f16_add(0x0001, 0x0801) => 0x0801
gcc 12.2 same calculations in _Float16 shows 0x0802

If nothing else it would probably be more appropriate to use int16_t instead of short. But even that should only be used internally IMHO. I think you should create your own type so it's clearer to people reading code using the API what is going on.

A simple typedef to int16_t would be an improvement, but I think a better solution would be something like typedef struct { int16_t val; } foo_float16; since it would trigger an error if people try to use arithmetic operators (+, -, *, /, etc.).

That said, some compilers have at least some support for 16-bit floats. Clang 6+ and GCC 4.5+ for starters. It would be nice if you could take advantage of that where available.

I'd also suggest you be careful about the name. float16_t is already taken by NEON, for example. Putting everything in a namespace would be an easy solution, but unfortunately calling the library "float16" is somewhat limiting there. FWIW, I probably would have been tempted to use something falcon-themed as a joke about the F-16 airplane. f16_t, maybe?

It would be nice to be able to convert to/from standard floats. Generically if possible, but at least if the system is using IEEE 754 (__STDC_IEC_559__ should be defined, though TBH I wouldn't be surprised if an MSVC exception is necessary).

FWIW, I'm considering this as a way to implement the float16_t stuff in NEON portably in SIMDe. I'm going to open a couple more issues, I just wanted you to understand the perspective I'm looking at it from since you seem to be focused on retrocomputing and so probably have different things in mind. If you're not interested in supporting my use case that's fine; please feel free to just close the issues if that's the case.

See https://gcc.gnu.org/onlinedocs/gcc/Common-Function-Attributes.html#index-const-function-attribute for documentation.

It's not really just GCC, several compilers support it… it would be great you supported at least clang, too, but if you want to just use the macro from Hedley that would be best IMHO. That said, I'm the sick bastard who wrote Hedley so obviously I'm biased.

These are useful, please expose them.

Since it would be better not to leak implementation details, I'd suggest that instead of macros you use f16_isnan and f16_isinf functions to match the standard C functions. It might also be nice to have f16_fpclassify and f16_isnormal too.