWeight<T> func(tmat, weight, input);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::MulGradWeight(const framework::Tensor& tmat,
-                                            framework::SelectedRows* weight,
-                                            const framework::Tensor& input) {
-  auto blas =
-      GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
-  size_t num_samples = tmat.dims()[0];
-  size_t input_width = input.dims()[1];
-  size_t tmat_width = tmat.dims()[1];
-  size_t weight_width = weight->value().dims()[1];
-  auto tmat_value = tmat.data<T>();
-  auto weight_value = weight->mutable_value()->data<T>();
-  auto input_value = input.data<T>();
-
-  std::unordered_map<int, std::vector<std::pair<T, const T*>>> ops;
-  ops.reserve(weight->rows().size());
-
-  for (size_t i = 0; i < num_samples; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    const T* input_value_row = input_value + input_width * i;
-    const T* tmat_row = tmat_value + i * tmat_width;
-    for (int j = 0; j < code_length; ++j) {
-      ops[code->calc_index(j)].emplace_back(tmat_row[j], input_value_row);
+struct MatrixBitCodeFunctorMulGradWeightSR
+    : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  framework::SelectedRows *weight_;
+  const framework::Tensor &input_;
+
+  MatrixBitCodeFunctorMulGradWeightSR(const framework::Tensor &tmat,
+                                      framework::SelectedRows *weight,
+                                      const framework::Tensor &input)
+      : tmat_(tmat), weight_(weight), input_(input) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    auto blas =
+        GetBlas<platform::CPUDeviceContext, T>(platform::CPUDeviceContext());
+    size_t num_samples = tmat_.dims()[0];
+    size_t input_width = input_.dims()[1];
+    size_t tmat_width = tmat_.dims()[1];
+    size_t weight_width = weight_->value().dims()[1];
+    auto tmat_value = tmat_.data<T>();
+    auto weight_value = weight_->mutable_value()->data<T>();
+    auto input_value = input_.data<T>();
+
+    std::unordered_map<int, std::vector<std::pair<T, const T *>>> ops;
+    ops.reserve(weight_->rows().size());
+
+    for (size_t i = 0; i < num_samples; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      const T *input_value_row = input_value + input_width * i;
+      const T *tmat_row = tmat_value + i * tmat_width;
+      for (int j = 0; j < code_length; ++j) {
+        ops[code.calc_index(j)].emplace_back(tmat_row[j], input_value_row);
+      }
     }
-  }
 
-  for (auto& row : weight->rows()) {
-    auto& op_in_row = ops[row];
-    for (auto& pair : op_in_row) {
-      auto& scale = pair.first;
-      auto* input_row = pair.second;
-      blas.AXPY(input_width, scale, input_row, weight_value);
+    for (auto &row : weight_->rows()) {
+      auto &op_in_row = ops[row];
+      for (auto &pair : op_in_row) {
+        auto &scale = pair.first;
+        auto *input_row = pair.second;
+        blas.AXPY(input_width, scale, input_row, weight_value);
+      }
+      weight_value += weight_width;
     }
-    weight_value += weight_width;
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::MulGradWeight(const framework::Tensor &tmat,
+                                            framework::SelectedRows *weight,
+                                            const framework::Tensor &input) {
+  MatrixBitCodeFunctorMulGradWeightSR<T> func(tmat, weight, input);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::MulGradError(const framework::Tensor& tmat,
-                                           const framework::Tensor& weight,
-                                           framework::Tensor* input) {
-  size_t num_samples = tmat.dims()[0];
-  size_t tmat_width = tmat.dims()[1];
-  size_t input_width = input->dims()[1];
-  size_t weight_width = weight.dims()[1];
-  auto tmat_value = tmat.data<T>();
-  auto weight_value = weight.data<T>();
-  auto input_value = input->data<T>();
-
-  for (size_t i = 0; i < num_samples; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      size_t index = code->calc_index(j);
-
-      for (size_t k = 0; k < input_width; ++k) {
-        input_value[input_width * i + k] +=
-            tmat_value[i * tmat_width + j] *
-            weight_value[weight_width * index + k];
+struct MatrixBitCodeFunctorMulGradError : public boost::static_visitor<void> {
+  const framework::Tensor &tmat_;
+  const framework::Tensor &weight_;
+  framework::Tensor *input_;
+
+  MatrixBitCodeFunctorMulGradError(const framework::Tensor &tmat,
+                                   const framework::Tensor &weight,
+                                   framework::Tensor *input)
+      : tmat_(tmat), weight_(weight), input_(input) {}
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    size_t num_samples = tmat_.dims()[0];
+    size_t tmat_width = tmat_.dims()[1];
+    size_t input_width = input_->dims()[1];
+    size_t weight_width = weight_.dims()[1];
+    auto tmat_value = tmat_.data<T>();
+    auto weight_value = weight_.data<T>();
+    auto input_value = input_->data<T>();
+
+    for (size_t i = 0; i < num_samples; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        size_t index = code.calc_index(j);
+
+        for (size_t k = 0; k < input_width; ++k) {
+          input_value[input_width * i + k] +=
+              tmat_value[i * tmat_width + j] *
+              weight_value[weight_width * index + k];
+        }
       }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::MulGradError(const framework::Tensor &tmat,
+                                           const framework::Tensor &weight,
+                                           framework::Tensor *input) {
+  MatrixBitCodeFunctorMulGradError<T> func(tmat, weight, input);
+  code_table_.apply_visitor(func);
 }
 
 template <typename T>
-void MatrixBitCodeFunctor<T>::Sub(framework::Tensor* tmat) {
-  size_t num_samples = tmat->dims()[0];
-  size_t o_width = tmat->dims()[1];
-  for (size_t i = 0; i < num_samples; ++i) {
-    auto code = code_table_->get_code(i);
-    int code_length = code->get_length();
-    for (int j = 0; j < code_length; ++j) {
-      if (code->calc_bit(j)) {
-        tmat->data<T>()[i * o_width + j] -= 1;
+struct MatrixBitCodeFunctorSub : public boost::static_visitor<void> {
+  framework::Tensor *tmat_;
+
+  explicit MatrixBitCodeFunctorSub(framework::Tensor *tmat) : tmat_(tmat) {}
+
+  template <typename CodeTable>
+  void operator()(const CodeTable &code_table) {
+    size_t num_samples = tmat_->dims()[0];
+    size_t o_width = tmat_->dims()[1];
+    auto *tmat_data = tmat_->data<T>();
+    for (size_t i = 0; i < num_samples; ++i) {
+      auto code = code_table.get_code(i);
+      int code_length = code.get_length();
+      for (int j = 0; j < code_length; ++j) {
+        if (code.calc_bit(j)) {
+          tmat_data[i * o_width + j] -= 1;
+        }
       }
     }
   }
+};
+
+template <typename T>
+void MatrixBitCodeFunctor<T>::Sub(framework::Tensor *tmat) {
+  MatrixBitCodeFunctorSub<T> func(tmat);
+  code_table_.apply_visitor(func);
 }
 
 template class MatrixBitCodeFunctor<float>;
diff --git a/paddle/fluid/operators/math/matrix_bit_code.h b/paddle/fluid/operators/math/matrix_bit_code.h
index 35ca73802b48982ddf3ed7485b56f50221c9f28c..01e4889d34ad6e409f1b8a9c4bf783800187e863 100644
--- a/paddle/fluid/operators/math/matrix_bit_code.h
+++ b/paddle/fluid/operators/math/matrix_bit_code.h
@@ -13,6 +13,7 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #pragma once
+#include <map>
 #include <unordered_map>
 #include <utility>
 #include <vector>
@@ -22,6 +23,7 @@ limitations under the License. */
 #include "paddle/fluid/framework/tensor.h"
 #include "paddle/fluid/operators/math/blas.h"
 #include "paddle/fluid/platform/device_context.h"
+#include "paddle/fluid/platform/variant.h"
 
 #if defined(_WIN32)
 #include <intrin.h>
@@ -98,24 +100,7 @@ inline int clz(const T& value) {
 
 inline size_t FindLastSet(size_t x) { return sizeof(size_t) * 8 - clz(x); }
 #endif  // !_WIN32
-// set a code interface to create multiple code
-class Code {
- public:
-  virtual ~Code() {}
-  virtual size_t calc_index(int bit) const = 0;
-  virtual bool calc_bit(int bit) const = 0;
-  virtual int get_length() const = 0;
-};
-// set a CodeTable interface to create multiple code table
-class CodeTable {
- public:
-  virtual std::unique_ptr<Code> get_code(int64_t code) const = 0;
-  virtual size_t size() const = 0;
-  virtual int get_max_code_length() const = 0;
-  virtual ~CodeTable() {}
-};
-
-class SimpleCode : public Code {
+class SimpleCode {
  public:
   SimpleCode(size_t code, size_t num_classes, const int64_t* ids)
       : c_(static_cast<size_t>(ids[code]) + num_classes) {}
@@ -137,16 +122,16 @@ class SimpleCode : public Code {
 };
 
 template <typename T>
-class CustomCode : public Code {
+class CustomCode {
  public:
   CustomCode(const framework::Tensor& ptable, const framework::Tensor& pcode,
-             const int64_t* ids, int index)
-      : ids_(ids), index_(index) {
-    ptable_ = ptable.Slice(index, index + 1);
-    pcode_ = pcode.Slice(index, index + 1);
+             const int64_t* ids, int index) {
+    seq_len_ = ptable.dims()[1];
+    ptable_data_ = ptable.data<T>() + seq_len_ * index;
+    pcode_data_ = pcode.data<T>() + seq_len_ * index;
   }
   /**
-   * Here the id of root shoud be 1 rather than 0, thus the encoding of class c
+   * Here the id of root should be 1 rather than 0, thus the encoding of class c
    * is `c + num_classes` and all siblings can get the same weight indice using
    * prefixes.
    * Weight index is the prefixes of encoding, thus leave out the right most
@@ -154,36 +139,37 @@ class CustomCode : public Code {
    * Binary classification path is the suffixes of encoding, thus leave out the
    * left most bit in calc_bit.
    */
-  size_t calc_index(int bit) const { return ptable_.data<T>()[bit]; }
-  bool calc_bit(int bit) const { return pcode_.data<T>()[bit]; }
-  int get_length() const {
-    int length = 0;
+  size_t calc_index(int bit) const { return ptable_data_[bit]; }
+  bool calc_bit(int bit) const { return pcode_data_[bit]; }
 
-    for (int i = 0; i < static_cast<int>(ptable_.dims()[1]); i++) {
-      if (ptable_.data<T>()[i] >= 0) {
-        length++;
-      } else {
-        return length;
-      }
+  // NOTE: this function is not thread-safe.
+  int get_length() const {
+    if (length_ < 0) {
+      auto len = seq_len_;
+      length_ =
+          static_cast<int>(std::find_if(ptable_data_, ptable_data_ + len,
+                                        [](const T& val) { return val < 0; }) -
+                           ptable_data_);
     }
-    return length;
+    return length_;
   }
 
  private:
-  framework::Tensor ptable_;
-  framework::Tensor pcode_;
-  const int64_t* ids_;
-  const int index_;
+  int64_t seq_len_;
+  const T* ptable_data_;
+  const T* pcode_data_;
+  mutable int length_{-1};
 };
 
-class SimpleCodeTable : public CodeTable {
+class SimpleCodeTable {
  public:
   SimpleCodeTable(size_t num_classes, const int64_t* ids)
       : num_classes_(num_classes), ids_(ids) {}
-  std::unique_ptr<Code> get_code(int64_t code) const {
-    std::unique_ptr<Code> coder(new SimpleCode(code, num_classes_, ids_));
-    return coder;
+
+  SimpleCode get_code(int64_t code) const {
+    return SimpleCode(code, num_classes_, ids_);
   }
+
   size_t size() const { return num_classes_; }
   int get_max_code_length() const { return FindLastSet(num_classes_ - 1); }
 
@@ -193,15 +179,14 @@ class SimpleCodeTable : public CodeTable {
 };
 
 template <typename T>
-class CustomCodeTable : public CodeTable {
+class CustomCodeTable {
  public:
   CustomCodeTable(const framework::Tensor& ptable,
                   const framework::Tensor& pcode, const int64_t* ids)
       : ptable_(ptable), pcode_(pcode), ids_(ids) {}
 
-  std::unique_ptr<Code> get_code(int64_t code) const {
-    std::unique_ptr<Code> coder(new CustomCode<T>(ptable_, pcode_, ids_, code));
-    return coder;
+  CustomCode<T> get_code(int64_t code) const {
+    return CustomCode<T>(ptable_, pcode_, ids_, code);
   }
 
   size_t size() const { return static_cast<size_t>(ptable_.dims()[1]); }
@@ -215,19 +200,21 @@ class CustomCodeTable : public CodeTable {
   const int64_t* ids_;
 };
 
+using CodeTable = boost::variant<SimpleCodeTable, CustomCodeTable<int64_t>>;
+
 template <typename T>
 class MatrixBitCodeFunctor {
  public:
   MatrixBitCodeFunctor(size_t num_classes, const int64_t* ids)
       : num_classes_(num_classes),
         ids_(ids),
-        code_table_(new SimpleCodeTable(num_classes, ids)) {}
+        code_table_(SimpleCodeTable(num_classes, ids)) {}
 
   MatrixBitCodeFunctor(const framework::Tensor& ptable,
                        const framework::Tensor& pcode, const int64_t* ids)
       : num_classes_(static_cast<size_t>(ptable.dims()[1])),
         ids_(ids),
-        code_table_(new CustomCodeTable<int64_t>(ptable, pcode, ids)) {}
+        code_table_(CustomCodeTable<int64_t>(ptable, pcode, ids)) {}
   /* For j < code_length
        tmat(i, j) += vec(0, index(i, j))
   */
@@ -277,7 +264,7 @@ class MatrixBitCodeFunctor {
 
   size_t num_classes_;
   const int64_t* ids_;
-  std::unique_ptr<CodeTable> code_table_;
+  CodeTable code_table_;
 };
 }  // namespace math
 }  // namespace operators
diff --git a/paddle/fluid/platform/dynload/mklml.h b/paddle/fluid/platform/dynload/mklml.h
index f0a973662360fd9ff35e1006cce937d86f3e563c..c3f9433503accf98d30ccaa57b9b4b8f3c68666a 100644
--- a/paddle/fluid/platform/dynload/mklml.h
+++ b/paddle/fluid/platform/dynload/mklml.h
@@ -82,6 +82,8 @@ extern void* mklml_dso_handle;
   __macro(vdSqr);                   \
   __macro(vsPowx);                  \
   __macro(vdPowx);                  \
+  __macro(vsInv);                   \
+  __macro(vdInv);                   \
   __macro(MKL_Set_Num_Threads)
 
 MKLML_ROUTINE_EACH(DECLARE_DYNAMIC_LOAD_MKLML_WRAP);