Category: Uniswap V3

Calculating the real reserves between two prices in the Uniswap V3 codebase In previous chapters, we derived formulas to calculate the real reserves of tokens X and Y between two…

The constant product formula in Uniswap v3 Our goal is to derive the constant product formula based on real reserves for a segment, given by $$ L^2 = (x_r+\frac{L}{\sqrt{p_u}})(y_r+L\sqrt{p_l})$$ and…

Real reserves in Uniswap v3 In the last chapter, we introduced two new concepts: real reserves and virtual reserves. The real reserves of a segment are the amount of tokens…

Real and virtual reserves in Uniswap v3 Uniswap v3 uses two types of reserves: real reserves and virtual reserves. Real reserves represent the actual amount of tokens present in a…

Square and Multiply Algorithm The square and multiply algorithm computes integer exponents in $\mathcal{O}(\log n)$ (logarithmic time). The naive way to compute an exponent $x^n$ is to multiply $x$ by…