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Comment by HPsquared | Hacker News Reader

Is there any advantage to doing it this way? Partitioning?

I’m not making claims about production graphics algorithms, but this gets really interesting if you consider using quad trees to represent images rather than bitmaps.

The algorithm as presented turns the image into a quadtree as it works, for then re-flattens it. But if we store the image as a quadtree to begin with, we obtain other advantages:

1. We can memoize operations like rotation so that the algorithm goes much faster for images that have large blocks of a single colour or pattern;

2. We can write other operations that recursively apply to the image, like changing one color to another.

http://raganwald.com/2016/12/27/recursive-data-structures.ht...

Original discussion:

https://news.ycombinator.com/item?id=13304487

I wouldn't do it exactly this way, but for a CPU implementation I would consider a blocked rotate that decomposes the image into square tiles of about [cache-line x cache-line] in size (e.g., 8x8 for RGBA8 data with a 32 byte cache line). Then cycle sets of four tiles and rotate within them in the process. E.g., cycle and rotate the four A tiles, cycle and rotate the four B tiles, etc:

    A B C D M I E A
    E F G H N J F B
    I J K L O K G C
    M N O P P L H D
    D H L P P O N M
    C G K O L K J I
    B F J N H G F E
    A E I M D C B A

With the right tile sizes and memory alignment you could parallelize these steps without false sharing.

It's easy to parallelize this, and at a certain recursion level the whole block will fit into cache, so this might avoid inefficient memory access compared to a naive for-loop that just moves every pixel to its rotated position.

Except you need to access each pixel log(n) times and it doesn’t obviously work for non-square images (or for non-right rotations).

Compare to the normal way you rotate things by right angles where e.g. new_image(x,y) = old_image(y, old_height - x), which is extremely embarrassingly parallel.

The actual reason is that it is fun.

> new_image(x,y) = old_image(y, old_height - x)

If you implement this as a view (rather than imperatively), you can get the compiler to optimize out four successive rotations to nothing :)

https://blog.cy.md/2014/03/21/functional-image-processing-in...

I assume that in an actual implementation you are not really processing every pixel log(n) times, but rather do something like new_image = rotate(old_image, 1), where 1 is the recursion level, and rotate(image, level) calls rotate(subset_of(image), level + 1) recursively until it reaches a single pixel, which is then returned as-is. Combined with return value optimization, that should avoid any temporaries being stored.

But yes, it's mostly fun :)

In that world doesn’t it just compile to the thing I wrote above (if you’re lucky)? In the GP you said it would be more cache-efficient or something but that’s just not true if it compiles to the same code is it?

No, the order in which things happen would be different, and this is what might make it more cache-efficient for rotating large images. It should look like this: https://en.wikipedia.org/wiki/Z-order_curve

I’m really confused by what you mean. If you’re not executing the line I wrote above (in parallel) then what are you doing? The things I could think you meant were:

- moving data in stages like the OP video which might be better for the cache (I don’t believe this) but would require writing to/from me more multiple times per pixel which I think would make it slower

- Accessing memory in a certain order when doing this on a cpu. Certainly that is a reasonable thing to expect to improve performance (roughly breaking the image into blocks that fit exactly into N cache lines, rotating in registers/memory, then writing into exactly N cache lines means you aren’t reading data from RAM/cache that you can’t use), but I don’t think that is related to the recursive process described in the article, unless you mean that you can use this process to get some operations like block(x,y,16) moves to block(s,t,16) and those could be executed cache-efficiently? But then this recursive method is more confusing and more restrictive on the image size than the thing I tried to describe at the start of this bullet point

Not really. It requires far too many memory accesses to be efficient.

No lookup tables

No rotate-by-ninety-degree algorithms use lookup tables.

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