lossless TryFrom<f{32,64}> implementations for f16 and bf16

[Robbepop]

Would it be possible to introduce lossless TryFrom implementations for bf16 and f16 types from Rust primitive f32 and f64 types so that for example f16::try_from(value).map(f16::to_f32) is either Err or Ok(value2) with value == value2 for all possible values?

This means that if TryFrom is Ok the conversion was lossless and it is possible to fully recover the f32 or f64 value later on if no mutations happen in between. If TryFrom yields Err then it is not possible to losslessly convert the particular f32 or f64 value. No rounding shall take place.

I actually need this if this can be implemented efficiently. :)