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Re: Should we be touching goops?

From: David Kastrup
Subject: Re: Should we be touching goops?
Date: Sun, 05 Jun 2022 16:42:52 +0200
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux)

Luca Fascione <> writes:

> On Sun, Jun 5, 2022 at 2:12 PM Jean Abou Samra <> 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

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

David Kastrup

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