TensorIterator.cpp

#include <ATen/native/TensorIterator.h>

#include <array>
#include <ATen/ExpandUtils.h>
#include <ATen/Parallel.h>
#include <ATen/native/TypeProperties.h>
#include <ATen/MemoryOverlap.h>
#include <ATen/native/Resize.h>
#include <ATen/TensorOperators.h>

#include <c10/util/irange.h>

namespace at {

using DimMask = TensorIteratorBase::DimMask;
using PtrVector = TensorIteratorBase::PtrVector;
using loop2d_t = TensorIteratorBase::loop2d_t;
using StrideVector = TensorIteratorBase::StrideVector;

/// Construction
TensorIteratorConfig& TensorIteratorConfig::add_output(const Tensor& output) {
  TORCH_INTERNAL_ASSERT(num_inputs_ == 0);
  tensors_.emplace_back(output);
  num_outputs_++;
  return *this;
}

TensorIteratorConfig& TensorIteratorConfig::add_input(const Tensor& input) {
  tensors_.emplace_back(input);
  num_inputs_++;
  return *this;
}

TensorIteratorConfig& TensorIteratorConfig::declare_static_dtype_and_device(ScalarType dtype, Device device) {
  TORCH_CHECK(!check_all_same_dtype_, "check_all_same_dtype(false) must be called before declare_static_dtype(...)");
  static_dtype_and_device_ = c10::make_optional(std::make_pair(dtype, device));
  return *this;
}

TensorIteratorConfig& TensorIteratorConfig::declare_static_shape(IntArrayRef shape) {
  // WARNING:
  //   This will bypass all shape checking in the TensorIterator. Kernels which call this method
  //   are expected to check shapes before calling `add_input` or `add_output`.
  TORCH_CHECK(!resize_outputs_, "resize_outputs() must be called before declare_static_shape(...)")
  static_shape_ = c10::make_optional(DimVector(shape));
  return *this;
}

TensorIteratorConfig& TensorIteratorConfig::declare_static_shape(IntArrayRef shape, IntArrayRef squash_dims) {
  declare_static_shape(shape);
  if (!static_shape_->size()) return *this;
  for (const auto& squash_dim : squash_dims) {
    TORCH_CHECK(squash_dim >= 0 && squash_dim < static_cast<int64_t>(static_shape_->size()),
                "squash_dim ", squash_dim, " must be in [0, ", static_shape_->size(), ").");
    (*static_shape_)[squash_dim] = 1;
  }
  return *this;
}

// NOTE: [Computing output strides]
// We use the following algorithm to compute output strides
// If correctly sized output is provided, we respect its stides and don't change them
// Otherwise, if provided output is of incorrect size or no output is provided,
// we try to recover permutation that was applied to the inputs
// by sorting the strides of the inputs. Precedence is given to the inputs in the order they were added,
// and to permutations involving non-broadcasted dimensions
// 1. we loop over inputs starting from the first
// 2. for all inputs strides of broadcasted dimensions are set to 0, and 0 compares equal to anything. If one
// of the dimensions being compared has a stride of 0, we move on to the next tensor to determine if
// these dimensions need to be swapped.
// 3. strides of dimensions equal to 1 participate in sorting
// 4. if 2 strides are equal and neither is 0, we try to break the tie by looking at the corresponding dimensions
// of the tensor. Dimensions were permuted if, when iterating from the end, dimensions corresponding to the
// same strides are increasing. If dimensions are non-increasing, we move on to the next input to break the tie.
//
// Instead of applying rule 4 for tie breaking, we could move on to the next tensor directly. This would result in possibly
// losing the correct permuation of the first tensor if there are permuted trivial dimensions, but could potentially
// improve traversal order of the second tensor. We chose the former option to better propagate channels last layout
// for example for a tensor with the sizes N1H1
// These rules result in the intuitive behavior that in most cases recovers permutation of either the first argument (if all
// arguments are of the same size) or the argument that is not broadcasted, regardless of its position.
// As a bonus, it also result in reasonably well-behaved traversal order of the inputs and outputs - in the kernels
// output is traversed linearly, and since it closely follows input layouts, inputs are traversed linearly as well
//
// Examples:
// full size tensor + broadcasted tensor with 0 or 1 non-trivial dimensions => strides of output are same
// as strides of full size input regardless of the order
// 2 tensors of same size but different strides => output strides are the same as first argument
//
// We also have fast path for memory-dense inputs with the same strides (or, trivially, single memory-dense input)
// that outputs a tensor with the same strides as inputs. The only difference in result with the algorithm described
// above is for strides for trivial (1) dimensions, where in ambiguous cases for performance reasons we default to
// contiguous strides.
// Example: tensor with sizes NC11 and strides C1CC will produce output with strides C111 (note differences are only
// in the strides of trivial dimensions, so physical layout is unaffected but permutation information is lost)
// We might change this behavior in future once performance considerations are resolved

void TensorIteratorBase::reorder_dimensions() {
  // Sort the dimensions based on strides in ascending order with reduced dims
  // at the front. NOTE: that this inverts the order of C-contiguous tensors.
  // strides[0] is the fastest moving dimension instead of strides[ndim - 1].
  // See NOTE: [Computing output strides] and inline  comments for more detailed description

  perm_.resize(ndim());
  if (ndim() == 1) {
    perm_[0] = 0;
    return;
  }

  // initialize perm with n-1, n-2, ..., 1, 0
  std::iota(perm_.rbegin(), perm_.rend(), 0);

  // returns 1 if the dim0 should come after dim1, -1 if dim0 should come
  // before dim1, and 0 if the comparison is ambiguous.
  auto should_swap = [&](size_t dim0, size_t dim1) {
    for (int arg = 0; arg < ntensors(); arg++) {
      // ignore undefined or incorrectly sized tensors
      if (operands_[arg].stride_bytes.empty() || operands_[arg].will_resize) {
        continue;
      }
      int64_t stride0 = operands_[arg].stride_bytes[dim0];
      int64_t stride1 = operands_[arg].stride_bytes[dim1];
      if (is_reduction_ && operands_[arg].is_output) {
        // move reduced dimensions to the front
        // strides of reduced dimensions are always set to 0 by review_reduce_result
        if ((stride0 == 0) != (stride1 == 0)) {
          return stride1 == 0 ? 1 : -1;
        }
      }
      //move on to the next input if one of the dimensions is broadcasted
      if (stride0 == 0 || stride1 == 0) {
        continue;
      // it is important to return here only with strict comparisons, for equal strides we try to break the tie later
      // by comparing corresponding dimensions or if that does not work, moving on to the next tensor
      } else if (stride0 < stride1) {
        return -1;
      } else  if (stride0 > stride1) {
        return 1;
      } else { //equal strides, use dimensions themselves as the tie-breaker.
        //at this point, with zero strides out of the way, we are guaranteed that operand dimensions are equal to shape_
         auto t_dim0 = shape_[dim0];
         auto t_dim1 = shape_[dim1];
         //return only if dimensions should be swapped, otherwise move on to the next tensor
         if (t_dim0 > t_dim1) {
             return 1;
         }
      }
    }
    return 0;
  };

  // insertion sort with support for ambiguous comparisons
  for (int i = 1; i < ndim(); i++) {
    int dim1 = i;
    for (int dim0 = i - 1; dim0 >= 0; dim0--) {
      int comparison = should_swap(perm_[dim0], perm_[dim1]);
      if (comparison > 0) {
        std::swap(perm_[dim0], perm_[dim1]);
        dim1 = dim0;
      } else if (comparison < 0) {
        break;
      }
    }
  }

  // perform re-ordering of shape and strides
  permute_dimensions(perm_);
}

// Computes a common dtype using type promotion
// See the [Common Dtype Computation] note
ScalarType TensorIteratorBase::compute_common_dtype() {
  at::native::ResultTypeState state = {};
  for (const auto& op : operands_) {
    if (op.is_output) {
      continue;
    }

    state = at::native::update_result_type_state(op.tensor, state);
  }

  common_dtype_ = at::native::result_type(state);
  TORCH_INTERNAL_ASSERT(common_dtype_ != ScalarType::Undefined);

  return common_dtype_;
}

TensorOptions original_options(const OperandInfo& op) {
  if (op.original_tensor.defined()) {
    return op.original_tensor.options();
  } else {
    return op.options();
  }
}

// Implements the the behavior of the following flags:
//   - check_all_same_dtype_
//   - check_all_same_device_
//   - enforce_safe_casting_to_output_
//   - promote_inputs_to_common_dtype_
//   - cast_common_dtype_to_outputs_
//
// See their descriptions in TensorIterator.h for details.
// NOTE: Checks for more specific behaviors (e.g. the first and second
//   inputs must share a dtype, but the third must have the long dtype)
//   should be implemented directly and outside of TensorIterator.
void TensorIteratorBase::compute_types(const TensorIteratorConfig& config) {
  // Reviews operands (1/2)
  //   - validates that all input tensors are defined
  //   - computes common device
  //   - determines if there are undefined outputs
  //   - determines if there are different dtypes and attempts
  //       to quickly acquire a common dtype
  Device common_device = kCPU;
  common_dtype_ = ScalarType::Undefined;
  // NB: despite output_dtype's generic sounding name, it only is
  // used in a nontrivial way if check_all_same_dtype is true
  ScalarType output_dtype = ScalarType::Undefined;
  bool has_different_input_dtypes = false;
  bool has_different_output_dtypes = false;
  bool has_undefined_outputs = false;

  for (auto& op : operands_) {
    // Validates that all inputs have type information, and that
    //   if an output is missing type information that we can infer
    //   the device it should be allocated on.
    if (!op.is_type_defined()) {
      TORCH_INTERNAL_ASSERT(op.is_output, "Found type undefined input tensor!");
      if (config.static_dtype_and_device_.has_value()) {
        op.target_dtype = config.static_dtype_and_device_->first;
        op.device = config.static_dtype_and_device_->second;
      } else {
        TORCH_INTERNAL_ASSERT(config.check_all_same_device_);
        has_undefined_outputs = true;
        continue;
      }
    }

    // Validates input tensors are defined
    if (!op.tensor.defined()) {
      TORCH_INTERNAL_ASSERT(op.is_output, "Found undefined input tensor!");
      continue;
    }

    TORCH_INTERNAL_ASSERT(op.target_dtype == op.current_dtype)

    // Acquires the first non-CPU device (if any) as the common device
    if (common_device == kCPU && !op.tensor.is_cpu()) {
      common_device = op.tensor.device();
    }

    if (!op.is_output) {
      // Determines if there are varying input dtypes
      // NOTE: the common dtype is set to the first defined input dtype observed
      if (op.target_dtype != common_dtype_) {
        if (common_dtype_ == ScalarType::Undefined) {
          common_dtype_ = op.target_dtype;
        } else {
          has_different_input_dtypes = true;
        }
      }
    } else {  // op.is_output
      // Determines if there are varying output dtypes
      // NOTE: the output dtype is set to the first defined output dtype observed
      if (op.target_dtype != output_dtype) {
        if (output_dtype == ScalarType::Undefined) {
          output_dtype = op.target_dtype;
        } else {
          has_different_output_dtypes = true;
        }
      }
    }
  }

  // Checks that either the computation type is computable or unneeded
  TORCH_INTERNAL_ASSERT(!(has_different_input_dtypes && !config.promote_inputs_to_common_dtype_ &&
                        (has_undefined_outputs || config.enforce_safe_casting_to_output_ ||
                        config.cast_common_dtype_to_outputs_)));

  // Checks that all inputs and defined outputs are the same dtype, if requested
  if (config.check_all_same_dtype_ &&
      (has_different_input_dtypes || has_different_output_dtypes ||
      (common_dtype_ != output_dtype && output_dtype != ScalarType::Undefined))) {
    // Throws an informative error message
    for (auto& op : operands_) {
      if (!op.tensor.defined()) {
        continue;
      }

      TORCH_CHECK(op.target_dtype == common_dtype_,
                  "Found dtype ", op.target_dtype, " but expected ", common_dtype_);
    }
  }

  // Short-circuits if no additional work required
  if (!has_undefined_outputs && !config.check_all_same_device_ &&
      !config.promote_inputs_to_common_dtype_ && !config.cast_common_dtype_to_outputs_ &&
      !config.enforce_safe_casting_to_output_) {
    // Invalidates common_dtype_ if it could not be inferred
    common_dtype_ = has_different_input_dtypes ? ScalarType::Undefined : common_dtype_;
    return;
  }

  // Computes a common dtype, if needed
  if (has_different_input_dtypes && config.promote_inputs_to_common_dtype_) {
    common_dtype_ = compute_common_dtype();
  }

  // Promotes common dtype to the default float scalar type, if needed
  if (config.promote_integer_inputs_to_float_ &&
      c10::isIntegralType(common_dtype_, /*includeBool=*/true)) {
    common_dtype_ = c10::typeMetaToScalarType(c10::get_default_dtype());
  }

  // Reviews operands (2/2)
  //   - sets metadata for undefined outputs
  //   - checks that all tensors are on the same device, if requested
  //   - checks that the common dtype can safely cast to each output, if requested
  //   - creates temporaries for CPU operations, if needed and requested
  int max_cpu_scalars_on_non_cpu = config.allow_cpu_scalars_ ? 1 : 0;
  int current_cpu_scalars_on_non_cpu = 0;
  for (auto& op : operands_) {
    if (!op.is_type_defined()) {
      op.target_dtype = common_dtype_;
      op.device = common_device;
      continue;
    }

    // Skips undefined tensors
    if (!op.tensor.defined()) {
      continue;
    }

    // Checks all tensors are on the same device, if requested
    if (config.check_all_same_device_) {
      // Handles CPU scalars on CUDA kernels that support them
      if (!common_device.is_cpu() &&
          config.allow_cpu_scalars_ && !op.is_output && op.tensor.dim() == 0 &&
          op.tensor.is_cpu()) {
        TORCH_CHECK(current_cpu_scalars_on_non_cpu < max_cpu_scalars_on_non_cpu,
                    "Trying to pass too many CPU scalars to non-CPU kernel!");
        ++current_cpu_scalars_on_non_cpu;
      } else if (op.device != common_device) {
        TORCH_CHECK(false,
                    "Expected all tensors to be on the same device, but "
                    "found at least two devices, ", common_device, " and ", op.device, "!");
      }
    }

    // Checks safe casting, if requested
    if (config.enforce_safe_casting_to_output_ && op.is_output && op.current_dtype != common_dtype_) {
      TORCH_CHECK(canCast(common_dtype_, op.current_dtype),
                  "result type ", common_dtype_, " can't be cast to the "
                  "desired output type ", op.current_dtype);
    }

    // Creates temporaries for CPU operations, if needed and requested
    // TODO: reuse temporaries when possible (e.g. for inplace operations)
    if (common_device == kCPU) {
      // Casts to outputs by creating temporaries of the correct dtype (if needed)
      // NB: we skip this on is_meta_, because the temporary allocation here is
      // unnecessary if we aren't going to actually do the compute
      if (config.cast_common_dtype_to_outputs_ && op.is_output && op.current_dtype != common_dtype_ && !is_meta_) {
        TORCH_INTERNAL_ASSERT(op.tensor.defined());
        // Marker [Output original_tensor is set]
        op.original_tensor = op.tensor;
        // NB: do NOT use set_output here, as the temporary is NOT a true output;
        // op.tensor is the true output and it was pre-provided for us.
        // TODO: The logic for cast_outputs will need to be handled by the
        // structured kernels implementation.  What probably should happen
        // is that we pass in the inferred dtype into the out kernel, and
        // then after calling the out kernel, do the conversion (which
        // is cast_outputs here), but integrating this with existing
        // TensorIterator will take a little doing
        op.tensor = at::empty_like(op.tensor,
                                   op.tensor.options().dtype(common_dtype_),
                                   LEGACY_CONTIGUOUS_MEMORY_FORMAT);
        if (!names_.empty()) {
          namedinference::propagate_names(op.tensor, names_);
        }
        op.current_dtype = common_dtype_;
        op.target_dtype = common_dtype_;
      }

      // Promotes inputs by creating temporaries of the correct dtype
      if (config.promote_inputs_to_common_dtype_ && !op.is_output && op.current_dtype != common_dtype_) {
        op.original_tensor = op.tensor;
        op.tensor = op.tensor.to(common_dtype_);
        op.current_dtype = common_dtype_;
        op.target_dtype = common_dtype_;
      }
    }
  }
}

StrideVector TensorIteratorBase::compatible_stride(int element_size) const {
  auto stride = StrideVector();
  int64_t next_stride = element_size;
  for (int dim = 0; dim < ndim(); dim++) {
    stride.push_back(next_stride);
    next_stride *= shape_[dim];
  }
  return stride;
}

DimVector TensorIteratorBase::invert_perm(IntArrayRef input) const {
  // Invert the permutation caused by reorder_dimensions. This is not valid
  // after coalesce_dimensions is called.
  TORCH_INTERNAL_ASSERT(!has_coalesced_dimensions_);
  TORCH_INTERNAL_ASSERT(input.size()==perm_.size());
  auto res = DimVector(input.size()); //no initialization needed, every value in res should be written to.
  for (int dim = 0; dim < ndim(); dim++) {
    res[perm_[dim]] = input[dim];
  }
  return res;
}

void TensorIteratorBase::allocate_or_resize_outputs() {
  for (int i = 0; i < num_outputs_; i++) {
    auto& op = operands_[i];
    if (!op.tensor.defined() || op.will_resize) {
      TORCH_INTERNAL_ASSERT(op.is_type_defined(), "no type for operand", i);
      int element_size = elementSize(op.target_dtype);
      op.stride_bytes = compatible_stride(element_size);
      // check if permutation is just an inverted order
      bool inverted = true;
      for (int i = 0; i < ndim(); i++) {
        if (perm_[i] != ndim() - i - 1) {
          inverted = false;
          break;
        }
      }
      auto tensor_shape = invert_perm(shape_);
      if (inverted) {
        // can just return contiguous output
        // it is faster because it avoids allocating 0 size tensor and
        // resizing and restriding it
        set_output(i, tensor_shape, {}, original_options(op), names_);
      } else {
        auto tensor_stride = invert_perm(op.stride_bytes);
        for (int dim = 0; dim < ndim(); dim++) {
          tensor_stride[dim] /= element_size;
        }
        set_output(i, tensor_shape, tensor_stride, original_options(op), names_);
      }
      op.current_dtype = op.target_dtype;
    } else if (op.tensor.defined()) {
      // Even if we don't resize, we still need to tell set_output about
      // the output, so that we properly set guard and propagate names
      set_output(i, op.tensor.sizes(), {}, original_options(op), names_);
    }
  }
}

void TensorIteratorBase::compute_names(const TensorIteratorConfig& config) {
  bool should_infer_names = std::any_of(
      operands_.begin(),
      operands_.end(),
      [](const OperandInfo& op) {
        return op.tensor.defined() && op.tensor.has_names();
      });
  if (!should_infer_names) {
    return;
  }

  for (auto& op : operands_) {
    if (!op.tensor.defined()) continue;
    // Don't include output tensors if we are resizing, since we will
    // clobber their names in any case.  (If the output tensor was
    // also an input tensor, we'll pick it up when it shows up again
    // in operands).
    if (config.resize_outputs_ && op.is_output) continue;
    // perform name inference
    if (names_.empty()) {
      names_ = op.tensor.names();
    } else {
      names_ = NameVector(unify_from_right(names_, op.tensor.names()));
    }
  }
}

void TensorIteratorBase::coalesce_dimensions() {
  if (ndim() <= 1) {
    return;
  }

  // We can coalesce two adjacent dimensions if either dim has size 1 or if:
  // shape[n] * stride[n] == shape[n + 1].
  auto can_coalesce = [&](int dim0, int dim1) {
    auto shape0 = shape_[dim0];
    auto shape1 = shape_[dim1];
    if (shape0 == 1 || shape1 == 1) {
      return true;
    }
    for (int i = 0; i < ntensors(); i++) {
      auto& stride = operands_[i].stride_bytes;
      if (shape0 * stride[dim0] != stride[dim1]) {
        return false;
      }
    }
    return true;
  };

  // replace each operands stride at dim0 with its stride at dim1
  auto replace_stride = [&](int dim0, int dim1) {
    for (int i = 0; i < ntensors(); i++) {
      auto& stride = operands_[i].stride_bytes;
      stride[dim0] = stride[dim1];
    }
  };

  int prev_dim = 0;
  for (int dim = 1; dim < ndim(); dim++) {
    if (can_coalesce(prev_dim, dim)) {
      if (shape_[prev_dim] == 1) {
        replace_stride(prev_dim, dim);
      }
      shape_[prev_dim] *= shape_[dim];
    } else {
      prev_dim++;
      if (prev_dim != dim) {
        replace_stride(prev_dim, dim);
        shape_[prev_dim] = shape_[dim];
      }
    }
  }

  shape_.resize(prev_dim + 1);
  for (int i = 0; i < ntensors(); i++) {
    operands_[i].stride_bytes.resize(ndim());
  }
  has_coalesced_dimensions_ = true;
}

int64_t TensorIteratorBase::numel() const {
  int64_t numel = 1;
  for (int64_t size : shape_) {
    numel *= size;
  }
  return numel;
}

StrideVector TensorIteratorBase::get_dim_strides(int dim) const {
  auto dims = ndim();
  auto inner_strides = StrideVector();
  for (auto& op : operands_) {
    inner_strides.push_back(dims == 0 ? 0 : op.stride_bytes[dim]);
  }
  return inner_strides;
}

SmallVector<char*, 4> TensorIteratorBase::get_data_ptrs(ArrayRef<char*> base, IntArrayRef counter) const {
  auto ptrs = SmallVector<char*, 4>(base);
  for (int dim = 0; dim < ndim(); dim++) {
    int64_t value = counter[dim];
    for (int arg = 0; arg < ntensors(); arg++) {
      ptrs[arg] += value * operands_[arg].stride_bytes[dim];
    }
  }
  return ptrs;
}

SmallVector<char*, 4> TensorIteratorBase::get_base_ptrs() const {
  auto ptrs = SmallVector<char*, 4>();
  for (int i = 0; i < ntensors(); i++) {
    ptrs.push_back((char*)data_ptr(i));
  }
  return ptrs;
}

bool TensorIteratorBase::is_dim_reduced(int dim) const {
  for (auto& op : operands_) {
    if (op.is_output && op.stride_bytes[dim] == 0 && shape_[dim] > 1) {
      return true;
    }
  }
  return false;
}

void TensorIteratorBase::permute_dimensions(IntArrayRef perm) {
  TORCH_INTERNAL_ASSERT(perm.size() == static_cast<unsigned>(ndim()));

  auto reorder = [perm](IntArrayRef data) {
    auto res = DimVector(data.size(), 0);
    for (size_t i = 0; i < perm.size(); i++) {
      res[i] = data[perm[i]];
    }
    return res;
  };

  // Update shape and strides
  shape_ = reorder(shape_);
  for (auto& op : operands_) {
    if (op.stride_bytes.size() > 0) {
      op.stride_bytes = reorder(op.stride_bytes);
    }
  }
}

int64_t TensorIteratorBase::num_output_elements() const {
  int64_t elem = 1;
  for (int dim = 0; dim < ndim(); dim++) {
    if (operands_[0].stride_bytes[dim] != 0 || shape_[dim] == 0)  {
      elem *= shape_[dim];
    }
  }
  return elem;
}

int TensorIteratorBase::num_reduce_dims() const {
  int count = 0;
  for (int dim = 0; dim < ndim(); dim++) {
    if (operands_[0].stride_bytes[dim] == 0) {
      count++;
    }
  }
  return count;
}

void TensorIteratorBase::for_each(loop2d_t loop, int64_t grain_size) {
  int64_t numel = this->numel();
  if (numel == 0) {
    return;
  } else if (numel < grain_size || at::get_num_threads() == 1) {
    return serial_for_each(loop, {0, numel});
  } else {
    at::parallel_for(0, numel, grain_size, [&](int64_t begin, int64_t end) {
      serial_for_each(loop, {begin, end});
    });
  }
}

StrideVector TensorIteratorBase::get_strides() const {
  StrideVector strides;
  for (int dim = 0; dim < ndim(); dim++) {
    for (int arg = 0; arg < ntensors(); arg++) {
      strides.push_back(operands_[arg].stride_bytes[dim]);
    }
  }
  return strides;
}

void TensorIteratorBase::serial_for_each(loop2d_t loop, Range range) const {
  if (range.size() == 0) {
    return;
  }
  auto strides = get_strides();
  while (strides.size() < 2U * ntensors()) {
    strides.push_back(0);
  }

  auto base_ptrs = get_base_ptrs();
  if (ndim() <= 1) {
    auto ptrs = get_data_ptrs(base_ptrs, { range.begin });
    loop(ptrs.data(), strides.data(), range.size(), 1);
  } else {
    auto counter = DimCounter(shape_, range);
    while (!counter.is_done()) {
      auto ptrs = get_data_ptrs(base_ptrs, counter.values);
      auto step = counter.max_2d_step();
      loop(ptrs.data(), strides.data(), step[0], step[1]);
      counter.increment(step);
    }
  }
}

bool TensorIteratorBase::is_trivial_1d() const {
  // TODO: check for casting once it's supported
  return ndim() == 1;
}

bool TensorIteratorBase::is_contiguous() const {
  if (numel() == 1) {
    return true;
  }
  if (ndim() != 1) {
    return false;
  }
  return has_contiguous_first_dim();
}


bool TensorIteratorBase::is_scalar(int arg) const {
  const auto& stride = operands_[arg].stride_bytes;
  for (int i = 0; i < ndim(); i++) {
    if (stride[i] != 0 && shape_[i] != 1) {
      return false;
    }
  }
  return true;
}

bool TensorIteratorBase::is_cpu_scalar(int arg) const {
  return is_scalar(arg) && device(arg).is_cpu();
}

void TensorIteratorBase::cast_outputs() {
  for (auto& op : operands_) {
    if (op.is_output && op.original_tensor.defined() &&
        op.original_tensor.scalar_type() != op.current_dtype) {
      // TODO: Now that set_output resizes both the original_tensor
      // and tensor, this condition should no longer ever be true
      if (op.original_tensor.sizes() != op.tensor.sizes()){
        op.original_tensor.resize_as_(op.tensor).as_strided_(op.tensor.sizes(), op.tensor.strides());
      }
      op.original_tensor.copy_(op.tensor);
      op.tensor = op.original_tensor;
    }
  }
}

void* TensorIteratorBase::data_ptr(int arg) const {
  return operands_[arg].data;
}

void TensorIteratorBase::remove_operand(int arg) {
  operands_.erase(operands_.begin() + arg);
}

void TensorIteratorBase::unsafe_replace_operand(int arg, void* data) {
  operands_[arg].data = data;
}

void TensorIteratorBase::narrow(int dim, int64_t start, int64_t size) {
  TORCH_INTERNAL_ASSERT(dim < ndim() && size >= 1);
  shape_[dim] = size;
  view_offsets_[dim] += start;
  for (auto& op : operands_) {
    op.data = ((char*)op.data) + op.stride_bytes[dim] * start;
  }
  if (size == 1 && !is_reduction_) {
    coalesce_dimensions();
  }
}

void TensorIteratorBase::select_all_keeping_dim(int start_dim, IntArrayRef indices) {
  TORCH_INTERNAL_ASSERT(start_dim <= ndim());
  for (int i = start_dim; i < ndim(); ++i) {
    for (auto& op : operands_) {
      op.data = ((char*)op.data) + op.stride_bytes[i] * indices[i - start_dim];
    }
    shape_[i] = 1;
  }
}

// Helper to construct a binary op that promotes integer inputs to float.
void TensorIteratorBase::build_binary_float_op(const Tensor& out, const Tensor& a, const Tensor& b) {
  build(TensorIteratorConfig()
     .set_check_mem_overlap(true)
     .add_output(out)
     .add_input(a)
     .add_input(b)
     .allow_cpu_scalars(true)
     .promote_inputs_to_common_dtype(true)
     .cast_common_dtype_to_outputs(true)
     .enforce_safe_casting_to_output(true)
     .promote_integer_inputs_to_float(true));
}

void TensorIteratorBase::build_binary_op(const Tensor& out, const Tensor& a, const Tensor& b) {
  build(TensorIteratorConfig()
    .set_check_mem_overlap(true)
    .add_output(out)
    .add_input(a)
    .add_input(b)
    .allow_cpu_scalars(true)
    .promote_inputs_to_common_dtype(true)
    .cast_common_dtype_to_outputs(true)
    .enforce_safe_casting_to_output(true));
}

void TensorIteratorBase::build_unary_float_op(const Tensor& out, const Tensor& a) {
  build(TensorIteratorConfig()
      .set_check_mem_overlap(true)
      .add_output(out)
      .add_input(a)
      .promote_inputs_to_common_dtype(true)
      .cast_common_dtype_to_outputs(true)
      .enforce_safe_casting_to_output(true)
      .promote_integer_inputs_to_float(true));
}

void TensorIteratorBase::build_unary_op(const Tensor& out, const Tensor& a) {
  build(TensorIteratorConfig()
      .set_check_mem_overlap(true)
      .add_output(out)
      .add_input(a)
      .cast_common_dtype_to_outputs(false)
      .enforce_safe_casting_to_output(false)
      .check_all_same_dtype(true));
}

TensorIterator TensorIterator::binary_op(Tensor& out, const Tensor& a, const Tensor& b) {
  TensorIterator iter;
  iter.build_binary_op(out, a, b);
  return iter;
}

TensorIterator TensorIterator::binary_float_op(Tensor& out, const Tensor& a, const Tensor& b) {
  TensorIterator iter;
  iter.build_binary_float_op(out, a, b);
  return iter;
}

TensorIterator TensorIterator::comparison_op(Tensor& out, const Tensor& a,
    const Tensor& b) {
  // Note [special-case bool outputs]
  // We explicitly don't call `cast_common_dtype_to_outputs` when the output tensor
  // has `bool` dtype. This is a performance optimization: the functional
  // version of all comparison/logical ops uses a bool output tensor, and we'd like to
  // avoid creating a temporary copy of the output.
  // However, note that all kernels using this TensorIterator will need to special-case when
  // the output tensor has bool dtype, and provide a lambda of type (scalar_t, scalar_t -> bool).
  if (out.scalar_type() == kBool) {
    return TensorIteratorConfig()
    .set_check_mem_overlap(true)
    .add_output(out)
    .add_input(a)
    .add_input(b)
    .allow_cpu_scalars(true)
    .promote_inputs_to_common_dtype(true)
    .build();
  } else {
    return TensorIteratorConfig()
    .set_check_mem_overlap(true)
    .add_output(out)
    .add_input(a)
    .add_input(b)
    .allow_cpu_scalars(true)
    .promote_inputs_to_common_dtype(true)
    .cast_common_dtype_to_outputs(true)
    .build();
  }
}

TensorIterator TensorIterator::unary_op(Tensor& out, const Tensor& a) {
  TensorIterator iter;
  iter.build_unary_op(out, a);
  return iter;
}

TensorIterator TensorIterator::unary_float_op(Tensor& out, const Tensor& a) {
  TensorIterator iter;
  iter.build_unary_float_op(out, a);
  return iter;
}

TensorIterator TensorIterator::nullary_op(Tensor& out) {
  return TensorIteratorConfig()
    .set_check_mem_overlap(true)
    .check_all_same_dtype(false)
    .add_output(out)
    // FIXME: workaround for bug: https://github.com/pytorch/pytorch/issues/20342
    .resize_outputs(false)
    .build();
}

TensorIterator TensorIterator::reduce_op(Tensor& out, const Tensor& a) {
  TORCH_INTERNAL_ASSERT(out.defined());
  return TensorIteratorConfig()
    .set_check_mem_overlap(false)
    .add_output(out)
    .add_input(a)
    .resize_outputs(false)
    .is_reduction(true)
    // TODO: not supporting casting to outputs is only really necessary for arg{min,max}
    .promote_inputs_to_common_dtype(true)
    .build();
}

TensorIterator TensorIterator::reduce_op(Tensor& out1, Tensor& out2, const Tensor& a) {
  TORCH_INTERNAL_ASSERT(out1.defined());
  TORCH_INTERNAL_ASSERT(out2.defined());
  TORCH_CHECK(a.device() == out1.device() && out1.device() == out2.device(),
      "reduce_op(): expected input and both outputs to be on same device, but input is on ", a.device(),
      ", output1 is on ", out1.device(), " and output2 is on", out2.device());
  TORCH_CHECK(out1.dim() == out2.dim(), "reduce_op(): expected both outputs to have same number of dims, but output1 has ", out1.dim(),
      " and output2 has ", out2.dim());
  TORCH_CHECK(out1.sizes() == out2.sizes(), "reduce_op(): expected both outputs to have same sizes, but output1 has ", out1.sizes(),
      " and output2 has ", out2.sizes());
  TORCH_CHECK(out1.strides() == out2.strides(), "reduce_op(): expected both outputs to have same strides, but output1 has ", out1.strides(),
      " and output2 has ", out2.strides());
  return TensorIteratorConfig()
    .set_check_mem_overlap(false)
    .add_output(out1)
    .add_output(out2)
    .add_input(a)
    .resize_outputs(false)
    .is_reduction(true)
    .check_all_same_dtype(false)
    .build();
}

void TensorIteratorBase::populate_operands(TensorIteratorConfig& config) {
  for (auto& tensor: config.tensors_) {
    // If *any* of the arguments is a meta tensor, the overall
    // computation is a meta computation (don't do any work,
    // just compute output information).  This aligns with
    // our multiple dispatch semantics.
    if (tensor.is_meta()) {
      is_meta_ = true;
    }
    operands_.emplace_back(std::move(tensor));
  }
  num_outputs_ = config.num_outputs_;
}

void TensorIteratorBase::mark_outputs() {
  // TODO: merge this into populate_operands
  for (int i = 0; i < num_outputs_; i++) {
    operands_[i].is_output = true;
    const auto& output = operands_[i].tensor;
    if (!output.defined()) continue;

    // check if output is also an input
    for (int arg = num_outputs_; arg < ntensors(); arg++) {
      const auto& input = operands_[arg].tensor;
      if (output.is_same(input)) {
        operands_[i].is_read_write = true;
      }
    }
  }
}

void TensorIteratorBase::mark_resize_outputs(const TensorIteratorConfig& config) {
  // Outputs cannot be broadcasted. Check that the shape of the outputs matches
  // the inferred shape. There's an exception for write-only tensors to support
  // our legacy behavior that functions with `out=` arguments resize their
  // outputs.
  if (config.static_shape_.has_value()) {
    return;
  }
  for (int i = 0; i < num_outputs_; i++) {
    const auto& output = operands_[i].tensor;
    if (output.defined() && !output.sizes().equals(shape_)) {
      if (config.resize_outputs_ && !operands_[i].is_read_write) {
        operands_[i].will_resize = true;
        continue;
      }
      // for reduction, output size does not match shape_, as output is reduced size, and shape_ is size of the input
      TORCH_CHECK(is_reduction_,  "output with shape ", output.sizes(), " doesn't match the broadcast shape ",
                 shape_);
    }
  }
}

void TensorIteratorBase::compute_mem_overlaps(const TensorIteratorConfig& config) {
  if (!config.check_mem_overlap_) {
    return;
  }
  for (int i = 0; i < num_outputs_; i++) {
    const auto& output = operands_[i].tensor;
    if (!output.defined()) continue;
    assert_no_internal_overlap(output);
    for (int j = num_outputs_; j < ntensors(); j++) {
      const auto& input = operands_[j].tensor;
      assert_no_partial_overlap(output, input);
    }
  }
}

void TensorIteratorBase::compute_shape(const TensorIteratorConfig& config) {
  if (config.static_shape_.has_value()) {
    shape_ = *config.static_shape_;
    return;
  }

  all_ops_same_shape_ = true;
  bool has_scalars = false;
  bool has_tensors = false;
  for (auto& op : operands_) {
    if (!op.tensor.defined()) continue;

    // For now, don't include output tensors when we're resizing outputs.
    // These shapes don't participate in shape computation.
    // This preserves the legacy behavior where torch.add(..., out=dst) resizes
    // the destination tensor.  If the output tensor is also an input, we'll
    // pick it up later in the operands.
    if (config.resize_outputs_ && op.is_output) continue;
    auto shape = op.tensor.sizes();
    if (shape.size() == 0) {
      has_scalars = true;
    } else {
      has_tensors = true;
    }
    if (has_scalars && has_tensors) {
      all_ops_same_shape_ = false;
    }
    if (shape_.empty()) {
      shape_ = shape;
    } else if (!shape.equals(shape_)) {
      all_ops_same_shape_ = false;
      shape_ = infer_size_dimvector(shape_, shape);
    }
  }
}

void TensorIteratorBase::compute_strides(const TensorIteratorConfig& config) {
  for (auto& op : operands_) {
    if (op.tensor.defined()) {
      IntArrayRef original_shape = config.static_shape_ ? shape_ : op.tensor.sizes();
      auto original_stride = op.tensor.strides();
      auto element_size_in_bytes = op.tensor.element_size();
      auto offset = ndim() - original_shape.size();
      if (offset > 0)
          op.stride_bytes.resize(ndim(), 0);
      else
          op.stride_bytes.resize(ndim());
      for (size_t i = 0; i < original_shape.size(); i++) {
        // see NOTE: [Computing output strides]
        if (original_shape[i] == 1 && shape_[offset + i] !=1) {
          op.stride_bytes[offset + i] = 0;
        } else {
          op.stride_bytes[offset + i] = original_stride[i] * element_size_in_bytes;
        }
      }
    }
  }
}

bool TensorIteratorBase::can_use_32bit_indexing() const {
  int64_t max_value = std::numeric_limits<int32_t>::max();
  if (numel() > max_value) {
    return false;
  }
  for (auto& op : operands_) {
    int64_t max_offset = 1;
    for (int dim = 0; dim < ndim(); dim++) {
      max_offset += (shape_[dim] - 1) * op.stride_bytes[dim];
    }
    if (max_offset > max_value) {
      return false;
    }
  }
  return true;
}

std::unique_ptr<TensorIterator> TensorIteratorBase::split(int dim) {
  TORCH_INTERNAL_ASSERT(dim >= 0 && dim < ndim() && shape()[dim] >= 2);
  std::unique_ptr<TensorIterator> copy(new TensorIterator(*this));

  bool overlaps = is_dim_reduced(dim);
  auto copy_size = shape_[dim] / 2;
  auto this_size = shape_[dim] - copy_size;
  copy->narrow(dim, 0, copy_size);
  copy->final_output_ &= !overlaps;
  this->narrow(dim, copy_size, this_size);
  this->accumulate_ |= overlaps;

  return copy;
}


int TensorIteratorBase::get_dim_to_split() const {
  TORCH_INTERNAL_ASSERT(ndim() >= 1);
  int64_t max_extent = -1;
  int dim_to_split = -1;
  for (int dim = ndim() - 1; dim >= 0; dim--) {
    if (shape_[dim] == 0) {
      continue;
    }
    int64_t size = shape_[dim];
    for (auto& op : operands_) {
      int64_t extent = (size - 1) * op.stride_bytes[dim];
      if (extent > max_extent) {
        max_extent = extent;
        dim_to_split = dim;
      }
    }
  }
  TORCH_INTERNAL_ASSERT(max_extent >= 0);
  return dim_to_split;
}

bool TensorIteratorBase::fast_set_up(const TensorIteratorConfig& config) {
  // This function tries to do a fast setup to avoid needless reordering of dimensions and tracking output strides
  // Return true if it can do fast setup or false otherwise
  // TODO enable fast handling for reductions
  FastSetupType setup_type = compute_fast_setup_type(config);
  if (setup_type == FastSetupType::NONE) {
    return false;
  }

  // allocate memory for output, memory format depends on setup_type
  switch (setup_type) {
    case FastSetupType::CONTIGUOUS:
      {
        for (int i = 0; i < num_outputs_; i++){
          auto& op = operands_[i];
          if (!op.tensor.defined()) {
            TORCH_INTERNAL_ASSERT(op.is_type_defined(), "no type for operand", i);
          }
          set_output(i, shape_, {}, original_options(op).memory_format(MemoryFormat::Contiguous), names_);
        }
        break;
      }
    case FastSetupType::CHANNELS_LAST:
      {
        for (int i = 0; i < num_outputs_; i++){
          auto& op = operands_[i];
          if (!op.tensor.defined()) {
            TORCH_INTERNAL_ASSERT(op.is_type_defined(), "no type for operand", i);
          }
          set_output(i, shape_, {}, original_options(op).memory_format(MemoryFormat::ChannelsLast), names_);
        }
        break;
      }
    case FastSetupType::NON_OVERLAPPING_DENSE:
      {
        // find the index of a defined tensor in operands_ start from input tensor
        int i_defined; // NOLINT(cppcoreguidelines-init-variables)
        for (i_defined = ntensors() - 1; i_defined >= 0; --i_defined) {
          if (operands_[i_defined].tensor.defined()) break;
        }
        TORCH_CHECK(i_defined >= 0, "Can not find a defined tensor when fast allocating memory to outputs");
        for (int i = 0; i < num_outputs_; i++){
          auto& op = operands_[i];
          if (!op.tensor.defined()) {
            TORCH_INTERNAL_ASSERT(op.is_type_defined(), "no type for operand", i);
          }
          set_output(i, shape_, operands_[i_defined].tensor.strides(), original_options(op), names_);
        }
        break;
      }
    default:
      TORCH_INTERNAL_ASSERT(false, "Unsupported fast setup type", c10::to_string((int)setup_type));
  }
  //coalescing dimensions consists of collapsing dimensions to 1 (we are limited to contiguous no-broadcast cases here)
  if (ndim() > 1){
    has_coalesced_dimensions_ = true;
  }
  if (ndim() >= 1) {
    shape_[0] = numel();
    shape_.resize(1);
  }
  for (auto& op : operands_ ) {
    auto element_size_in_bytes = op.tensor.element_size();
    op.stride_bytes.resize(ndim());
    if (ndim()>0) {
      op.stride_bytes[0] = element_size_in_bytes;
    }
  }
  return true;
}

FastSetupType TensorIteratorBase::compute_fast_setup_type(const TensorIteratorConfig& config) {
  if (is_reduction_ || !all_ops_same_shape_) {
    return FastSetupType::NONE;
  }

  bool is_contiguous = true;
  bool is_channels_last = true;
  bool is_non_overlapping_and_dense = true;
  for (const auto& op : operands_) {
    if (op.tensor.defined() && !op.will_resize) {
      is_contiguous &= op.tensor.is_contiguous(at::MemoryFormat::Contiguous);
      is_channels_last &= op.tensor.is_contiguous(at::MemoryFormat::ChannelsLast);
      is_non_overlapping_and_dense &= op.tensor.is_non_overlapping_and_dense();
    }
  }
  // TODO this leads to ambiguous cases (NC11) to be always treated as contiguous
  if (is_contiguous) {
    return FastSetupType::CONTIGUOUS;
  }
  if (is_channels_last) {
    return FastSetupType::CHANNELS_LAST;
  }
  if (is_non_overlapping_and_dense) {
    int64_t prev = -1;
    // Fast setup is allowed only when all the defined tensors have the same shape and strides,
    // Iterate from back to check input tensors' strides first, then output tensors'.
    for (int64_t i = ntensors() - 1; i >= 0; --i) {
      const auto& op = operands_[i];
      if (op.tensor.defined() && !op.will_resize) {
        if (prev < 0) {
          prev = i;
          continue;
        }
        if (!operands_[prev].tensor.strides().equals(op.tensor.strides())) {
          // [Note: stride check for non contiguous tensors in fast setup]
          // We prevent 3 cases doing fast setup here:
          // 1. input tensors have different strides.
          // 2. output tensors won't be resized and have different strides.
          // 3. input tensors have the same strides, but output tensors have different strides with input tensors.
          //    We don't allow re-stride output tensors in this case since it is not compatible with
          //    numpy. The behavior in numpy is that if the output tensor has same shape as the input
          //    tensor but different strides, the strides of output tensor will be preserved, so we do
          //    the same in tensor iterator.
          return FastSetupType::NONE;
        }
      }
    }
    return FastSetupType::NON_OVERLAPPING_DENSE;
  }
  return FastSetupType::NONE;
}

TensorIteratorBase::TensorIteratorBase() = default;

void TensorIteratorBase::build(TensorIteratorConfig& config) {
  // populate some persistent configuration fields
  is_reduction_ = config.is_reduction_;

  // fill in operands_ based on configuration
  populate_operands(config);
  // set is_output and is_read_write flags on appropriate tensors
  mark_outputs();
  // Check that the outputs have no internal overlap
  // and do not share memory with inputs.
  compute_mem_overlaps(config);
  // Check that input dimensions are aligned correctly & compute outnames.
  compute_names(config);
  // compute the broadcasted shape
  compute_shape(config);
  // mark outputs for resizing if necessary
  mark_resize_outputs(config);
  // compute the result dtype and device
  compute_types(config);
  // try fast setup output tensor, if failed, fallback to normal setup
  if (!fast_set_up(config)) {
    // compute each tensor's stride after broadcasting
    compute_strides(config);
    // re-order dimensions to improve coalescing
    reorder_dimensions();
    // allocate the output tensor if it's not provided
    allocate_or_resize_outputs();
    // coalesce adjacent dimensions when possible
    if (!is_meta_) coalesce_dimensions();
  }

  if (is_meta_) return;

  for (auto& op : operands_) {
    TORCH_INTERNAL_ASSERT(op.tensor.defined());
    op.data = op.tensor.data_ptr();
  }

  // zero out offsets
  // If the tensor is a scalar, we leave room for it
  // So index translations in reduction can access
  // a valid value for the offset
  int64_t ndim_offsets = (ndim() ? ndim() : 1);
  view_offsets_ = DimVector(ndim_offsets, 0);
}

// This is the structured kernels implementation of set_output.  It is
// NEVER actually called directly; instead, a subclass of TensorIteratorBase
// will override set_output to actually do the operation, and then call
// set_output on the TensorIteratorBase to setup TI's metadata.
// The precondition for this function is that maybe_get_output() now
// unconditionally returns a real Tensor (prior to output setting,
// this function may return an undefined tensor.)
void TensorIteratorBase::set_output(int64_t output_idx, IntArrayRef sizes, IntArrayRef strides, TensorOptions options, DimnameList names) {
  auto& op = operands_[output_idx];
  TORCH_INTERNAL_ASSERT_DEBUG_ONLY(output_idx < num_outputs_);
  const auto& t = maybe_get_output(output_idx);
  TORCH_INTERNAL_ASSERT(t.defined());
  if (!op.tensor.defined()) {
    op.tensor = t;
    op.current_dtype = op.target_dtype;
  } else if (op.will_resize) {
    if (op.original_tensor.defined()) {
      // OK, so this is pretty weird.  To understand how we can end up in
      // this situation, first look at Marker [Output original_tensor is set].
      // That is the sole site where original_tensor may be set on an
      // output operand.  Essentially, when we are given an explicit output
      // tensor whose dtype doesn't match the computed common dtype from
      // the input operands, we do a switcheroo: we replace the (incorrectly
      // typed) output tensor with a correctly typed, *temporary* tensor,
      // and remember the original tensor in original_tensor (which will
      // then get written back to when we cast_outputs).
      //
      // Now, what if the given output tensor also happened to be zero
      // size (meaning that we will_resize it)?  Well, at the call site
      // above, we don't necessarily(*) know what the correct shape should
      // be, so we give the temporary tensor the same shape as the original.
      // At the time of set_output is when we DO know what the correct size
      // is, and the subclass's implementation of set_output in structured class
      // responsible for resizing original_tensor.  But we still have this
      // incorrectly sized temporary output which the structured subclass
      // knows nothing about, so we are obligated to also resize it here.
      //
      // This is a slight memory pessimization, because previously
      // original_tensor only got resized at the end of the computation, rather
      // than at the beginning (as happens here).  However, the peak memory
      // usage is the same, since you need to materialize both original tensor
      // and temporary tensor to do the copy.
      //
      // (*) Actually, technically, we probably do know what the shape
      // should be, since we do shape computation before dtype computation.
      // So hypothetically we could figure out what the correct shape is
      // at that point in time and directly allocate the temporary at
      // the right size.
      //
      // But a better solution is to delay allocation of temporaries until
      // after TensorIterator builder, waiting until we actually want
      // to do the computation.  That would also remove the necessity
      // for the is_meta_ test.
      TORCH_INTERNAL_ASSERT(op.original_tensor.is_same(t));
      TORCH_INTERNAL_ASSERT(!op.tensor.is_same(t));
      // fastpath CPU to skip a dispatcher trip
      if (op.tensor.is_cpu()) {
        at::native::resize_output_cpu(op.tensor, sizes);
      } else {
        at::native::resize_output(op.tensor, sizes);
      }
      if (!strides.empty()) {
        TORCH_INTERNAL_ASSERT(!options.memory_format_opt().has_value());
        op.tensor.as_strided_(sizes, strides);
      } else if (options.memory_format_opt().has_value()) {
        op.tensor.unsafeGetTensorImpl()->empty_tensor_restride(*options.memory_format_opt());
      }
    }
  }
}

// This is the "traditional" implementation of set_output.  On TensorIterator
// instances, it is invoked directly from various call sites in this file.  No
// funny business.
void TensorIterator::set_output(int64_t output_idx, IntArrayRef sizes, IntArrayRef strides, TensorOptions options, DimnameList names) {
  // NB: intentionally no superclass call
  auto& op = operands_[output_idx];
  TORCH_INTERNAL_ASSERT_DEBUG_ONLY(output_idx < num_outputs_);
  if (!op.tensor.defined()) {
      if (strides.empty()) {
        op.tensor = at::empty(sizes, options);
      } else {
        op.tensor = at::empty_strided(sizes, strides, options);
      }
      op.current_dtype = op.target_dtype;
  } else if (op.will_resize) {
      // fastpath CPU to skip a dispatcher trip
      if (op.tensor.is_cpu()) {
        at::native::resize_output_cpu(op.tensor, sizes);
      } else {
        at::native::resize_output(op.tensor, sizes);
      }
      if (!strides.empty()) {
        TORCH_INTERNAL_ASSERT(!options.memory_format_opt().has_value());
        op.tensor.as_strided_(sizes, strides);
      } else if (options.memory_format_opt().has_value()) {
        op.tensor.unsafeGetTensorImpl()->empty_tensor_restride(*options.memory_format_opt());
      }
  }
  if (!names.empty()) {
    TORCH_INTERNAL_ASSERT(op.tensor.defined());
    namedinference::propagate_names(op.tensor, names);
  }
}

// Not actually used by anything (TensorIterator subclass calls
// its own implementation of set_output which knows exactly where
// all the outputs are), but we have to provide all pure virtual methods
// for MetaBase
const Tensor& TensorIterator::maybe_get_output(int64_t output_idx) {
  return operands_[output_idx].tensor;
}

SplitUntil32Bit TensorIteratorBase::with_32bit_indexing() const {
  return SplitUntil32Bit(*this);
}

/// SplitUntil32Bit. Recursively splits an iterator into sub-iterators that
/// can use 32-bit indexing.

SplitUntil32Bit::iterator::iterator(const TensorIteratorBase& iter) {
  vec.emplace_back(new TensorIterator(iter));
  vec.emplace_back(nullptr); // ++ first pops the last element
  ++(*this);
}

SplitUntil32Bit::iterator& SplitUntil32Bit::iterator::operator++() {
  vec.pop_back();
  while (!vec.empty() && !vec.back()->can_use_32bit_indexing()) {
    auto& iter = *vec.back();
    int64_t split_dim = iter.get_dim_to_split();
    vec.emplace_back(iter.split(split_dim));
  }
  return *this;
}

TensorIterator& SplitUntil32Bit::iterator::operator*() const {
  return *vec.back();
}

SplitUntil32Bit::iterator SplitUntil32Bit::begin() const {
  return SplitUntil32Bit::iterator(iter);
}

SplitUntil32Bit::iterator SplitUntil32Bit::end() const {
  return SplitUntil32Bit::iterator();
}

DimCounter::DimCounter(IntArrayRef shape, Range range)
  : shape(shape)
  , range(range)
  , values(shape.size(), 0)
  , offset(range.begin) {
  int64_t linear_offset = range.begin;
  int64_t ndim = values.size();
  for (const auto dim : c10::irange(ndim)) {
    int64_t size = shape[dim];
    if (size > 0) {
      values[dim] = linear_offset % size;
      linear_offset /= size;
    }
  }
  TORCH_INTERNAL_ASSERT(linear_offset == 0);
}

bool DimCounter::is_done() const {
  return offset >= range.end;
}

void DimCounter::increment(const std::array<int64_t, 2>& step) {
  offset += step[0] * step[1];
  int64_t ndim = values.size();
  int64_t overflow = step[0];
  int i = 0;
  if (step[1] != 1) {
    TORCH_INTERNAL_ASSERT(step[0] == shape[0] && values[0] == 0);
    i = 1;
    overflow = step[1];
  }
  for (; i < ndim && overflow > 0; i++) {
    auto size = shape[i];
    auto prev = values[i];
    auto value = prev + overflow;
    if (value >= size) {
      overflow = 1;
      value -= size;
      TORCH_INTERNAL_ASSERT(value < size);
    } else {
      overflow = 0;
    }
    values[i] = value;
  }
  TORCH_INTERNAL_ASSERT(overflow == 0 || overflow == 1);
}

std::array<int64_t, 2> DimCounter::max_2d_step() const {
  int64_t step0 = std::min(shape[0] - values[0], range.end - offset);
  int64_t step1 = 1;
  if (step0 == shape[0] && shape.size() >= 1) {
    step1 = std::min(shape[1] - values[1], (range.end - offset) / shape[0]);
  }
  return {step0, step1};
}

}  // namespace at