--- Log opened Thu Mar 02 00:00:58 2023
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14:16 < real_or_random> sipa: https://github.com/bitcoin-core/secp256k1/pull/943#discussion_r729889981
14:16 < real_or_random> remembering now
14:17 < sipa> Ahaaa!
14:19 < real_or_random> which is a bit arbitrary... we could have taken uint32_t, which is the smallest limb type
14:19 < real_or_random> but yeah, whatever
14:20 < sipa> uint8_t would also work
14:20 < sipa> but int suffices
14:20 < real_or_random> who will ever need numbers greater than 0x7FFF ?
14:20 < sipa> Yeah let's switch to secp15k1
14:20 < real_or_random> certainly not cryptographic implementations
14:21 < real_or_random> much faster for sure
14:21 < sipa> i mean it might be like 17 times less secure because it's smaller
14:21 < sipa> but just run it 17 times
14:22 < real_or_random> lol
14:22 < real_or_random> I wasn't sure how to articulate what confused me about https://github.com/bitcoin-core/secp256k1/pull/1118#discussion_r1122015946
14:22 < real_or_random> but I think I know now: the notation is somewhat non-standard
14:23 < sipa> I get that it's confusing, because those +- before the square roots ultimately don't matter.
14:23 < real_or_random> when I see multiple +-, I think they are synchronized
14:23 < sipa> Ah, I see.
14:23 < real_or_random> like +-5 * +-6 = 30
14:23 < real_or_random> and +-5 * -+6 = -30
14:24 < sipa> Would it be better to just drop them from the formulas, and add a footnote/comment that other signs work too.
14:24 < real_or_random> plus of course the fact that usual arithmetic rules for sqrts don't apply
14:25 < real_or_random> hmm, yeah, or just consider |y| instead of y
14:25 < real_or_random> oh no, that means we need to define |.|
14:25 < sipa> Actually, I think that the sqrt function (defined as sqrt(x) = x^((p-1)/4), is fully multiplicative.
14:26 < sipa> Though such a fully-multiplicative sqrt may not exist for every field, nor is it actually essential for the argument here that our sqrt happens to have that property.
14:27 < sipa> "function is fully multiplicative" meaning f(x)f(y) = f(xy)
14:27 < real_or_random> ok you're right
14:27 < sipa> Based on that, I think I'll just drop the +- and add a short comment.
14:27 < real_or_random> I guess you could also just write +-  (y * sqrt(d^3*g^3)) and that will be less confusing already
14:27 < real_or_random> but I guess a comment is more explicit
14:28 < real_or_random> by the way, it took me at least 3 reviews of this PR to figure out why you choose n and d as variable names 
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14:54 < sipa> I made a few changes to the PR.
14:54 < sipa> (well, the comments)
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--- Log closed Fri Mar 03 00:00:59 2023