Optimize doubling: secp256k1 has no y=0 point #120

This gives a 1.5% verification improvement when using the endomorphism, 2.3% improvement when not.

Add a comment that the assigment in the if is intentional or otherwise we're going to get bug reports for it. (or leave the original handling for that branch, ... doesn't it generate the same code?)

And yes, our curve has no point of order 2, so this must be safe.

My chat backscroll suggests you used a somewhat different argument, about -7 having a cube root mod p. I guess the whole argument goes something like:

"For some group element Q of curve E, if 2Q = Infinity, thus Q+Q = Q + -Q, thus Q = -Q, which means that Q.{x,y} = Q.{x,-y}, so this could only be true if there is some point on the curve with y=0, which is only true there exists a cube root of [...]".

Might be useful to include the argument lest someone reviewing the code think it was just forgotten. :)

Fixed.

ACK. As semi-aside: Technically, do we even need the branch and return on infinity? just copy it over. Doen't matter what the rest is... the common case is uh, not trying to double infinities. :P The branch should be perfectly predicted, so it may not matter at all though.

I tried not branching and just setting infinity correctly, which seemed slower. I can't explain why, as this should not be a common case.

Some test doing something dumb? Might just be a matter of stirring the alignment. No big deal in any case.