Concentrated liquidity AMM

A constant-product AMM whose liquidity is concentrated into a bounded price range [sqrtPriceMin, sqrtPriceMax]. Inside the range the pool prices swaps on the x × y = k curve; outside it the pool stops pricing. This archetype is analogous to Uniswap V3, though the internal math and fee composition differ.

A concentrated strategy is one instruction program priced by SwapVM (the Aqua swap engine) and run through the single AquaSwapVMRouter. The archetype is selected by the program bytes below, not by a dedicated contract.

The "pool" here is a virtual accounting construct, not a custodial vault. Each maker's tokens stay in their own wallet under a revocable, per-chain, per-token allowance; the protocol holds no tokens and moves them only when a taker fills a swap atomically.

Core instructions

Instruction Role
_dynamicBalancesXD Load reserves; persist after swap
_xycConcentrateGrowLiquidity2D Apply price-range bounds to reserves
_xycSwapXD Compute x × y = k pricing within bounded state

_xycConcentrateGrowLiquidity2D is a pre-swap modifier. It transforms balanceIn and balanceOut before the swap formula runs, and _xycSwapXD then operates on the adjusted reserves.

Program

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Program memory program = ProgramBuilder.init(_opcodes());
bytes memory bytecode = bytes.concat(
    program.build(_dynamicBalancesXD, BalancesArgsBuilder.build(
        dynamic([tokenLt, tokenGt]),
        dynamic([uint256(1_000e18), uint256(1_000e18)])
    )),
    program.build(_xycConcentrateGrowLiquidity2D, XYCConcentrateArgsBuilder.build2D(
        sqrtPriceMin,
        sqrtPriceMax
    )),
    program.build(_xycSwapXD)
);

Token ordering: tokenLt is the token with the lower address (price denominator); tokenGt is the token with the higher address. P = tokenGt / tokenLt.

Args (from XYCConcentrate)

Field Size Type Description
sqrtPriceMin 32 bytes uint256 Lower bound of price range (sqrt of P)
sqrtPriceMax 32 bytes uint256 Upper bound of price range (sqrt of P)

Total: 64 bytes, packed via abi.encodePacked.

Price range behavior

Condition Behavior
P inside [sqrtPriceMin², sqrtPriceMax²] Normal swap pricing
P at or beyond lower bound Pool is fully in tokenLt; no more sells of tokenGt accepted
P at or beyond upper bound Pool is fully in tokenGt; no more sells of tokenLt accepted

Optional modifiers

Goal Add
Flat fee _flatFeeAmountInXD before _xycConcentrateGrowLiquidity2D
MEV protection _decayXD before the fee
Expiry _deadline before balance setup

  • XYCConcentrate: instruction args and bounds math

  • XYCSwap: underlying constant-product formula

  • Constant Product: unbounded variant

  • Pegged Swap: low-slippage alternative for stable pairs

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