algorithmic trading
Joined July 2020
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1/ What does (7.8 choose 3) mean? A riddle, a real solution, and a bad but maybe not so silly solution:
There are n teams of m hares, and one team of t tortoises. The participants race, and finish in a random order. Teams are ranked by their slowest member.
Time for solutions to 'the tortoise and the n teams of m hares' problem that I asked about a while ago on here! Congrats to @GaussianProcess for solving.
The answer is Γ(1/m + 1)Γ(n+1)/Γ(1/m+n+1)
7/ That works if t/m is an integer, *but it also gives the correct answer* when t/m isn't an integer! So it's a sensible way to combinatorially define binomial coefficients like (7.8 choose 3) = (7 choose 3) / P(4 tortoises beat at least 3 out of 7 teams of 5 hares) = 51.272
9/ 128 bits seems just out of reach, maybe with some careful parameter tuning and enough time or with a more advanced factoooring method it can be done. I'd love to hear if anyone was able to make this work!
cc @samczsun @paradigm_ctf
1/ A New Fastest Solidity Square Root?
It's closely based on the solmate implementation, and should be ~50 gas cheaper on average.
Here's a brief thread to explain the method:
github.com/Gaussian-Process/…
5/ This gives us an initial estimate within a factor of ~3 of the true square root, which is still good enough that just seven iterations of the Babylonian method suffice.
6/ Thanks to @wardbradt for discussion, and for help with forge and testing.
cc @transmissions11, @boredGenius