How Concentrated Liquidity in Uniswap V3 Works This article explains how Uniswap V3 implements concentrated liquidity. We assume the reader already understands Uniswap V2. To understand concentrated...

Computing the Current Tick Given sqrtPriceX96 In the previous chapters, we saw that the protocol stores the square root of the price instead of the price itself. Therefore, it is necessary to relate...

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 contained in that segment—...

Square Root Price in Uniswap V3 In Uniswap V2, the protocol tracks token reserves and derives the spot price, $p_x=y/x$, and total liquidity, $L=xy$, where $x$ and $y$ are the reserves of tokens X...

Uniswap V3 Factory and the Relationship Between Tick Spacing and Fees In early chapters, we introduced the concept of ticks, which discretize the price curve. A tick is a price defined by the formula...

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 $x$...

Tickmath getSqrtRatioAtTick This article explains how the function in Uniswap V3 TickMath library works. The function takes a tick index and returns the square root price at that exact tick as a...

Uniswap v2 router code walkthrough The Router contracts provide a user-facing smart contract for safely minting and burning LP tokens (adding and removing liquidity) safely swapping pair tokens They...

Uniswap V2 Architecture: An Introduction to Automated Market Makers Uniswap is a DeFi app that enables traders to swap one token for another in a trustless manner. It was one of the early automated...

Breaking Down the Uniswap V2 Swap Function Uniswap V2’s swap function is cleverly designed, but many devs find its logic counterintuitive the first time they encounter it. This article explains how...