Does CSIS (Canada) perform an equivalent function to that of both the American CIA and NSA?
No, CSIS is only responsible for domestic intelligence concerns. The CIA takes care of foreign intelligence, whereas I believe the NSA is responsible for signal intelligence. Canada has no government agency for foreign intelligence. Officially, anyway. And probably unofficially, too, but who knows what the spooks do when no one’s watching them.
I was unaware that CSIS had any function at all, actually. 
CSE takes care of foreign sigint.
Right, I forgot about them. But no Canadian agency for human intelligence exists, anyway.
As Gest noted above, the CSE takes care of the NSA gig, doing difficult electronic stuff.
CSIS, having had a disc full of plaintext intelligence information (which included names of informants) found in a phone booth by a random civillian and having had a senior official leave classified documents in the trunk of her car to be stolen while she was attending a hockey game, takes care of the role of the CIA: scaring the living crap out of the people they’re protecting.
Roughly:
CSE = NSA
CSIS = CIA
RCMP = FBI
DND also does a lot of the human intelligence.