At first, there is 16 fetches per row x column, 1024 in total. Then, it is observed that an input row needs to be fetched only once per output row, reducing the amount to 8 fetches per row, plus 8 per row x column, 8 * 8 + 8 * 64 = 576 in total. This requires the same amount of 16 numbers to be kept in registers.
But then it is claimed that by doing one quadrant at a time, all that is needed is 64 fetches per quadrant or 256 fetches in total. But that assumes we can keep 4 rows and 4 columns, 8 numbers per row or column = 64 numbers in registers! If we can only keep 16 numbers like above, each row of the quadrant is going to take 40 fetches, and we get 160 fetches per quadrant or 640 fetches in total, a pessimization from 576 fetches!
There is something off with the explanation.
At first, there is 16 fetches per row x column, 1024 in total. Then, it is observed that an input row needs to be fetched only once per output row, reducing the amount to 8 fetches per row, plus 8 per row x column, 8 * 8 + 8 * 64 = 576 in total. This requires the same amount of 16 numbers to be kept in registers.
But then it is claimed that by doing one quadrant at a time, all that is needed is 64 fetches per quadrant or 256 fetches in total. But that assumes we can keep 4 rows and 4 columns, 8 numbers per row or column = 64 numbers in registers! If we can only keep 16 numbers like above, each row of the quadrant is going to take 40 fetches, and we get 160 fetches per quadrant or 640 fetches in total, a pessimization from 576 fetches!
See https://en.wikipedia.org/wiki/Block_matrix#Multiplication