[flohofwoe]

There's actually a better solution if you allow the compiler some wiggle room:

Zig and C23 (and probably a couple other languages) support arbitrary width integers, so integer types like u15, i3, i1 or even u512 etc... are something entirely 'normal', and even useful in day-to-day coding when mixing signed and unsigned integer math (for instance Zig disallows to assign an unsigned integer to a signed integer of the same width, but it's perfectly fine to assign a 7-bit unsigned integer to an 8-bit signed integer).

Down on the CPU such operations happen on the register width, and if the integer width exceeds the register width, are unrolled into a chain of op-with-carry instructions (same way we did 16- or 32-bit math back on 8-bit processors).