/* Copyright 2017 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.
==============================================================================*/

#include "tensorflow/compiler/xla/service/cpu/shape_partition.h"

namespace xla {
namespace cpu {

std::vector<int64> ShapePartitionAssigner::Run(int64 target_partition_count) {
  // Gather outer-most dims where dim_size >= 'target_partition_count'.
  // Note: always leave inner-dim static for vectorization/optimizations.
  std::vector<int64> outer_dims;
  int64 outer_dim_size = 1;
  // TODO(b/27458679) Consider reserving enough minor dimensions (based on
  // target vector register width) to enable vector instructions.
  for (int i = shape_.layout().minor_to_major_size() - 1; i >= 1; --i) {
    const int64 dimension = shape_.layout().minor_to_major(i);
    outer_dims.push_back(dimension);
    outer_dim_size *= shape_.dimensions(dimension);
    if (outer_dim_size >= target_partition_count) {
      break;
    }
  }

  // Clip target partition count if outer dim size is insufficient to cover.
  target_partition_count = std::min(outer_dim_size, target_partition_count);

  // Calculate the target number of partitions per-dimension, by factoring
  // 'target_partition_count' into 'num_outer_dims' equal terms.
  // EX:
  // *) target_partition_count = 16
  // *) out_dim_count = 2
  // *) target_dim_partition_count = 16 ^ (1.0 / 2) == 4
  const int64 target_dim_partition_count = std::pow(
      static_cast<double>(target_partition_count), 1.0 / outer_dims.size());

  // Assign feasible dimension partitions based on 'target_dim_partition_count'
  // and actual dimension sizes from 'shape_'.
  std::vector<int64> dimension_partition_counts(outer_dims.size());
  for (int64 i = 0; i < outer_dims.size(); ++i) {
    dimension_partition_counts[i] =
        std::min(static_cast<int64>(shape_.dimensions(outer_dims[i])),
                 target_dim_partition_count);
  }

  // Check if total partition count is below 'target_partition_count'.
  // This can occur if some dimensions in 'shape_' are below the
  // 'target_dim_partition_count' threshold.
  if (GetTotalPartitionCount(dimension_partition_counts) <
      target_partition_count) {
    // Assign additional partitions (greedily to outer dimensions), if doing
    // so would keep the total number of partitions <= 'target_partition_count',
    // using one pass over 'dimension_partition_counts'.
    for (int64 i = 0; i < dimension_partition_counts.size(); ++i) {
      const int64 current_dim_partition_count = dimension_partition_counts[i];
      const int64 other_dims_partition_count =
          GetTotalPartitionCount(dimension_partition_counts) /
          current_dim_partition_count;
      // Constraint: (current + additional) * other <= target
      // Calculate: additional = target / other - current
      int64 additional_partition_count =
          target_partition_count / other_dims_partition_count -
          current_dim_partition_count;
      // Clip 'additional_partition_count' by current dimension size.
      additional_partition_count = std::min(
          shape_.dimensions(outer_dims[i]) - dimension_partition_counts[i],
          additional_partition_count);
      if (additional_partition_count > 0) {
        dimension_partition_counts[i] += additional_partition_count;
      }
    }
  }

  return dimension_partition_counts;
}

int64 ShapePartitionAssigner::GetTotalPartitionCount(
    const std::vector<int64>& dimension_partition_counts) {
  int64 total_partition_count = 1;
  for (int64 dim_partition_count : dimension_partition_counts) {
    total_partition_count *= dim_partition_count;
  }
  return total_partition_count;
}

ShapePartitionIterator::ShapePartitionIterator(
    const Shape& shape, const std::vector<int64>& dimension_partition_counts)
    : shape_(shape),
      dimension_partition_counts_(dimension_partition_counts),
      dimensions_(dimension_partition_counts_.size()),
      dimension_partition_sizes_(dimension_partition_counts_.size()),
      dimension_partition_strides_(dimension_partition_counts_.size()) {
  // Store partitioned outer dimensions from 'shape_'.
  for (int i = 0; i < dimensions_.size(); ++i) {
    dimensions_[i] = shape_.layout().minor_to_major(
        shape_.layout().minor_to_major_size() - 1 - i);
  }

  // Calculate partition size for each dimension (note that the size of
  // the last partition in each dimension may be different if the dimension
  // size is not a multiple of partition size).
  for (int i = 0; i < dimension_partition_sizes_.size(); ++i) {
    const int64 dim_size = shape_.dimensions(dimensions_[i]);
    dimension_partition_sizes_[i] =
        std::max(1LL, dim_size / dimension_partition_counts_[i]);
  }

  // Calculate the partition strides for each dimension.
  dimension_partition_strides_[dimension_partition_strides_.size() - 1] = 1;
  for (int i = dimension_partition_strides_.size() - 2; i >= 0; --i) {
    dimension_partition_strides_[i] = dimension_partition_strides_[i + 1] *
                                      dimension_partition_counts_[i + 1];
  }
}

std::vector<std::pair<int64, int64>> ShapePartitionIterator::GetPartition(
    int64 index) const {
  // Calculate and return the partition for 'index'.
  // Returns for each dimension: (partition_start, partition_size).
  std::vector<std::pair<int64, int64>> partition(dimensions_.size());
  for (int64 i = 0; i < partition.size(); ++i) {
    // Calculate the index for dimension 'i'.
    const int64 partition_index = index / dimension_partition_strides_[i];
    // Calculate dimension partition start at 'partition_index'.
    partition[i].first = partition_index * dimension_partition_sizes_[i];
    // Calculate dimension partition size (note that the last partition size
    // may be adjusted if dimension size is not a multiple of partition size).
    if (partition_index == dimension_partition_counts_[i] - 1) {
      // Last partition in this dimension.
      partition[i].second =
          shape_.dimensions(dimensions_[i]) - partition[i].first;
    } else {
      partition[i].second = dimension_partition_sizes_[i];
    }
    CHECK_GT(partition[i].second, 0);
    // Update index to remove conribution from current dimension.
    index -= partition_index * dimension_partition_strides_[i];
  }
  return partition;
}

int64 ShapePartitionIterator::GetTotalPartitionCount() const {
  return ShapePartitionAssigner::GetTotalPartitionCount(
      dimension_partition_counts_);
}

}  // namespace cpu
}  // namespace xla
