Which compiler are you using where std::isinf breaks? Hopefully it was also clear that my experience leans toward CUDA, and I think the inf & nan support works there in the presence of NVCC’s fast-math.
Even if I don't care about the accuracy differences, I still need a way to check for invalid input data. The upshot is that I had to roll my own isnan and isinf to be able to use -Ofast (because it's actually the underlying __builtin_xxx intrinsics that are broken), which still seems wrong to me.