Does anyone know a formula we can use for a scan that lets us know when a price crosses a moving average up or down?

I'll use a 20 period simple moving average as an example. Crossing up could be written as follows.

C > AVGC20 AND C1 <= AVGC20.1

Crossing down could be written as follows.

C < AVGC20 AND C1 >= AVGC20.1

Crossing in either direction could be written as either:

(C > AVGC20 AND C1 <= AVGC20.1) OR (C < AVGC20 AND C1 >= AVGC20.1)

Or as:

SGN(C - AVGC20) <> SGN(C1 - AVGC20.1)