-- cumsum xs:L n > L n — running-sum list. Output length matches input.
--
-- The classic trick: a window-k moving sum over xs can be computed in
-- O(n) by taking differences of cumsum at offsets k apart. Dividing by k
-- gives the moving average. Below we show the running-sum directly, and
-- a window-2 moving sum computed from cumsum differences.
-- Basic running sum
running>L n;cumsum [1, 2, 3, 4]
-- Empty input → empty output
empty>L n;cumsum []
-- Window-2 moving sum via cumsum diff: pairs of adjacent xs summed.
-- xs = [10, 20, 30, 40]; cumsum = [10, 30, 60, 100]
-- window-2 sums = [30, 50, 70] = [cs[1], cs[2]-cs[0], cs[3]-cs[1]]
pairsum>L n;xs=[10, 20, 30, 40];cs=cumsum xs;a=at cs 1;b=-(at cs 2) (at cs 0);c=-(at cs 3) (at cs 1);[a, b, c]
-- run: running
-- out: [1, 3, 6, 10]
-- run: empty
-- out: []
-- run: pairsum
-- out: [30, 50, 70]