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How is it 2X lower arithmetic intensity than 2D blur? I thought N times lower arithmetic intensity.


I think the lower arithmetic intensity has to do with the memory accesses vs work. Although the amount of work is less, there are more memory accesses due to the extra storage.


Some costs we had to pay in order to get this lower arithmetic intensity include having to allocate an extra image, which may not be trivial depending on the size of the image, and increasing the amount of bandwidth we need. Now we need to load the input, write to tmp, read the tmp, and write the output, whereas before, we only needed to load the input image and write the output image. This could possibly have made the program bandwidth bound, and it's also using a lot more energy because of the reads and writes.

1_1 This is a good read and looks at the example of this two-stage blur algorithm.