My first kitten was called Rails, but be run away. The second one, Ruby, but she died from sickness the second day we had her home. The third one was Rails 2, but we called him just Rails, he’s 10 yo now. The fourth one wad called PowerBI, buy ny wife didn’t like and it was a lame name anyway so we changed it to Sushi.
Serious answer: Posits seem cool, like they do most of what floats do, but better (in a given amount of space). I think supporting them in hardware would be awesome, but of course there’s a chicken and egg problem there with supporting them in programming languages.
Posits aside, that page had one of the best, clearest explanations of how floating point works that I’ve ever read. The authors of my college textbooks could have learned a thing or two about clarity from this writer.
I had the great honour of seeing John Gustafson give a presentation about unums shortly after he first proposed posits (type III unums). The benefits over floating point arithmetic seemed incredible, and they seemed largely much more simple.
I also got to chat with him about “Gustafson’s Law”, which kinda flips Amdahl’s Law on its head. Parallel computing has long been a bit of an interest for me I was also in my last year of computer science studies then and we were covering similar subjects at the time. I found that timing to be especially amusing.
I have been thinking that maybe modern programming languages should move away from supporting IEEE 754 all within one data type.
Like, we’ve figured out that having a null value for everything always is a terrible idea. Instead, we’ve started encoding potential absence into our type system with Option or Result types, which also encourages dealing with such absence at the edges of our program, where it should be done.
Well, NaN is null all over again. Instead, we could make the division operator an associated function which returns a Result<f64> and disallow f64 from ever being NaN.
My main concern is interop with the outside world. So, I guess, there would still need to be a IEEE 754 compliant data type. But we could call it ieee_754_f64 to really get on the nerves of anyone wanting to use it when it’s not strictly necessary.
Well, and my secondary concern, which is that AI models would still want to just calculate with tons of floats, without error-handling at every intermediate step, even if it sometimes means that the end result is a shitty vector of NaNs, that would be supported with that, too.
Well, that is what I meant. That NaN is effectively an error state. It’s only like null in that any float can be in this error state, because you can’t rule out this error state via the type system.
Why do you feel like it’s not a great solution to make NaN an explicit error?
Theres plenty of cases where I would like to do some large calculation that can potentially give a NaN at many intermediate steps. I prefer to check for the NaN at the end of the calculation, rather than have a bunch of checks in every intermediate step.
How I handle the failed calculation is rarely dependent on which intermediate step gave a NaN.
This feels like people want to take away a tool that makes development in the engineering world a whole lot easier because “null bad”, or because they can’t see the use of multiplying 1e27 with 1e-30.
Well, I’m not saying that I want to take tools away. I’m explicitly saying that a ieee_754_f64 type could exist. I just want it to be named annoyingly, so anyone who doesn’t know why they should use it, will avoid it.
If you chain a whole bunch of calculations where you don’t care for NaN, that’s also perfectly unproblematic. I just think, it would be helpful to:
Nudge people towards doing a NaN check after such a chain of calculations, because it can be a real pain, if you don’t do it.
Document in the type system that this check has already taken place. If you know that a float can’t be NaN, then you have guarantees that, for example, addition will never produce a NaN. It allows you to remove some of the defensive checks, you might have felt the need to perform on parameters.
Special cases are allowed to exist and shouldn’t be made noticeably more annoying. I just want it to not be the default, because it’s more dangerous and in the average applications, lots of floats are just passed through, so it would make sense to block NaNs right away.
What do you do about a dataset which contains 11999 fine numbers, but one of them is NaN because George called in sick that week? Throw away the whole dataset because it doesn’t fit the data type?
but in statistics, you deal with NaNs all the time. Data is absent from the data set. If it would be an error every time, you wouldn’t get anything done.
My thinking is that a call to the safe division method would check after the division, whether the result is a NaN. And if it is, then it returns an Error-value, which you can handle.
Obviously, you could do the same with a NaN by just throwing an if-else after any division statement, but I would like to enforce it in the type system that this check is done.
I agree with moving away from floats but I have a far simpler proposal… just use a struct of two integers - a value and an offset. If you want to make it an IEEE standard where the offset is a four bit signed value and the value is just a 28 or 60 bit regular old integer then sure - but I can count the number of times I used floats on one hand and I can count the number of times I wouldn’t have been better off just using two integers on -0 hands.
Floats specifically solve the issue of how to store a ln absurdly large range of values in an extremely modest amount of space - that’s not a problem we need to generalize a solution for. In most cases having values up to the million magnitude with three decimals of precision is good enough. Generally speaking when you do float arithmetic your numbers will be with an order of magnitude or two… most people aren’t adding the length of the universe in seconds to the width of an atom in meters… and if they are floats don’t work anyways.
I think the concept of having a fractionally defined value with a magnitude offset was just deeply flawed from the get-go - we need some way to deal with decimal values on computers but expressing those values as fractions is needlessly imprecise.
While I get your proposal, I’d think this would make dealing with float hell. Do you really want to .unwrap() every time you deal with it? Surely not.
One thing that would be great, is that the / operator could work between Result and f64, as well as between Result and Result. Would be like doing a .map(|left| left / right) operation.
Well, not every time. Only if I do a division or get an ieee_754_f64 from the outside world. That doesn’t happen terribly often in the applications I’ve worked on.
And if it does go wrong, I do want it to explode right then and there. Worst case would be, if it writes random NaNs into some database and no one knows where they came from.
As for your suggestion with the slash accepting Results, yeah, that could resolve some pain, but I’ve rarely seen multiple divisions being necessary back-to-back and I don’t want people passing around a Result<f64> in the codebase. Then you can’t see where it went wrong anymore either.
So, personally, I wouldn’t put that division operator into the stdlib, but having it available as a library, if someone needs it, would be cool, yeah.
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