Re: Should we be touching goops?

[Luca Fascione]

Oh yes absolutely, the growth is normally much slower than worse case
unless the addends come from really weird-ass distributions, no doubt.
Round to even helps a lot with that

And indeed our numbers not coming from measurements will in practice only
have low significant bits in a handful of specific patterns (and all
divides by power of two have a lot lot of low significant zeroes, which
further helps)

(Do you guys have a sense in practice how rare "odd" divisor groupings are?
It seems like anything that's not a triplet or maybe a quintuplet would be
real rare, no?)

L

On Sun, 5 Jun 2022, 16:42 David Kastrup, <dak@gnu.org> wrote:

> 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
>