> Another one is that single precision floating point doesn't have enough precision to represent both planet scale and human scale in the same coordinate system (let alone solar system scale or galaxy scale), yet GPUs don't support double precision well.
Could you do double-single computations on a GPU? (By that I mean something like double-double arithmetic, only with two singles instead of two doubles.)
Sure, with a performance penalty. Some GPUs do support double precision, though again at a performance penalty. You might run into issues with the fixed function parts of the GPU being single precision even on GPUs that support double precision types in shaders, depending on how you do things. Also, shading languages probably don't have nice libraries for double single precision so you'd have to roll your own, and probably without niceties like operator overloading.
It's not required for space rendering, as once everything is in camera coordinates you no longer have any visible precision issues (as long as you are using a float reverse Z buffer). You just have to be careful to make sure your world to camera transforms are done on the CPU, and you break large objects like planets into small LOD chunks with their own local coordinate systems, which you need to do anyway.
If I recall correctly, on a CPU, the penalty of doing "double-X" is something like 1:7 or so compared to just doing X. On most consumer GPUs, the penalty of doing doubles instead of singles would be a 1:24 or 1:32 these days, wouldn't it? So there should still be a fourfold speedup or so. Mixed binary operations with one single and one double-single should be cheaper, whenever applicable.
As for "rolling your own", this is a compiler transformation, effectively. So it may depend on your workflow whether it's painful or not.
Could you do double-single computations on a GPU? (By that I mean something like double-double arithmetic, only with two singles instead of two doubles.)