A lack of arbitrary precision makes GPUs unsuitable for deeper Mandelbrot zoom levels, so "solved" is overstating it.
I agree the worse floating point precision of GPUs puts them at a disadvantage but they still do better for massively parallel problems like fractal renders. (http://www.bealto.com/mp-mandelbrot_benchmarks.html)
Most GPUs can, at reduced speed, do double precision, which is 53 bits.
The maximum precision for this zoom movie is 960 bits.
So, unless you write code to compose high-precision math operations out of double-precision math then the GPU cannot even participate. And once you do that you will find that the GPU's speed advantage is mostly or entirely lost.
That means that GPUs are not very good at doing high-precision math. They lose a lot more efficiency implementing high-precision math than CPUs do. And GPUs are also worse at doing parallel calculations that end up following different paths, which inevitably happens when one pixel diverges before another.
My back-of-the-envelope estimates show that GPUs are not worth it for this use-case. I will change my mind when I see a GPU-based deep zoom fractal program.
And you can do add-with-carry manually on the AMD GPU using two instructions: ADDC_UINT to get the carry flag from an addition followed by ADD_PREV to add it.
It would be interesting to see how well a GPU can do compared to a CPU. Doing 64-bit math gives an automatic four-to-one advantage (it takes four 32x32 multiplies to replicate a single 64x64 multiply) so the GPU would be starting out at a disadvantage, plus GPUs run at lower clock rates and have other disadvantages, but perhaps their many many cores would be enough to overcome this.