amm

Automated Market Maker (AMM)

A simple constant product AMM (x * y = k) for decentralized token swaps.

Features Demonstrated

• Constant product formula (Uniswap V2 style)
• Liquidity provider (LP) tokens
• Swap fee mechanism
• Slippage protection
• Price calculation
• Square root calculation
• Internal helper functions

How It Works

Constant Product Formula

The AMM maintains the invariant: reserveA * reserveB = k

When swapping:

amountOut = (amountIn * reserveOut) / (reserveIn + amountIn)

Liquidity Provision

LPs deposit both tokens proportionally and receive LP tokens representing their share:

lpTokens = min(
  (amountA * totalLP) / reserveA,
  (amountB * totalLP) / reserveB
)

Fees

Swap fees (in basis points) are deducted from input:

• 30 basis points = 0.3% fee
• Fees remain in the pool, benefiting LPs

Contract Interface

Initialization

• initialize(tokenA, tokenB, amountA, amountB) - Create pool with initial liquidity

Liquidity Management

• addLiquidity(amountA, amountB, minLP) - Add liquidity, receive LP tokens
• removeLiquidity(lpTokens, minA, minB) - Burn LP tokens, receive underlying

Swaps

• swapAForB(amountIn, minOut) - Swap token A for B
• swapBForA(amountIn, minOut) - Swap token B for A

View Functions

• getReserves() - Current pool reserves
• getPriceAtoB() - Spot price A/B
• getPriceBtoA() - Spot price B/A
• getAmountOut(amountIn, aToB) - Quote expected output
• getLPBalance(account) - LP token balance

Admin

• setSwapFee(fee) - Update swap fee (max 10%)

Example Usage

// Deploy AMM with 0.3% fee
constructor(30)

// Initialize pool with 1000 of each token
initialize(tokenA, tokenB, 1000, 1000)

// Add more liquidity
addLiquidity(500, 500, 400)  // Expect ~500 LP tokens

// Swap 100 A for B
swapAForB(100, 80)  // Min 80 B out

// Check price
getPriceAtoB()  // Returns price with 6 decimal precision

// Remove liquidity
removeLiquidity(200, 180, 180)  // Burn 200 LP, expect ~200 of each

Build & Deploy

solscript check amm.sol
solscript build amm.sol

Key Concepts

Price Impact

Larger trades relative to reserves cause more price impact (slippage).

Impermanent Loss

LPs may experience IL when prices diverge from entry point.

Arbitrage

Price differences with other markets create arbitrage opportunities that rebalance the pool.

Security Considerations

• Minimum liquidity locked to prevent manipulation
• Slippage protection on all operations
• Fee caps to prevent abuse
• Consider flash loan protection for production