26 Jun
2006
26 Jun
'06
10:15 p.m.
On Jun 26, 2006, at 5:41 PM, Schroeppel, Richard wrote:
or Quarter-Squares,
Q(N) = floor[N^2 / 4]
x * y = Q(x+y) - Q(x-y).
The key idea in each case is to use a table that's a function of one variable in a clever way to compute a two-variable result.
Essentially every analog computer ever built uses a quarter-square approach to computing products. It's pretty easy to build analog circuits that square, and quite difficult to do multiply in other ways. I believe even the mechanical servomechanism computers used this approach.