Using the latest gcc compiler, do I still have to think about these types of manual loop optimizations, or will the compiler take care of them for me well enough?
Check the generated assembly and see for yourself. See if the computation for the loop-invariant code is being done inside the loop or outside the loop in the assembly code that your compiler generates. If it's failing to do the loop hoisting, do the hoisting yourself.
But as others have said, you should always profile first to find your bottlenecks. Once you've determined that this is in fact a bottleneck, only then should you check to see if the compiler's performing loop hoisting (aka loop-invariant code motion) in the hot spots. If it's not, help it out.