It's not quite as bad as it sounds, because the only difference is that the representation of NaN (the sign and the payload bits) isn't guaranteed to be stable. If you're not relying on any specific representation of NaN, then floating-point math in const fn is identical, and observed differences would be considered a soundness bug in the Rust compiler.
I had to look this up because it is a while that I tried to use floating point math in a const fn and it seems that the differences you described have been decided to be acceptable.
Oh, nice. Sometime I find it really hard to track the status of new Rust features. For example the tracking issue I linked is still open with "Stabilize" missing.
what happens if you compile on a system that has a different precision than the system you run on? like suppose you compile on a 64 bit system targetting 32 bit embedded with an fp accelerator or a 16 bit system with softfloat?
I'm not personally familiar with the implementation, but Rust's const fn is evaluated using an interpreter called MIRI with its own softfloat implementation, and therefore isn't limited by the precision of the host platform. The act of cross-compilation shouldn't pose a problem, and would be a soundness issue in the compiler if it did.
As long as the target is compliant with IEEE 754, which is what Rust expects, it shouldn't be an issue. The only platform that I know of that causes problems is extremely old pre-SSE 32-bit x86, where floats sometimes have 80-bit precision and which can't be worked around because of LLVM limitations which nobody's going to fix because the target is so obscure. Rust will probably just end up deprecating that target and replacing it with a softfloat equivalent.
Last time I checked the float functions that have no bit-identical results (mostly transcendental functions) were missing from Rust's const fn for exactly that reason.