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Right, I didn't think people would actually want to read the paper; I just wanted to make the point that, rather than being difficult, this was solved over 20 years ago. (And I was an undergrad at the time!)

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The article claims that the provable bounds for rounding errors are significantly worse than the empirical bounds used by y-cruncher, so an provably correct algorithm would not have competitive performance.

I'm not sure if you claim that the bounds proven in your paper are tight enough to be competitive, or if you simply confirm that there are slower conservative implementations that are provably correct.

This is indeed the issue. Using provable bounds loses too many bits for complex FFTs to make sense for long multiplies.

I (a) proved bounds, and (b) showed that those bounds were tight by constructing inputs which came close to the error bounds. The "empirical bounds" demonstrably don't work for some inputs.

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