Total wattage means very little when it comes to PSUs. It all depends on the +12V rail(s) of the PSU. That is the rail that powers all the heavy load devices. Older and cheaper PSUs used to put all the load capacity on the other voltage rails.
Normall, the HD-7870 would require a 500W PSU. But there again, it depends on the +12V rail's amps and total watts.