// integral image split in 2 vertical stripes so creation is 2-parallel

final sclass BWIntegralImage_twoParts implements MakesBufferedImage, IBWIntegralImage {

  int w, h, th;

  IBWIntegralImage top, bottom;

  *() {}

  *(File f) { this(loadImage2(f)); }

  *(MakesBufferedImage img) { this(toBufferedImage(img)); }

  *(BufferedImage image) {

    this(image, (img, idx) -> BWIntegralImage(img));

  }

  *(BufferedImage image, IF2<BufferedImage, Int, IBWIntegralImage> makeSubImage) {

    this(null, image, makeSubImage);

  }

  *(ThreadPoolExecutor executor, BufferedImage image, IF2<BufferedImage, Int, IBWIntegralImage> makeSubImage) ctex {

    w = image.getWidth();

    h = image.getHeight();

    th = (h+1)/2;

    L<IBWIntegralImage> l = parallelEval(executor,

      () -> makeSubImage.get(virtualClipBufferedImage(image, 0, 0, w, th), 0),

      () -> h <= th ? null : makeSubImage.get(virtualClipBufferedImage(image, 0, th, w, h-th), 1)

    );

    top = first(l);

    bottom = second(l);

  }

  public int getIIValue(int x, int y) {

    ret y < th ? top.getIIValue(x, y)

      : top.getIIValue(x, th-1) + bottom.getIIValue(x, y-th);

  }

  // optimization over default method

  public int getPixelSum(int x1, int y1, int x2, int y2) {

    if (y2 <= th)

      ret top.getPixelSum(x1, y1, x2, y2);

    if (y1 >= th)

      ret bottom.getPixelSum(x1, y1-th, x2, y2-th);

    // rectangle straddles top and bottom stripe

    //ret bwIntegralImage_sumRect(this, x1, y1, x2, y2);

    int topLeft     = top.getIIValue(x1-1, y1-1);

    int topRight    = top.getIIValue(x2-1, y1-1);

    int mediumLeft  = top.getIIValue(x1-1, th-1);

    int mediumRight = top.getIIValue(x2-1, th-1);

    int bottomLeft  = bottom.getIIValue(x1-1, y2-th-1);

    int bottomRight = bottom.getIIValue(x2-1, y2-th-1);

    ret bottomRight-bottomLeft+mediumRight-mediumLeft+topLeft-topRight;

  }

  public int getWidth() { ret w; }

  public int getHeight() { ret h; }

}