Summed Area Table AKA Integral Image
It precomputes sums of all rows and columns in a 2d array for fast O(1)
querying of sums of areas within it.
It does this:
let mut sum = 0;
for row in y1..y2
but faster:
// precompute
let s = new;
// now it's fast:
let sum = s.sum_range;