  static Status ProcessDimensions(
      const OpInputList& inputs,
      const gtl::InlinedVector<bool, 2>& input_has_ellipsis,
      const bool output_has_ellipsis, OperandLabels* input_labels,
      Labels* output_labels, std::vector<DimensionType>* label_types,
      OperandLabelCounts* input_label_counts, LabelCounts* output_label_counts,
      LabelToDimSizes* label_to_dim_sizes) {
    if (inputs.size() != input_labels->size()) {
      return errors::InvalidArgument("Expected ", input_labels->size(),
                                     " inputs but got: ", inputs.size());
    }
    const int num_inputs = inputs.size();

    // We infer the number of broadcasting dimensions by taking the maximum rank
    // among the broadcasting subshapes of the input.
    int max_bcast_dims = 0;
    const int num_named_labels = label_types->size();
    label_to_dim_sizes->resize(num_named_labels);
    for (int i = 0; i < num_inputs; ++i) {
      Labels* labels = &(*input_labels)[i];

      if (!input_has_ellipsis[i]) {
        if (inputs[i].dims() != labels->size()) {
          return errors::InvalidArgument("Expected input ", i, " to have rank ",
                                         labels->size(),
                                         " but got: ", inputs[i].dims());
        }
        for (int label_idx = 0; label_idx < labels->size(); ++label_idx) {
          const int label = (*labels)[label_idx];
          TF_RETURN_IF_ERROR(RecordLabelToDimension(label, label_idx, inputs[i],
                                                    label_to_dim_sizes));
        }
        continue;
      }

      // Input has an ellipsis.
      if (inputs[i].dims() + 1 < labels->size()) {
        return errors::InvalidArgument(
            "Expected input ", i, " to have rank at least ", labels->size() - 1,
            " but got: ", inputs[i].dims());
      }
      int ellipsis_axis = -1;
      const int num_bcast_dims = inputs[i].dims() - labels->size() + 1;
      for (int label_idx = 0; label_idx < labels->size(); ++label_idx) {
        const int label = (*labels)[label_idx];
        if (label == kEllipsisLabel) {
          ellipsis_axis = label_idx;
          continue;
        }
        // Current label is not an ellipsis.
        const int axis =
            label_idx + (ellipsis_axis == -1 ? 0 : num_bcast_dims - 1);
        TF_RETURN_IF_ERROR(
            RecordLabelToDimension(label, axis, inputs[i], label_to_dim_sizes));
      }
      // Found an ellipsis. Replace 'kEllipsisLabel' with broadcasting
      // dimensions.
      if (ellipsis_axis != -1) {
        InsertBroadcastLabels(num_bcast_dims, num_named_labels, ellipsis_axis,
                              labels, &input_label_counts->at(i));
        max_bcast_dims = std::max(max_bcast_dims, num_bcast_dims);
      }
    }
    if (!absl::c_linear_search(input_has_ellipsis, true) &&
        !output_has_ellipsis) {
      return Status::OK();
    }
    // Insert broadcasting dimensions in the output labels.
    auto it =
        std::find(output_labels->begin(), output_labels->end(), kEllipsisLabel);
    if (it != output_labels->end()) {
      const int ellipsis_axis = it - output_labels->begin();
      InsertBroadcastLabels(max_bcast_dims, num_named_labels, ellipsis_axis,
                            output_labels, output_label_counts);
    } else if (max_bcast_dims > 0) {
      return errors::InvalidArgument(
          "Output contains ", max_bcast_dims,
          " broadcasting dimension(s) but no ellipsis "
          "(...) was found in the output subscripts.");
    }
    // Populate DimensionType for the new broadcasting labels.
    label_types->resize(num_named_labels + max_bcast_dims, kBroadcasting);
    return Status::OK();
  }
  static Status ProcessDimensions(
      const OpInputList& inputs,
      const gtl::InlinedVector<bool, 2>& input_has_ellipsis,
      const bool output_has_ellipsis, OperandLabels* input_labels,
      Labels* output_labels, std::vector<DimensionType>* label_types,
      OperandLabelCounts* input_label_counts, LabelCounts* output_label_counts,
      LabelToDimSizes* label_to_dim_sizes) {
    if (inputs.size() != input_labels->size()) {
      return errors::InvalidArgument("Expected ", input_labels->size(),
                                     " inputs but got: ", inputs.size());
    }
    const int num_inputs = inputs.size();

     
     
    int max_bcast_dims = 0;
    const int num_named_labels = label_types->size();
    label_to_dim_sizes->resize(num_named_labels);
    for (int i = 0; i < num_inputs; ++i) {
      Labels* labels = &(*input_labels)[i];

      if (!input_has_ellipsis[i]) {
        if (inputs[i].dims() != labels->size()) {
          return errors::InvalidArgument("Expected input ", i, " to have rank ",
                                         labels->size(),
                                         " but got: ", inputs[i].dims());
        }
        for (int label_idx = 0; label_idx < labels->size(); ++label_idx) {
          const int label = (*labels)[label_idx];
          TF_RETURN_IF_ERROR(RecordLabelToDimension(label, label_idx, inputs[i],
                                                    label_to_dim_sizes));
        }
        continue;
      }

       
      if (inputs[i].dims() + 1 < labels->size()) {
        return errors::InvalidArgument(
            "Expected input ", i, " to have rank at least ", labels->size() - 1,
            " but got: ", inputs[i].dims());
      }
      int ellipsis_axis = -1;
      const int num_bcast_dims = inputs[i].dims() - labels->size() + 1;
      for (int label_idx = 0; label_idx < labels->size(); ++label_idx) {
        const int label = (*labels)[label_idx];
        if (label == kEllipsisLabel) {
          ellipsis_axis = label_idx;
          continue;
        }
         
        const int axis =
            label_idx + (ellipsis_axis == -1 ? 0 : num_bcast_dims - 1);
        TF_RETURN_IF_ERROR(
            RecordLabelToDimension(label, axis, inputs[i], label_to_dim_sizes));
      }
       
       
      if (ellipsis_axis != -1) {
        InsertBroadcastLabels(num_bcast_dims, num_named_labels, ellipsis_axis,
                              labels, &input_label_counts->at(i));
        max_bcast_dims = std::max(max_bcast_dims, num_bcast_dims);
      }
    }
    if (!absl::c_linear_search(input_has_ellipsis, true) &&
        !output_has_ellipsis) {
      return Status::OK();
    }
     
    auto it =
        std::find(output_labels->begin(), output_labels->end(), kEllipsisLabel);
    if (it != output_labels->end()) {
      const int ellipsis_axis = it - output_labels->begin();
      InsertBroadcastLabels(max_bcast_dims, num_named_labels, ellipsis_axis,
                            output_labels, output_label_counts);
    } else if (max_bcast_dims > 0) {
      return errors::InvalidArgument(
          "Output contains ", max_bcast_dims,
          " broadcasting dimension(s) but no ellipsis "
          "(...) was found in the output subscripts.");
    }
     
    label_types->resize(num_named_labels + max_bcast_dims, kBroadcasting);
    return Status::OK();
  }