get_D() and get_y() in Curve StableSwap This article shows algebraically step-by-step how the code for get_D() and get_y() are derived from the StableSwap invariant. Given the StableSwap Invariant: $$ An^n\sum x_i +D=An^nD+\frac{D^{n+1}}{n^n\prod x_i} $$ There are two frequent math operations we wish to conduct with it: Compute $D$ given fixed values for $A$, and the […]
Fixed Point Arithmetic in Solidity (Using Solady, Solmate, and ABDK as Examples) A fixed-point number is an integer that stores only the numerator of a fraction — while the denominator is implied. This type of arithmetic is not necessary in most programming languages because they have floating point numbers. It is necessary in Solidity because […]
Uniswap V2: Calculating the Settlement Price of an AMM Swap This article explains how to determine the price settlement of a trading pair in an Automated Market Maker (AMM). It answers the question of “How many token X can be swapped for token Y from the AMM?”. The swap() function on Uniswap V2 requires you […]
How Chainlink Price Feeds Work Chainlink price oracles are smart contracts with public view functions that return the price of a particular asset denominated in USD. Off-chain nodes collect the prices from various sources like exchanges and write the price data to the smart contract. Here is the smart contract for getting the price of […]
How Compound V3 Allocates COMP Rewards Compound issues rewards in COMP tokens to lenders and borrowers in proportion to their share of the a market’s lending and borrowing. The algorithm is extremely similar to the MasterChef Staking Algorithm, so the reader should familiarize themselves with that first. High level overview of Compound V3 rewards Similar […]
Bulkers in Compound V3 The bulker contracts in Compound V3 are multicall-like contracts for batching several transactions. For example, if we wanted to supply Ether, LINK, and wBTC as collateral and borrow USDC against it in one transaction, we can do that. We can also reduce the collateral holdings and withdraw a loan in one […]
Understanding Collateral, Liquidations, and Reserves in Compound V3 In this chapter we will examine the following topics about Compound V3: collateral valuation absorbing insufficiently collateralized loans (liquidations) selling absorbed collateral what reserves are and how reserves affect liquidations. These are a lot of topics to go over in one article, but they are all heavily […]
cUSDC V3 (Compound V3) as a non-standard Rebasing Token, CometExt.sol The Compound V3 contract behaves like a rebasing ERC 20 token. A rebasing token is a token which has an algorithmically adjusted supply rather than a fixed one. The “token” here represents the present value of positive USDC balances. That is, lenders can transfer the […]
DeFi Interest Rate Indexes: Principal value and Present Value in Compound V3 The intuitive way to track lender deposits is to record the amount of USDC they deposited and the time they deposited. Compound V3 does not do this. Instead, similar to SushiSwap Masterchef Staking Algorithm, Compound V3 tracks the hypothetical gain of one dollar […]