PeggedSwap

PeggedSwap is a square-root linear swap curve optimized for pegged assets (stablecoins, wrapped tokens, and LSTs with fixed ratios). It provides minimal slippage near the peg and uses an analytical solution, so no iterative solver is required.

PeggedSwap is one of the instructions in the Aqua opcode set (AquaOpcodes), executed by SwapVM, the Aqua swap engine, on the AquaSwapVMRouter. The full deployed set is Controls, XYCSwap, XYCConcentrate, Decay, Fee, PeggedSwap, and Extruction.

Source: src/instructions/PeggedSwap.sol

Curve formula: √(x/X₀) + √(y/Y₀) + A(x/X₀ + y/Y₀) = 1 + A (curvature p = 0.5, hardcoded)

Args encoding

All fields are 32-byte uint256 values, packed via abi.encodePacked:

Field Offset Size Description
x0 0 32 bytes Initial reserve normalization factor for tokenLt (token with lower address)
y0 32 32 bytes Initial reserve normalization factor for tokenGt (token with higher address)
linearWidth 64 32 bytes Linear component coefficient A in 1e27 scale; max 5000 × 1e27; higher = tighter peg
rateLt 96 32 bytes Decimal scale multiplier for tokenLt
rateGt 128 32 bytes Decimal scale multiplier for tokenGt

Total: 160 bytes. Build with PeggedSwapArgsBuilder.build(PeggedSwapArgsBuilder.Args memory args).

Rate multipliers normalize tokens to a common precision. When token addresses determine lt/gt, assign rates so that balance × rate is in the same scale for both tokens.

Example: USDC (6 decimals, lower address) and DAI (18 decimals, higher address):

rateLt = 1e12   // scales 1000e6 USDC → 1000e18
rateGt = 1      // 1000e18 DAI stays as-is
x0 = 1000e18    // normalized initial USDC reserve
y0 = 1000e18    // normalized initial DAI reserve

When to use: Suitable for pairs that maintain a fixed or near-fixed ratio (USDC/USDT, WETH/stETH with hardcoded rate). Not suitable for pairs where the peg ratio drifts over time (e.g. WETH/wstETH with an ever-increasing exchange rate), because the curve has finite reserves and a hard price boundary.

Instructions

_peggedSwapGrowPriceRange2D

Solidity
1
function _peggedSwapGrowPriceRange2D(Context memory ctx, bytes calldata args) internal pure

Behavior

  1. Parses args and determines (rateIn, rateOut, x0_init, y0_init) based on tokenIn < tokenOut
  2. Normalizes real balances: x0 = balanceIn × rateIn, y0 = balanceOut × rateOut
  3. Computes the curve invariant from (x0, y0, x0_init, y0_init, linearWidth)
  4. exactIn: finds y1 (new normalized output reserve) that satisfies the invariant given x1 = x0 + amountIn × rateIn, then converts back: amountOut = (y0 − y1) / rateOut
  5. exactOut: finds x1 from y1 = y0 − amountOut × rateOut, then: amountIn = ⌈(x1 − x0) / rateIn⌉

All rounding protects the maker: amountOut rounds down, amountIn rounds up.

Errors

Error Condition
PeggedSwapRecomputeDetected() amountOut != 0 (exactIn) or amountIn != 0 (exactOut)
PeggedSwapBothBalancesZero() Both balanceIn and balanceOut are zero
PeggedSwapInvalidArgsLength(length) Args shorter than 160 bytes
PeggedSwapInvalidLinearWidth(linearWidth) linearWidth > 5000e27 (MAX_LINEAR_WIDTH = 5000 × 1e27)
PeggedSwapInvalidInitialBalances(x0, y0) Either x0 or y0 is zero
PeggedSwapInvalidRates(rateLt, rateGt) Either rate is zero
  • XYCSwap: constant-product AMM for non-pegged pairs
  • XYCConcentrate: concentrated liquidity for non-pegged pairs
  • Balances: provides balanceIn/balanceOut

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