text: /* Copyright 2015 The TensorFlow 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.
  ==============================================================================*/
  
  #if GOOGLE_CUDA
  
  #define EIGEN_USE_GPU
  
  #include "tensorflow/core/kernels/training_ops.h"
  #include "tensorflow/core/framework/register_types.h"
  
  namespace tensorflow {
  
  typedef Eigen::GpuDevice GPUDevice;
  
  namespace functor {
  template <typename T>
  struct ApplyGradientDescent<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      var.device(d) -= lr.reshape(single).broadcast(bcast) * grad;
    }
  };
  
  template <typename T>
  struct ApplyAdagrad<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat accum,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstFlat grad) {
      accum.device(d) += grad.square();
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      var.device(d) -= lr.reshape(single).broadcast(bcast) * grad * accum.rsqrt();
    }
  };
  
  template <typename T>
  struct ApplyAdadelta<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat accum,
                    typename TTypes<T>::Flat accum_update,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar rho,
                    typename TTypes<T>::ConstScalar epsilon,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
  
      accum.device(d) = accum * rho.reshape(single).broadcast(bcast) +
                        grad.square() * (grad.constant(T(1)) -
                                         rho.reshape(single).broadcast(bcast));
      const auto update =
          (accum_update + epsilon.reshape(single).broadcast(bcast)).sqrt() *
          (accum + epsilon.reshape(single).broadcast(bcast)).rsqrt() * grad;
      var.device(d) -= update * lr.reshape(single).broadcast(bcast);
      accum_update.device(d) =
          accum_update * rho.reshape(single).broadcast(bcast) +
          update.square() *
              (grad.constant(T(1)) - rho.reshape(single).broadcast(bcast));
    }
  };
  
  template <typename T>
  struct ApplyMomentum<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat accum,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstFlat grad,
                    typename TTypes<T>::ConstScalar momentum, bool use_nesterov) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      accum.device(d) = accum * momentum.reshape(single).broadcast(bcast) + grad;
      if (use_nesterov) {
        var.device(d) -= grad * lr.reshape(single).broadcast(bcast) +
                         accum * momentum.reshape(single).broadcast(bcast) *
                             lr.reshape(single).broadcast(bcast);
      } else {
        var.device(d) -= lr.reshape(single).broadcast(bcast) * accum;
      }
    }
  };
  
  template <typename T>
  struct ApplyAdam<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat m, typename TTypes<T>::Flat v,
                    typename TTypes<T>::ConstScalar beta1_power,
                    typename TTypes<T>::ConstScalar beta2_power,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar beta1,
                    typename TTypes<T>::ConstScalar beta2,
                    typename TTypes<T>::ConstScalar epsilon,
                    typename TTypes<T>::ConstFlat grad, bool use_nesterov) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      const auto one = static_cast<T>(1.0);
      m.device(d) =
          m +
          (beta1.constant(one) - beta1).reshape(single).broadcast(bcast) *
              (grad - m);
      v.device(d) =
          v +
          (beta2.constant(one) - beta2).reshape(single).broadcast(bcast) *
              (grad.square() - v);
  
      if (use_nesterov) {
        var.device(d) -=
            (lr * (beta2_power.constant(one) - beta2_power).sqrt() /
             (beta1_power.constant(one) - beta1_power))
                .reshape(single)
                .broadcast(bcast) *
            (m * beta1.reshape(single).broadcast(bcast) +
             (beta1.constant(one) - beta1).reshape(single).broadcast(bcast) *
                 grad) /
            (epsilon.reshape(single).broadcast(bcast) + v.sqrt());
      } else {
        var.device(d) -= (lr * (beta2_power.constant(one) - beta2_power).sqrt() /
                          (beta1_power.constant(one) - beta1_power))
                             .reshape(single)
                             .broadcast(bcast) *
                         m /
                         (epsilon.reshape(single).broadcast(bcast) + v.sqrt());
      }
    }
  };
  
  template <typename T>
  struct ApplyRMSProp<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat ms, typename TTypes<T>::Flat mom,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar rho,
                    typename TTypes<T>::ConstScalar momentum,
                    typename TTypes<T>::ConstScalar epsilon,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      const auto one = static_cast<T>(1.0);
      ms.device(d) = ms +
                     (rho.constant(one) - rho).reshape(single).broadcast(bcast) *
                         (grad.square() - ms);
      mom.device(d) =
          mom * momentum.reshape(single).broadcast(bcast) +
          lr.reshape(single).broadcast(bcast) * grad /
              ((epsilon.reshape(single).broadcast(bcast) + ms).sqrt());
      var.device(d) -= mom;
    }
  };
  
  template <typename T>
  struct ApplyCenteredRMSProp<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat mg, typename TTypes<T>::Flat ms,
                    typename TTypes<T>::Flat mom,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar rho,
                    typename TTypes<T>::ConstScalar momentum,
                    typename TTypes<T>::ConstScalar epsilon,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
      const auto one = static_cast<T>(1.0);
      const auto one_minus_rho =
          (rho.constant(one) - rho).reshape(single).broadcast(bcast);
      ms.device(d) = ms + one_minus_rho * (grad.square() - ms);
      mg.device(d) = mg + one_minus_rho * (grad - mg);
      auto denom = (ms - mg.square()) + epsilon.reshape(single).broadcast(bcast);
      mom.device(d) = mom * momentum.reshape(single).broadcast(bcast) +
                      lr.reshape(single).broadcast(bcast) * grad / denom.sqrt();
      var.device(d) -= mom;
    }
  };
  
  template <typename T>
  struct ApplyAddSign<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat m,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar alpha,
                    typename TTypes<T>::ConstScalar sign_decay,
                    typename TTypes<T>::ConstScalar beta,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
  
      // The following is the GPU equivalent of the CPU version:
      // m.device(d) = m * beta() + grad * (static_cast<T>(1) - beta());
      const auto one = static_cast<T>(1.0);
      auto beta_bcast = beta.reshape(single).broadcast(bcast);
      auto one_minus_beta =
          (beta.constant(one) - beta).reshape(single).broadcast(bcast);
      m.device(d) =  m * beta_bcast + grad * one_minus_beta;
  
      // The following is the GPU equivalent of the CPU version:
      // var.device(d) -= lr() * (alpha() + sign_decay() * sign_gm) * grad;
      auto sign_gm = grad.sign() * m.sign();
      auto lr_bcast = lr.reshape(single).broadcast(bcast);
      auto alpha_bcast = alpha.reshape(single).broadcast(bcast);
      auto sign_decay_bcast = sign_decay.reshape(single).broadcast(bcast);
      var.device(d) -=
          lr_bcast * (alpha_bcast + sign_decay_bcast * sign_gm) * grad;
    }
  };
  
  template <typename T>
  struct ApplyPowerSign<GPUDevice, T> {
    void operator()(const GPUDevice& d, typename TTypes<T>::Flat var,
                    typename TTypes<T>::Flat m,
                    typename TTypes<T>::ConstScalar lr,
                    typename TTypes<T>::ConstScalar logbase,
                    typename TTypes<T>::ConstScalar sign_decay,
                    typename TTypes<T>::ConstScalar beta,
                    typename TTypes<T>::ConstFlat grad) {
      Eigen::array<typename TTypes<T>::Tensor::Index, 1> bcast;
      bcast[0] = grad.dimension(0);
      Eigen::Sizes<1> single;
  
      // The following is the GPU equivalent of the CPU version:
      // m.device(d) = m * beta() + grad * (static_cast<T>(1) - beta());
      const auto one = static_cast<T>(1.0);
      auto beta_bcast = beta.reshape(single).broadcast(bcast);
      auto one_minus_beta =
          (beta.constant(one) - beta).reshape(single).broadcast(bcast);
      m.device(d) =  m * beta_bcast + grad * one_minus_beta;
  
      // The following is the GPU equivalent of the CPU version:
      // auto grad_scale = (logbase() * sign_decay() * sign_gm).exp();
      // var.device(d) -= lr() * grad_scale * grad;
      auto sign_gm = grad.sign() * m.sign();
      auto lr_bcast = lr.reshape(single).broadcast(bcast);
      auto logbase_bcast = logbase.reshape(single).broadcast(bcast);
      auto sign_decay_bcast = sign_decay.reshape(single).broadcast(bcast);
      auto grad_scale =  (logbase_bcast * sign_decay_bcast * sign_gm).exp();
      var.device(d) -= lr_bcast * grad_scale * grad;
    }
  };
  
  }  // namespace functor
  
  template struct functor::ApplyGradientDescent<GPUDevice, Eigen::half>;
  template struct functor::ApplyGradientDescent<GPUDevice, float>;
  template struct functor::ApplyGradientDescent<GPUDevice, double>;
  
  template struct functor::ApplyAdagrad<GPUDevice, Eigen::half>;
  template struct functor::ApplyAdagrad<GPUDevice, float>;
  template struct functor::ApplyAdagrad<GPUDevice, double>;
  
  template struct functor::ApplyAdadelta<GPUDevice, Eigen::half>;
  template struct functor::ApplyAdadelta<GPUDevice, float>;
  template struct functor::ApplyAdadelta<GPUDevice, double>;
  
  template struct functor::ApplyMomentum<GPUDevice, Eigen::half>;
  template struct functor::ApplyMomentum<GPUDevice, float>;
  template struct functor::ApplyMomentum<GPUDevice, double>;
  
  template struct functor::ApplyAdam<GPUDevice, Eigen::half>;
  template struct functor::ApplyAdam<GPUDevice, float>;
  template struct functor::ApplyAdam<GPUDevice, double>;
  
  template struct functor::ApplyRMSProp<GPUDevice, Eigen::half>;
  template struct functor::ApplyRMSProp<GPUDevice, float>;
  template struct functor::ApplyRMSProp<GPUDevice, double>;
  
  template struct functor::ApplyCenteredRMSProp<GPUDevice, Eigen::half>;
  template struct functor::ApplyCenteredRMSProp<GPUDevice, float>;
  template struct functor::ApplyCenteredRMSProp<GPUDevice, double>;
  
  template struct functor::ApplyAddSign<GPUDevice, Eigen::half>;
  template struct functor::ApplyAddSign<GPUDevice, float>;
  template struct functor::ApplyAddSign<GPUDevice, double>;
  
  template struct functor::ApplyPowerSign<GPUDevice, Eigen::half>;
  template struct functor::ApplyPowerSign<GPUDevice, float>;
  template struct functor::ApplyPowerSign<GPUDevice, double>;
  
  }  // end namespace tensorflow
  
  #endif  // GOOGLE_CUDA
  