A much simpler and much faster classify-ival-periodic

[pavpanchekha]

The core logic is this:

• Values with exponent < 0 are < 1 and therefore are near-0
• Values with ulp > 0 have minimum difference of > 1 and therefore are too wide
• Otherwise, range-reduce

This isn't maximally precise, but points right on the boundary should be rare anyway.

[AYadrov]

We may have to add (bfnan?) conditions, because exponent of +nan.bf is -2147483646 - which can be considered as 'near-0 case. Another value I am thinking of is: min.bf = (bf "-2.382564904887951073216169781732674520415e-323228497"), the exponent is equal to -1073741823.
We maybe want check whether lo-exp < 1 = xlo < 1.bf, depends whether we want to classify values closer to 1.bf as 'near-0 as well.

[pavpanchekha]

Hmm, ok. I don't know if we need to deal with +nan.bf. It shouldn't be possible to have +nan.bf as the endpoint of an interval unless it's the illegal interval, in which case we can special-case that.

I think min.bf should be handled fine, right? It's exponent is small, so it'll be near-0, which I think is fine?

Comparing the exp to 1 instead of 0 is fine but would require reasoning about the periodicity. I imagine it doesn't actually matter that much: since these values are small, the precision we ultimately choose for the range reduction will also be small, and it's only one binade.

[AYadrov]

Yeah, I see, min.bf is not a problem.
By the way, that's impressive how this implementation fits Herbie