Re: Should we be touching goops?

[Luca Fascione]

On Sun, 5 Jun 2022, 17:39 David Kastrup, <dak@gnu.org> wrote:

> Luca Fascione <l.fascione@gmail.com> writes:
>
> > 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)
>
> There is no "low significance" for answering the question whether two
> music events are simultaneous or not and could share a stem.
>

Sorry I meant that if you look at the bits of X/2^n t all the bits on the
left will be zeros from a certain point on, because dividing by a power of
2 alters the exponent only, not the significand (assuming X is a smallish
number). All this to imply rounding is not tricky


> > (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?)
>
> Frequent enough that we would want to support it.  Sextuplets are pretty
> frequent (and differ in musical accent from identically timed triplets).
>

Yes of course, but sextuplet bits and triplet bits are the same (X/6 has
the same significand bits as X/3, only the exponent is one lower). So if I
understand right it's only rounding when you'd have strange recombinations
of complicated fractions, which I'd imagine is very rare (if nothing else
because it'd be hard to read for the musicians).

That being said, of course rationals are just perfect for this application,
I'm not suggesting we'd change anything I'm just musing/geeking out.

L


> --
> David Kastrup
>