/*
Copyright (c) MONAI Consortium
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
    http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

#include <torch/extension.h>
#include <vector>

// s'(z) = (1 - s(z)) * s(z)
torch::Tensor d_sigmoid(torch::Tensor z) {
  auto s = torch::sigmoid(z);
  return (1 - s) * s;
}

// tanh'(z) = 1 - tanh^2(z)
torch::Tensor d_tanh(torch::Tensor z) {
  return 1 - z.tanh().pow(2);
}

// elu'(z) = relu'(z) + { alpha * exp(z) if (alpha * (exp(z) - 1)) < 0, else 0}
torch::Tensor d_elu(torch::Tensor z, torch::Scalar alpha = 1.0) {
  auto e = z.exp();
  auto mask = (alpha * (e - 1)) < 0;
  return (z > 0).type_as(z) + mask.type_as(z) * (alpha * e);
}

std::vector<torch::Tensor> lltm_cpu_forward(
    torch::Tensor input,
    torch::Tensor weights,
    torch::Tensor bias,
    torch::Tensor old_h,
    torch::Tensor old_cell) {
  auto X = torch::cat({old_h, input}, /*dim=*/1);

  auto gate_weights = torch::addmm(bias, X, weights.transpose(0, 1));
  auto gates = gate_weights.chunk(3, /*dim=*/1);

  auto input_gate = torch::sigmoid(gates[0]);
  auto output_gate = torch::sigmoid(gates[1]);
  auto candidate_cell = torch::elu(gates[2], /*alpha=*/1.0);

  auto new_cell = old_cell + candidate_cell * input_gate;
  auto new_h = torch::tanh(new_cell) * output_gate;

  return {new_h, new_cell, input_gate, output_gate, candidate_cell, X, gate_weights};
}

std::vector<torch::Tensor> lltm_cpu_backward(
    torch::Tensor grad_h,
    torch::Tensor grad_cell,
    torch::Tensor new_cell,
    torch::Tensor input_gate,
    torch::Tensor output_gate,
    torch::Tensor candidate_cell,
    torch::Tensor X,
    torch::Tensor gate_weights,
    torch::Tensor weights) {
  auto d_output_gate = torch::tanh(new_cell) * grad_h;
  auto d_tanh_new_cell = output_gate * grad_h;
  auto d_new_cell = d_tanh(new_cell) * d_tanh_new_cell + grad_cell;

  auto d_old_cell = d_new_cell;
  auto d_candidate_cell = input_gate * d_new_cell;
  auto d_input_gate = candidate_cell * d_new_cell;

  auto gates = gate_weights.chunk(3, /*dim=*/1);
  d_input_gate *= d_sigmoid(gates[0]);
  d_output_gate *= d_sigmoid(gates[1]);
  d_candidate_cell *= d_elu(gates[2]);

  auto d_gates = torch::cat({d_input_gate, d_output_gate, d_candidate_cell}, /*dim=*/1);

  auto d_weights = d_gates.t().mm(X);
  auto d_bias = d_gates.sum(/*dim=*/0, /*keepdim=*/true);

  auto d_X = d_gates.mm(weights);
  const auto state_size = grad_h.size(1);
  auto d_old_h = d_X.slice(/*dim=*/1, 0, state_size);
  auto d_input = d_X.slice(/*dim=*/1, state_size);

  return {d_old_h, d_input, d_weights, d_bias, d_old_cell};
}