I couldn't figure out just now whether to use "swam" or "swum".
Googled around a bit for something authoritative and came up with a page from A semantic approach to English grammar by Robert M W Dixon.
This morning I swam. I have swum today. I swam already. I've already swum. Should have known it'd be that simple, really -- it seems if you use the verb "have" as an auxiliary you use the "swum" form. The technical term for when you use "swum" seems to be the "previous perfective aspect", both in the present ("I have swum") and past ("I had swum") -- otherwise use "swam" (or "swim", but it's obvious when to use that).