--- Log opened Mon Jul 24 00:00:08 2023
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08:43 < roconnor> For safegcd, IIUC, there is a theorem that goes something like this:  If we are in a state where g is odd (and f is odd) and delta <= 0, then forall n such that 1 <= n <= 1 - delta, the transition matrix for the next n steps is [[ 2^n 0 ][ w 1]] where w = -g · f^-1 (mod 2^n).
08:44 < roconnor> Does that sound right?  I will need to figure out how to prove this.
08:44 < roconnor> Presumably the induction on n will be straightforward.
09:18 < sipa> Something like that should hold, yes.
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10:35 < roconnor> Okay I wrote up a proof on a "napkin".  I should be able to formalize this.
10:36 < sipa> I for one look forward to Formal Napkin.
10:36 < roconnor> An there will be a similar theorem for when delta is positive.
10:38 < roconnor> I guess delta is immediately negated when it is positive, so it probably uses this non-positive case as a lemma.
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16:09 < roconnor> I kinda feel like this theorem might still be true even when g is even.
16:09 < roconnor> it holds for n=1 at least.
16:11 < roconnor> I can check once I'm done with the formal proof if I ever use the hypothesis.
16:12 < roconnor> yeah, I'm half way through the proof and I haven't used it yet.
16:12 < roconnor> I doubt I will be using it on the second part.
16:16 < roconnor> Presumably g being odd is needed for the delta is positive theorem.
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--- Log closed Tue Jul 25 00:00:09 2023