Tim Peters <t...@python.org> added the comment:

[Mark]
> The idea is no more than: "compute an extra bit, then use
> that extra bit to determine which way to round".

Thanks! Despite that this is what the derivation I sketched boiled down to, I 
was still missing how general the underlying principle was. Duh! Indeed, 
nothing special about sqrt here. So I'm delightfully surprised again :-)

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<https://bugs.python.org/issue46187>
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