// Copyright (c) 2018 MathInf GmbH, Thomas Viehmann
// Licensed under the BSD-3-Clause license
// This is the CPU implementation of the Connectionist Temporal Loss.
// We mostly follow Graves.
// 1. Graves et al: http://www.cs.toronto.edu/~graves/icml_2006.pdf
// We use the equations from above link, but note that [1] has 1-based indexing and we (of course) use 0-based.
// Graves et al call the probabilities y, we use log_probs (also calling them inputs)

#include <ATen/ATen.h>
#include <ATen/Dispatch.h>
#include <ATen/Parallel.h>
#include <ATen/TensorUtils.h>

#include <numeric>
#include <type_traits>

namespace at {
namespace native {

namespace {

// this ad-hoc converts from targets (l in [1]) to augmented targets (l' in [1]) note that no bound-checking is done
template<typename target_t>
static inline int64_t get_target_prime(target_t* target, int64_t offset, int64_t stride, int64_t idx, int64_t BLANK) {
  if (idx % 2 == 0) {
    return BLANK;
  } else {
    return target[offset + stride * (idx / 2)];
  }
}

// This kernel is a relatively straightforward implementation of the alpha calculation in the forward backward algorithm (section 4.1).
// A (minor) twist is that we are using log-calculations to enhance numerical stability (log_probs and log_alpha).
// The function returns the loss and the alphas, the alphas are kept for the backward step. The wrapper (ctc_loss below) hides
// the alphas from the user by only returning the loss.
template<typename scalar_t, ScalarType target_scalar_type>
std::tuple<Tensor, Tensor> ctc_loss_cpu_template(const Tensor& log_probs, const Tensor& targets, IntArrayRef input_lengths, IntArrayRef target_lengths, int64_t BLANK) {
  // log_probs: input_len x batch_size x num_labels
  // targets [int64]: batch_size x target_length OR sum(target_lengths)
  constexpr scalar_t neginf = -std::numeric_limits<scalar_t>::infinity();
  using target_t = typename std::conditional<target_scalar_type == kInt, int, int64_t>::type;

  CheckedFrom c = "ctc_loss_cpu";
  auto log_probs_arg = TensorArg(log_probs, "log_probs", 1);
  auto targets_arg = TensorArg(targets, "targets", 2);
  checkScalarType(c, targets_arg, target_scalar_type);
  checkDim(c, log_probs_arg, 3);
  checkDimRange(c, targets_arg, 1, 3);

  int64_t batch_size = log_probs.size(1);
  int64_t num_labels = log_probs.size(2);
  TORCH_CHECK((0 <= BLANK) && (BLANK < num_labels), "blank must be in label range");
  TORCH_CHECK((int64_t) input_lengths.size() == batch_size, "input_lengths must be of size batch_size");
  TORCH_CHECK((int64_t) target_lengths.size() == batch_size, "target_lengths must be of size batch_size");

  size_t tg_target_stride;
  int64_t max_target_length = 0;
  std::vector<int64_t> tg_batch_offsets(batch_size);
  if (targets.dim() == 1) { // concatenated targets
    int64_t pos = 0;
    for (int64_t i = 0; i < batch_size; i++) {
      tg_batch_offsets[i] = pos;
      pos += target_lengths[i];
      if (max_target_length < target_lengths[i])
         max_target_length = target_lengths[i];
    }
    tg_target_stride = targets.stride(0);
    checkSize(c, targets_arg, 0, pos);
  }
  else { // batch x max_target_length
    // dim is 2
    int64_t tg_batch_stride = targets.stride(0);
    for (int64_t i = 0; i < batch_size; i++) {
      tg_batch_offsets[i] = i * tg_batch_stride;
      if (max_target_length < target_lengths[i])
        max_target_length = target_lengths[i];
    }
    tg_target_stride = targets.stride(1);
    checkSize(c, targets_arg, 0, batch_size);
    TORCH_CHECK(targets.size(1) >= max_target_length,
             "Expected tensor to have size at least ", max_target_length, " at dimension 1, but got size ", targets.size(1), " for ", targets_arg,
             " (while checking arguments for ", c, ")");
  }
  int64_t max_input_length = log_probs.size(0);
  for (int64_t b = 0; b < batch_size; b++) {
    TORCH_CHECK(input_lengths[b] <= max_input_length,
             "Expected tensor to have size at least ", max_input_length, " at dimension 1, but got size ", input_lengths[b], " for ", log_probs_arg,
             " (while checking arguments for ", c, ")");
  }

  Tensor log_alpha = at::empty({batch_size, log_probs.size(0), 2*max_target_length+1}, log_probs.options());
  Tensor neg_log_likelihood = at::empty({batch_size}, log_probs.options());

  auto lpp  = log_probs.permute({1,0,2});
  auto log_probs_a_global = lpp.accessor<scalar_t, 3>();
  auto log_alpha_a_global = log_alpha.accessor<scalar_t, 3>();
  auto targets_data = targets.data<target_t>();
  auto neg_log_likelihood_a = neg_log_likelihood.accessor<scalar_t, 1>();

  // alpha calculation for the first row, the three equations for alpha_1 above eq (6)
  // first the default
  log_alpha.narrow(1, 0, 1).fill_(neginf);
  at::parallel_for(0, batch_size, 0, [&](int64_t start, int64_t end) {
    for (int64_t b = start; b < end; b++) {
      int64_t input_length = input_lengths[b];
      int64_t target_length = target_lengths[b];
      auto log_probs_a = log_probs_a_global[b];
      auto log_alpha_a = log_alpha_a_global[b];
      int64_t tg_batch_offset = tg_batch_offsets[b];

      // the first two items of alpha_t above eq (6)
      log_alpha_a[0][0] = log_probs_a[0][BLANK];
      if (target_length > 0)
        log_alpha_a[0][1] = log_probs_a[0][get_target_prime(targets_data, tg_batch_offset, tg_target_stride, 1, BLANK)];

      // now the loop over the inputs
      for (int64_t t=1; t<input_length; t++) {
        for (int64_t s=0; s<2*target_length+1; s++) {
          auto current_target_prime = get_target_prime(targets_data, tg_batch_offset, tg_target_stride, s, BLANK);
          // this loop over s could be parallel/vectorized, too, but the required items are one index apart
          // alternatively, one might consider moving s to the outer loop to cache current_target_prime more (but then it needs to be descending)
          // for the cuda implementation, that gave a speed boost.
          // This is eq (6) and (7), la1,2,3 are the three summands. We keep track of the maximum for the logsumexp calculation.

          scalar_t la1 = log_alpha_a[t-1][s];
          scalar_t lamax = la1;
          scalar_t la2, la3;
          if (s > 0) {
            la2 = log_alpha_a[t-1][s-1];
            if (la2 > lamax)
              lamax = la2;
          } else {
            la2 = neginf;
          }
          if ((s > 1) && (get_target_prime(targets_data, tg_batch_offset, tg_target_stride, s-2, BLANK) !=
                          current_target_prime)) {
            la3 = log_alpha_a[t-1][s-2];
            if (la3 > lamax)
              lamax = la3;
          } else {
            la3 = neginf;
          }
          if (lamax == neginf) // cannot do neginf-neginf
            lamax = 0;
          // this is the assignment of eq (6)
          log_alpha_a[t][s] = std::log(std::exp(la1-lamax)+std::exp(la2-lamax)+std::exp(la3-lamax))+lamax + log_probs_a[t][current_target_prime];
        }
      }
      // the likelihood is the the sum of the last two alphas, eq (8), the loss is the negative log likelihood
      scalar_t l1 = log_alpha_a[input_length-1][target_length*2];
      scalar_t l2 = log_alpha_a[input_length-1][target_length*2-1];
      scalar_t m = std::max(l1, l2);
      m = ((m == neginf) ? 0 : m);
      scalar_t log_likelihood = std::log(std::exp(l1-m)+std::exp(l2-m))+m;
      neg_log_likelihood_a[b] = -log_likelihood;
    }
  });

  return std::make_tuple(neg_log_likelihood, log_alpha);
}

// This is the backward. It consists of two phases:
// a) computing the beta analogous to the alphas in the forward (backward half of the forward-backward algorithm) (eq (10) and (11))
// b) collecting the per-activation characters for all s and wrapping the gradient (eq (16), the collection is the sum)
template<typename scalar_t, ScalarType target_scalar_type>
Tensor ctc_loss_backward_cpu_template(const Tensor& grad_out, const Tensor& log_probs, const Tensor& targets, IntArrayRef input_lengths, IntArrayRef target_lengths,
                                      const Tensor& neg_log_likelihood, const Tensor& log_alpha, int64_t BLANK, bool zero_infinity) {
  constexpr scalar_t neginf = -std::numeric_limits<scalar_t>::infinity();
  using target_t = typename std::conditional<target_scalar_type == kInt, int, int64_t>::type;
  int64_t max_input_length = log_probs.size(0);
  int64_t batch_size = log_probs.size(1);
  int64_t num_labels = log_probs.size(2);
  Tensor grad = at::full_like(log_probs, neginf); // at this point, this is log of empty sum

  // The admin bits. We don't do much checking and assume that the forward did.
  int64_t tg_target_stride;
  int64_t max_target_length;
  std::vector<int64_t> tg_batch_offsets(batch_size);

  if (targets.dim() == 1) { // concatenated targets
    int64_t pos = 0;
    max_target_length = 0;
    for (int64_t i = 0; i < batch_size; i++) {
      tg_batch_offsets[i] = pos;
      pos += target_lengths[i];
      if (max_target_length < target_lengths[i])
        max_target_length = target_lengths[i];
    }
    tg_target_stride = targets.stride(0);
  }
  else { // batch x max_target_length
    // dim is 2
    int64_t tg_batch_stride = targets.stride(0);
    for (int64_t i = 0; i < batch_size; i++) {
      tg_batch_offsets[i] = i * tg_batch_stride;
    }
    tg_target_stride = targets.stride(1);
    max_target_length = targets.size(1);
  }

  Tensor log_beta = at::empty_like(log_alpha);  // could be optimized to use only 2 rows
  auto lpp  = log_probs.permute({1,0,2});
  auto log_probs_a_global = lpp.accessor<scalar_t, 3>();
  auto log_alpha_a_global = log_alpha.accessor<scalar_t, 3>();
  auto log_beta_a_global = log_beta.accessor<scalar_t, 3>();
  auto gp = grad.permute({1,0,2});
  auto grad_a_global = gp.accessor<scalar_t, 3>();
  auto targets_data = targets.data<target_t>();

  at::parallel_for(0, batch_size, 0, [&](int64_t start, int64_t end) {
    for (int64_t b = start; b < end; b++) {
      scalar_t nll = neg_log_likelihood.accessor<scalar_t, 1>()[b];
      if (zero_infinity &&  nll == std::numeric_limits<scalar_t>::infinity()) {
        grad.narrow(1, b, 1).zero_();
        continue;
      }

      auto log_probs_a = log_probs_a_global[b];
      auto log_alpha_a = log_alpha_a_global[b];
      auto log_beta_a = log_beta_a_global[b];
      auto grad_a = grad_a_global[b];
      int64_t input_length = input_lengths[b];
      int64_t target_length = target_lengths[b];
      int64_t tg_batch_offset = tg_batch_offsets[b];

      // the initialization of beta before eq (10)
      // here we do the fill for each batch item separately, as the input lengths will differ, so the t in which
      // we start varies
      if (input_length > 0) {
        log_beta.narrow(0, b, 1).narrow(1, input_length-1, 1).fill_(neginf);
        log_beta_a[input_length-1][2*target_length] = log_probs_a[input_length-1][BLANK];
        grad_a[input_length-1][BLANK] = log_alpha_a[input_length-1][2*target_length] + log_beta_a[input_length-1][2*target_length];

        if (target_length > 0) {
          auto current_target_prime = get_target_prime(targets_data, tg_batch_offset, tg_target_stride, 2*target_length-1, BLANK);
          log_beta_a[input_length-1][2*target_length-1] = log_probs_a[input_length-1][current_target_prime];

          // the first two are a blank and a non-blank, so we know they are different and we don't need to do log+
          grad_a[input_length-1][current_target_prime] = log_alpha_a[input_length-1][2*target_length-1] + log_beta_a[input_length-1][2*target_length-1];
        }
      }

      // now loop applying eq (10) / (11)
      for (int64_t t=input_length-2; t>=0; t--) {
        // this loop over s could be parallel/vectorized and doesn't really need to be descending...
        // alternatively, one might consider moving s to the outer loop to cache current_target_prime more (but then it needs to be descending)
        // for the cuda implementation, that gave a speed boost.
        for (int64_t s=2*target_length; s>=0; s--) {
          scalar_t lb1 = log_beta_a[t+1][s];
          scalar_t lbmax = lb1;
          scalar_t lb2, lb3;
          auto current_target_prime = get_target_prime(targets_data, tg_batch_offset, tg_target_stride, s, BLANK);
          if (s < 2*target_length) {
            lb2 = log_beta_a[t+1][s+1];
            if (lb2 > lbmax)
              lbmax = lb2;
          } else {
            lb2 = neginf;
          }
          if ((s < 2*target_length-1) && (get_target_prime(targets_data, tg_batch_offset, tg_target_stride, s+2, BLANK) !=
                                          current_target_prime)) {
            lb3 = log_beta_a[t+1][s+2];
            if (lb3 > lbmax)
              lbmax = lb3;
          } else {
            lb3 = neginf;
          }
          if (lbmax == neginf)
            lbmax = 0;

          log_beta_a[t][s] = std::log(std::exp(lb1-lbmax)+std::exp(lb2-lbmax)+std::exp(lb3-lbmax))+lbmax + log_probs_a[t][current_target_prime];
          // one might check whether one can vectorize this better when done after the t-loop...
          // now that we have beta, we fill in the sum of alpha*beta in eq (16)
          // in contrast to the cuda implementation, we only parallelize over the batch, so we don't have a concurrency
          // issue (several s can map to the same target character)
          // collected[b, t, target'[s]] "log+=" log_alpha[t, s]+log_beta[t, s]
          scalar_t log_alpha_beta =  log_alpha_a[t][s] + log_beta_a[t][s];
          scalar_t &lcab = grad_a[t][current_target_prime];
          if (lcab == neginf) {
            lcab = log_alpha_beta;
          } else {
            scalar_t max = std::max(lcab, log_alpha_beta);
            lcab = std::log(std::exp(lcab-max)+std::exp(log_alpha_beta-max))+max;
          }
        }
      }

      // now grad has the sum of eq (16)
      // now we wrap up the calculation by adding in the remaining items of eq (16)
      // this could be a great target for further vectorization.
      // grad is the output gradient, nll is the loss. Note that the likelihood -nll is the Z of eq (16)
      scalar_t gr =  grad_out.accessor<scalar_t, 1>()[b];
      for (int64_t t = 0; t < input_length; t++) { // or go for the full thing?
        for (int64_t c = 0; c < num_labels; c++) {
          scalar_t& res = grad_a[t][c];
          scalar_t lp = log_probs_a[t][c];
          res = (std::exp(lp)-std::exp(res + nll - lp)) * gr;
        }
      }
      // zero the remainder
      if (input_length < max_input_length) {
        grad.narrow(0, input_length, max_input_length - input_length).narrow(1, b, 1).zero_();
      }
    }
  });
  return grad;
}

} // namespace

std::tuple<Tensor, Tensor> ctc_loss_cpu(const Tensor& log_probs, const Tensor& targets, IntArrayRef input_lengths, IntArrayRef target_lengths, int64_t BLANK, bool zero_infinity) {
  (void)zero_infinity; // only used for backwards
  return AT_DISPATCH_FLOATING_TYPES(log_probs.scalar_type(), "ctc_loss_cpu", [&] {
      if (targets.scalar_type() == kLong) {
        return ctc_loss_cpu_template<scalar_t, kLong>(log_probs, targets, input_lengths, target_lengths, BLANK);
      } else {
        return ctc_loss_cpu_template<scalar_t, kInt>(log_probs, targets, input_lengths, target_lengths, BLANK);
      }
  });
}

Tensor ctc_loss_backward_cpu(const Tensor& grad, const Tensor& log_probs, const Tensor& targets, IntArrayRef input_lengths, IntArrayRef target_lengths,
                             const Tensor& neg_log_likelihood, const Tensor& log_alpha, int64_t BLANK, bool zero_infinity) {
  return AT_DISPATCH_FLOATING_TYPES(log_probs.scalar_type(), "ctc_loss_backward_cpu", [&] {
      if (targets.scalar_type() == kLong) {
        return ctc_loss_backward_cpu_template<scalar_t,kLong>(grad, log_probs, targets, input_lengths, target_lengths, neg_log_likelihood, log_alpha, BLANK, zero_infinity);
      } else {
        return ctc_loss_backward_cpu_template<scalar_t,kInt>(grad, log_probs, targets, input_lengths, target_lengths, neg_log_likelihood, log_alpha, BLANK, zero_infinity);
      }
  });
}

// this wrapper function dispatches to the native and cudnn implementations and hides the alpha/grad from the user (by just returning the loss)
// the gradient is implemented for _cudnn_ctc_loss (just in derivatives.yaml) and _ctc_loss and this function has automatic gradients
// it also handles the reduction if desired
Tensor ctc_loss(const Tensor& log_probs, const Tensor& targets, IntArrayRef input_lengths, IntArrayRef target_lengths, int64_t BLANK, int64_t reduction, bool zero_infinity) {
  auto& ctx = at::globalContext();

  bool use_cudnn =
    detail::getCUDAHooks().compiledWithCuDNN() &&
    (detail::getCUDAHooks().versionCuDNN() >= 7000) &&
    ctx.userEnabledCuDNN() &&
    (BLANK == 0) && (targets.dim()==1) &&
    (log_probs.scalar_type() == at::kFloat) &&
    (targets.scalar_type() == at::kInt) &&
    (log_probs.type().backend() == Backend::CUDA);

  if (use_cudnn) {
    // we don't know that input_lengths and target_lengths have the same size (they should, but we didn't check yet)
    int64_t max_input_length = log_probs.size(0);
    for (int64_t b = 0; b < input_lengths.size(); b++) {
      use_cudnn &= (input_lengths[b] == max_input_length);
    }
    for (int64_t b = 0; b < target_lengths.size(); b++) {
      // target length < 256 is documented, but we see illegal memory accesses when target lengths > input lengths for CuDNN
      use_cudnn &= (target_lengths[b] <= 256) & (target_lengths[b] <= input_lengths[b]);
    }
  }

  Tensor res;
  if (use_cudnn) {
    res = std::get<0>(at::_cudnn_ctc_loss(log_probs, targets, input_lengths, target_lengths, BLANK, ctx.deterministicCuDNN(), zero_infinity));
  } else {
    res = std::get<0>(at::_ctc_loss(log_probs, targets, input_lengths, target_lengths, BLANK, zero_infinity));
    if (zero_infinity) {
      res = at::where(res == Scalar(std::numeric_limits<double>::infinity()), at::zeros({}, res.options()), res);
    }
  }
  if (reduction == Reduction::Mean) {
    auto target_lengths_t = at::tensor(target_lengths, res.options());
    return (res / target_lengths_t).mean();
  } else if (reduction == Reduction::Sum) {
    return res.sum();
  }
  return res;
}

// Convenience function accepting Tensors
Tensor ctc_loss(const Tensor& log_probs, const Tensor& targets, const Tensor& input_lengths, const Tensor& target_lengths, int64_t BLANK, int64_t reduction, bool zero_infinity) {
  TORCH_CHECK(isIntegralType(input_lengths.scalar_type()), "input_lenghts must be integral");
  TORCH_CHECK(isIntegralType(target_lengths.scalar_type()), "target_lenghts must be integral");

  Tensor ilc = input_lengths.toType(kLong).toBackend(Backend::CPU).contiguous();
  Tensor tlc = target_lengths.toType(kLong).toBackend(Backend::CPU).contiguous();
  IntArrayRef il(ilc.data<int64_t>(), ilc.numel());
  IntArrayRef tl(tlc.data<int64_t>(), tlc.numel());
  return at::native::ctc_loss(log_probs, targets, il, tl, BLANK, reduction, zero_infinity);
}

} } // at::native
