balancer-v3-gyro-pool

name	Balancer V3 Gyro Pool
description	This skill should be used when the user asks about "Gyro pool", "2-CLP", "E-CLP", "concentrated liquidity", "sqrtAlpha", "sqrtBeta", "ellipse curve", "Gyroscope", "pricing range", or needs to understand Balancer V3 Gyro Pool implementations.
version	0.1.0

Balancer V3 Gyro Pools

Gyro pools are Concentrated Liquidity Pools (CLPs) that allow liquidity to be focused within specific price ranges, providing higher capital efficiency than traditional AMMs.

Overview

Balancer V3 includes two types of Gyro pools:

Pool Type	Tokens	Curve Shape	Best For
Gyro2CLP	2	Hyperbolic (like Uniswap v3)	General concentrated liquidity
GyroECLP	2	Ellipse	Stable pairs with asymmetric behavior

Gyro 2-CLP Pool

Concentrates liquidity within a pricing range [α, β].

Invariant Formula

L² = (x + a)(y + b)

where:
  a = L / sqrt(β)    // Virtual offset for token X
  b = L * sqrt(α)    // Virtual offset for token Y
  L = Invariant

Gyro2CLPPool Contract

contract Gyro2CLPPool is IGyro2CLPPool, BalancerPoolToken, PoolInfo, Version {
    uint256 private immutable _sqrtAlpha;  // sqrt(lower price bound)
    uint256 private immutable _sqrtBeta;   // sqrt(upper price bound)

    struct GyroParams {
        string name;
        string symbol;
        uint256 sqrtAlpha;   // sqrt of minimum price
        uint256 sqrtBeta;    // sqrt of maximum price
        string version;
    }

    constructor(GyroParams memory params, IVault vault) {
        // sqrtAlpha must be less than sqrtBeta
        if (params.sqrtAlpha >= params.sqrtBeta) {
            revert SqrtParamsWrong();
        }
        _sqrtAlpha = params.sqrtAlpha;
        _sqrtBeta = params.sqrtBeta;
    }
}

Price Range Configuration

// Price range [α, β] defines where liquidity is concentrated
// Example: For a 0.95 - 1.05 price range:
// sqrtAlpha = sqrt(0.95e18) ≈ 974679434480896e3
// sqrtBeta = sqrt(1.05e18) ≈ 1024695076595960e3

// The tighter the range, the higher the capital efficiency
// but also the higher the impermanent loss risk

Swap Calculation

function onSwap(PoolSwapParams calldata request) external view returns (uint256) {
    bool tokenInIsToken0 = request.indexIn == 0;

    // Calculate virtual offsets based on current invariant
    (uint256 virtualParamIn, uint256 virtualParamOut) = _getVirtualOffsets(
        request.balancesScaled18[request.indexIn],
        request.balancesScaled18[request.indexOut],
        tokenInIsToken0
    );

    if (request.kind == SwapKind.EXACT_IN) {
        return Gyro2CLPMath.calcOutGivenIn(
            balanceIn, balanceOut, amountIn, virtualParamIn, virtualParamOut
        );
    } else {
        return Gyro2CLPMath.calcInGivenOut(
            balanceIn, balanceOut, amountOut, virtualParamIn, virtualParamOut
        );
    }
}

Gyro2CLPPoolFactory

contract Gyro2CLPPoolFactory is BasePoolFactory {
    function create(
        string memory name,
        string memory symbol,
        TokenConfig[] memory tokens,      // Exactly 2 tokens
        uint256 sqrtAlpha,
        uint256 sqrtBeta,
        PoolRoleAccounts memory roleAccounts,
        uint256 swapFeePercentage,
        address poolHooksContract,
        bytes32 salt
    ) external returns (address pool);
}

Gyro E-CLP Pool

Trading occurs along part of an ellipse curve, providing more flexible price behavior.

E-CLP Parameters

struct EclpParams {
    int256 alpha;   // Lower price bound
    int256 beta;    // Upper price bound
    int256 c;       // cos(phi) - rotation angle
    int256 s;       // sin(phi) - rotation angle
    int256 lambda;  // Stretching parameter
}

struct DerivedEclpParams {
    Vector2 tauAlpha;  // Derived from alpha
    Vector2 tauBeta;   // Derived from beta
    int256 u, v, w, z; // Derived coefficients
    int256 dSq;        // Denominator squared
}

GyroECLPPool Contract

contract GyroECLPPool is IGyroECLPPool, BalancerPoolToken, PoolInfo, Version {
    // E-CLP parameters (immutable)
    int256 internal immutable _paramsAlpha;
    int256 internal immutable _paramsBeta;
    int256 internal immutable _paramsC;
    int256 internal immutable _paramsS;
    int256 internal immutable _paramsLambda;

    // Derived parameters (38 decimal precision)
    int256 internal immutable _tauAlphaX;
    int256 internal immutable _tauAlphaY;
    int256 internal immutable _tauBetaX;
    int256 internal immutable _tauBetaY;
    int256 internal immutable _u, _v, _w, _z;
    int256 internal immutable _dSq;

    struct GyroECLPPoolParams {
        string name;
        string symbol;
        EclpParams eclpParams;
        DerivedEclpParams derivedEclpParams;  // Pre-computed off-chain
        string version;
    }
}

E-CLP Math

// Invariant calculation with error bounds
function calculateInvariantWithError(
    uint256[] memory balances,
    EclpParams memory params,
    DerivedEclpParams memory derived
) internal pure returns (int256 invariant, int256 error);

// Swap calculations
function calcOutGivenIn(
    uint256[] memory balances,
    uint256 amountIn,
    bool tokenInIsToken0,
    EclpParams memory params,
    DerivedEclpParams memory derived,
    Vector2 memory invariant
) internal pure returns (uint256 amountOut, ...);

function calcInGivenOut(
    uint256[] memory balances,
    uint256 amountOut,
    bool tokenInIsToken0,
    EclpParams memory params,
    DerivedEclpParams memory derived,
    Vector2 memory invariant
) internal pure returns (uint256 amountIn, ...);

GyroECLPPoolFactory

contract GyroECLPPoolFactory is BasePoolFactory {
    function create(
        string memory name,
        string memory symbol,
        TokenConfig[] memory tokens,
        EclpParams memory eclpParams,
        DerivedEclpParams memory derivedEclpParams,
        PoolRoleAccounts memory roleAccounts,
        uint256 swapFeePercentage,
        address poolHooksContract,
        bytes32 salt
    ) external returns (address pool);
}

Fee Bounds

// Gyro pools have wide fee ranges
function getMinimumSwapFeePercentage() external pure returns (uint256) {
    return 1e12; // 0.0001%
}

function getMaximumSwapFeePercentage() external pure returns (uint256) {
    return 1e18; // 100% (for extreme cases)
}

Invariant Ratio Bounds

// 2-CLP: No bounds (unlimited unbalanced operations)
function getMinimumInvariantRatio() returns (uint256) { return 0; }
function getMaximumInvariantRatio() returns (uint256) { return type(uint256).max; }

// E-CLP: Has bounds
uint256 constant MIN_INVARIANT_RATIO = ...; // Pool specific
uint256 constant MAX_INVARIANT_RATIO = ...; // Pool specific

Querying Pool Data

2-CLP

function getGyro2CLPPoolDynamicData() external view returns (Gyro2CLPPoolDynamicData memory);
function getGyro2CLPPoolImmutableData() external view returns (Gyro2CLPPoolImmutableData memory);

struct Gyro2CLPPoolImmutableData {
    IERC20[] tokens;
    uint256[] decimalScalingFactors;
    uint256 sqrtAlpha;
    uint256 sqrtBeta;
}

E-CLP

function getECLPParams() external view returns (EclpParams memory, DerivedEclpParams memory);
function getGyroECLPPoolDynamicData() external view returns (GyroECLPPoolDynamicData memory);
function getGyroECLPPoolImmutableData() external view returns (GyroECLPPoolImmutableData memory);

Factory Usage Examples

2-CLP Pool

// Create a concentrated USDC/DAI pool (0.99 - 1.01 range)
uint256 sqrtAlpha = 995037190209989e3;  // sqrt(0.99e18)
uint256 sqrtBeta = 1004987562112089e3;  // sqrt(1.01e18)

TokenConfig[] memory tokens = new TokenConfig[](2);
tokens[0] = TokenConfig({
    token: IERC20(USDC),
    tokenType: TokenType.STANDARD,
    rateProvider: IRateProvider(address(0)),
    paysYieldFees: false
});
tokens[1] = TokenConfig({
    token: IERC20(DAI),
    tokenType: TokenType.STANDARD,
    rateProvider: IRateProvider(address(0)),
    paysYieldFees: false
});

address pool = gyro2ClpFactory.create(
    "USDC-DAI 2CLP",
    "USDC-DAI-2CLP",
    tokens,
    sqrtAlpha,
    sqrtBeta,
    PoolRoleAccounts(address(0), address(0), address(0)),
    0.0001e16,  // 0.01% swap fee
    address(0), // no hooks
    keccak256("my-2clp-salt")
);

E-CLP Pool

// E-CLP requires pre-computed derived parameters
// These are typically computed off-chain using the Gyroscope SDK

EclpParams memory params = EclpParams({
    alpha: ...,
    beta: ...,
    c: ...,      // cos(phi)
    s: ...,      // sin(phi)
    lambda: ...  // stretching
});

DerivedEclpParams memory derived = EclpParams({
    tauAlpha: Vector2(..., ...),
    tauBeta: Vector2(..., ...),
    u: ..., v: ..., w: ..., z: ...,
    dSq: ...
});

address pool = gyroEclpFactory.create(
    "WETH-wstETH ECLP",
    "WETH-wstETH-ECLP",
    tokens,
    params,
    derived,
    roleAccounts,
    swapFeePercentage,
    address(0),
    salt
);

Use Cases

Pool Type	Best For
2-CLP	Stablecoin pairs, pegged assets, predictable ranges
E-CLP	LST pairs (wstETH/ETH), asymmetric price behavior

Reference Files

• pkg/pool-gyro/contracts/Gyro2CLPPool.sol - 2-CLP implementation
• pkg/pool-gyro/contracts/Gyro2CLPPoolFactory.sol - 2-CLP factory
• pkg/pool-gyro/contracts/GyroECLPPool.sol - E-CLP implementation
• pkg/pool-gyro/contracts/GyroECLPPoolFactory.sol - E-CLP factory
• pkg/pool-gyro/contracts/lib/Gyro2CLPMath.sol - 2-CLP math
• pkg/pool-gyro/contracts/lib/GyroECLPMath.sol - E-CLP math
• Gyroscope Docs