Depending on the model, a 7800 needs about 4 - 6 amps. A 3850 needs about 5 - 7 amps.
Your PSU is an old design with relatively heavy 3.3 and 5 volt rails and a pretty light 12 volt rail. A modern 450 watt PSU should produce at least 30 amps.
need a new PSU.
Replace it. Get something like an Antec EA 380D or Corsair CX 430 V2. Both have 28+ Amps on the 12v rail and is of good build quality while affordable (even more so when on sale).
I would prefer the Antec over the Corsair CX430.
Second, PSU companies are required to have that table showing voltage etc but there is no specific thing that says they have to say. So crappy companies put their MAX
voltage current while good companies put CONTINUOUS voltage current and the certifications and tests that say they're good quality. BIG distinction between those two. Not to mention the wattage doesn't have to come from the 12v line but can also be from the 5v and 3.5v.
In modern systems, the CPU and GPU (the two things that consume the most power) are powered from the 12 volt lines.