activation_op.h

/* Copyright (c) 2018 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. */

#pragma once
#include <glog/logging.h>
#include <algorithm>
#include <memory>
#include <string>
#include <unordered_set>
#include <utility>
#include <vector>

#include <cmath>
#ifndef _USE_MATH_DEFINES
#define _USE_MATH_DEFINES
#endif

#include "paddle/fluid/framework/eigen.h"
#include "paddle/fluid/framework/op_registry.h"
#include "paddle/fluid/operators/math/blas.h"
#include "paddle/fluid/platform/enforce.h"
#include "paddle/fluid/platform/float16.h"

#ifdef PADDLE_WITH_MKLDNN
#include "paddle/fluid/platform/mkldnn_helper.h"
#endif

namespace paddle {
namespace operators {

using framework::To32BitIndex;

enum ActBwdOpFwdDeps {
  kNoDeps = 0x00,  // Do not need any forward input/output
  kDepX = 0x01,    // Only need forward input X
  kDepOut = 0x02,  // Only need forward output Out
};

/* The following operator can be used to process SelectedRows, because the
 * output of those operator for zero is zero too.
 */
static std::unordered_set<std::string> CanBeUsedBySelectedRows = {
    "abs", "abs_grad", "square", "square_grad", "sqrt", "sqrt_grad"};

inline void ExtractActivationTensor(const framework::ExecutionContext& context,
                                    const framework::Tensor** X,
                                    framework::Tensor** Out) {
  auto x_var = context.InputVar("X");
  auto out_var = context.OutputVar("Out");
  PADDLE_ENFORCE_NOT_NULL(x_var,
                          platform::errors::NotFound(
                              "Cannot get input Variable X, variable name = %s",
                              context.InputName("X")));
  PADDLE_ENFORCE_NOT_NULL(
      out_var, platform::errors::NotFound(
                   "Cannot get output Variable Out, variable name = %s",
                   context.OutputName("Out")));
  if (CanBeUsedBySelectedRows.count(context.Type())) {
    *X = paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*x_var);
    *Out = paddle::framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(
        out_var);
  } else {
    *X = context.Input<framework::Tensor>("X");
    *Out = context.Output<framework::Tensor>("Out");
  }

  PADDLE_ENFORCE_NOT_NULL(*Out, platform::errors::NotFound(
                                    "Cannot get the tensor from the Variable "
                                    "Output(Out), variable name = %s",
                                    context.OutputName("Out")));
}

template <ActBwdOpFwdDeps kDepValue>
inline void ExtractActivationGradTensor(
    const framework::ExecutionContext& context, const framework::Tensor** X,
    const framework::Tensor** Out, const framework::Tensor** dOut,
    framework::Tensor** dX) {
  auto out_grad_var = context.InputVar(framework::GradVarName("Out"));
  auto x_grad_var = context.OutputVar(framework::GradVarName("X"));
  const framework::Variable* out_var = nullptr;

  if (static_cast<int>(kDepValue) & static_cast<int>(kDepOut)) {
    out_var = context.InputVar("Out");
    PADDLE_ENFORCE_NOT_NULL(
        out_var, platform::errors::NotFound(
                     "Cannot get input Variable Out, variable name = %s",
                     context.InputName("Out")));
  }

  PADDLE_ENFORCE_NOT_NULL(
      out_grad_var, platform::errors::NotFound(
                        "Cannot get input Variable %s, variable name = %s",
                        framework::GradVarName("Out"),
                        context.InputName(framework::GradVarName("Out"))));
  PADDLE_ENFORCE_NOT_NULL(
      x_grad_var, platform::errors::NotFound(
                      "Cannot get output Variable %s, variable name = %s",
                      framework::GradVarName("X"),
                      context.OutputName(framework::GradVarName("X"))));

  if (CanBeUsedBySelectedRows.count(context.Type())) {
    *dOut = paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(
        *out_grad_var);
    *dX = paddle::framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(
        x_grad_var);

    if (out_var) {
      *Out =
          paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*out_var);
    } else {
      *Out = *dOut;  // fake out
    }

  } else {
    *Out = context.Input<framework::Tensor>("Out");
    *dOut = context.Input<framework::Tensor>(framework::GradVarName("Out"));
    *dX = context.Output<framework::Tensor>(framework::GradVarName("X"));

    if (out_var) {
      *Out = &(out_var->Get<framework::LoDTensor>());
    } else {
      *Out = *dOut;  // fake out
    }
  }

  PADDLE_ENFORCE_NOT_NULL(*dX,
                          platform::errors::NotFound(
                              "Cannot get the tensor from the Variable "
                              "Output(Out), variable name = %s",
                              context.OutputName(framework::GradVarName("X"))));

  if (static_cast<int>(kDepValue) & static_cast<int>(kDepX)) {
    auto x_var = context.InputVar("X");
    PADDLE_ENFORCE_NOT_NULL(x_var, platform::errors::NotFound(
                                       "Cannot get the tensor from the "
                                       "Variable Input(X), variable name = %s",
                                       context.InputName("X")));
    if (CanBeUsedBySelectedRows.count(context.Type())) {
      *X = paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*x_var);
    } else {
      *X = context.Input<framework::Tensor>("X");
    }
  } else {
    VLOG(10) << " Inplace activation of Op : " << context.Type();
    *X = *dX;
  }
}

template <typename DeviceContext, typename Functor>
class ActivationKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;

  void Compute(const framework::ExecutionContext& context) const override {
    const framework::Tensor* X = nullptr;
    framework::Tensor* Out = nullptr;
    ExtractActivationTensor(context, &X, &Out);
    Out->mutable_data<T>(context.GetPlace());

    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "Activation"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Output", "Out", "Activation"));
    auto* place =
        context.template device_context<DeviceContext>().eigen_device();
    Functor functor;

    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = context.Attr<float>(attr.first);
    }
    // use 32bit index to speed up computation
    bool use_32bit_index = out.size() < Eigen::NumTraits<int>::highest();
    bool is_gpu_place = platform::is_gpu_place(context.GetPlace());
    if (use_32bit_index && is_gpu_place) {
      functor(*place, To32BitIndex(x), To32BitIndex(out));
    } else {
      functor(*place, x, out);
    }
  }
};

template <typename DeviceContext, typename Functor>
class ActivationGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& context) const override {
    const framework::Tensor *X, *Out, *dOut;
    framework::Tensor* dX = nullptr;
    X = Out = dOut = nullptr;
    ExtractActivationGradTensor<Functor::FwdDeps()>(context, &X, &Out, &dOut,
                                                    &dX);
    dX->mutable_data<T>(context.GetPlace());
    auto dout = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(dOut, "Input", "Out@GRAD", "ActivationGrad"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Input", "Out", "ActivationGrad"));
    auto dx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(dX, "Input", "X@GRAD", "ActivationGrad"));
    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "ActivationGrad"));
    auto* place =
        context.template device_context<DeviceContext>().eigen_device();
    Functor functor;
    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = context.Attr<float>(attr.first);
    }
    // use 32bit index to speed up computation
    bool use_32bit_index = out.size() < Eigen::NumTraits<int>::highest();
    bool is_gpu_place = platform::is_gpu_place(context.GetPlace());
    if (use_32bit_index && is_gpu_place) {
      functor(*place, To32BitIndex(x), To32BitIndex(out), To32BitIndex(dout),
              To32BitIndex(dx));
    } else {
      functor(*place, x, out, dout, dx);
    }
  }
};

template <typename T>
struct BaseActivationFunctor {
  using ELEMENT_TYPE = T;

  using AttrPair = std::vector<std::pair<const char*, float*>>;

  AttrPair GetAttrs() { return AttrPair(); }
};

// sigmoid(x) = 1 / (1 + exp(-x))
template <typename T>
struct SigmoidFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = static_cast<T>(1) / (static_cast<T>(1) + (-x).exp());
  }
};

template <typename T>
struct SigmoidGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * out * (static_cast<T>(1) - out);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// Originally: logsigmoid(x) = -log (1 + exp(-x))
// For numerical stability, we can use the log-sum-exp trick:
// https://hips.seas.harvard.edu/blog/2013/01/09/computing-log-sum-exp/
// We can rewrite the above equation as:
// out = -log( exp(0) + exp(-x)) [since exp(0) = 1]
//   = -log( exp(max(-x, 0) - max(-x, 0)) + exp(-x + max(-x, 0) - max(-x, 0)))
//   = -log( exp(max(-x, 0)) * exp(-max(-x, 0)) - exp(max(-x, 0)) * exp(-x -
//           max(-x, 0)))
//   = -log( exp(max(-x, 0)) * (exp(-max(-x, 0)) + exp(-x - max(-x, 0))))
//   = -log( exp(max(-x, 0)) - log(exp(-max(-x, 0)) + exp(-x - max(-x, 0)))
//
// Hence, logsigmoid(x) = - (max(-x, 0) + log(exp(-max(-x, 0))
// + exp(-x - max(-x, 0))))
template <typename T>
struct LogSigmoidFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto temp = (-x).cwiseMax(static_cast<T>(0));  // temp = max(-x, 0)
    out.device(d) = -temp - (((-temp).exp() + (-x - temp).exp()).log());
  }
};

// Originally: f' = exp(-x) / (1 + exp(-x))
// For numerical stability: f' = exp(-x - max(-x, 0)) / (exp(-max(-x, 0)) +
// exp(-x - max(-x, 0)))
template <typename T>
struct LogSigmoidGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto temp = (-x).cwiseMax(static_cast<T>(0));  // temp = max(-x, 0)
    dx.device(d) =
        dout * ((-x - temp).exp() / ((-temp).exp() + (-x - temp).exp()));
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// exp(x) = e^x
template <typename T>
struct ExpFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.exp();
  }
};

template <typename T>
struct ExpGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * out;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// relu(x) = max(x, 0)
template <typename T>
struct ReluFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.cwiseMax(static_cast<T>(0));
  }
};

template <typename T>
struct ReluGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * (out > static_cast<T>(0)).template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
template <typename T>
struct TanhFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.tanh();
  }
};

template <typename T>
struct TanhGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * (static_cast<T>(1) - out * out);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// tanhshrink(x) = x - tanh(x)
// where tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
template <typename T>
struct TanhShrinkFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x - x.tanh();
  }
};

template <typename T>
struct TanhShrinkGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * (x.tanh() * x.tanh());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// tanhshrink(x) = x - tanh(x)
// where tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
template <typename T>
struct HardShrinkFunctor : public BaseActivationFunctor<T> {
  float threshold;

  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto temp1 = x < static_cast<T>(threshold * -1.f);
    auto temp2 = x > static_cast<T>(threshold);
    out.device(d) = x * (temp1 + temp2 > 0).template cast<T>();
  }
};

template <typename T>
struct HardShrinkGradFunctor : public BaseActivationFunctor<T> {
  float threshold;

  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto temp1 = x < static_cast<T>(threshold * -1.f);
    auto temp2 = x > static_cast<T>(threshold);
    dx.device(d) = dout * (temp1 + temp2 > 0).template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// softshrink(x) = x - lambda, if x > lambda; x + lambda, if x < -lambda; 0
// otherwise
template <typename T>
struct SoftShrinkFunctor : public BaseActivationFunctor<T> {
  float lambda;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"lambda", &lambda}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto lambdaT = static_cast<T>(lambda);
    auto temp1 = (x > lambdaT).template cast<T>();
    auto temp2 = (x < -lambdaT).template cast<T>();
    out.device(d) = temp1 * (x - lambdaT) + temp2 * (x + lambdaT);
  }
};

template <typename T>
struct SoftShrinkGradFunctor : public BaseActivationFunctor<T> {
  float lambda;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"lambda", &lambda}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto lambdaT = static_cast<T>(lambda);
    auto temp1 = (x > lambdaT).template cast<T>();
    auto temp2 = (x < -lambdaT).template cast<T>();
    dx.device(d) = dout * (temp1 + temp2).template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// sqrt(x) = x^(1/2)
template <typename T>
struct SqrtFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.sqrt();
  }
};

template <typename T>
struct SqrtGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = static_cast<T>(0.5) * dout / out;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// rsqrt(x) = x^(-1/2)
template <typename T>
struct RsqrtFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.rsqrt();
  }
};

template <typename T>
struct RsqrtGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = static_cast<T>(-0.5) * dout * out * out * out;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// ceil(x) = ceiling(x)
template <typename T>
struct CeilFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.ceil();
  }
};

template <typename T>
struct ZeroGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = static_cast<T>(0) * out;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kNoDeps; }
};

// floor(x) = flooring(x)
template <typename T>
struct FloorFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.floor();
  }
};

template <typename T>
struct Sine {
  HOSTDEVICE T operator()(const T& val) const { return sin(val); }
};

template <>
struct Sine<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(sin(static_cast<float>(val)));
  }
};

template <typename T>
struct Cosine {
  HOSTDEVICE T operator()(const T& val) const { return cos(val); }
};

template <>
struct Cosine<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(cos(static_cast<float>(val)));
  }
};

// cosine'(x) = -sin(x)
template <typename T>
struct CosGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = -dout * x.unaryExpr(Sine<T>());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// cosine(x) = cos(x)
template <typename T>
struct CosFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Cosine<T>());
  }
};

// sine'(x) = cos(x)
template <typename T>
struct SinGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * x.unaryExpr(Cosine<T>());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// sine(x) = sin(x)
template <typename T>
struct SinFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Sine<T>());
  }
};

template <typename T>
struct Sinh {
  HOSTDEVICE T operator()(const T& val) const { return sinh(val); }
};

template <>
struct Sinh<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(sinhf(static_cast<float>(val)));
  }
};

template <typename T>
struct Cosh {
  HOSTDEVICE T operator()(const T& val) const { return cosh(val); }
};

template <>
struct Cosh<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(coshf(static_cast<float>(val)));
  }
};

// sinh(x) = sinh(x)
template <typename T>
struct SinhFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Sinh<T>());
  }
};

// cosh(x) = cosh(x)
template <typename T>
struct CoshFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Cosh<T>());
  }
};

// sinh'(x) = cosh(x)
template <typename T>
struct SinhGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * x.unaryExpr(Cosh<T>());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// cosh'(x) = sinh(x)
template <typename T>
struct CoshGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * x.unaryExpr(Sinh<T>());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct Acos {
  HOSTDEVICE T operator()(const T& val) const { return acos(val); }
};

template <>
struct Acos<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(acos(static_cast<float>(val)));
  }
};

// Acos(x) = acos(x)
template <typename T>
struct AcosFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Acos<T>());
  }
};

// acos'(x) = -1/sqrt(1-x^2)
template <typename T>
struct AcosGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) =
        -dout * static_cast<T>(1) / (static_cast<T>(1) - x.square()).sqrt();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct Asin {
  HOSTDEVICE T operator()(const T& val) const { return asin(val); }
};

template <>
struct Asin<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(asin(static_cast<float>(val)));
  }
};

// Asin(x) = asin(x)
template <typename T>
struct AsinFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Asin<T>());
  }
};

// asin'(x) = 1/sqrt(1-x^2)
template <typename T>
struct AsinGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) =
        dout * static_cast<T>(1) / (static_cast<T>(1) - x.square()).sqrt();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct Atan {
  HOSTDEVICE T operator()(const T& val) const { return atan(val); }
};

template <>
struct Atan<platform::float16> {
  HOSTDEVICE platform::float16 operator()(const platform::float16& val) const {
    return platform::float16(atan(static_cast<float>(val)));
  }
};

// Atan(x) = atan(x)
template <typename T>
struct AtanFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.unaryExpr(Atan<T>());
  }
};

// atan'(x) =  1 / (1 + x^2)
template <typename T>
struct AtanGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * static_cast<T>(1) / (static_cast<T>(1) + x.square());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// round(x) = [x]
template <typename T>
struct RoundFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.round();
  }
};

// abs(x) = |x|
template <typename T>
struct AbsFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.abs();
  }
};

template <typename T>
struct AbsGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * x.sign();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// reciprocal(x) = 1 / x
template <typename T>
struct ReciprocalFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = static_cast<T>(1) / x;
  }
};

template <typename T>
struct ReciprocalGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * static_cast<T>(-1) * out * out;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// log(x) = natural logarithm of x
template <typename T>
struct LogFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.log();
  }
};

template <typename T>
struct LogGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * (static_cast<T>(1) / x);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// log1p(x) = natural logarithm of x+1
template <typename T>
struct Log1pFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = (static_cast<T>(1) + x).log();
  }
};

template <typename T>
struct Log1pGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * (static_cast<T>(1) / (x + static_cast<T>(1)));
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// square(x) = x^2
template <typename T>
struct SquareFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.square();
  }
};

template <typename T>
struct SquareGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * static_cast<T>(2) * x;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct BReluFunctor : public BaseActivationFunctor<T> {
  float t_min;
  float t_max;

  // NOTE: Explicit hides the `BaseActivationFunctor<T>::GetAttrs`
  // not polymorphism for speed.
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"t_min", &t_min}, {"t_max", &t_max}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) =
        x.cwiseMax(static_cast<T>(t_min)).cwiseMin(static_cast<T>(t_max));
  }
};

template <typename T>
struct BReluGradFunctor : public BaseActivationFunctor<T> {
  float t_min;
  float t_max;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"t_min", &t_min}, {"t_max", &t_max}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout *
                   ((x > static_cast<T>(t_min)) * (x < static_cast<T>(t_max)))
                       .template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// relu6(x) = min(max(0, x), 6)
template <typename T>
struct Relu6Functor : public BaseActivationFunctor<T> {
  float threshold;

  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) =
        x.cwiseMax(static_cast<T>(0)).cwiseMin(static_cast<T>(threshold));
  }
};

template <typename T>
struct Relu6GradFunctor : public BaseActivationFunctor<T> {
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) =
        dout *
        ((out > static_cast<T>(0)) * (out < static_cast<T>(threshold)))
            .template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

// HardSwish = min(max(0, x+3), 6) * x / 6
template <typename T>
struct HardSwishFunctor : public BaseActivationFunctor<T> {
  float threshold;
  float scale;
  float offset;

  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}, {"scale", &scale}, {"offset", &offset}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = (x + static_cast<T>(offset))
                        .cwiseMax(static_cast<T>(0))
                        .cwiseMin(static_cast<T>(threshold)) *
                    x / static_cast<T>(scale);
  }
};

template <typename T>
struct HardSwishGradFunctor : public BaseActivationFunctor<T> {
  float threshold;
  float scale;
  float offset;

  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}, {"scale", &scale}, {"offset", &offset}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto tmp = ((x + static_cast<T>(offset)) < static_cast<T>(threshold))
                   .template cast<T>();
    dx.device(d) =
        dout *
        (((x + static_cast<T>(offset)) > static_cast<T>(0)).template cast<T>() *
             (static_cast<T>(2) * x + static_cast<T>(offset)) /
             static_cast<T>(scale) * tmp +
         static_cast<T>(1) * (static_cast<T>(1) - tmp));
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// For numerical stability, using the following formula instead of softplus(x) =
// log(1 + exp(x))
// softplus(x) = log(1 + exp(beta * x)) / beta when beta * x <= threshold(beta =
// 1, threshold = 20 by default), otherwise x
template <typename T>
struct SoftplusFunctor : public BaseActivationFunctor<T> {
  float beta;
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"beta", &beta}, {"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) {
    auto x_beta = static_cast<T>(beta) * x;
    out.device(d) = (x_beta > static_cast<T>(threshold))
                        .select(x, (static_cast<T>(1) + x_beta.exp()).log() /
                                       static_cast<T>(beta));
  }
};

// For numerical stability, using the following formula instead of
// d(softplus(x))/dx = 1 / (1 + exp(-x))
// d(softplus(x))/dx = 1 / (1 + exp(-beta * x)) when beta * x <= threshold(beta
// = 1, threshold = 20 by default), otherwise x
template <typename T>
struct SoftplusGradFunctor : public BaseActivationFunctor<T> {
  float beta;
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"beta", &beta}, {"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) {
    auto x_beta = static_cast<T>(beta) * x;
    dx.device(d) =
        (x_beta > static_cast<T>(threshold))
            .select(dout, dout / (static_cast<T>(1) + (-x_beta).exp()));
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// softsign(x) = x / (1 + |x|)
template <typename T>
struct SoftsignFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) {
    out.device(d) = x / (static_cast<T>(1) + x.abs());
  }
};

// d(softsign(x))/dx = 1 / (1 + |x|)^2
// Taken from https://en.wikipedia.org/wiki/Activation_function
template <typename T>
struct SoftsignGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) {
    dx.device(d) =
        dout * (static_cast<T>(1) / (static_cast<T>(1) + x.abs()).square());
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct SoftReluFunctor : public BaseActivationFunctor<T> {
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto tmp = static_cast<T>(threshold);
    auto temp = x.cwiseMax(-tmp).cwiseMin(tmp);
    out.device(d) = (static_cast<T>(1) + temp.exp()).log();
  }
};

template <typename T>
struct SoftReluGradFunctor : public BaseActivationFunctor<T> {
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto tmp = static_cast<T>(threshold);
    auto temp = ((out > -tmp) * (out < tmp)).template cast<T>();
    dx.device(d) = dout * (static_cast<T>(1) - (-out).exp()) * temp;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

template <typename T>
struct LeakyReluFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    if (alpha < 1.f) {
      out.device(d) = x.cwiseMax(static_cast<T>(alpha) * x);
    } else {
      out.device(d) = x.cwiseMin(static_cast<T>(alpha) * x);
    }
  }
};

template <typename T>
struct LeakyReluGradFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto temp1 =
        static_cast<T>(alpha) * (x < static_cast<T>(0)).template cast<T>();
    auto temp2 = (x >= static_cast<T>(0)).template cast<T>();
    dx.device(d) = dout * (temp1 + temp2).template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct ELUFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.cwiseMax(static_cast<T>(0)) +
                    (static_cast<T>(alpha) * (x.exp() - static_cast<T>(1)))
                        .cwiseMin(static_cast<T>(0));
  }
};

template <typename T>
struct ELUGradFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto temp_a_pos = static_cast<T>(alpha > 0);
    auto temp_a_neg = static_cast<T>(alpha <= 0);
    auto temp_x_pos = (x > static_cast<T>(0)).template cast<T>();
    auto temp_x_neg = (x <= static_cast<T>(0)).template cast<T>();

    // dx = dout, if alpha > 0 and x > 0
    // dx = dout * alpha * x.exp(), if alpha > 0 and x <= 0
    // dx = dout * (1 + alpha * x.exp()), if alpha <= 0 and x > 0
    // dx = 0, if alpha <= 0 and x <=0
    dx.device(d) =
        dout * temp_a_pos * temp_x_pos +
        dout * static_cast<T>(alpha) * x.exp() * temp_a_pos * temp_x_neg +
        dout * (static_cast<T>(1) + static_cast<T>(alpha) * x.exp()) *
            temp_a_neg * temp_x_pos;
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// FIXME(qijun) https://github.com/PaddlePaddle/Paddle/issues/5198
template <typename T>
struct PowFunctor : public BaseActivationFunctor<T> {
  float factor;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"factor", &factor}};
  }
  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x.pow(static_cast<T>(factor));
  }
};

template <typename T>
struct PowGradFunctor : public BaseActivationFunctor<T> {
  float factor;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"factor", &factor}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout * static_cast<T>(factor) *
                   x.pow(static_cast<T>(factor) - static_cast<T>(1));
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct STanhFunctor : public BaseActivationFunctor<T> {
  float scale_a;
  float scale_b;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"scale_a", &scale_a}, {"scale_b", &scale_b}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) =
        static_cast<T>(scale_b) * (static_cast<T>(scale_a) * x).tanh();
  }
};

template <typename T>
struct STanhGradFunctor : public BaseActivationFunctor<T> {
  float scale_a;
  float scale_b;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"scale_a", &scale_a}, {"scale_b", &scale_b}};
  }

  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto a = static_cast<T>(scale_a);
    auto b = static_cast<T>(scale_b);
    auto temp = (a * x).tanh() * (a * x).tanh();
    dx.device(d) = dout * a * b * (static_cast<T>(1) - temp);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct ThresholdedReluFunctor : public BaseActivationFunctor<T> {
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto th = static_cast<T>(threshold);
    out.device(d) = (x > th).template cast<T>() * x;
  }
};

template <typename T>
struct ThresholdedReluGradFunctor : public BaseActivationFunctor<T> {
  float threshold;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"threshold", &threshold}};
  }

  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    auto th = static_cast<T>(threshold);
    dx.device(d) = dout * (x > th).template cast<T>();
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct HardSigmoidFunctor : public BaseActivationFunctor<T> {
  float slope;
  float offset;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"slope", &slope}, {"offset", &offset}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    auto temp = x * static_cast<T>(slope) + static_cast<T>(offset);
    out.device(d) =
        temp.cwiseMax(static_cast<T>(0)).cwiseMin(static_cast<T>(1));
  }
};

template <typename T>
struct HardSigmoidGradFunctor : public BaseActivationFunctor<T> {
  float slope;
  float offset;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"slope", &slope}, {"offset", &offset}};
  }
  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
    dx.device(d) = dout *
                   ((out > static_cast<T>(0)) * (out < static_cast<T>(1)))
                       .template cast<T>() *
                   static_cast<T>(slope);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

template <typename T>
struct SwishFunctor : public BaseActivationFunctor<T> {
  float beta;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"beta", &beta}};
  }

  template <typename Device, typename X, typename Out>
  void operator()(Device d, X x, Out out) const {
    out.device(d) = x / (static_cast<T>(1) + (static_cast<T>(-beta) * x).exp());
  }
};

template <typename T>
struct SwishGradFunctor : public BaseActivationFunctor<T> {
  float beta;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"beta", &beta}};
  }

  template <typename Device, typename X, typename Out, typename dOut,
            typename dX>
  void operator()(Device d, X x, Out fake_out, dOut dout, dX dx) const {
    auto temp1 = static_cast<T>(1) /
                 (static_cast<T>(1) + (static_cast<T>(-beta) * x).exp());
    auto out = x * temp1;
    auto temp2 = temp1 * (static_cast<T>(1) - (static_cast<T>(beta) * out));
    dx.device(d) = dout * ((static_cast<T>(beta) * out) + temp2);
  }

  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

/*
 * in arguments: x, out, ddx
 * out arguments: ddout, dout, dx
 */
template <ActBwdOpFwdDeps kDepValue>
inline void ExtractActivationDoubleGradTensor(
    const framework::ExecutionContext& ctx, const framework::Tensor** X,
    const framework::Tensor** Out, const framework::Tensor** ddX,
    framework::Tensor** dX, framework::Tensor** dOut,
    framework::Tensor** ddOut) {
  auto ddx_var = ctx.InputVar("DDX");
  auto ddo_var = ctx.OutputVar("DDOut");
  PADDLE_ENFORCE_NOT_NULL(
      ddx_var, platform::errors::NotFound(
                   "Cannot get input Variable Out, variable name = %s",
                   ctx.InputName("DDX")));
  if (CanBeUsedBySelectedRows.count(ctx.Type())) {
    *ddX = paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*ddx_var);
    if (ddo_var) {
      *ddOut = paddle::framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(
          ddo_var);
    }
  } else {
    *ddX = ctx.Input<framework::Tensor>("DDX");
    if (ddo_var) {
      *ddOut = ctx.Output<framework::Tensor>("DDOut");
    }
  }
  PADDLE_ENFORCE_NOT_NULL(
      *ddX,
      platform::errors::NotFound(
          "Cannot get the tensor from the Variable Output, variable name = %s",
          ctx.OutputName("DDX")));

  if (static_cast<int>(kDepValue) & static_cast<int>(kDepX)) {
    auto x_var = ctx.InputVar("X");
    PADDLE_ENFORCE_NOT_NULL(
        x_var, platform::errors::NotFound(
                   "Cannot get input Variable Out, variable name = %s",
                   ctx.InputName("X")));
    auto dx_var = ctx.OutputVar("DX");
    if (CanBeUsedBySelectedRows.count(ctx.Type())) {
      *X = paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*x_var);
      if (dx_var) {
        *dX = paddle::framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(
            dx_var);
      }
    } else {
      *X = ctx.Input<framework::Tensor>("X");
      if (dx_var) {
        *dX = ctx.Output<framework::Tensor>("DX");
      }
    }
  } else {
    VLOG(10) << "Inplace activation of Op: " << ctx.Type();
    *X = *ddX;
  }
  if (static_cast<int>(kDepValue) & static_cast<int>(kDepOut)) {
    auto out_var = ctx.InputVar("Out");
    PADDLE_ENFORCE_NOT_NULL(
        out_var,
        platform::errors::NotFound(
            "Cannot get the tensor from the Variable Out, variable name = %s",
            ctx.InputName("Out")));
    auto dout_var = ctx.OutputVar("DOut");
    if (CanBeUsedBySelectedRows.count(ctx.Type())) {
      *Out =
          paddle::framework::GetLoDTensorOrSelectedRowsValueFromVar(*out_var);
      if (dout_var) {
        *dOut =
            paddle::framework::GetMutableLoDTensorOrSelectedRowsValueFromVar(
                dout_var);
      }
    } else {
      *Out = ctx.Input<framework::Tensor>("Out");
      if (dout_var) {
        *dOut = ctx.Output<framework::Tensor>("DOut");
      }
    }
  } else {
    VLOG(10) << "Inplace activation of Op: " << ctx.Type();
    *Out = *ddX;
  }
}

template <typename DeviceContext, typename Functor>
class ActivationDoubleGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& ctx) const override {
    const framework::Tensor *X, *Out, *ddX;
    X = Out = ddX = nullptr;
    framework::Tensor *ddOut, *dOut, *dX;
    ddOut = dOut = dX = nullptr;

    ExtractActivationDoubleGradTensor<Functor::FwdDeps()>(ctx, &X, &Out, &ddX,
                                                          &dX, &dOut, &ddOut);

    if (ddOut) ddOut->mutable_data<T>(ctx.GetPlace());
    if (dOut) dOut->mutable_data<T>(ctx.GetPlace());
    if (dX) dX->mutable_data<T>(Out->dims(), ctx.GetPlace());

    auto& place = ctx.template device_context<DeviceContext>();

    Functor functor;
    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = ctx.Attr<float>(attr.first);
    }
    functor(place, X, Out, ddX, ddOut, dOut, dX);
  }
};

template <typename T>
struct AbsGradGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* X,
                  const framework::Tensor* Out, const framework::Tensor* ddX,
                  framework::Tensor* ddOut, framework::Tensor* dOut,
                  framework::Tensor* dX) const {
    auto* d = dev.eigen_device();
    auto ddx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(ddX, "Input", "DDX", "AbsGradGrad"));
    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "AbsGradGrad"));
    if (ddOut) {
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "AbsGradGrad"));
      ddout.device(*d) = ddx * x.sign();
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct ReluGradGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* X,
                  const framework::Tensor* Out, const framework::Tensor* ddX,
                  framework::Tensor* ddOut, framework::Tensor* dOut,
                  framework::Tensor* dX) const {
    auto* d = dev.eigen_device();
    auto ddx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(ddX, "Input", "DDX", "ReluGradGrad"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Output", "Out", "ReluGradGrad"));
    if (ddOut) {
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "ReluGradGrad"));
      ddout.device(*d) = ddx * (out > static_cast<T>(0)).template cast<T>();
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

template <typename T>
struct LeakyReluGradGradFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* X,
                  const framework::Tensor* Out, const framework::Tensor* ddX,
                  framework::Tensor* ddOut, framework::Tensor* dOut,
                  framework::Tensor* dX) const {
    if (ddOut) {
      auto* d = dev.eigen_device();
      auto ddx = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddX, "Input", "DDX", "LeakyReluGradGrad"));
      auto x = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(X, "Input", "X", "LeakyReluGradGrad"));
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DOut", "LeakyReluGradGrad"));
      ddout.device(*d) =
          ddx *
          ((x > static_cast<T>(0)).template cast<T>() +
           static_cast<T>(alpha) * (x <= static_cast<T>(0)).template cast<T>())
              .template cast<T>();
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct ELUGradGradFunctor : public BaseActivationFunctor<T> {
  float alpha;
  typename BaseActivationFunctor<T>::AttrPair GetAttrs() {
    return {{"alpha", &alpha}};
  }
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* X,
                  const framework::Tensor* ddX, framework::Tensor* ddOut,
                  const framework::Tensor* dOut, framework::Tensor* dX) const {
    auto* d = dev.eigen_device();
    auto ddx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(ddX, "Input", "DDX", "ELUGradGrad"));
    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "ELUGradGrad"));

    if (dX) {
      auto dx = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dX, "Output", "DX", "ELUGradGrad"));
      auto dout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dOut, "Output", "DOut", "ELUGradGrad"));
      dx.device(*d) = ddx * dout * static_cast<T>(alpha) * x.exp() *
                      (x < static_cast<T>(0)).template cast<T>();
    }

    if (ddOut) {
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "ELUGradGrad"));
      ddout.device(*d) = ddx *
                         ((x > static_cast<T>(0)).template cast<T>() +
                          static_cast<T>(alpha) * x.exp() *
                              (x <= static_cast<T>(0)).template cast<T>())
                             .template cast<T>();
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

template <typename T>
struct SqrtGradGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* Out,
                  const framework::Tensor* ddX, framework::Tensor* ddOut,
                  framework::Tensor* dOut, const framework::Tensor* dX) const {
    auto* d = dev.eigen_device();
    auto ddx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(ddX, "Input", "DDX", "SqrtGradGrad"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Output", "Out", "SqrtGradGrad"));
    // sqrt GradGrad: ddy = 0.5 * ddx / y, dy = -1 * dx * ddx
    // calculate dy first, so ddy can inplace ddx
    if (dOut) {
      auto dx = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dX, "Output", "DX", "SqrtGradGrad"));
      auto dout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dOut, "Output", "DOut", "SqrtGradGrad"));
      dout.device(*d) = dx * ddx * static_cast<T>(-1) / out;
    }
    if (ddOut) {
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "SqrtGradGrad"));
      ddout.device(*d) = ddx * static_cast<T>(0.5) / out;
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepOut; }
};

template <typename T>
struct SquareGradGradFunctor : public BaseActivationFunctor<T> {
  template <typename Device>
  void operator()(const Device& dev, const framework::Tensor* X,
                  const framework::Tensor* ddX, framework::Tensor* ddOut,
                  const framework::Tensor* dOut, framework::Tensor* dX) const {
    auto* d = dev.eigen_device();
    auto ddx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(ddX, "Input", "DDX", "SquareGradGrad"));
    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "SquareGradGrad"));
    // square GradGrad: ddy=2x*ddx, dx=2dy*ddx
    // calculate dx first, so ddy can inplace ddx
    if (dX) {
      auto dx = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dX, "Output", "DX", "SquareGradGrad"));
      auto dout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(dOut, "Output", "DOut", "SquareGradGrad"));
      dx.device(*d) = ddx * static_cast<T>(2) * dout;
    }
    if (ddOut) {
      auto ddout = framework::EigenVector<T>::Flatten(
          GET_DATA_SAFELY(ddOut, "Output", "DDOut", "SquareGradGrad"));
      ddout.device(*d) = ddx * static_cast<T>(2) * x;
    }
  }
  static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }
};

// TODO(dengkaipeng): double gradient calculation for Square/Sqrt need
// DOut(dy) as input(not output), tensor extraction is different from
// others. Impliment extraction kernel seperately here.
inline void ExtractDoubleGradTensorWithInputDOut(
    const framework::ExecutionContext& ctx, const framework::Tensor** X,
    const framework::Tensor** ddX, framework::Tensor** dX,
    const framework::Tensor** dOut, framework::Tensor** ddOut) {
  // extract ddX(output), ddOut(input)
  auto ddx_var = ctx.InputVar("DDX");
  auto ddo_var = ctx.OutputVar("DDOut");
  PADDLE_ENFORCE_NOT_NULL(
      ddx_var, platform::errors::NotFound(
                   "Cannot get input Variable Out, variable name = %s",
                   ctx.InputName("DDX")));
  *ddX = ctx.Input<framework::Tensor>("DDX");
  if (ddo_var) {
    *ddOut = ctx.Output<framework::Tensor>("DDOut");
  }
  PADDLE_ENFORCE_NOT_NULL(
      ddX,
      platform::errors::NotFound(
          "Cannot get the tensor from the Variable DDX, variable name = %s",
          ctx.OutputName("DDX")));

  // extract x(input), dx(output)
  auto x_var = ctx.InputVar("X");
  PADDLE_ENFORCE_NOT_NULL(
      x_var, platform::errors::NotFound(
                 "Cannot get input Variable Out, variable name = %s",
                 ctx.InputName("X")));
  auto dx_var = ctx.OutputVar("DX");
  *X = ctx.Input<framework::Tensor>("X");
  if (dx_var) {
    *dX = ctx.Output<framework::Tensor>("DX");
  }

  // extract dOut(input)
  auto dout_var = ctx.InputVar("DOut");
  if (dout_var) {
    *dOut = ctx.Input<framework::Tensor>("DOut");
  }
}

template <typename DeviceContext, typename Functor>
class SquareDoubleGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& ctx) const override {
    const framework::Tensor *X, *ddX, *dOut;
    X = ddX = dOut = nullptr;
    framework::Tensor *dX, *ddOut;
    dX = ddOut = nullptr;

    ExtractDoubleGradTensorWithInputDOut(ctx, &X, &ddX, &dX, &dOut, &ddOut);

    if (dX) dX->mutable_data<T>(X->dims(), ctx.GetPlace());
    if (ddOut) ddOut->mutable_data<T>(ctx.GetPlace());

    auto& place = ctx.template device_context<DeviceContext>();

    Functor functor;
    functor(place, X, ddX, ddOut, dOut, dX);
  }
};

template <typename DeviceContext, typename Functor>
class ELUDoubleGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& ctx) const override {
    const framework::Tensor *X, *ddX, *dOut;
    X = ddX = dOut = nullptr;
    framework::Tensor *dX, *ddOut;
    dX = ddOut = nullptr;

    ExtractDoubleGradTensorWithInputDOut(ctx, &X, &ddX, &dX, &dOut, &ddOut);

    if (dX) dX->mutable_data<T>(X->dims(), ctx.GetPlace());
    if (ddOut) ddOut->mutable_data<T>(ctx.GetPlace());

    auto& place = ctx.template device_context<DeviceContext>();

    Functor functor;
    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = ctx.Attr<float>(attr.first);
    }
    functor(place, X, ddX, ddOut, dOut, dX);
  }
};

template <typename DeviceContext, typename Functor>
class SqrtDoubleGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& ctx) const override {
    const framework::Tensor *Out, *dX, *ddX;
    Out = dX = ddX = nullptr;
    framework::Tensor *ddOut, *dOut;
    ddOut = dOut = nullptr;

    // extract ddx(input), ddout(output)
    auto ddx_var = ctx.InputVar("DDX");
    auto ddo_var = ctx.OutputVar("DDOut");
    PADDLE_ENFORCE_NOT_NULL(
        ddx_var, platform::errors::NotFound(
                     "Cannot get input Variable DDX, variable name = %s",
                     ctx.InputName("DDX")));
    ddX = ctx.Input<framework::Tensor>("DDX");
    if (ddo_var) {
      ddOut = ctx.Output<framework::Tensor>("DDOut");
    }
    PADDLE_ENFORCE_NOT_NULL(
        ddX, platform::errors::NotFound(
                 "Cannot get input Variable DDX, variable name = %s",
                 ctx.InputName("DDX")));

    // extract out(input), dout(output)
    auto out_var = ctx.InputVar("Out");
    PADDLE_ENFORCE_NOT_NULL(
        out_var, platform::errors::NotFound(
                     "Cannot get input Variable Out, variable name = %s",
                     ctx.InputName("Out")));
    auto dout_var = ctx.OutputVar("DOut");
    Out = ctx.Input<framework::Tensor>("Out");
    if (dout_var) {
      dOut = ctx.Output<framework::Tensor>("DOut");
    }

    // extract dx(input)
    auto dx_var = ctx.InputVar("DX");
    PADDLE_ENFORCE_NOT_NULL(
        dx_var, platform::errors::NotFound(
                    "Cannot get input Variable DX, variable name = %s",
                    ctx.InputName("DX")));
    if (dx_var) {
      dX = ctx.Input<framework::Tensor>("DX");
    }

    if (dOut) dOut->mutable_data<T>(Out->dims(), ctx.GetPlace());
    if (ddOut) ddOut->mutable_data<T>(Out->dims(), ctx.GetPlace());

    auto& place = ctx.template device_context<DeviceContext>();

    Functor functor;
    functor(place, Out, ddX, ddOut, dOut, dX);
  }
};

template <typename DeviceContext, typename Functor>
class PowKernel : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;

  void Compute(const framework::ExecutionContext& context) const override {
    const framework::Tensor* X = nullptr;
    framework::Tensor* Out = nullptr;
    ExtractActivationTensor(context, &X, &Out);
    Out->mutable_data<T>(context.GetPlace());

    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "Pow"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Output", "Out", "Pow"));
    auto* place =
        context.template device_context<DeviceContext>().eigen_device();
    Functor functor;
    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = context.Attr<float>(attr.first);
    }
    // get FactorTensor
    auto* factor_tensor = context.HasInput("FactorTensor")
                              ? context.Input<framework::Tensor>("FactorTensor")
                              : nullptr;
    if (factor_tensor) {
      auto* factor_data = factor_tensor->data<float>();
      framework::Tensor cpu_factor_tensor;
      if (platform::is_gpu_place(factor_tensor->place())) {
        TensorCopySync(*factor_tensor, platform::CPUPlace(),
                       &cpu_factor_tensor);
        factor_data = cpu_factor_tensor.data<float>();
      }
      auto factor =
          std::vector<float>(factor_data, factor_data + factor_tensor->numel());
      PADDLE_ENFORCE_EQ(
          factor.size(), 1,
          platform::errors::InvalidArgument(
              "The shape of factor(tensor) must be [1] rather than %d",
              factor.size()));
      for (auto& attr : attrs) {
        *attr.second = factor[0];
      }
    }
    functor(*place, x, out);
  }
};

template <typename DeviceContext, typename Functor>
class PowGradKernel
    : public framework::OpKernel<typename Functor::ELEMENT_TYPE> {
 public:
  using T = typename Functor::ELEMENT_TYPE;
  void Compute(const framework::ExecutionContext& context) const override {
    const framework::Tensor *X, *Out, *dOut;
    framework::Tensor* dX = nullptr;
    X = Out = dOut = nullptr;
    ExtractActivationGradTensor<Functor::FwdDeps()>(context, &X, &Out, &dOut,
                                                    &dX);
    dX->mutable_data<T>(context.GetPlace());
    auto dout = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(dOut, "Input", "Out@GRAD", "PowGrad"));
    auto out = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(Out, "Input", "Out", "PowGrad"));
    auto dx = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(dX, "Output", "X@GRAD", "PowGrad"));
    auto x = framework::EigenVector<T>::Flatten(
        GET_DATA_SAFELY(X, "Input", "X", "PowGrad"));
    auto* place =
        context.template device_context<DeviceContext>().eigen_device();
    Functor functor;
    auto attrs = functor.GetAttrs();
    for (auto& attr : attrs) {
      *attr.second = context.Attr<float>(attr.first);
    }
    // get FactorTensor
    auto* factor_tensor =
        context.HasInput("FactorTensor")
            ? context.Input<framework::LoDTensor>("FactorTensor")
            : nullptr;
    if (factor_tensor) {
      auto* factor_data = factor_tensor->data<float>();
      framework::Tensor cpu_factor_tensor;
      if (platform::is_gpu_place(factor_tensor->place())) {
        TensorCopySync(*factor_tensor, platform::CPUPlace(),
                       &cpu_factor_tensor);
        factor_data = cpu_factor_tensor.data<float>();
      }
      auto factor =
          std::vector<float>(factor_data, factor_data + factor_tensor->numel());
      PADDLE_ENFORCE_EQ(
          factor.size(), 1,
          platform::errors::InvalidArgument(
              "The shape of factor(tensor) must be [1] rather than %d",
              factor.size()));
      for (auto& attr : attrs) {
        *attr.second = factor[0];
      }
    }
    functor(*place, x, out, dout, dx);
  }
};
}  // namespace operators
}  // namespace paddle

#define FOR_EACH_ACTIVATION_OP(__macro)                                       \
  __macro(sigmoid, Sigmoid, SigmoidFunctor, SigmoidGradFunctor);              \
  __macro(logsigmoid, LogSigmoid, LogSigmoidFunctor, LogSigmoidGradFunctor);  \
  __macro(tanh, Tanh, TanhFunctor, TanhGradFunctor);                          \
  __macro(atan, Atan, AtanFunctor, AtanGradFunctor);                          \
  __macro(softshrink, SoftShrink, SoftShrinkFunctor, SoftShrinkGradFunctor);  \
  __macro(rsqrt, Rsqrt, RsqrtFunctor, RsqrtGradFunctor);                      \
  __macro(ceil, Ceil, CeilFunctor, ZeroGradFunctor);                          \
  __macro(floor, Floor, FloorFunctor, ZeroGradFunctor);                       \
  __macro(cos, Cos, CosFunctor, CosGradFunctor);                              \
  __macro(acos, Acos, AcosFunctor, AcosGradFunctor);                          \
  __macro(sin, Sin, SinFunctor, SinGradFunctor);                              \
  __macro(asin, Asin, AsinFunctor, AsinGradFunctor);                          \
  __macro(sinh, Sinh, SinhFunctor, SinhGradFunctor);                          \
  __macro(cosh, Cosh, CoshFunctor, CoshGradFunctor);                          \
  __macro(round, Round, RoundFunctor, ZeroGradFunctor);                       \
  __macro(reciprocal, Reciprocal, ReciprocalFunctor, ReciprocalGradFunctor);  \
  __macro(log, Log, LogFunctor, LogGradFunctor);                              \
  __macro(log1p, Log1p, Log1pFunctor, Log1pGradFunctor);                      \
  __macro(brelu, BRelu, BReluFunctor, BReluGradFunctor);                      \
  __macro(soft_relu, SoftRelu, SoftReluFunctor, SoftReluGradFunctor);         \
  __macro(stanh, STanh, STanhFunctor, STanhGradFunctor);                      \
  __macro(softplus, Softplus, SoftplusFunctor, SoftplusGradFunctor);          \
  __macro(softsign, Softsign, SoftsignFunctor, SoftsignGradFunctor);          \
  __macro(relu6, Relu6, Relu6Functor, Relu6GradFunctor);                      \
  __macro(tanh_shrink, TanhShrink, TanhShrinkFunctor, TanhShrinkGradFunctor); \
  __macro(hard_shrink, HardShrink, HardShrinkFunctor, HardShrinkGradFunctor); \
  __macro(hard_sigmoid, HardSigmoid, HardSigmoidFunctor,                      \
          HardSigmoidGradFunctor);                                            \
  __macro(swish, Swish, SwishFunctor, SwishGradFunctor);                      \
  __macro(thresholded_relu, ThresholdedRelu, ThresholdedReluFunctor,          \
          ThresholdedReluGradFunctor);                                        \
  __macro(hard_swish, HardSwish, HardSwishFunctor, HardSwishGradFunctor);