Question for those with cats?

I don't know if this is an okay topic to post on an app like this but recently we adopted a 2 year old cat who basically wags his tail like a dog. All the time. Even when no one is near him. I know that's not usually a good sign when a cat has his tail going, so I was wondering what could be the problem. He'll be purring when he does it sometimes too. Other times hell do it really fast like when someone gets too close to him, which is when I KNOW he's angry cause hell swat right after. The few times he isn't wagging his tail is when he's in a deep sleep or really sitting down, but I would say it's about 3% of the time he isn't wagging it a bit. But the usual tail wagging is kind of slow or medium paced, no matter where he is or what he's doing. Is this normal?