You're missing the other major problem, which is that range is mutually-exclusive with precision. The scientific community discovered a long time ago that exponential notation is the superior way to represent both for very large and very small values because the mantissa is shifted to the place where precision is needed most.
>In 3D modelling/video games, almost certainly not.
A 32-bit integer divided into a 16-bit whole and a 16-bit fraction would be limited to only representing values between -32768 and 32767 while also having worse precision than a 32-bit ieee std754 floating-point at values near 0.
>In accounting software...probably?
Representing money in terms of cents instead of dollars removes the need for real-numbers entirely outside of "Office Space" scenarios where tracking fractions of cents over millions of transactions adds up to tangible amounts of money.
>Across the whole universe of programs: who could say?
Most computer programs don't need real numbers of any sort, and the ones that do need to be written by people who understand basic mathematical concepts like precision.
> A 32-bit integer divided into a 16-bit whole and a 16-bit fraction would be limited to only representing values between -32768 and 32767 while also having worse precision than a 32-bit ieee std754 floating-point at values near 0
...OK? I'm not sure how that relates to my supposition that trigonometric operations are likely to be more common in 3D modelling cases. I'm not arguing for or against any particular representation of numbers therein.
> Representing money in terms of cents instead of dollars removes the need for real-numbers entirely
I wasn't imagining dollars-and-cents, but rather rates - X per Y, the most natural way in which division arises in real life.
> Most computer programs don't need real numbers of any sort...
You're again arguing against a case I'm not making. I'm not making any claims about the necessity (or otherwise) of real numbers in programs, but simply wondering about the prevalence of particular operations.
> and the ones that do need to be written by people who understand basic mathematical concepts like precision.
A snide insult motivated by your own misunderstanding of my point. I understand precision, and it's irrelevant to my point.
I had thought this was also to do with gpu physics at some level of precision in the float it matters so one machine configuration will not precisely match another machine doing the same calculation. Or something like that.
>In 3D modelling/video games, almost certainly not.
A 32-bit integer divided into a 16-bit whole and a 16-bit fraction would be limited to only representing values between -32768 and 32767 while also having worse precision than a 32-bit ieee std754 floating-point at values near 0.
>In accounting software...probably?
Representing money in terms of cents instead of dollars removes the need for real-numbers entirely outside of "Office Space" scenarios where tracking fractions of cents over millions of transactions adds up to tangible amounts of money.
>Across the whole universe of programs: who could say?
Most computer programs don't need real numbers of any sort, and the ones that do need to be written by people who understand basic mathematical concepts like precision.