IEEE 754 is what you get if you started with the idea of sign, exponent, and fraction and made the most efficient hardware implementation of it possible. It's not "beautiful", but it falls out pretty straightforwardly from those starting assumptions, even the seemingly weirder parts like -0, subnormals and all the rounding modes. It was not really democratically designed, but done by numerical computing experts coupled with hardware design experts. Every "simplified" implementation of floating point that has appeared (e.g. auto-FTZ mode in vector units) has eventually been dragged kicking and screaming back to the IEEE standard.
Another way to see it is that floating point is the logical extension of fixed point math to log space to deal with numbers across a large orders of magnitude. I don't know if "beautiful" is exactly the right word, but it's an incredibly solid bit of engineering.
I feel like your description comes across as more negative on the design of IEEE-754 floats than you intend. Is there something else you think would have been better? Maybe I’m misreading it.
Maybe the hardware focus can be blamed for the large exponents and small mantissas.
The reasonable only non-IEEE things that comes to mind for me are:
- bfloat16 which just works with the most significant half of a float32.
- log8 which is almost all exponent.
I guess in both cases they are about getting more out of available memory bandwidth and the main operation is f32 + x * y -> f32 (ie multiply and accumulate into f32 result).
Maybe they will be (or already are) incorporated into IEEE standards though
Well, I do know some people who really hate subnormals because they are really slow on Intel and kinda slow on Arm. Subnormals I can see being a pain for graphics HW designers. I for one neither love nor hate IEEE 754, other than -0. I have spent far, far too many hours dealing with it. IMHO, it's an encoding artifact masquerading as a feature.
> what you get if you started with the idea of sign, exponent, and fraction and made the most efficient hardware implementation of it possible. It's not "beautiful", but it falls out pretty straightforwardly from those starting assumptions
This implies a strange way of defining what "beautiful" means in this context.
