#include <string>
#include <fstream>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cmath>
#include <cassert>
#include <cstring>
#include <chrono>
#include <cstdlib>

#include <xmmintrin.h>
#include <emmintrin.h>

using namespace std;

//
//
// Point
//

template <typename T>
struct TPoint {
  T x;
  T y;

  TPoint(T a, T b)
  : x(a)
  , y(b)
  {}
};

typedef TPoint<int> Point;
typedef TPoint<double> DPoint; // absolute point, can be negative
template<typename Elem, typename Traits, typename T>

std::basic_ostream<Elem, Traits>& operator << (std::basic_ostream<Elem, Traits>& o, TPoint<T> const& p)
{
  o << "(" << p.x << ", " << p.y << ")";
  return o;
}

struct PackedPixel {
  uint32_t r;
  uint32_t g;
  uint32_t b;

  PackedPixel()
  : r(0)
  , g(0)
  , b(0)
  {}
};

uint8_t interpolate_packed(uint32_t pack, double x, double x_inv, double y, double y_inv)
{
  return (((pack >> 24) & 0x000f) * x_inv + ((pack >> 16) & 0x000f) * x) * y_inv
         + (((pack >> 8) & 0x000f) * x_inv + (pack & 0x000f) * x) * y;
}



//
//
// Image
//

struct Image {
  unsigned int width;
  unsigned int height;
  uint8_t* buffer;

  Image()
  : width(0)
  , height(0)
  , buffer(NULL)
  {}

  virtual ~Image()
  {
    delete [] buffer;
  }

  Image(unsigned int w, unsigned int h)
  {
    this->width = w;
    this->height = h;
    buffer = new uint8_t[width * height * 3];
    memset(buffer, 0, width * height * 3 * sizeof (uint8_t));
  }

  Image(string const& path)
  : Image()
  {
    ifstream is(path);
    if (!is.is_open())
    {
      cerr << "Cannot open file '" << path << "'" << endl;
      abort();
    }

    if (!this->read_header(is))
    {
      cerr << "Invalid header." << endl;
      abort();
    }

    if (!this->read_body(is))
    {
      delete buffer;
      buffer = nullptr;

      cerr << "Invalid header." << endl;
      abort();
    }
  }

  bool save(string const& path) const
  {
    ofstream os(path);
    if (!os.is_open())
    {
      cerr << "Cannot open file '" << path << "'" << endl;
      return false;
    }
    this->write_header(os);
    this->write_body(os);
    return true;
  }

  void set_pixel(unsigned int x, unsigned int y, uint8_t r, uint8_t g, uint8_t b)
  {
    if (x >= width || y >= height)
    {
//        cerr << __LINE__ << " | Point (" << x << ", " << y << ") out of bounds" << endl;
//        cerr << " Image dimensions: " << width << " x " << height << endl;
//        assert(false);
        return;
    }
    int index = (y * width + x) * 3;
    buffer[index++] = r;
    buffer[index++] = g;
    buffer[index++] = b;
  }

  void set_pixel(Point const& p, uint8_t r, uint8_t g, uint8_t b)
  {
    this->set_pixel(p.x, p.y, r, g, b);
  }


  protected:
    bool read_header(std::ifstream& istr)
    {
      // check magic
      if (istr.get() != 'P' )
      {
        return false;
      }

      char type = static_cast<char>(istr.get());
      if (type != '6')
      {
        return false;
      }

      if (istr.get() != '\n')
      {
        return false;
      }

      // skip comments
      while (istr.peek() == '#')
      {
        std::string line;
        std::getline(istr, line);
      }

      // get size
      istr >> width >> height;
      if (width == 0 || height == 0)
      {
        return false;
      }

      // get maxvalue
      if (istr.get() != '\n')
      {
        return false;
      }

      int max_value = -1;
      istr >> max_value;
      if (max_value > 255)
      {
        return false;
      }

      if (istr.get() != '\n')
      {
        return false;
      }

      // cout << "width: " << width << endl;
      // cout << "height: " << height << endl;

      return true;
    }

    bool write_header(std::ofstream& ostr) const
    {
      ostr << "P6" << endl;
      ostr << width << " " << height << endl;
      ostr << "255" << endl;
      return true;
    }

    virtual bool read_body(std::ifstream& istr)
    {
      unsigned int const nb_pixels = width * height;
      buffer = new uint8_t[nb_pixels * 3];

      uint8_t* buf_index = buffer;
      for (unsigned int i = 0; i < nb_pixels * 3; ++i)
      {
        *buf_index = istr.get();
        ++buf_index;
      }

      return true;
    }

    virtual bool write_body(std::ofstream& ostr) const
    {
      unsigned int const nb_pixels = width * height;
      uint8_t* buf_index = buffer;
      for (unsigned int i = 0; i < nb_pixels * 3; ++i)
      {
        ostr << (char) *buf_index;
        ++buf_index;
      }

      return true;
    }
};

template<unsigned int W, unsigned int H>
struct TiledImage : public Image {
  uint8_t* tiles;
  unsigned int static const tile_w = W;
  unsigned int static const tile_h = H;
  unsigned int static const tile_size = W * H;
  unsigned int nb_col_tile;
  unsigned int nb_row_tile;

  TiledImage()
  : Image()
  , tiles(NULL)
  , nb_col_tile(0)
  , nb_row_tile(0)
  {}

  ~TiledImage()
  {
    delete [] tiles;
  }

  TiledImage(unsigned int w, unsigned int h)
  {
    allocate_memory(w, h);
  }

  TiledImage(string const& path)
  : TiledImage()
  {
      ifstream is(path);
      if (!is.is_open())
      {
          cerr << "Cannot open file '" << path << "'" << endl;
          abort();
      }

      if (!this->read_header(is))
      {
          cerr << "Invalid header." << endl;
          abort();
      }

      if (!this->read_body(is))
      {
          // TODO: delete tiles
          cerr << "Invalid header." << endl;
          abort();
      }
  }

  uint8_t*
  access_pixel(unsigned int x, unsigned int y)
  {
    if (x >= width || y >= height)
      return nullptr;

    unsigned int const tile_width = tile_w * 3;

    unsigned int const tile_index = (y / tile_h) * nb_col_tile + (x / tile_w);
    uint8_t* tile = tiles + tile_index * tile_size * 3;
    unsigned int const tile_j = y % tile_h;
    unsigned int const tile_i = x % tile_w;
    return tile + tile_j * tile_width + (tile_i * 3);
  }

  uint8_t const*
  get_tile(unsigned int index) const
  {
    if (index >= nb_col_tile * nb_row_tile)
      return nullptr;

    return tiles + index * tile_size * 3;
  }

  uint8_t*
  get_tile(unsigned int index)
  {
    if (index >= nb_col_tile * nb_row_tile)
      return nullptr;

    return tiles + index * tile_size * 3;
  }

  uint8_t const*
  access_pixel(unsigned int x, unsigned int y) const
  {
    if (x >= width || y >= height)
      return nullptr;

    unsigned int const tile_width = tile_w * 3;

    unsigned int const tile_index = (y / tile_h) * nb_col_tile + (x / tile_w);
    const uint8_t* tile = this->get_tile(tile_index);
    unsigned int const tile_j = y % tile_h;
    unsigned int const tile_i = x % tile_w;
    return tile + tile_j * tile_width + (tile_i * 3);
  }

  PackedPixel
  get_packed_pixels(unsigned int x, unsigned int y) const
  {
    PackedPixel pack;

    this->insert_pixel(pack, x, y);
    pack.r = pack.r << 8;
    pack.g = pack.g << 8;
    pack.b = pack.b << 8;

    this->insert_pixel(pack, x + 1, y);
    pack.r = pack.r << 8;
    pack.g = pack.g << 8;
    pack.b = pack.b << 8;

    this->insert_pixel(pack, x, y + 1);
    pack.r = pack.r << 8;
    pack.g = pack.g << 8;
    pack.b = pack.b << 8;

    this->insert_pixel(pack, x + 1, y + 1);

    return pack;
  }

  void
  print_tile(unsigned int index) const
  {
    cout << "Tile[" << index << "]" << endl;
    uint8_t const* tile = this->get_tile(index);
    unsigned int const tile_width = tile_w * 3;
    for (unsigned int j = 0; j < tile_h; ++j)
    {
      for (unsigned int i = 0; i < tile_w; ++i)
      {
        if (i != 0)
          cout << ", ";
        uint8_t const* p = tile + j * tile_width + i * 3;
        cout << (int) *p << " " << (int) *(p + 1) << " " << (int) *(p + 2);

      }
      cout << endl;
    }
    cout << endl;
  }


  protected:
    void insert_pixel(PackedPixel& pack, unsigned int x, unsigned int y) const
    {
      unsigned int const tile_width = tile_w * 3;
      unsigned int const tile_index = (y / tile_h) * nb_col_tile + (x / tile_w);
      if (tile_index >= nb_col_tile * nb_row_tile)
        return;
      uint8_t const* tile = tiles[tile_index];
      unsigned int const tile_j = y % tile_h;
      unsigned int const tile_i = x % tile_w;
      unsigned int index = tile_j * tile_width + (tile_i * 3);
      pack.r += tile[index];
      pack.g += tile[index + 1] + 1;
      pack.b += tile[index + 2] + 1;
    }

    void allocate_memory(unsigned int w, unsigned int h)
    {
      width = w;
      height = h;

      nb_col_tile = width / tile_w;
      if (width % tile_w != 0)
        ++nb_col_tile;

      nb_row_tile = height / tile_h;
      if (height % tile_h != 0)
        ++nb_row_tile;

      unsigned int const nb_tiles = nb_col_tile * nb_row_tile;
      tiles = new uint8_t[nb_tiles * tile_size * 3];
      memset(tiles, 0, nb_tiles * tile_size * 3 * sizeof (uint8_t));
    }

    virtual bool read_body(std::ifstream& istr)
    {
      this->allocate_memory(width, height);

      // Pixel loading
      for (unsigned int j = 0; j < height; ++j)
        for (unsigned int i = 0; i < width; ++i)
        {
          uint8_t* tile = this->access_pixel(i, j);
          *(tile++) = istr.get();
          *(tile++) = istr.get();
          *(tile++) = istr.get();
        }

      return true;
    }

    virtual bool write_body(std::ofstream& ostr) const override
    {
      for (unsigned int j = 0; j < height; ++j)
        for (unsigned int i = 0; i < width; ++i)
        {
          uint8_t const* tile = this->access_pixel(i, j);
          ostr << (char) *(tile++);
          ostr << (char) *(tile++);
          ostr << (char) *(tile++);
        }

      return true;
    }

};



//
//
// Trigonometry
//

DPoint convert_grid_coord(Image const& img, Point const& p)
{
  return DPoint(p.x - img.width / 2.0f + 0.5, p.y - img.height / 2.0f + 0.5);
}

double convert_radian(Image const& img, Point const& p, double const ratio)
{
  DPoint centered = convert_grid_coord(img, p);
  double const cos_value = centered.x * ratio;
  double const sin_value = - (centered.y * ratio);
  double angle = acos(cos_value);
  if (sin_value < 0)
  {
    angle = (2 * M_PI) - angle;
  }

  return angle;
}

DPoint convert_abs_coord(double const angle, double const ratio)
{
  return DPoint(cos(angle) / ratio, - sin(angle) / ratio);
}

Point convert_img_coord(Image const& img, DPoint const& p)
{
  int x = round(p.x + (img.width / 2.0f) - 0.5);
  int y = round(p.y + (img.height / 2.0f) - 0.5);
  return Point(x, y);
}

DPoint convert_img_coord_precision(Image const& img, DPoint const& p)
{
  double x = p.x + (img.width / 2.0f) - 0.5;
  double y = p.y + (img.height / 2.0f) - 0.5;
  return DPoint(x, y);
}

void convert_abs_to_polar_coord(DPoint const& p, double& angle, double& dist)
{
  angle = atan2(-p.y, p.x);
  dist = sqrt(p.x * p.x + p.y * p.y);
}

DPoint convert_polar_to_grid_coord(double const angle, double const distance)
{
  return DPoint(cos(angle) * distance, - (sin(angle) * distance));
}

double compute_ratio(Image const& img)
{
  double const trigo_length = (sqrt(img.width * img.width + img.height * img.height) - 1) / 2;
  return 1.0f / trigo_length;
}

void compute_output_size(Image const& src, double const rotation, unsigned int& width, unsigned int& height)
{
  double const ratio = compute_ratio(src);
  double min_w = 0;
  double max_w = 0;
  double min_h = 0;
  double max_h = 0;

  Point p(0, 0);
  double angle = convert_radian(src, p, ratio);
  DPoint tl = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, tl.x);
  max_w = max(max_w, tl.x);
  min_h = min(min_h, tl.y);
  max_h = max(max_h, tl.y);

  p = Point(src.width - 1, 0);
  angle = convert_radian(src, p, ratio);
  DPoint tr = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, tr.x);
  max_w = max(max_w, tr.x);
  min_h = min(min_h, tr.y);
  max_h = max(max_h, tr.y);

  p = Point(0, src.height - 1);
  angle = convert_radian(src, p, ratio);
  DPoint bl = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, bl.x);
  max_w = max(max_w, bl.x);
  min_h = min(min_h, bl.y);
  max_h = max(max_h, bl.y);

  p = Point(src.width - 1, src.height - 1);
  angle = convert_radian(src, p, ratio);
  DPoint br = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, br.x);
  max_w = max(max_w, br.x);
  min_h = min(min_h, br.y);
  max_h = max(max_h, br.y);

  width = (int) (max_w - min_w) + 1;
  height = (int) (max_h - min_h) + 1;
}



//
//
// Math approximation
//

void round_if_very_small(double& d)
{
  if (abs(d) < 1.0e-10)
    d = 0.0;

  if (abs(d - 1) < 1.0e-10)
    d = 1.0;
}

inline
bool fequal(float a, float b, float sigma)
{
  return abs(a - b) < sigma;
}



//
//
// Image rotation
//

DPoint get_mapped_point(Image const& src, Point const& p, double const rotation)
{
  DPoint const d = convert_grid_coord(src, p);
  double p_angle = 0;
  double dist = 0;
  convert_abs_to_polar_coord(d, p_angle, dist);
  return convert_polar_to_grid_coord(p_angle + rotation, dist);
}

inline
void rotate_pixel(Image const& src,
                  Point const& src_rotated_point,
                  unsigned int const src_limit,
                  uint8_t* rotate_buffer, unsigned int rot_index)
{
  unsigned int const quantize = 8;

  int const src_x = src_rotated_point.x >> 3;
  int const src_y = src_rotated_point.y >> 3;

  unsigned int src_index = (src_y * src.width + src_x) * 3;

  // Bilinear interpolation
  unsigned int src_index_1 = src_index;
  unsigned int src_index_2 = src_index_1 + 3;
  unsigned int src_index_3 = src_index_1 + 3 * src.width;
  unsigned int src_index_4 = src_index_3 + 3;

  // Out-of-bounds check
  if (src_index_4 >= src_limit)
    return;

  unsigned int x_delta = src_rotated_point.x & 0x07;;
  unsigned int y_delta = src_rotated_point.y & 0x07;
  unsigned int const inv_x = quantize - x_delta;
  unsigned int const inv_y = quantize - y_delta;

  // No SIMD
  rotate_buffer[rot_index] = ((src.buffer[src_index_1] * inv_x + src.buffer[src_index_2] * x_delta) * inv_y
                           + (src.buffer[src_index_3] * inv_x + src.buffer[src_index_4] * x_delta) * y_delta) >> 6;
  rotate_buffer[rot_index + 1] = ((src.buffer[src_index_1 + 1] * inv_x + src.buffer[src_index_2 + 1] * x_delta) * inv_y
                               + (src.buffer[src_index_3 + 1] * inv_x + src.buffer[src_index_4 + 1] * x_delta) * y_delta) >> 6;
  rotate_buffer[rot_index + 2] = ((src.buffer[src_index_1 + 2] * inv_x + src.buffer[src_index_2 + 2] * x_delta) * inv_y
                               + (src.buffer[src_index_3 + 2] * inv_x + src.buffer[src_index_4 + 2] * x_delta) * y_delta) >> 6;
}

Image* rotate(Image const& src, double angle)
{
  double const rotation = (angle / 180.0f) * M_PI;
  unsigned int w = 0;
  unsigned int h = 0;
  compute_output_size(src, rotation, w, h);
  Image* rotated = new Image(w, h);

  // corner points in rotated image
  // TODO: add one ligne for smooth border
  DPoint const tl_grid = get_mapped_point(src, Point(0, 0), rotation);
  Point const tl = convert_img_coord(*rotated, tl_grid);

  // corner points in source image
  DPoint src_tl = get_mapped_point(*rotated, tl, -rotation);
  src_tl = convert_img_coord_precision(src, src_tl);

  DPoint const src_origin = get_mapped_point(*rotated, Point(0, 0), -rotation);
  DPoint src_delta_x = get_mapped_point(*rotated, Point(1, 0), -rotation);
  DPoint src_delta_y = get_mapped_point(*rotated, Point(0, 1), -rotation);

  src_delta_x.x = src_delta_x.x - src_origin.x;
  src_delta_x.y = src_delta_x.y - src_origin.y;
  round_if_very_small(src_delta_x.x);
  round_if_very_small(src_delta_x.y);
  src_delta_y.x = src_delta_y.x - src_origin.x;
  src_delta_y.y = src_delta_y.y - src_origin.y;
  round_if_very_small(src_delta_y.x);
  round_if_very_small(src_delta_y.y);

  unsigned int const src_limit = src.width * src.height * 3;

  DPoint const rot_origin_in_src_grid = get_mapped_point(*rotated, Point(0, 0), -rotation);
  DPoint const rot_origin_in_src = convert_img_coord_precision(src, rot_origin_in_src_grid);

  unsigned int buffer_index = 0;
  uint8_t* buffer = rotated->buffer;

  unsigned int const quantize = 8;
  int const& src_qwidth = src.width * quantize;
  int const& src_qheight = src.height * quantize;

  for (unsigned int y = 0; y < rotated->height; ++y)
  {
    Point const src_rotated_point((rot_origin_in_src.x + y * src_delta_y.x) * quantize,
                                  (rot_origin_in_src.y + y * src_delta_y.y) * quantize);

    for (unsigned int x = 0; x < rotated->width; ++x)
    {
      Point const src_runner(src_rotated_point.x + x * src_delta_x.x * quantize,
                             src_rotated_point.y + x * src_delta_x.y * quantize);

      if (src_runner.x >= 0 && src_runner.x < src_qwidth
          && src_runner.y >= 0 && src_runner.y < src_qheight)
      {
        rotate_pixel(src, src_runner,
                     src_limit,
                     buffer, buffer_index * 3);
      }

      ++buffer_index;
    }
  }

  return rotated;
}

//
//
// Tile rotation
//

template<unsigned int W, unsigned int H>
void rotate_pixel(TiledImage<W, H> const& src,
                  Point const& src_rotated_point,
                  uint8_t* rot_tile)
{
  unsigned int const quantize = 8;

  int const src_x = src_rotated_point.x >> 3;
  int const src_y = src_rotated_point.y >> 3;

  uint8_t const* src_index_1 = src.access_pixel(src_x, src_y);
  uint8_t const* src_index_2 = src.access_pixel(src_x + 1, src_y);
  uint8_t const* src_index_3 = src.access_pixel(src_x, src_y + 1);
  uint8_t const* src_index_4 = src.access_pixel(src_x + 1, src_y + 1);

  // FIXME: deal with image border
  if (!src_index_4)
    return;

  unsigned int x_delta = src_rotated_point.x & 0x07;;
  unsigned int y_delta = src_rotated_point.y & 0x07;
  unsigned int const inv_x = quantize - x_delta;
  unsigned int const inv_y = quantize - y_delta;

  // No SIMD
  rot_tile[0] = ((src_index_1[0] * inv_x + src_index_2[0] * x_delta) * inv_y
              + (src_index_3[0] * inv_x + src_index_4[0] * x_delta) * y_delta) >> 6;
  rot_tile[1] = ((src_index_1[1] * inv_x + src_index_2[1] * x_delta) * inv_y
              + (src_index_3[1] * inv_x + src_index_4[1] * x_delta) * y_delta) >> 6;
  rot_tile[2] = ((src_index_1[2] * inv_x + src_index_2[2] * x_delta) * inv_y
              + (src_index_3[2] * inv_x + src_index_4[2] * x_delta) * y_delta) >> 6;
}

template<unsigned int W, unsigned int H>
TiledImage<W, H>*
rotate(TiledImage<W, H> const& src, double angle)
{
  double const rotation = (angle / 180.0f) * M_PI;
  unsigned int w = 0;
  unsigned int h = 0;
  compute_output_size(src, rotation, w, h);
  auto rotated = new TiledImage<W, H>(w, h);

  DPoint src_origin = get_mapped_point(*rotated, Point(0, 0), -rotation);
  DPoint src_delta_x = get_mapped_point(*rotated, Point(1, 0), -rotation);
  DPoint src_delta_y = get_mapped_point(*rotated, Point(0, 1), -rotation);

  src_delta_x.x = src_delta_x.x - src_origin.x;
  src_delta_x.y = src_delta_x.y - src_origin.y;
  round_if_very_small(src_delta_x.x);
  round_if_very_small(src_delta_x.y);
  src_delta_y.x = src_delta_y.x - src_origin.x;
  src_delta_y.y = src_delta_y.y - src_origin.y;
  round_if_very_small(src_delta_y.x);
  round_if_very_small(src_delta_y.y);

  DPoint const rot_origin_in_src_grid = get_mapped_point(*rotated, Point(0, 0), -rotation);
  DPoint const rot_origin_in_src = convert_img_coord_precision(src, rot_origin_in_src_grid);

  unsigned int const quantize = 8;
  int const& src_qwidth = src.width * quantize;
  int const& src_qheight = src.height * quantize;

  for (unsigned int y = 0; y < rotated->nb_row_tile; ++y)
  {
    for (unsigned int x = 0; x < rotated->nb_col_tile; ++x)
    {
      unsigned int const rot_tile_index = y * rotated->nb_col_tile + x;
      uint8_t* runner = rotated->get_tile(rot_tile_index);

      for (unsigned int j = 0; j < H; ++j)
      {
        int const y_index = y * H + j;
        int x_index = x * W;
        DPoint const src_rotated_point((rot_origin_in_src.x + x_index * src_delta_x.x + y_index * src_delta_y.x) * quantize,
                                       (rot_origin_in_src.y + x_index * src_delta_x.y + y_index * src_delta_y.y) * quantize);

        for (unsigned int i = 0; i < W; ++i)
        {
          Point const src_runner(src_rotated_point.x + i * src_delta_x.x * quantize,
                                 src_rotated_point.y + i * src_delta_x.y * quantize);

          if (src_runner.x >= 0 && src_runner.x < src_qwidth
              && src_runner.y >= 0 && src_runner.y < src_qheight)
          {
            rotate_pixel(src, src_runner, runner);
          }

          runner += 3;
        }
      }
    }
  }

  return rotated;
}



//
//
// Check
//

bool check_points()
{
  Image five(5, 5);
  Point origin(0, 0);
  DPoint d1 = convert_grid_coord(five, origin);
  assert(d1.x == -2);
  assert(d1.y == -2);

  return true;
}

bool check_trigo()
{
  Image square(500, 500);
  double const ratio = compute_ratio(square);
  double const sigma = 1.0e-2;
  if (!fequal(ratio, 1 / 707.106, sigma))
  {
    cerr << __LINE__ << " | Invalid ratio: " << ratio << " != " << 1 / 707.106 << endl;
    return false;
  }

  // Check that the origin of a square image is at sqrt(2) / 2
  double const angle = convert_radian(square, Point(0, 0), ratio);

  if (!fequal(angle, 3 * M_PI / 4, sigma))
  {
    cerr << __LINE__ << " | Invalid angle value: " << angle << " != " << 3 * M_PI / 4 << endl;
    return false;
  }

  // Check that we can reverse the origin point.
  DPoint const abs_reverse_point = convert_abs_coord(angle, ratio);
  Point const reverse_point = convert_img_coord(square, abs_reverse_point);
  if (!fequal(0.0, reverse_point.x, sigma)
    || !fequal(0.0, reverse_point.y, sigma))
  {
    cerr << __LINE__ << "Reverse origin fail" << endl;
    cerr << " " << reverse_point << " != (0, 0)" << endl;
    cerr << " abs point " << abs_reverse_point << endl;
    return false;
  }

  // Check that when rotating the origin by 45 degrees
  double const rotation = M_PI / 4; // 45 degrees
  unsigned int w = 0;
  unsigned int h = 0;
  compute_output_size(square, rotation, w, h);

  if (!fequal(w, square.width * sqrt(2), sigma * square.width)
      || !fequal(h, square.height * sqrt(2), sigma * square.height))
  {
    cerr << "Invalid rotated image dimensions " << w << " x " << h << endl;
    cerr << " expected " << (int) ceil(square.width * sqrt(2)) << " x " << (int) ceil(square.height * sqrt(2)) << endl;
    return false;
  }


  Image rotated(w, h);

  DPoint const a_p45 = convert_abs_coord(angle + rotation, ratio);
  Point const p45 = convert_img_coord(rotated, a_p45);
  if (!fequal(0, p45.x, sigma))
  {
    cerr << __LINE__ << " > Rotation origin by 45 degrees:" << endl;
    cerr << " invalid x value: " << p45.x << " != " << 0 << endl;
    cerr << " absolute point: " << a_p45 << endl;
    cerr << " relative point: " << p45 << endl;
    return false;
  }
  if (!fequal(p45.y, (h - 1) / 2.0f, sigma))
  {
    cerr << __LINE__ << " > Rotation origin by 45 degrees:" << endl;
    cerr << "Invalid y value: " << p45.y << " != " << (h - 1) / 2.0f << endl;
    cerr << " absolute point: " << a_p45 << endl;
    cerr << " relative point: " << p45 << endl;
    return false;
  }

  // Polar coordinates
  {
    DPoint const d(-42.5, 37.5);
    double angle = 0;
    double dist = 0;
    convert_abs_to_polar_coord(d, angle, dist);
    DPoint const reversed = convert_polar_to_grid_coord(angle, dist);
    if (!fequal(d.x, reversed.x, sigma)
        || !fequal(d.y, reversed.y, sigma))
    {
      cerr << __LINE__ << " > Reverse polar coordinates:" << endl;
      cerr << reversed << " != " << d << endl;
      cerr << "polar (" << angle << ", " << dist << ")" << endl;
      return false;
    }
  }

  return true;
}

bool check_90(string const& path)
{
  Image const src(path);
  Image const* rotated = rotate(src, 90);

  for (unsigned int y = 0; y < rotated->height; ++y)
  {
    for (unsigned int x = 0; x < rotated->width; ++x)
    {
      unsigned rot_index = (y * rotated->width + x) * 3;
      unsigned src_index = (x * src.width + (src.width - 1 - y)) * 3;
      if (memcmp(&rotated->buffer[rot_index], &src.buffer[src_index], 3 * sizeof (uint8_t)) != 0)
      {
        Point r(x, y);
        Point s((src.width - 1 - y), x);
        cerr << __LINE__ << " | R: " << r << " != S:" << s << endl;
        cerr << "R dim: " << rotated->width << " x " << rotated->height << endl;
        cerr << "S dim: " << src.width << " x " << src.height << endl;
        return false;
      }
    }
  }

  delete rotated;

  return true;
}



//
//
// Main
//
string get_save_path(string const& base, unsigned int i)
{
    stringstream filename;
    //filename << "/tmp/";
    filename << base << "_";

    if (i < 100)
      filename << "0";
    if (i < 10)
      filename << "0";
    filename << i << ".ppm";

    return filename.str();
}

int main(int argc, char* argv[])
{
  if (argc < 2)
  {
    cout << "Usage: " << argv[0] << " image.ppm" << endl;
    return 1;
  }

  bool perform_check = false;

  if (perform_check)
  {
    if (!check_points())
      return 1;

    if (!check_trigo())
      return 1;

    if (!check_90(argv[1]))
    {
      cerr << __LINE__ << " | 90 degrees check failed" << endl << endl;
//      return 1;
    }
  }


  // No tile
  Image img(argv[1]);
  float average = 0.0;
  int i = 0;
  for (double rotation = 0; rotation < 360; rotation += 45)
  {
    auto const before = chrono::high_resolution_clock::now();
    Image* const rotated = rotate(img, rotation);
    auto const after = chrono::high_resolution_clock::now();
    auto const duration_ms = std::chrono::duration_cast<std::chrono::milliseconds>(after - before);
    average += duration_ms.count();

    cout << "rotate(" << rotation << "): " << duration_ms.count() << " ms" << endl;

    rotated->save(get_save_path("rotated", rotation));
    delete rotated;
    ++i;
  }
  cout << "---------" << endl;
  cout << " average: " << average / i << "ms" << endl << endl;

  // Tile
  TiledImage<8, 8> tiled_img(argv[1]);
  average = 0.0;
  i = 0;
  for (double rotation = 0; rotation < 360; rotation += 45)
  {
    auto const before = chrono::high_resolution_clock::now();
    auto const rotated = rotate(tiled_img, rotation);
    auto const after = chrono::high_resolution_clock::now();
    auto const duration_ms = std::chrono::duration_cast<std::chrono::milliseconds>(after - before);
    average += duration_ms.count();

    cout << "rotate tiled(" << rotation << "): " << duration_ms.count() << " ms" << endl;

    rotated->save(get_save_path("rotated_tiled", rotation));
    delete rotated;
    ++i;
  }
  cout << "---------" << endl;
  cout << " average: " << average / i << "ms" << endl;

  return 0;
}