uniswap-simplified.py

from math import sqrt


class Uniswap:
    def __init__(self, xs):
        self.xs = xs
        self.lastK = sqrt(xs[0] * xs[1])

    def swap(self, i, dx):
        d = self.xs[0] * self.xs[1]
        y = self.xs[0] if i == 1 else self.xs[1]
        ny = d / (self.xs[i] + dx * 0.997)
        self.xs[i] = self.xs[i] + dx
        dy = y - ny
        self.xs[0 if i == 1 else 1] = ny
        return self.xs, dy

    def getFee(self):
        K = sqrt(self.xs[0] * self.xs[1])
        p = (K - self.lastK) / (K + self.lastK)
        return [p * self.xs[0], p * self.xs[1]]

    def collectFee(self):
        K = sqrt(self.xs[0] * self.xs[1])
        p = (K - self.lastK) / (K + self.lastK)
        self.xs = [x * (1 - p) for x in self.xs]
        self.lastK = sqrt(self.xs[0] * self.xs[1])


u = Uniswap([40, 80])

print(u.swap(1, 1))
print(u.getFee())
u.collectFee()
print(u.getFee())
print(u.swap(1, 0.8))
print(u.getFee())
u.collectFee()

print()

u = Uniswap([40, 60])

print(u.swap(0, 1))
print(u.getFee())
u.collectFee()
print(u.swap(0, 0.2))
print(u.getFee())
u.collectFee()