CFMM Implementation in Mage DEX

Mage DEX’s Constant Function Market Maker (CFMM) model combines dynamic reserve management with a dual-reserve bonding curve system to deliver both price precision and liquidity consistency.

Core Implementation

• Platform Integration:
  • Constructed for the Solana Virtual Machine (SVM) using the robust Anchor framework.
• Dual-Reserve System:
  • Virtual Reserves: Facilitate high-precision pricing and effective slippage control.
  • Real Reserves: Maintain the on-chain token balances and enforce liquidity constraints.
• Invariant Maintenance:
  • The product of the virtual reserves is preserved through all swap operations, ensuring consistent pricing.

Bonding Curve Mechanism

• Dynamic Reserve Adjustment:
  • Swap operations adjust both virtual and real reserves to sustain the invariant.
  • The bonding curve mechanism dynamically recalculates reserves in response to liquidity events.
• Pricing Functions:
  • Detailed methods update reserve levels when processing buy and sell operations.

Deposit and Withdrawal Calculations

• Liquidity events trigger a recalibration routine that synchronizes virtual reserves with actual token balances, ensuring that changes in liquidity are immediately reflected in pricing.

Bonding Curve Calculation Details

• Buy Operation:

  1. Compute the invariant product:
     product = virtualSOL × virtualTOKEN
  2. Adjust the virtual token reserve:
     new_virtualTOKEN = virtualTOKEN − Δ tokens
  3. Derive the new virtual SOL reserve:
     new_virtualSOL = (product ÷ new_virtualTOKEN) + 1
  4. Determine the SOL cost:
     SOL cost = new_virtualSOL − virtualSOL

• Sell Operation:

  • A similar process applies, dynamically adjusting reserves based on the token amount sold while maintaining the invariant.

Note: These formulas represent the robust mechanism underpinning Mage DEX’s swap operations, ensuring market-responsive pricing with precision and reliability.