rotate-me-fast/rotation.cpp

#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>
#include <tmmintrin.h>

#include "image.h"

using namespace std;

#define LOG cout << __FUNCTION__ << ": " << __LINE__ << " | "
#define ERRLOG cerr << __FUNCTION__ << ": " << __LINE__ << " | "


//
//
// 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 const 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 const 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 const 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 const 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;
}

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);
}



//
//
// 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;
}



//
//
// Padding
//

uint16_t* generate_padding_table(Image const& rotated,
                                 Point src_rotated_origin,
                                 Point const& qdx, Point const& qdy,
                                 int src_qwidth, int src_qheight)
{
  uint16_t* padding_table = new uint16_t[rotated.height];
  // We suppose the image is square.
  if (qdx.x == 0 || qdx.y == 0)
  {
    memset(padding_table, 0, sizeof (uint16_t) * rotated.height);
    return padding_table;
  }

  for (unsigned int i = 0; i < rotated.height; ++i)
  {
    int y_range = 0;
    if (src_rotated_origin.y < 0)
    {
      y_range = ceil((-src_rotated_origin.y) / (float) qdx.y);
    }
    else if (src_rotated_origin.y >= src_qheight)
    {
      y_range = ceil((float) (src_rotated_origin.y - src_qheight + 1) / (float) (-qdx.y));
    }
    if (y_range < 0)
    {
      cout << "Negative Y range" << endl;
      abort();
    }

    int x_range = 0;
    if (src_rotated_origin.x < 0)
    {
      x_range = ceil((-src_rotated_origin.x) / (float) qdx.x);
    }
    else if (src_rotated_origin.x >= src_qwidth)
    {
      x_range = ceil((float) (src_rotated_origin.x - src_qwidth + 1) / (float) (-qdx.x));
    }
    if (x_range < 0)
    {
      cout << "Negative X range" << endl;
      abort();
    }

    padding_table[i] = max(x_range, y_range);

    {
      Point test(src_rotated_origin.x + padding_table[i] * qdx.x,
                 src_rotated_origin.y + padding_table[i] * qdx.y);
      if (test.x < 0 || test.y < 0
         || test.x >= src_qwidth || test.y >= src_qheight)
      {
        cout << "Padding issue at line " << i << endl;
        cout << "  src:    " << src_rotated_origin << endl;
        cout << "  test:   " << test << endl;
        cout << "  q dim:  " << src_qwidth << " x " << src_qheight << endl;
        cout << "  " << padding_table[i] << " x " << qdx << endl;
        cout << "  x diff = " << src_rotated_origin.x - src_qwidth + 1 << endl;
        cout << "  x coef = " << (float) (src_rotated_origin.x - src_qwidth + 1) / (float) (-qdx.x) << endl;
        abort();
      }
    }

    src_rotated_origin += qdy;
  }

  return padding_table;
}

uint16_t* generate_padding_table_back_q(Image const& rotated,
                                        Point src_rotated_origin,
                                        Point const& qdx,
                                        Point const& qdy,
                                        int src_qwidth,
                                        int src_qheight,
                                        uint16_t const* front_padding)
{
  uint16_t* padding_table = new uint16_t[rotated.height];
  // We suppose the image is square.
  if (qdx.x == 0 || qdx.y == 0)
  {
    memset(padding_table, 0, sizeof (uint16_t) * rotated.height);
    return padding_table;
  }

  src_rotated_origin.x = (rotated.width - 1) * qdx.x;
  src_rotated_origin.y = (rotated.width - 1) * qdx.y;

  for (unsigned int i = 0; i < rotated.height; ++i)
  {
    int y_range = 0;
    if (src_rotated_origin.y < 0)
    {
      y_range = ceil((-src_rotated_origin.y) / (float) qdx.y);
    }
    else if (src_rotated_origin.y >= src_qheight)
    {
      y_range = ceil((float) (src_rotated_origin.y - src_qheight + 1) / (float) (qdx.y));
    }
    if (y_range < 0)
    {
      cout << "Negative back Y range at line " << i << endl;
      abort();
    }

    int x_range = 0;
    if (src_rotated_origin.x < 0)
    {
      x_range = ceil((-src_rotated_origin.x) / (float) qdx.x);
    }
    else if (src_rotated_origin.x >= src_qwidth)
    {
      x_range = ceil((float) (src_rotated_origin.x - src_qwidth + 1) / abs(qdx.x));
    }
    if (x_range < 0)
    {
      cout << "Negative back X range at line " << i << endl;
      cout << "  src origin: " << src_rotated_origin << endl;
      cout << "  q dim:      " << src_qwidth << " x " << src_qheight << endl;
      abort();
    }

    padding_table[i] = max(x_range, y_range);

    {
      Point test(src_rotated_origin.x - padding_table[i] * qdx.x,
                 src_rotated_origin.y - padding_table[i] * qdx.y);
      if (test.x < 0 || test.y < 0
         || test.x >= src_qwidth || test.y >= src_qheight)
      {
        padding_table[i] = rotated.width - front_padding[i];
//        cout << "Back padding issue at line " << i << endl;
//        cout << "  src origin: " << src_rotated_origin << endl;
//        cout << "  test:       " << test << endl;
//        cout << "  q dim:      " << src_qwidth << " x " << src_qheight << endl;
//        cout << "  " << padding_table[i] << " x " << qdx << endl;
//        cout << "  X range     " << x_range << endl;
//        cout << "  Y range     " << y_range << endl;
//        cout << "    height diff = " << src_rotated_origin.y - src_qheight + 1 << endl;
//        cout << "    coef = " << (float) (src_rotated_origin.y - src_qheight + 1) / (float) qdx.y << endl;
//        abort();
      }
    }

    src_rotated_origin += qdy;
  }

  return padding_table;
}

void print_padding_table(uint16_t const* padding_table,
                         uint16_t const* border_table,
                         Image const& image)
{
  cout << "Padding table:" << endl;

  for (unsigned int i = 0; i < image.height; ++i)
  {
    int left_padding = padding_table[i];
    int left_border = border_table[i];
    int right_padding = padding_table[image.height - 1 - i];
    int right_border = border_table[image.height - 1 - i];
    int core_pixels = image.width - left_padding - right_padding - left_border - right_border;

    if (core_pixels < 0)
    {
      cout << "Too much padding + border at line " << i << endl;
      cout << "  left padding  = " << left_padding << endl;
      cout << "  left border   = " << left_border << endl;
      cout << "  right border  = " << right_border << endl;
      cout << "  right padding = " << right_padding << endl;
      cout << "  total         = " << left_padding + left_border + right_border + right_padding << endl;
      cout << "  width         = " << image.width << endl;
      abort();
    }

    cout << "  " << i << " [";
    for (int j = 0; j < left_padding; ++j)
      cout << " ";
    for (int j = 0; j < left_border; ++j)
      cout << ".";
    for (int j = 0; j < core_pixels; ++j)
      cout << "x";
    for (int j = 0; j < right_border; ++j)
      cout << ".";
    for (int j = 0; j < right_padding; ++j)
      cout << " ";
    cout << "]" << endl;
  }
}



//
//
// Border
//

uint16_t* generate_border_table(uint16_t const* padding_table, Image const& image)
{
  uint16_t* border_table = new uint16_t[image.height];
  if (image.width - padding_table[0] - padding_table[image.height - 1] == 0)
  {
    cout << "No room for top border" << endl;
    border_table[0] = 0;
  }
  else
    border_table[0] = 1;

  for (unsigned int i = 1; i < image.height - 1; ++i)
  {
    if (padding_table[i] == padding_table[i - 1])
    {
      border_table[i] = 1;
    }
    else
    {
      if (padding_table[i - 1] > padding_table[i])
      {
        border_table[i] = padding_table[i - 1] - padding_table[i] + 1;
      }
      else
      {
        border_table[i - 1] = padding_table[i] - padding_table[i - 1] + 1;
        border_table[i] = 1;
      }
    }
  }

  // Check that we don't add too much border
  for (unsigned int i = 1; i < image.height - 1; ++i)
  {
    if (padding_table[i] + border_table[i]
      + padding_table[image.height - 1 - i] + border_table[image.height - 1 - i]
      > (int) image.width)
    {
      cout << "Too much border!" << endl;
      cout << "  border[" << i << "]: " << border_table[i] << endl;
      cout << "  border[" << image.height - 1 - i << "]: " << border_table[image.height - 1 - i] << endl;
      if (border_table[i] > border_table[image.height - 1 - i])
        border_table[i] -= 1;
      else
        border_table[image.height - 1 - i] -= 1;
    }
  }

  border_table[image.height - 1] = image.width - padding_table[0] - padding_table[image.height - 1] - border_table[0];
  if (border_table[image.height - 1] > image.width)
  {
    cout << "That shit cray" << endl;
    cout << "  width = " << image.width << endl;
    cout << "  left padding = " << padding_table[0] << endl;
    cout << "  left border = " << border_table[0] << endl;
    cout << "  right border = " << border_table[image.height - 1] << endl;
    cout << "  right padding = " << padding_table[image.height - 1] << endl;
    cout << "  ~ " << image.width << endl;
    cout << "  ~ " << image.width - padding_table[0] << endl;
    cout << "  ~ " << image.width - padding_table[0] - padding_table[image.height - 1] << endl;
    cout << "  ~ " << image.width - padding_table[0] - padding_table[image.height - 1] - border_table[0] << endl;
  }

  return border_table;
}



//
//
// Image rotation
//

inline
void rotate_pixel(Image const& src,
                  Point const& src_rotated_point,
                  pvalue_t* rotate_buffer, unsigned int rot_index,
                  int q_pow)
{
  // Quantize on a 8x8 grid
  int const q_inter_pow = 3;
  int const q_inter = 1 << q_inter_pow;
  int const mask = 0x07;

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

  // Bilinear interpolation
  unsigned int const src_index_1 = (src_y * src.width + src_x) * src.pixel_size;
  unsigned int const src_index_2 = src_index_1 + src.pixel_size;
  unsigned int const src_index_3 = src_index_1 + src.pixel_size * src.width;
  unsigned int const src_index_4 = src_index_3 + src.pixel_size;

  pvalue_t const src_tl = src.buffer[src_index_1];
  pvalue_t const src_tr = src.buffer[src_index_2];
  pvalue_t const src_bl = src.buffer[src_index_3];
  pvalue_t const src_br = src.buffer[src_index_4];

  unsigned int const x_delta = (src_rotated_point.x >> (q_pow - q_inter_pow)) & mask;
  unsigned int const y_delta = (src_rotated_point.y >> (q_pow - q_inter_pow)) & mask;
  unsigned int const inv_x = q_inter - x_delta;
  unsigned int const inv_y = q_inter - y_delta;

#ifndef SIMD

  pvalue_t interpolated = ((src_tl * inv_x + src_tr * x_delta) * inv_y
                         + (src_bl * inv_x + src_br * x_delta) * y_delta) >> (q_inter_pow << 1);
  rotate_buffer[rot_index] = interpolated;
  // 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;

#else

  // X-axis
  __m128i top = _mm_loadu_si128((__m128i*) &src.buffer[src_index_1]);
  __m128i bottom = _mm_loadu_si128((__m128i*) &src.buffer[src_index_3]);
  __m128i coef = _mm_set_epi16(x_delta, x_delta, x_delta, x_delta, inv_x, inv_x, inv_x, inv_x);
  top = _mm_mullo_epi16(top, coef);
  bottom = _mm_mullo_epi16(bottom, coef);

  // Y-axis
  coef = _mm_set1_epi16(inv_y);
  top = _mm_mullo_epi16(top, coef);
  coef = _mm_set1_epi16(y_delta);
  bottom = _mm_mullo_epi16(bottom, coef);
  top = _mm_add_epi16(top, bottom);

  top = _mm_srli_epi16(top, 2 * q_pow);

  rotate_buffer[rot_index] = _mm_extract_epi16(top, 0) + _mm_extract_epi16(top, 4);
  // rotate_buffer[rot_index + 1] = _mm_extract_epi16(top, 1) + _mm_extract_epi16(top, 5);
  // rotate_buffer[rot_index + 2] = _mm_extract_epi16(top, 2) + _mm_extract_epi16(top, 6);


#endif // ! SIMD
}

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, src.type);

  DPoint const src_origin = get_mapped_point(*rotated, Point(0, 0), -rotation);
  DPoint src_delta_x = get_mapped_point(*rotated, Point(src.width, 0), -rotation);
  DPoint src_delta_y = get_mapped_point(*rotated, Point(0, src.height), -rotation);
  src_delta_x -= src_origin;
  src_delta_y -= src_origin;

  // Quantized position on a grid
  int const q_pos_pow = 10;
  int const q_pos = 1 << q_pos_pow;

  // TODO: we could have only one delta and deduce the other one
  Point const qdx(ceil(src_delta_x.x * q_pos / src.width), ceil(src_delta_x.y * q_pos / src.width));
  Point const qdy(ceil(src_delta_y.x * q_pos / src.height), ceil(src_delta_y.y * q_pos / src.height));

  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;
  pvalue_t* buffer = rotated->buffer;

  int const width = rotated->width;
  int const height = rotated->height;
  int const& src_qwidth = src.width * q_pos;
  int const& src_qheight = src.height * q_pos;

  Point src_rotated_origin(rot_origin_in_src.x * q_pos,
                           rot_origin_in_src.y * q_pos);
  // Padding
  uint16_t* padding_table = generate_padding_table(*rotated, src_rotated_origin,
                                                   qdx, qdy,
                                                   src_qwidth, src_qheight);
 // uint16_t* back_padding_table = generate_padding_table_back_q(*rotated, src_rotated_origin,
 //                                                              qdx, qdy,
 //                                                              src_qwidth, src_qheight,
 //                                                              padding_table);
  //uint16_t* border_table = generate_border_table(padding_table, *rotated);
  //print_padding_table(padding_table, border_table, *rotated);

  for (int y = 0; y < height; ++y)
  {

    // TODO: compact these structure to increase locality
    int const left_padding = padding_table[y];
    int const left_border = 0;
    int const right_padding = 0;
    int const right_border = padding_table[height - 1 - y];
    int const core_pixels = width - left_padding - left_border - right_border - right_padding;

    // Left padding
    for (int x = 0; x < left_padding; ++x, ++buffer_index)
    {
      // Set to black value
      // TODO: memset
      buffer[buffer_index] = 50;
    }

    // Border
    for (int x = 0; x < left_border; ++x, ++buffer_index)
    {
      buffer[buffer_index] = 0; // TODO: handle border
    }

    Point src_rotated_point(src_rotated_origin.x + (left_padding + left_border) * qdx.x,
                            src_rotated_origin.y + (left_padding + left_border) * qdx.y);

    // Body
    for (int x = 0; x < core_pixels; ++x, ++buffer_index)
    {
      if (src_rotated_point.x < 0 || src_rotated_point.y < 0
          || src_rotated_point.x >= src_qwidth || src_rotated_point.y >= src_qheight)
      {
        LOG << "Out-of-bounds point!" << endl;
//        cout << "  x: " << x << endl;
//        cout << "  src_rotated_point: " << src_rotated_point << endl;
//        cout << "  qdx: " << qdx << endl;
//        cout << "  q_pos: " << q_pos << endl;
//        cout << "  rotated point: (" << x + left_padding + left_border << ", " << y << ")" << endl;
//        cout << "  src point: (" << (src_rotated_point.x >> q_pos_pow) << ", " << (src_rotated_point.y >> q_pos_pow) << ")" << endl;
//        cout << "  src point: (" << (src_rotated_point.x / q_pos) << ", " << (src_rotated_point.y / q_pos) << ")" << endl;
//        cout << "  width: " << width << endl;
//        cout << "  left padding: " << left_padding << endl;
//        cout << "   left border: " << left_border << endl;
//        cout << "    core pixels: " << core_pixels << endl;
//        cout << "   right border: " << right_border << endl;
//        cout << "  right padding: " << right_padding << endl;
        buffer[buffer_index] = 255;
      }
      else
      {
        rotate_pixel(src, src_rotated_point, buffer, buffer_index, q_pos_pow);
      }

      src_rotated_point += qdx;
    }

    // Border
    for (int x = 0; x < right_border; ++x, ++buffer_index)
    {
      buffer[buffer_index] = 0; // TODO: handle border
      src_rotated_point += qdx;
    }

    // Right padding
    for (int x = 0; x < right_padding; ++x, ++buffer_index)
    {
      // Set to black value
      // TODO: memset
      buffer[buffer_index] = 100;
    }

    src_rotated_origin += qdy;
  }
//  cout << endl;

  return rotated;
}



//
//
// Check
//

bool check_points()
{
  Image five(5, 5, pnm::Format::PGM);
  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, pnm::Format::PGM);
  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, pnm::Format::PGM);

  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_00(string const& path)
{
  Image const src(path);
  Image const* rotated = rotate(src, 0);

  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) * rotated->pixel_size;
      unsigned src_index = (y * src.width + x) * src.pixel_size;
      if (memcmp(&rotated->buffer[rot_index], &src.buffer[src_index], src.pixel_size * sizeof (pvalue_t)) != 0)
      {
        Point r(x, y);
        Point s(x, y);
        LOG << "R" << r << " != S" << s << endl;
        LOG << "R: " << rot_index << " != S: " << src_index << endl;
        LOG << rotated->buffer[rot_index] << " != " << src.buffer[src_index] << endl;
        LOG << "R dim: " << rotated->width << " x " << rotated->height << endl;
        LOG << "S dim: " << src.width << " x " << src.height << endl;
        return false;
      }
    }
  }

  delete rotated;

  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) * rotated->pixel_size;
      unsigned src_index = (x * src.width + (src.width - 1 - y)) * src.pixel_size;
      if (memcmp(&rotated->buffer[rot_index], &src.buffer[src_index], src.pixel_size * sizeof (pvalue_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 << ".pnm";

    return filename.str();
}

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

  bool perform_check = true;

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

    if (!check_trigo())
      return 1;

    if (!check_00(argv[1]))
    {
      ERRLOG << "0 degree check failed" << endl << endl;
      return 1;
    }

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

  double const step = 5;
  bool save_output_img = true;
  bool print_each_run = true;

  // No tile
  Image img(argv[1]);
  float average = 0.0;
  int i = 0;
  for (double rotation = 0; rotation < 360; rotation += step)
  {
    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();

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

    if (save_output_img)
      rotated->save(get_save_path("rotated", rotation));

    delete rotated;
    ++i;
  }
  cout << "---------" << endl;
  cout << " average: " << average / i << "ms" << endl << endl;

  return 0;
}