FWIW, well-implemented round-to-nearest conversion routines (e.g. Python and IIRC Glibc, although MSVC is historically bad about this) will roundtrip IEEE>decimal>IEEE if you use the correct number of digits (at least 9 for singles and 17 for doubles), for reasons of mathematics and not implementation. (The other way around also works, barring exponent under- and overflow, but for at most 6 and 15 digits respectively, so I wouldn’t call bijective, strictly speaking.)
The conversions are not even that hard ... unless you want to deal with arbitrary (and arbitrarily long) decimal representations and not just those that arise from IEEE numbers. Essentially the only choice to make is whether the conversion to decimal will emit all the digits all the time (simpler) or the shortest number of digits that will round to the requested IEEE float when read back (less liable to be mocked in webcomics[1]).
Of course, using hex floats is much simpler than even the simplest implementation of the above; I just want to point out that IEEE floats are perfectly roundtrippable through decimal.
The conversions are not even that hard ... unless you want to deal with arbitrary (and arbitrarily long) decimal representations and not just those that arise from IEEE numbers. Essentially the only choice to make is whether the conversion to decimal will emit all the digits all the time (simpler) or the shortest number of digits that will round to the requested IEEE float when read back (less liable to be mocked in webcomics[1]).
Of course, using hex floats is much simpler than even the simplest implementation of the above; I just want to point out that IEEE floats are perfectly roundtrippable through decimal.
[1] https://www.smbc-comics.com/comic/2013-06-05