Re: Should we be touching goops?

[David Kastrup]

Luca Fascione <l.fascione@gmail.com> writes:

> On Sun, Jun 5, 2022 at 2:12 PM Jean Abou Samra <jean@abou-samra.fr> wrote:
>
>> As David already said, the part of LilyPond we're discussing is using
>> rationals. Furthermore, (a + b) + c being close but not equal to
>> a + (b + c) for floats is not really an issue for most parts of LilyPond.
>>
>
> Yes, agreed on all points. I'd be surprised this would make a big practical
> difference.
> The difference is there, but at worst it's one least significant bit per
> operation when floats are involved.
> It's tiny in practice.

There tends to be "weak associativity" in that (((a+b)-b)+b)-b tends to
be the same as ((a+b)-b)+(b-b) in IEEE FP arithmetic using
"round-to-even" which helps a bit constraining progressive error
accumulation.

But algebraically that isn't a lot of help, of course.

-- 
David Kastrup