I'd like to extend my skill set into GPU computing. I am familiar with raytracing and realtime graphics(OpenGL), but the next generation of graphics and high performance computing seems to be in GPU computing or something like it.
I currently use an AMD HD 7870 graphics card on my home computer. Could I write CUDA code for this? (my intuition is no, but since Nvidia released the compiler binaries I might be wrong).
A second more general question is, Where do I start with GPU computing? I'm certain this is an often asked question, but the best I saw was from 08' and I figure the field has changed quite a bit since then.
Nope, you can't use CUDA for that. CUDA is limited to NVIDIA hardware. OpenCL would be the best alternative.
Khronos itself has a list of resources. As does the StreamComputing.eu website. For your AMD specific resources, you might want to have a look at AMD's APP SDK page.
Note that at this time there are several initiatives to translate/cross-compile CUDA to different languages and APIs. One such an example is HIP. Note however that this still does not mean that CUDA runs on AMD GPUs.