Positions in Uniswap v3 Adding liquidity to an AMM means depositing tokens into the AMM pool. Liquidity providers do this in the hope of earning fees from users who swap with that pool. In Uniswap...

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 prices in a segment....

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 $$ L^2 = (x_r+\frac{L}{\sqrt{p_u}})(y_r+L\sqrt{p_l}) $$...

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—...

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 segment. Each...

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...

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 $x$...

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...

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...

Tick limits in Uniswap V3 The smallest tick in Uniswap v3 is -887,272 and the largest tick is 887,272. This chapter explains the rationale behind this range, which is based on finding the tick that...

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...

Introducing ticks in Uniswap V3 This article explains what ticks are in Uniswap V3. Ticks enable gas-efficient accounting of concentrated liquidity, so let’s quickly review concentrated liquidity...