For integers it really doesn’t exist. An algorithm for multiplying an integer with -1 is: Invert all bits and add 1 to the right-most bit. You can do that for 0 of course, it won’t hurt.
There are probably a lot of scientific applications (e.g. statistics, audio, 3D graphics) where exponential notation is the norm and there’s an understanding about precision and significant digits/bits. It’s a space where fixed-point would absolutely destroy performance, because you’d need as many bits as required to store your largest terms. Yes, NaN and negative zero are utter disasters in the corners of the IEEE spec, but so is trying to do math with 256bit integers.
For a practical explanation about how stark a difference this is, the PlayStation (one) uses an integer z-buffer (“fixed point”). This is responsible for the vertex popping/warping that the platform is known for. Floating-point z-buffers became the norm almost immediately after the console’s launch, and we’ve used them ever since.
What’s the problem with -0?
It conceptually makes sense for to negativ values to close to 0 to be represented as -0.
In practice I have never seen a problem with -0.
On NaN: While its use cases can nowadays be replaced with language constructs like result types, it was created before exceptions or sum types. The way it propagates kind of mirrors Haskells monadic Maybe.
We should be demanding more and better wrapper types from our language/standard library designers.
Obviously floating point is of huge benefit for many audio dsp calculations, from my observations (non-programmer, just long time DAW user, from back in the day when fixed point with relatively low accumulators was often what we had to work with, versus now when 64bit floating point for processing happens more as the rule) - e.g. fixed point equalizers can potentially lead to dc offset in the results. I don’t think peeps would be getting as close to modeling non-linear behavior of analog processors with just fixed point math either.
Audio, like a lot of physical systems, involve logarithmic scales, which is where floating-point shines. Problem is, all the other physical systems, which are not logarithmic, only get to eat the scraps left over by IEEE 754. Floating point is a scam!
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