Contract Source Code:

pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/utils/cryptography/EIP712Upgradeable.sol";
import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "./interfaces/engine/ISpotEngine.sol";
import "./interfaces/engine/IPerpEngine.sol";
import "./interfaces/engine/IProductEngine.sol";
import "./interfaces/IEndpoint.sol";
import {SpotEngine} from "./SpotEngine.sol";
import "./PerpEngine.sol";
import "./Endpoint.sol";
import "./Verifier.sol";
import "./WithdrawPool.sol";

contract ContractOwner is EIP712Upgradeable, OwnableUpgradeable {
    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor() {
        _disableInitializers();
    }

    function initialize(
        address multisig,
        address _deployer,
        address _spotEngine,
        address _perpEngine,
        address _endpoint,
        address _clearinghouse,
        address _verifier
    ) external initializer {
        require(_deployer == msg.sender, "expected deployed to initialize");
        __Ownable_init();
        transferOwnership(multisig);
        deployer = _deployer;
        spotEngine = SpotEngine(_spotEngine);
        perpEngine = PerpEngine(_perpEngine);
        endpoint = Endpoint(_endpoint);
        clearinghouse = IClearinghouse(_clearinghouse);
        verifier = Verifier(_verifier);
    }

    address deployer;
    SpotEngine spotEngine;
    PerpEngine perpEngine;
    Endpoint endpoint;
    IClearinghouse clearinghouse;
    Verifier verifier;
    LegacySpotAddProductCall[] spotAddProductCalls; // deprecated
    PerpAddProductCall[] perpAddProductCalls; // deprecated
    bytes[] internal updateProductTxs;

    // using `bytes[]` in case we will change the layout of the calls.
    bytes[] internal rawSpotAddProductCalls;
    bytes[] internal rawPerpAddProductCalls;

    modifier onlyDeployer() {
        require(msg.sender == deployer, "sender must be deployer");
        _;
    }

    struct LegacySpotAddProductCall {
        uint32 productId;
        address book;
        int128 sizeIncrement;
        int128 minSize;
        int128 lpSpreadX18;
        ISpotEngine.Config config;
        RiskHelper.RiskStore riskStore;
    }

    struct SpotAddProductCall {
        uint32 productId;
        uint32 quoteId;
        address book;
        int128 sizeIncrement;
        int128 minSize;
        int128 lpSpreadX18;
        ISpotEngine.Config config;
        RiskHelper.RiskStore riskStore;
    }

    struct PerpAddProductCall {
        uint32 productId;
        address book;
        int128 sizeIncrement;
        int128 minSize;
        int128 lpSpreadX18;
        RiskHelper.RiskStore riskStore;
    }

    function submitSpotAddProductCall(
        uint32 productId,
        uint32 quoteId,
        address book,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18,
        ISpotEngine.Config calldata config,
        RiskHelper.RiskStore calldata riskStore
    ) external onlyDeployer {
        uint32[] memory pendingIds = pendingSpotAddProductIds();
        for (uint256 i = 0; i < pendingIds.length; i++) {
            require(
                productId != pendingIds[i],
                "trying to add a spot product twice."
            );
        }
        rawSpotAddProductCalls.push(
            abi.encode(
                SpotAddProductCall(
                    productId,
                    quoteId,
                    book,
                    sizeIncrement,
                    minSize,
                    lpSpreadX18,
                    config,
                    riskStore
                )
            )
        );
    }

    function submitPerpAddProductCall(
        uint32 productId,
        address book,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18,
        RiskHelper.RiskStore calldata riskStore
    ) external onlyDeployer {
        uint32[] memory pendingIds = pendingPerpAddProductIds();
        for (uint256 i = 0; i < pendingIds.length; i++) {
            require(
                productId != pendingIds[i],
                "trying to add a perp product twice."
            );
        }
        rawPerpAddProductCalls.push(
            abi.encode(
                PerpAddProductCall(
                    productId,
                    book,
                    sizeIncrement,
                    minSize,
                    lpSpreadX18,
                    riskStore
                )
            )
        );
    }

    function clearSpotAddProductCalls() external onlyDeployer {
        delete rawSpotAddProductCalls;
    }

    function clearPerpAddProductCalls() external onlyDeployer {
        delete rawPerpAddProductCalls;
    }

    function addProducts(uint32[] memory spotIds, uint32[] memory perpIds)
        external
        onlyOwner
    {
        for (uint256 i = 0; i < rawSpotAddProductCalls.length; i++) {
            SpotAddProductCall memory call = abi.decode(
                rawSpotAddProductCalls[i],
                (SpotAddProductCall)
            );
            require(spotIds[i] == call.productId, "spot id doesn't match.");
            spotEngine.addProduct(
                call.productId,
                call.quoteId,
                call.book,
                call.sizeIncrement,
                call.minSize,
                call.lpSpreadX18,
                call.config,
                call.riskStore
            );
        }
        delete rawSpotAddProductCalls;

        for (uint256 i = 0; i < rawPerpAddProductCalls.length; i++) {
            PerpAddProductCall memory call = abi.decode(
                rawPerpAddProductCalls[i],
                (PerpAddProductCall)
            );
            require(perpIds[i] == call.productId, "perp id doesn't match.");
            perpEngine.addProduct(
                call.productId,
                call.book,
                call.sizeIncrement,
                call.minSize,
                call.lpSpreadX18,
                call.riskStore
            );
        }
        delete rawPerpAddProductCalls;
    }

    function pendingSpotAddProductIds() public view returns (uint32[] memory) {
        uint32[] memory productIds = new uint32[](
            rawSpotAddProductCalls.length
        );
        for (uint256 i = 0; i < rawSpotAddProductCalls.length; i++) {
            SpotAddProductCall memory call = abi.decode(
                rawSpotAddProductCalls[i],
                (SpotAddProductCall)
            );
            productIds[i] = call.productId;
        }
        return productIds;
    }

    function pendingPerpAddProductIds() public view returns (uint32[] memory) {
        uint32[] memory productIds = new uint32[](
            rawPerpAddProductCalls.length
        );
        for (uint256 i = 0; i < rawPerpAddProductCalls.length; i++) {
            PerpAddProductCall memory call = abi.decode(
                rawPerpAddProductCalls[i],
                (PerpAddProductCall)
            );
            productIds[i] = call.productId;
        }
        return productIds;
    }

    function hasPendingAddProductCalls() public view returns (bool) {
        return
            rawPerpAddProductCalls.length > 0 ||
            rawSpotAddProductCalls.length > 0;
    }

    function submitUpdateProductTx(bytes calldata slowModeTx)
        external
        onlyDeployer
    {
        updateProductTxs.push(slowModeTx);
    }

    function clearUpdateProductTxs() external onlyDeployer {
        delete updateProductTxs;
    }

    function batchSubmitUpdateProductTxs(bytes[] calldata slowModeTxs)
        external
        onlyDeployer
    {
        for (uint256 i = 0; i < slowModeTxs.length; i++) {
            bytes memory txn = slowModeTxs[i];
            updateProductTxs.push(txn);
        }
    }

    function updateProducts() external onlyOwner {
        for (uint256 i = 0; i < updateProductTxs.length; i++) {
            bytes memory txn = updateProductTxs[i];
            endpoint.submitSlowModeTransaction(txn);
        }
        delete updateProductTxs;
    }

    function withdrawInsurance(uint128 amount, address sendTo)
        external
        onlyOwner
    {
        IEndpoint.WithdrawInsurance memory _txn = IEndpoint.WithdrawInsurance(
            amount,
            sendTo
        );
        bytes memory txn = abi.encodePacked(uint8(27), abi.encode(_txn));
        endpoint.submitSlowModeTransaction(txn);
    }

    function hasPendingUpdateProductTxs() public view returns (bool) {
        return updateProductTxs.length > 0;
    }

    function addEngine(
        address engine,
        address offchainExchange,
        IProductEngine.EngineType engineType
    ) external onlyOwner {
        clearinghouse.addEngine(engine, offchainExchange, engineType);
    }

    function assignPubKey(
        uint256 i,
        uint256 x,
        uint256 y
    ) public onlyOwner {
        verifier.assignPubKey(i, x, y);
    }

    function deletePubkey(uint256 index) public onlyOwner {
        verifier.deletePubkey(index);
    }

    function spotUpdateRisk(
        uint32 productId,
        RiskHelper.RiskStore memory riskStore
    ) external onlyOwner {
        spotEngine.updateRisk(productId, riskStore);
    }

    function perpUpdateRisk(
        uint32 productId,
        RiskHelper.RiskStore memory riskStore
    ) external onlyOwner {
        perpEngine.updateRisk(productId, riskStore);
    }

    function setWithdrawPool(address _withdrawPool) external onlyOwner {
        clearinghouse.setWithdrawPool(_withdrawPool);
    }

    function removeWithdrawPoolLiquidity(
        uint32 productId,
        uint128 amount,
        address sendTo
    ) external onlyOwner {
        WithdrawPool withdrawPool = WithdrawPool(
            clearinghouse.getWithdrawPool()
        );
        withdrawPool.removeLiquidity(productId, amount, sendTo);
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./common/Constants.sol";
import "./common/Errors.sol";
import "./interfaces/engine/ISpotEngine.sol";
import "./interfaces/clearinghouse/IClearinghouse.sol";
import "./libraries/MathHelper.sol";
import "./libraries/MathSD21x18.sol";
import "./libraries/RiskHelper.sol";
import "./BaseEngine.sol";
import "./SpotEngineState.sol";
import "./SpotEngineLP.sol";

contract SpotEngine is SpotEngineLP {
    using MathSD21x18 for int128;

    function initialize(
        address _clearinghouse,
        address _offchainExchange,
        address _quote,
        address _endpoint,
        address _admin
    ) external {
        _initialize(_clearinghouse, _offchainExchange, _endpoint, _admin);

        configs[QUOTE_PRODUCT_ID] = Config({
            token: _quote,
            interestInflectionUtilX18: 8e17, // .8
            interestFloorX18: 1e16, // .01
            interestSmallCapX18: 4e16, // .04
            interestLargeCapX18: ONE // 1
        });
        _risk().value[QUOTE_PRODUCT_ID] = RiskHelper.RiskStore({
            longWeightInitial: 1e9,
            shortWeightInitial: 1e9,
            longWeightMaintenance: 1e9,
            shortWeightMaintenance: 1e9,
            priceX18: ONE
        });
        states[QUOTE_PRODUCT_ID] = State({
            cumulativeDepositsMultiplierX18: ONE,
            cumulativeBorrowsMultiplierX18: ONE,
            totalDepositsNormalized: 0,
            totalBorrowsNormalized: 0
        });
        productIds.push(QUOTE_PRODUCT_ID);
        emit AddProduct(QUOTE_PRODUCT_ID);
    }

    /**
     * View
     */

    function getEngineType() external pure returns (EngineType) {
        return EngineType.SPOT;
    }

    function getConfig(uint32 productId) external view returns (Config memory) {
        return configs[productId];
    }

    /**
     * Actions
     */

    /// @notice adds a new product with default parameters
    function addProduct(
        uint32 productId,
        uint32 quoteId,
        address book,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18,
        Config calldata config,
        RiskHelper.RiskStore calldata riskStore
    ) public onlyOwner {
        require(productId != QUOTE_PRODUCT_ID);
        _addProductForId(
            productId,
            quoteId,
            book,
            sizeIncrement,
            minSize,
            lpSpreadX18,
            riskStore
        );

        configs[productId] = config;
        states[productId] = State({
            cumulativeDepositsMultiplierX18: ONE,
            cumulativeBorrowsMultiplierX18: ONE,
            totalDepositsNormalized: 0,
            totalBorrowsNormalized: 0
        });

        lpStates[productId] = LpState({
            supply: 0,
            quote: Balance({amount: 0, lastCumulativeMultiplierX18: ONE}),
            base: Balance({amount: 0, lastCumulativeMultiplierX18: ONE})
        });
    }

    function updateProduct(bytes calldata rawTxn) external onlyEndpoint {
        UpdateProductTx memory txn = abi.decode(rawTxn, (UpdateProductTx));
        RiskHelper.RiskStore memory riskStore = txn.riskStore;

        if (txn.productId != QUOTE_PRODUCT_ID) {
            require(
                riskStore.longWeightInitial <=
                    riskStore.longWeightMaintenance &&
                    riskStore.shortWeightInitial >=
                    riskStore.shortWeightMaintenance &&
                    configs[txn.productId].token == txn.config.token,
                ERR_BAD_PRODUCT_CONFIG
            );

            RiskHelper.RiskStore memory r = _risk().value[txn.productId];
            r.longWeightInitial = riskStore.longWeightInitial;
            r.shortWeightInitial = riskStore.shortWeightInitial;
            r.longWeightMaintenance = riskStore.longWeightMaintenance;
            r.shortWeightMaintenance = riskStore.shortWeightMaintenance;
            _risk().value[txn.productId] = r;

            _exchange().updateMarket(
                txn.productId,
                type(uint32).max,
                address(0),
                txn.sizeIncrement,
                txn.minSize,
                txn.lpSpreadX18
            );
        }

        configs[txn.productId] = txn.config;
    }

    function updateQuoteFromInsurance(bytes32 subaccount, int128 insurance)
        external
        returns (int128)
    {
        _assertInternal();
        State memory state = states[QUOTE_PRODUCT_ID];
        BalanceNormalized memory balanceNormalized = balances[QUOTE_PRODUCT_ID][
            subaccount
        ].balance;
        int128 balanceAmount = balanceNormalizedToBalance(
            state,
            balanceNormalized
        ).amount;
        if (balanceAmount < 0) {
            int128 topUpAmount = MathHelper.max(
                MathHelper.min(insurance, -balanceAmount),
                0
            );
            insurance -= topUpAmount;
            _updateBalanceNormalized(state, balanceNormalized, topUpAmount);
        }
        states[QUOTE_PRODUCT_ID] = state;
        balances[QUOTE_PRODUCT_ID][subaccount].balance = balanceNormalized;
        return insurance;
    }

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta,
        int128 quoteDelta
    ) external {
        require(productId != QUOTE_PRODUCT_ID, ERR_INVALID_PRODUCT);
        _assertInternal();
        State memory state = states[productId];
        State memory quoteState = states[QUOTE_PRODUCT_ID];

        BalanceNormalized memory balance = balances[productId][subaccount]
            .balance;

        BalanceNormalized memory quoteBalance = balances[QUOTE_PRODUCT_ID][
            subaccount
        ].balance;

        _updateBalanceNormalized(state, balance, amountDelta);
        _updateBalanceNormalized(quoteState, quoteBalance, quoteDelta);

        balances[productId][subaccount].balance = balance;
        balances[QUOTE_PRODUCT_ID][subaccount].balance = quoteBalance;

        states[productId] = state;
        states[QUOTE_PRODUCT_ID] = quoteState;

        _balanceUpdate(productId, subaccount);
        _balanceUpdate(QUOTE_PRODUCT_ID, subaccount);
    }

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta
    ) external {
        _assertInternal();

        State memory state = states[productId];

        BalanceNormalized memory balance = balances[productId][subaccount]
            .balance;
        _updateBalanceNormalized(state, balance, amountDelta);
        balances[productId][subaccount].balance = balance;

        states[productId] = state;
        _balanceUpdate(productId, subaccount);
    }

    // only check on withdraw -- ensure that users can't withdraw
    // funds that are in the Vertex contract but not officially
    // 'deposited' into the Vertex system and counted in balances
    // (i.e. if a user transfers tokens to the clearinghouse
    // without going through the standard deposit)
    function assertUtilization(uint32 productId) external view {
        (State memory _state, ) = getStateAndBalance(productId, X_ACCOUNT);
        int128 totalDeposits = _state.totalDepositsNormalized.mul(
            _state.cumulativeDepositsMultiplierX18
        );
        int128 totalBorrows = _state.totalBorrowsNormalized.mul(
            _state.cumulativeBorrowsMultiplierX18
        );
        require(totalDeposits >= totalBorrows, ERR_MAX_UTILIZATION);
    }

    function socializeSubaccount(bytes32 subaccount) external {
        require(msg.sender == address(_clearinghouse), ERR_UNAUTHORIZED);

        uint32[] memory _productIds = getProductIds();
        for (uint128 i = 0; i < _productIds.length; ++i) {
            uint32 productId = _productIds[i];

            State memory state = states[productId];
            Balance memory balance = balanceNormalizedToBalance(
                state,
                balances[productId][subaccount].balance
            );
            if (balance.amount < 0) {
                int128 totalDeposited = state.totalDepositsNormalized.mul(
                    state.cumulativeDepositsMultiplierX18
                );

                state.cumulativeDepositsMultiplierX18 = (totalDeposited +
                    balance.amount).div(state.totalDepositsNormalized);

                require(state.cumulativeDepositsMultiplierX18 > 0);

                state.totalBorrowsNormalized += balance.amount.div(
                    state.cumulativeBorrowsMultiplierX18
                );

                balances[productId][subaccount].balance.amountNormalized = 0;

                if (productId == QUOTE_PRODUCT_ID) {
                    for (uint32 j = 0; j < _productIds.length; ++j) {
                        uint32 baseProductId = _productIds[j];
                        if (baseProductId == QUOTE_PRODUCT_ID) {
                            continue;
                        }
                        LpState memory lpState = lpStates[baseProductId];
                        _updateBalanceWithoutDelta(state, lpState.quote);
                        lpStates[baseProductId] = lpState;
                        _productUpdate(baseProductId);
                    }
                } else {
                    LpState memory lpState = lpStates[productId];
                    _updateBalanceWithoutDelta(state, lpState.base);
                    lpStates[productId] = lpState;
                }
                states[productId] = state;
                _balanceUpdate(productId, subaccount);
            }
        }
    }

    function manualAssert(
        int128[] calldata totalDeposits,
        int128[] calldata totalBorrows
    ) external view {
        for (uint128 i = 0; i < totalDeposits.length; ++i) {
            uint32 productId = productIds[i];
            State memory state = states[productId];
            require(
                state.totalDepositsNormalized.mul(
                    state.cumulativeDepositsMultiplierX18
                ) == totalDeposits[i],
                ERR_DSYNC
            );
            require(
                state.totalBorrowsNormalized.mul(
                    state.cumulativeBorrowsMultiplierX18
                ) == totalBorrows[i],
                ERR_DSYNC
            );
        }
    }

    function getToken(uint32 productId) external view returns (address) {
        return address(configs[productId].token);
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/cryptography/draft-EIP712Upgradeable.sol";
import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "./common/Errors.sol";
import "./libraries/MathHelper.sol";
import "./interfaces/IVerifier.sol";

contract Verifier is EIP712Upgradeable, OwnableUpgradeable, IVerifier {
    Point[8] internal pubkeys;
    Point[256] internal aggregatePubkey;
    bool[256] internal isAggregatePubkeyLatest;
    uint256 internal nSigner;

    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor() {
        _disableInitializers();
    }

    function initialize(Point[8] memory initialSet) external initializer {
        __Ownable_init();
        for (uint256 i = 0; i < 8; ++i) {
            if (!isPointNone(initialSet[i])) {
                _assignPubkey(i, initialSet[i].x, initialSet[i].y);
            }
        }
    }

    function revertGasInfo(uint256 i, uint256 gasUsed) external pure {
        revert(
            string.concat(
                "G ",
                MathHelper.uint2str(uint128(i)),
                " ",
                MathHelper.uint2str(uint128(gasUsed))
            )
        );
    }

    function assignPubKey(
        uint256 i,
        uint256 x,
        uint256 y
    ) public onlyOwner {
        _assignPubkey(i, x, y);
    }

    function _assignPubkey(
        uint256 i,
        uint256 x,
        uint256 y
    ) internal {
        require(i < 8);
        if (isPointNone(pubkeys[i])) {
            nSigner += 1;
        }
        pubkeys[i] = Point(x, y);
        for (uint256 s = (1 << i); s < 256; s = (s + 1) | (1 << i)) {
            isAggregatePubkeyLatest[s] = false;
        }
    }

    function deletePubkey(uint256 index) public onlyOwner {
        if (!isPointNone(pubkeys[index])) {
            nSigner -= 1;
            delete pubkeys[index];
        }
    }

    function getPubkey(uint8 index) public view returns (Point memory) {
        return pubkeys[index];
    }

    function getPubkeyAddress(uint8 index) public view returns (address) {
        Point memory p = getPubkey(index);
        return address(uint160(uint256(keccak256(abi.encode(p.x, p.y)))));
    }

    function getAggregatePubkey(uint8 signerBitmask)
        internal
        returns (Point memory)
    {
        if (signerBitmask == 0 || isAggregatePubkeyLatest[signerBitmask])
            return aggregatePubkey[signerBitmask];
        Point memory res;
        for (uint256 i = 0; i < 8; ++i) {
            if ((signerBitmask >> i) % 2 == 1) {
                require(!isPointNone(pubkeys[i]));
                res = pointAdd(
                    getAggregatePubkey(signerBitmask ^ uint8(1 << i)),
                    pubkeys[i]
                );
                break;
            }
        }
        aggregatePubkey[signerBitmask] = res;
        isAggregatePubkeyLatest[signerBitmask] = true;
        return res;
    }

    // determine if 2/3 of the signers are included in this signing mask
    // and if the keys are present
    function checkQuorum(uint8 signerBitmask) internal view returns (bool) {
        uint256 nSigned = 0;
        for (uint256 i = 0; i < 8; ++i) {
            bool signed = ((signerBitmask >> i) & 1) == 1;
            if (signed) {
                if (isPointNone(pubkeys[i])) {
                    return false;
                }
                nSigned += 1;
            }
        }
        return nSigned * 2 > nSigner;
    }

    function requireValidSignature(
        bytes32 message,
        bytes32 e,
        bytes32 s,
        uint8 signerBitmask
    ) public {
        require(checkQuorum(signerBitmask));
        Point memory pubkey = getAggregatePubkey(signerBitmask);
        require(
            verify(
                pubkey.y % 2 == 0 ? 27 : 28,
                bytes32(pubkey.x),
                message,
                e,
                s
            ),
            "Verification failed"
        );
    }

    /// SCHNORR IMPLEMENTATION BELOW
    // secp256k1 group order
    uint256 public constant Q =
        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141;

    // parity := public key y-coord parity (27 or 28)
    // px := public key x-coord
    // message := 32-byte message
    // e := schnorr signature challenge
    // s := schnorr signature
    function verify(
        uint8 parity,
        bytes32 px,
        bytes32 message,
        bytes32 e,
        bytes32 s
    ) internal pure returns (bool) {
        // ecrecover = (m, v, r, s);
        bytes32 sp = bytes32(Q - mulmod(uint256(s), uint256(px), Q));
        bytes32 ep = bytes32(Q - mulmod(uint256(e), uint256(px), Q));

        require(sp != 0);
        // the ecrecover precompile implementation checks that the `r` and `s`
        // inputs are non-zero (in this case, `px` and `ep`), thus we don't need to
        // check if they're zero.
        address R = ecrecover(sp, parity, px, ep);
        require(R != address(0), "ecrecover failed");
        return e == keccak256(abi.encodePacked(R, uint8(parity), px, message));
    }

    uint256 public constant _P =
        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F;

    struct Point {
        uint256 x;
        uint256 y;
    }

    function pow(
        uint256 a,
        uint256 b,
        uint256 mod
    ) internal pure returns (uint256) {
        // a ^ b % mod
        uint256 res = 1;
        while (b > 0) {
            if (b % 2 == 1) {
                res = mulmod(res, a, mod);
            }
            a = mulmod(a, a, mod);
            b /= 2;
        }
        return res;
    }

    function isPointNone(Point memory u) internal pure returns (bool) {
        return u.x == 0 && u.y == 0;
    }

    function pointAdd(Point memory u, Point memory v)
        internal
        pure
        returns (Point memory)
    {
        if (isPointNone(u)) return v;
        if (isPointNone(v)) return u;
        uint256 lam = 0;
        if (u.x == v.x) {
            if (u.y != v.y) return Point(0, 0);
            lam = mulmod(3, u.x, _P);
            lam = mulmod(lam, u.x, _P);
            lam = mulmod(lam, pow(mulmod(2, v.y, _P), _P - 2, _P), _P);
        } else {
            lam = mulmod(
                addmod(v.y, _P - u.y, _P),
                pow(addmod(v.x, _P - u.x, _P), _P - 2, _P),
                _P
            );
        }
        uint256 x3 = mulmod(lam, lam, _P);
        x3 = addmod(x3, _P - u.x, _P);
        x3 = addmod(x3, _P - v.x, _P);
        uint256 y3 = addmod(u.x, _P - x3, _P);
        y3 = mulmod(y3, lam, _P);
        y3 = addmod(y3, _P - u.y, _P);
        return Point(x3, y3);
    }

    function checkIndividualSignature(
        bytes32 digest,
        bytes memory signature,
        uint8 signerIndex
    ) public view returns (bool) {
        address expectedAddress = getPubkeyAddress(signerIndex);
        address recovered = ECDSA.recover(digest, signature);
        return expectedAddress == recovered;
    }

    function requireValidTxSignatures(
        bytes calldata txn,
        uint64 idx,
        bytes[] calldata signatures
    ) public {
        bytes32 data = keccak256(
            abi.encodePacked(uint256(block.chainid), uint256(idx), txn)
        );
        bytes32 hashedMsg = keccak256(
            abi.encodePacked("\x19Ethereum Signed Message:\n32", data)
        );

        uint256 nSignatures = 0;
        for (uint256 i = 0; i < signatures.length; i++) {
            if (signatures[i].length > 0) {
                nSignatures += 1;
                require(
                    checkIndividualSignature(
                        hashedMsg,
                        signatures[i],
                        uint8(i)
                    ),
                    "invalid signature"
                );
            }
        }
        require(nSignatures == nSigner, "not enough signatures");
    }

    function validateSignature(
        bytes32 sender,
        address linkedSigner,
        bytes32 digest,
        bytes memory signature
    ) public pure {
        address recovered = ECDSA.recover(digest, signature);
        require(
            (recovered != address(0)) &&
                ((recovered == address(uint160(bytes20(sender)))) ||
                    (recovered == linkedSigner)),
            ERR_INVALID_SIGNATURE
        );
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/cryptography/draft-EIP712Upgradeable.sol";
import "./interfaces/IEndpoint.sol";
import "./interfaces/IOffchainExchange.sol";
import "./interfaces/clearinghouse/IClearinghouse.sol";
import "./EndpointGated.sol";
import "./common/Errors.sol";
import "./libraries/ERC20Helper.sol";
import "./libraries/MathHelper.sol";
import "./libraries/Logger.sol";
import "./interfaces/engine/ISpotEngine.sol";
import "./interfaces/engine/IPerpEngine.sol";
import "./interfaces/IERC20Base.sol";
import "./interfaces/IVerifier.sol";

interface ISanctionsList {
    function isSanctioned(address addr) external view returns (bool);
}

contract Endpoint is IEndpoint, EIP712Upgradeable, OwnableUpgradeable {
    using ERC20Helper for IERC20Base;

    IERC20Base private quote; // deprecated
    IClearinghouse public clearinghouse;
    ISpotEngine private spotEngine;
    IPerpEngine private perpEngine;
    ISanctionsList private sanctions;

    address internal sequencer;
    int128 private sequencerFees;

    mapping(bytes32 => uint64) internal subaccountIds;
    mapping(uint64 => bytes32) internal subaccounts;
    uint64 internal numSubaccounts;

    // healthGroup -> (spotPriceX18, perpPriceX18)
    mapping(uint32 => Prices) private pricesX18; // deprecated
    mapping(uint32 => address) private books; // deprecated
    mapping(address => uint64) internal nonces;

    uint64 public nSubmissions;

    SlowModeConfig internal slowModeConfig;
    mapping(uint64 => SlowModeTx) internal slowModeTxs;

    struct Times {
        uint128 perpTime;
        uint128 spotTime;
    }

    Times internal times;

    mapping(uint32 => int128) internal sequencerFee;

    mapping(bytes32 => address) internal linkedSigners;

    int128 private slowModeFees;

    // invitee -> referralCode
    mapping(address => string) public referralCodes;

    // address -> whether can call `BurnLpAndTransfer`.
    mapping(address => bool) internal transferableWallets;

    mapping(uint32 => int128) internal priceX18;
    address internal offchainExchange;

    string internal constant LIQUIDATE_SUBACCOUNT_SIGNATURE =
        "LiquidateSubaccount(bytes32 sender,bytes32 liquidatee,uint32 productId,bool isEncodedSpread,int128 amount,uint64 nonce)";
    string internal constant TRANSFER_QUOTE_SIGNATURE =
        "TransferQuote(bytes32 sender,bytes32 recipient,uint128 amount,uint64 nonce)";
    string internal constant WITHDRAW_COLLATERAL_SIGNATURE =
        "WithdrawCollateral(bytes32 sender,uint32 productId,uint128 amount,uint64 nonce)";
    string internal constant MINT_LP_SIGNATURE =
        "MintLp(bytes32 sender,uint32 productId,uint128 amountBase,uint128 quoteAmountLow,uint128 quoteAmountHigh,uint64 nonce)";
    string internal constant BURN_LP_SIGNATURE =
        "BurnLp(bytes32 sender,uint32 productId,uint128 amount,uint64 nonce)";
    string internal constant LINK_SIGNER_SIGNATURE =
        "LinkSigner(bytes32 sender,bytes32 signer,uint64 nonce)";

    IVerifier private verifier;

    function _updatePrice(uint32 productId, int128 _priceX18) internal {
        require(_priceX18 > 0, ERR_INVALID_PRICE);
        address engine = clearinghouse.getEngineByProduct(productId);
        if (engine != address(0)) {
            priceX18[productId] = _priceX18;
            IProductEngine(engine).updatePrice(productId, _priceX18);
        }
    }

    function initialize(
        address _sanctions,
        address _sequencer,
        address _offchainExchange,
        IClearinghouse _clearinghouse,
        address _verifier,
        int128[] memory initialPrices
    ) external initializer {
        __Ownable_init();
        __EIP712_init("Vertex", "0.0.1");
        sequencer = _sequencer;
        clearinghouse = _clearinghouse;
        offchainExchange = _offchainExchange;
        verifier = IVerifier(_verifier);
        sanctions = ISanctionsList(_sanctions);
        spotEngine = ISpotEngine(
            clearinghouse.getEngineByType(IProductEngine.EngineType.SPOT)
        );

        perpEngine = IPerpEngine(
            clearinghouse.getEngineByType(IProductEngine.EngineType.PERP)
        );

        quote = IERC20Base(clearinghouse.getQuote());

        slowModeConfig = SlowModeConfig({timeout: 0, txCount: 0, txUpTo: 0});

        for (uint32 i = 0; i < initialPrices.length; i++) {
            priceX18[i] = initialPrices[i];
        }
    }

    // NOTE: we want DepositCollateral to be the first action anybody takes on Vertex
    // so we can record the existence of their subaccount on-chain
    // unfortunately, there are some edge cases where an empty account can place an order
    // or do an AMM swap that passes health checks without going through a deposit, so
    // we block those functions unless there has been a deposit first
    function _recordSubaccount(bytes32 subaccount) internal {
        if (subaccountIds[subaccount] == 0) {
            subaccountIds[subaccount] = ++numSubaccounts;
            subaccounts[numSubaccounts] = subaccount;
        }
    }

    function requireSubaccount(bytes32 subaccount) private view {
        require(
            subaccount == X_ACCOUNT || (subaccountIds[subaccount] != 0),
            ERR_REQUIRES_DEPOSIT
        );
    }

    function validateSubmissionIdx(uint64 idx) private view {
        require(idx == nSubmissions, ERR_INVALID_SUBMISSION_INDEX);
    }

    function validateNonce(bytes32 sender, uint64 nonce) internal virtual {
        require(
            nonce == nonces[address(uint160(bytes20(sender)))]++,
            ERR_WRONG_NONCE
        );
    }

    function chargeFee(bytes32 sender, int128 fee) internal {
        chargeFee(sender, fee, QUOTE_PRODUCT_ID);
    }

    function chargeFee(
        bytes32 sender,
        int128 fee,
        uint32 productId
    ) internal {
        spotEngine.updateBalance(productId, sender, -fee);
        sequencerFee[productId] += fee;
    }

    function chargeSlowModeFee(IERC20Base token, address from)
        internal
        virtual
    {
        require(address(token) != address(0));
        token.safeTransferFrom(
            from,
            address(this),
            clearinghouse.getSlowModeFee()
        );
    }

    function getLinkedSigner(bytes32 subaccount)
        public
        view
        virtual
        returns (address)
    {
        return
            RiskHelper.isIsolatedSubaccount(subaccount)
                ? linkedSigners[
                    IOffchainExchange(offchainExchange).getParentSubaccount(
                        subaccount
                    )
                ]
                : linkedSigners[subaccount];
    }

    function validateSignature(
        bytes32 sender,
        bytes32 digest,
        bytes memory signature
    ) internal virtual {
        verifier.validateSignature(
            sender,
            getLinkedSigner(sender),
            digest,
            signature
        );
    }

    function safeTransferFrom(
        IERC20Base token,
        address from,
        uint256 amount
    ) internal virtual {
        token.safeTransferFrom(from, address(this), amount);
    }

    function safeTransferTo(
        IERC20Base token,
        address to,
        uint256 amount
    ) internal virtual {
        token.safeTransfer(to, amount);
    }

    function handleDepositTransfer(
        IERC20Base token,
        address from,
        uint256 amount
    ) internal {
        require(address(token) != address(0));
        safeTransferFrom(token, from, amount);
        safeTransferTo(token, address(clearinghouse), amount);
    }

    function validateSender(bytes32 txSender, address sender) internal view {
        require(
            address(uint160(bytes20(txSender))) == sender ||
                sender == address(this),
            ERR_SLOW_MODE_WRONG_SENDER
        );
    }

    function setReferralCode(address sender, string memory referralCode)
        internal
    {
        if (bytes(referralCodes[sender]).length == 0) {
            referralCodes[sender] = referralCode;
        }
    }

    function depositCollateral(
        bytes12 subaccountName,
        uint32 productId,
        uint128 amount
    ) external {
        depositCollateralWithReferral(
            bytes32(abi.encodePacked(msg.sender, subaccountName)),
            productId,
            amount,
            DEFAULT_REFERRAL_CODE
        );
    }

    function depositCollateralWithReferral(
        bytes12 subaccountName,
        uint32 productId,
        uint128 amount,
        string calldata referralCode
    ) external {
        depositCollateralWithReferral(
            bytes32(abi.encodePacked(msg.sender, subaccountName)),
            productId,
            amount,
            referralCode
        );
    }

    function depositCollateralWithReferral(
        bytes32 subaccount,
        uint32 productId,
        uint128 amount,
        string memory referralCode
    ) public {
        require(bytes(referralCode).length != 0);
        require(
            !RiskHelper.isIsolatedSubaccount(subaccount) && productId != 145,
            ERR_UNAUTHORIZED
        );

        address sender = address(bytes20(subaccount));

        // depositor / depositee need to be unsanctioned
        requireUnsanctioned(msg.sender);
        requireUnsanctioned(sender);

        // no referral code allowed for remote deposit
        setReferralCode(
            sender,
            sender == msg.sender ? referralCode : DEFAULT_REFERRAL_CODE
        );

        if (subaccount != X_ACCOUNT && (subaccountIds[subaccount] == 0)) {
            clearinghouse.requireMinDeposit(productId, amount);
        }

        handleDepositTransfer(
            IERC20Base(spotEngine.getToken(productId)),
            msg.sender,
            uint256(amount)
        );
        // copy from submitSlowModeTransaction
        SlowModeConfig memory _slowModeConfig = slowModeConfig;

        slowModeTxs[_slowModeConfig.txCount++] = SlowModeTx({
            executableAt: uint64(block.timestamp) + 259200, // hardcoded to three days
            sender: sender,
            tx: abi.encodePacked(
                uint8(TransactionType.DepositCollateral),
                abi.encode(
                    DepositCollateral({
                        sender: subaccount,
                        productId: productId,
                        amount: amount
                    })
                )
            )
        });
        slowModeConfig = _slowModeConfig;
    }

    function requireUnsanctioned(address sender) internal view virtual {
        require(!sanctions.isSanctioned(sender), ERR_WALLET_SANCTIONED);
    }

    function submitSlowModeTransaction(bytes calldata transaction) external {
        TransactionType txType = TransactionType(uint8(transaction[0]));

        // special case for DepositCollateral because upon
        // slow mode submission we must take custody of the
        // actual funds

        address sender = msg.sender;

        if (txType == TransactionType.DepositCollateral) {
            revert();
        } else if (txType == TransactionType.DepositInsurance) {
            DepositInsurance memory txn = abi.decode(
                transaction[1:],
                (DepositInsurance)
            );
            handleDepositTransfer(_getQuote(), sender, uint256(txn.amount));
        } else if (txType == TransactionType.UpdateProduct) {
            require(sender == owner());
        } else if (txType == TransactionType.BurnLpAndTransfer) {
            require(transferableWallets[sender], ERR_WALLET_NOT_TRANSFERABLE);
            BurnLpAndTransfer memory txn = abi.decode(
                transaction[1:],
                (BurnLpAndTransfer)
            );
            setReferralCode(
                address(uint160(bytes20(txn.recipient))),
                DEFAULT_REFERRAL_CODE
            );
        } else if (txType == TransactionType.WithdrawInsurance) {
            require(sender == owner());
        } else {
            chargeSlowModeFee(_getQuote(), sender);
            slowModeFees += SLOW_MODE_FEE;
        }

        SlowModeConfig memory _slowModeConfig = slowModeConfig;
        requireUnsanctioned(sender);
        slowModeTxs[_slowModeConfig.txCount++] = SlowModeTx({
            executableAt: uint64(block.timestamp) + 259200, // hardcoded to three days
            sender: sender,
            tx: transaction
        });
        // TODO: to save on costs we could potentially just emit something
        // for now, we can just create a separate loop in the engine that queries the remote
        // sequencer for slow mode transactions, and ignore the possibility of a reorgy attack
        slowModeConfig = _slowModeConfig;
    }

    function _executeSlowModeTransaction(
        SlowModeConfig memory _slowModeConfig,
        bool fromSequencer
    ) internal {
        require(
            _slowModeConfig.txUpTo < _slowModeConfig.txCount,
            ERR_NO_SLOW_MODE_TXS_REMAINING
        );
        SlowModeTx memory txn = slowModeTxs[_slowModeConfig.txUpTo];
        delete slowModeTxs[_slowModeConfig.txUpTo++];

        require(
            fromSequencer || (txn.executableAt <= block.timestamp),
            ERR_SLOW_TX_TOO_RECENT
        );

        if (block.chainid == 31337) {
            // for testing purposes, we don't fail silently when the chainId is hardhat's default.
            this.processSlowModeTransaction(txn.sender, txn.tx);
        } else {
            uint256 gasRemaining = gasleft();
            try this.processSlowModeTransaction(txn.sender, txn.tx) {} catch {
                // we need to differentiate between a revert and an out of gas
                // the issue is that in evm every inner call only 63/64 of the
                // remaining gas in the outer frame is forwarded. as a result
                // the amount of gas left for execution is (63/64)**len(stack)
                // and you can get an out of gas while spending an arbitrarily
                // low amount of gas in the final frame. we use a heuristic
                // here that isn't perfect but covers our cases.
                // having gasleft() <= gasRemaining / 2 buys us 44 nested calls
                // before we miss out of gas errors; 1/2 ~= (63/64)**44
                // this is good enough for our purposes

                if (gasleft() <= 250000 || gasleft() <= gasRemaining / 2) {
                    assembly {
                        invalid()
                    }
                }

                // try return funds now removed
            }
        }
    }

    function executeSlowModeTransaction() external {
        SlowModeConfig memory _slowModeConfig = slowModeConfig;
        _executeSlowModeTransaction(_slowModeConfig, false);
        slowModeConfig = _slowModeConfig;
    }

    // TODO: these do not need senders or nonces
    // we can save some gas by creating new structs
    function processSlowModeTransaction(
        address sender,
        bytes calldata transaction
    ) public {
        require(msg.sender == address(this));
        TransactionType txType = TransactionType(uint8(transaction[0]));
        if (txType == TransactionType.LiquidateSubaccount) {
            LiquidateSubaccount memory txn = abi.decode(
                transaction[1:],
                (LiquidateSubaccount)
            );
            validateSender(txn.sender, sender);
            requireSubaccount(txn.sender);
            clearinghouse.liquidateSubaccount(txn);
        } else if (txType == TransactionType.DepositCollateral) {
            DepositCollateral memory txn = abi.decode(
                transaction[1:],
                (DepositCollateral)
            );
            validateSender(txn.sender, sender);
            _recordSubaccount(txn.sender);
            clearinghouse.depositCollateral(txn);
        } else if (txType == TransactionType.WithdrawCollateral) {
            WithdrawCollateral memory txn = abi.decode(
                transaction[1:],
                (WithdrawCollateral)
            );

            validateSender(txn.sender, sender);
            clearinghouse.withdrawCollateral(
                txn.sender,
                txn.productId,
                txn.amount,
                address(0),
                nSubmissions
            );
        } else if (txType == TransactionType.SettlePnl) {
            clearinghouse.settlePnl(transaction);
        } else if (txType == TransactionType.DepositInsurance) {
            clearinghouse.depositInsurance(transaction);
        } else if (txType == TransactionType.MintLp) {
            MintLp memory txn = abi.decode(transaction[1:], (MintLp));
            require(
                clearinghouse.getEngineByProduct(txn.productId) ==
                    clearinghouse.getEngineByType(
                        IProductEngine.EngineType.SPOT
                    ),
                ERR_INVALID_PRODUCT
            );
            validateSender(txn.sender, sender);
            clearinghouse.mintLp(txn);
        } else if (txType == TransactionType.BurnLp) {
            BurnLp memory txn = abi.decode(transaction[1:], (BurnLp));
            validateSender(txn.sender, sender);
            clearinghouse.burnLp(txn);
        } else if (txType == TransactionType.SwapAMM) {
            SwapAMM memory txn = abi.decode(transaction[1:], (SwapAMM));
            validateSender(txn.sender, sender);
            requireSubaccount(txn.sender);
            IOffchainExchange(offchainExchange).swapAMM(txn);
        } else if (txType == TransactionType.UpdateProduct) {
            UpdateProduct memory txn = abi.decode(
                transaction[1:],
                (UpdateProduct)
            );
            IProductEngine(txn.engine).updateProduct(txn.tx);
        } else if (txType == TransactionType.LinkSigner) {
            LinkSigner memory txn = abi.decode(transaction[1:], (LinkSigner));
            validateSender(txn.sender, sender);
            requireSubaccount(txn.sender);
            linkedSigners[txn.sender] = address(uint160(bytes20(txn.signer)));
        } else if (txType == TransactionType.BurnLpAndTransfer) {
            BurnLpAndTransfer memory txn = abi.decode(
                transaction[1:],
                (BurnLpAndTransfer)
            );
            validateSender(txn.sender, sender);
            _recordSubaccount(txn.recipient);
            clearinghouse.burnLpAndTransfer(txn);
        } else if (txType == TransactionType.WithdrawInsurance) {
            clearinghouse.withdrawInsurance(transaction, nSubmissions);
        } else {
            revert();
        }
    }

    function processTransaction(bytes calldata transaction) internal {
        TransactionType txType = TransactionType(uint8(transaction[0]));
        if (txType == TransactionType.LiquidateSubaccount) {
            SignedLiquidateSubaccount memory signedTx = abi.decode(
                transaction[1:],
                (SignedLiquidateSubaccount)
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(LIQUIDATE_SUBACCOUNT_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.liquidatee,
                            signedTx.tx.productId,
                            signedTx.tx.isEncodedSpread,
                            signedTx.tx.amount,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            requireSubaccount(signedTx.tx.sender);
            chargeFee(signedTx.tx.sender, LIQUIDATION_FEE);
            clearinghouse.liquidateSubaccount(signedTx.tx);
        } else if (txType == TransactionType.WithdrawCollateral) {
            SignedWithdrawCollateral memory signedTx = abi.decode(
                transaction[1:],
                (SignedWithdrawCollateral)
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(WITHDRAW_COLLATERAL_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.productId,
                            signedTx.tx.amount,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            chargeFee(
                signedTx.tx.sender,
                clearinghouse.getWithdrawFee(signedTx.tx.productId),
                signedTx.tx.productId
            );
            clearinghouse.withdrawCollateral(
                signedTx.tx.sender,
                signedTx.tx.productId,
                signedTx.tx.amount,
                address(0),
                nSubmissions
            );
        } else if (txType == TransactionType.SpotTick) {
            SpotTick memory txn = abi.decode(transaction[1:], (SpotTick));
            Times memory t = times;
            uint128 dt = t.spotTime == 0 ? 0 : txn.time - t.spotTime;
            spotEngine.updateStates(dt);
            t.spotTime = txn.time;
            times = t;
        } else if (txType == TransactionType.PerpTick) {
            PerpTick memory txn = abi.decode(transaction[1:], (PerpTick));
            Times memory t = times;
            uint128 dt = t.perpTime == 0 ? 0 : txn.time - t.perpTime;
            perpEngine.updateStates(dt, txn.avgPriceDiffs);
            t.perpTime = txn.time;
            times = t;
        } else if (txType == TransactionType.UpdatePrice) {
            UpdatePrice memory txn = abi.decode(transaction[1:], (UpdatePrice));
            _updatePrice(txn.productId, txn.priceX18);
        } else if (txType == TransactionType.SettlePnl) {
            clearinghouse.settlePnl(transaction);
        } else if (
            txType == TransactionType.MatchOrders ||
            txType == TransactionType.MatchOrdersRFQ
        ) {
            MatchOrders memory txn = abi.decode(transaction[1:], (MatchOrders));
            requireSubaccount(txn.taker.order.sender);
            requireSubaccount(txn.maker.order.sender);
            MatchOrdersWithSigner memory txnWithSigner = MatchOrdersWithSigner({
                matchOrders: txn,
                takerLinkedSigner: getLinkedSigner(txn.taker.order.sender),
                makerLinkedSigner: getLinkedSigner(txn.maker.order.sender)
            });
            IOffchainExchange(offchainExchange).matchOrders(txnWithSigner);
        } else if (txType == TransactionType.MatchOrderAMM) {
            MatchOrderAMM memory txn = abi.decode(
                transaction[1:],
                (MatchOrderAMM)
            );
            requireSubaccount(txn.taker.order.sender);
            IOffchainExchange(offchainExchange).matchOrderAMM(
                txn,
                getLinkedSigner(txn.taker.order.sender)
            );
        } else if (txType == TransactionType.ExecuteSlowMode) {
            SlowModeConfig memory _slowModeConfig = slowModeConfig;
            _executeSlowModeTransaction(_slowModeConfig, true);
            slowModeConfig = _slowModeConfig;
        } else if (txType == TransactionType.MintLp) {
            SignedMintLp memory signedTx = abi.decode(
                transaction[1:],
                (SignedMintLp)
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(MINT_LP_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.productId,
                            signedTx.tx.amountBase,
                            signedTx.tx.quoteAmountLow,
                            signedTx.tx.quoteAmountHigh,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            chargeFee(signedTx.tx.sender, HEALTHCHECK_FEE);
            clearinghouse.mintLp(signedTx.tx);
        } else if (txType == TransactionType.BurnLp) {
            SignedBurnLp memory signedTx = abi.decode(
                transaction[1:],
                (SignedBurnLp)
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(BURN_LP_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.productId,
                            signedTx.tx.amount,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            chargeFee(signedTx.tx.sender, HEALTHCHECK_FEE);
            clearinghouse.burnLp(signedTx.tx);
        } else if (txType == TransactionType.DumpFees) {
            IOffchainExchange(offchainExchange).dumpFees();
        } else if (txType == TransactionType.ClaimSequencerFees) {
            ClaimSequencerFees memory txn = abi.decode(
                transaction[1:],
                (ClaimSequencerFees)
            );
            uint32[] memory spotIds = spotEngine.getProductIds();
            int128[] memory fees = new int128[](spotIds.length);
            for (uint256 i = 0; i < spotIds.length; i++) {
                fees[i] = sequencerFee[spotIds[i]];
                sequencerFee[spotIds[i]] = 0;
            }
            requireSubaccount(txn.subaccount);
            clearinghouse.claimSequencerFees(txn, fees);
        } else if (txType == TransactionType.ManualAssert) {
            clearinghouse.manualAssert(transaction);
        } else if (txType == TransactionType.LinkSigner) {
            SignedLinkSigner memory signedTx = abi.decode(
                transaction[1:],
                (SignedLinkSigner)
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(LINK_SIGNER_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.signer,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            linkedSigners[signedTx.tx.sender] = address(
                uint160(bytes20(signedTx.tx.signer))
            );
        } else if (txType == TransactionType.UpdateFeeRates) {
            UpdateFeeRates memory txn = abi.decode(
                transaction[1:],
                (UpdateFeeRates)
            );
            IOffchainExchange(offchainExchange).updateFeeRates(
                txn.user,
                txn.productId,
                txn.makerRateX18,
                txn.takerRateX18
            );
        } else if (txType == TransactionType.TransferQuote) {
            SignedTransferQuote memory signedTx = abi.decode(
                transaction[1:],
                (SignedTransferQuote)
            );
            _recordSubaccount(signedTx.tx.recipient);
            validateSignature(
                signedTx.tx.sender,
                _hashTypedDataV4(
                    keccak256(
                        abi.encode(
                            keccak256(bytes(TRANSFER_QUOTE_SIGNATURE)),
                            signedTx.tx.sender,
                            signedTx.tx.recipient,
                            signedTx.tx.amount,
                            signedTx.tx.nonce
                        )
                    )
                ),
                signedTx.signature
            );
            validateNonce(signedTx.tx.sender, signedTx.tx.nonce);
            chargeFee(signedTx.tx.sender, HEALTHCHECK_FEE);
            clearinghouse.transferQuote(signedTx.tx);
        } else if (txType == TransactionType.RebalanceXWithdraw) {
            RebalanceXWithdraw memory txn = abi.decode(
                transaction[1:],
                (RebalanceXWithdraw)
            );

            clearinghouse.withdrawCollateral(
                X_ACCOUNT,
                txn.productId,
                txn.amount,
                txn.sendTo,
                nSubmissions
            );
        } else if (txType == TransactionType.UpdateMinDepositRate) {
            UpdateMinDepositRate memory txn = abi.decode(
                transaction[1:],
                (UpdateMinDepositRate)
            );

            spotEngine.updateMinDepositRate(
                txn.productId,
                txn.minDepositRateX18
            );
        } else if (txType == TransactionType.AssertCode) {
            clearinghouse.assertCode(transaction);
        } else if (txType == TransactionType.CreateIsolatedSubaccount) {
            CreateIsolatedSubaccount memory txn = abi.decode(
                transaction[1:],
                (CreateIsolatedSubaccount)
            );
            bytes32 newIsolatedSubaccount = IOffchainExchange(offchainExchange)
                .createIsolatedSubaccount(
                    txn,
                    getLinkedSigner(txn.order.sender)
                );
            _recordSubaccount(newIsolatedSubaccount);
        } else {
            revert();
        }
    }

    function submitTransactionsChecked(
        uint64 idx,
        bytes[] calldata transactions,
        bytes32 e,
        bytes32 s,
        uint8 signerBitmask
    ) external {
        validateSubmissionIdx(idx);
        require(msg.sender == sequencer);
        // TODO: if one of these transactions fails this means the sequencer is in an error state
        // we should probably record this, and engage some sort of recovery mode

        bytes32 digest = keccak256(abi.encode(idx));
        for (uint256 i = 0; i < transactions.length; ++i) {
            digest = keccak256(abi.encodePacked(digest, transactions[i]));
        }
        verifier.requireValidSignature(digest, e, s, signerBitmask);

        for (uint256 i = 0; i < transactions.length; i++) {
            bytes calldata transaction = transactions[i];
            processTransaction(transaction);
            nSubmissions += 1;
        }
    }

    function submitTransactionsCheckedWithGasLimit(
        uint64 idx,
        bytes[] calldata transactions,
        uint256 gasLimit
    ) external {
        uint256 gasUsed = gasleft();
        validateSubmissionIdx(idx);
        for (uint256 i = 0; i < transactions.length; i++) {
            bytes calldata transaction = transactions[i];
            processTransaction(transaction);
            if (gasUsed - gasleft() > gasLimit) {
                verifier.revertGasInfo(i, gasUsed);
            }
        }
        verifier.revertGasInfo(transactions.length, gasUsed - gasleft());
    }

    function getSubaccountId(bytes32 subaccount)
        external
        view
        returns (uint64)
    {
        return subaccountIds[subaccount];
    }

    function _getQuote() internal view returns (IERC20Base) {
        return IERC20Base(spotEngine.getToken(QUOTE_PRODUCT_ID));
    }

    function getPriceX18(uint32 productId)
        public
        view
        returns (int128 _priceX18)
    {
        _priceX18 = priceX18[productId];
        require(_priceX18 != 0, ERR_INVALID_PRODUCT);
    }

    function getTime() external view returns (uint128) {
        Times memory t = times;
        uint128 _time = t.spotTime > t.perpTime ? t.spotTime : t.perpTime;
        require(_time != 0, ERR_INVALID_TIME);
        return _time;
    }

    function getOffchainExchange() external view returns (address) {
        return offchainExchange;
    }

    function getSequencer() external view returns (address) {
        return sequencer;
    }

    function getSlowModeTx(uint64 idx)
        external
        view
        returns (
            SlowModeTx memory,
            uint64,
            uint64
        )
    {
        return (
            slowModeTxs[idx],
            slowModeConfig.txUpTo,
            slowModeConfig.txCount
        );
    }

    function getNonce(address sender) external view returns (uint64) {
        return nonces[sender];
    }

    function updateSanctions(address _sanctions) external onlyOwner {
        sanctions = ISanctionsList(_sanctions);
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/utils/cryptography/draft-EIP712Upgradeable.sol";
import "./libraries/MathHelper.sol";
import "./interfaces/IEndpoint.sol";
import "./Verifier.sol";
import "./interfaces/engine/ISpotEngine.sol";
import "./interfaces/IERC20Base.sol";
import "./libraries/ERC20Helper.sol";
import "./common/Constants.sol";

contract WithdrawPool is EIP712Upgradeable, OwnableUpgradeable {
    using ERC20Helper for IERC20Base;
    using MathSD21x18 for int128;

    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor() {
        _disableInitializers();
    }

    function initialize(address _clearinghouse, address _verifier)
        external
        initializer
    {
        __Ownable_init();
        clearinghouse = _clearinghouse;
        verifier = _verifier;
    }

    address internal clearinghouse;

    address internal verifier;

    // submitted withdrawal idxs
    mapping(uint64 => bool) public markedIdxs;

    // collected withdrawal fees in native token decimals
    mapping(uint32 => int128) public fees;

    uint64 public minIdx;

    function submitFastWithdrawal(
        uint64 idx,
        bytes calldata transaction,
        bytes[] calldata signatures
    ) public {
        require(!markedIdxs[idx], "Withdrawal already submitted");
        require(idx > minIdx, "idx too small");
        markedIdxs[idx] = true;

        Verifier v = Verifier(verifier);
        v.requireValidTxSignatures(transaction, idx, signatures);

        IEndpoint.SignedWithdrawCollateral memory signedTx = abi.decode(
            transaction[1:],
            (IEndpoint.SignedWithdrawCollateral)
        );

        IERC20Base token = getToken(signedTx.tx.productId);

        address sendTo = address(uint160(bytes20(signedTx.tx.sender)));
        uint128 transferAmount = signedTx.tx.amount;

        require(transferAmount <= INT128_MAX, ERR_CONVERSION_OVERFLOW);

        int128 fee = fastWithdrawalFeeAmount(
            token,
            signedTx.tx.productId,
            transferAmount
        );

        require(transferAmount > uint128(fee), "Fee larger than balance");
        transferAmount -= uint128(fee);
        fees[signedTx.tx.productId] += fee;

        handleWithdrawTransfer(token, sendTo, transferAmount);
    }

    function submitWithdrawal(
        IERC20Base token,
        address sendTo,
        uint128 amount,
        uint64 idx
    ) public {
        require(msg.sender == clearinghouse);

        if (markedIdxs[idx]) {
            return;
        }
        markedIdxs[idx] = true;
        // set minIdx to most recent withdrawal submitted by sequencer
        minIdx = idx;

        handleWithdrawTransfer(token, sendTo, amount);
    }

    function fastWithdrawalFeeAmount(
        IERC20Base token,
        uint32 productId,
        uint128 amount
    ) public view returns (int128) {
        uint8 decimals = token.decimals();
        require(decimals <= MAX_DECIMALS);
        int256 multiplier = int256(10**(MAX_DECIMALS - uint8(decimals)));
        int128 amountX18 = int128(amount) * int128(multiplier);

        int128 proportionalFeeX18 = FAST_WITHDRAWAL_FEE_RATE.mul(amountX18);
        int128 minFeeX18 = 5 *
            IClearinghouse(clearinghouse).getWithdrawFee(productId);

        int128 feeX18 = MathHelper.max(proportionalFeeX18, minFeeX18);
        return feeX18 / int128(multiplier);
    }

    function removeLiquidity(
        uint32 productId,
        uint128 amount,
        address sendTo
    ) external onlyOwner {
        handleWithdrawTransfer(getToken(productId), sendTo, amount);
    }

    function checkMarkedIdxs(uint64[] calldata idxs)
        public
        view
        returns (bool[] memory)
    {
        bool[] memory marked = new bool[](idxs.length);
        for (uint256 i = 0; i < idxs.length; i++) {
            marked[i] = markedIdxs[idxs[i]];
        }
        return marked;
    }

    function checkProductBalances(uint32[] calldata productIds)
        public
        view
        returns (uint256[] memory)
    {
        uint256[] memory balances = new uint256[](productIds.length);
        for (uint256 i = 0; i < productIds.length; i++) {
            IERC20Base token = getToken(productIds[i]);
            balances[i] = token.balanceOf(address(this));
        }
        return balances;
    }

    function handleWithdrawTransfer(
        IERC20Base token,
        address to,
        uint128 amount
    ) internal virtual {
        token.safeTransfer(to, uint256(amount));
    }

    function safeTransferFrom(
        IERC20Base token,
        address from,
        uint256 amount
    ) internal virtual {
        token.safeTransferFrom(from, address(this), amount);
    }

    function getToken(uint32 productId) internal view returns (IERC20Base) {
        IERC20Base token = IERC20Base(spotEngine().getConfig(productId).token);
        require(address(token) != address(0));
        return token;
    }

    function spotEngine() internal view returns (ISpotEngine) {
        return
            ISpotEngine(
                IClearinghouse(clearinghouse).getEngineByType(
                    IProductEngine.EngineType.SPOT
                )
            );
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "hardhat/console.sol";

import "./common/Constants.sol";
import "./common/Errors.sol";
import "./interfaces/engine/IProductEngine.sol";
import "./interfaces/engine/IPerpEngine.sol";
import "./interfaces/clearinghouse/IClearinghouse.sol";
import "./libraries/MathHelper.sol";
import "./libraries/MathSD21x18.sol";
import "./BaseEngine.sol";
import "./PerpEngineLp.sol";

contract PerpEngine is PerpEngineLp {
    using MathSD21x18 for int128;

    function initialize(
        address _clearinghouse,
        address _offchainExchange,
        address,
        address _endpoint,
        address _admin
    ) external {
        _initialize(_clearinghouse, _offchainExchange, _endpoint, _admin);
    }

    function getEngineType() external pure returns (EngineType) {
        return EngineType.PERP;
    }

    /**
     * Actions
     */

    /// @notice adds a new product with default parameters
    function addProduct(
        uint32 productId,
        address book,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18,
        RiskHelper.RiskStore calldata riskStore
    ) public onlyOwner {
        _addProductForId(
            productId,
            QUOTE_PRODUCT_ID,
            book,
            sizeIncrement,
            minSize,
            lpSpreadX18,
            riskStore
        );

        states[productId] = State({
            cumulativeFundingLongX18: 0,
            cumulativeFundingShortX18: 0,
            availableSettle: 0,
            openInterest: 0
        });

        lpStates[productId] = LpState({
            supply: 0,
            lastCumulativeFundingX18: 0,
            cumulativeFundingPerLpX18: 0,
            base: 0,
            quote: 0
        });
    }

    /// @notice changes the configs of a product, if a new book is provided
    /// also clears the book
    function updateProduct(bytes calldata rawTxn) external onlyEndpoint {
        UpdateProductTx memory txn = abi.decode(rawTxn, (UpdateProductTx));
        RiskHelper.RiskStore memory riskStore = txn.riskStore;

        require(
            riskStore.longWeightInitial <= riskStore.longWeightMaintenance &&
                riskStore.shortWeightInitial >=
                riskStore.shortWeightMaintenance,
            ERR_BAD_PRODUCT_CONFIG
        );

        RiskHelper.RiskStore memory r = _risk().value[txn.productId];
        r.longWeightInitial = riskStore.longWeightInitial;
        r.shortWeightInitial = riskStore.shortWeightInitial;
        r.longWeightMaintenance = riskStore.longWeightMaintenance;
        r.shortWeightMaintenance = riskStore.shortWeightMaintenance;
        _risk().value[txn.productId] = r;

        _exchange().updateMarket(
            txn.productId,
            type(uint32).max,
            address(0),
            txn.sizeIncrement,
            txn.minSize,
            txn.lpSpreadX18
        );
    }

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta,
        int128 vQuoteDelta
    ) external {
        // Only a market book can apply deltas
        _assertInternal();
        State memory state = states[productId];
        Balance memory balance = balances[productId][subaccount];

        _updateBalance(state, balance, amountDelta, vQuoteDelta);

        states[productId] = state;
        balances[productId][subaccount] = balance;
        _balanceUpdate(productId, subaccount);
    }

    function settlePnl(bytes32 subaccount, uint256 productIds)
        external
        returns (int128)
    {
        _assertInternal();
        int128 totalSettled = 0;

        while (productIds != 0) {
            uint32 productId = uint32(productIds & ((1 << 32) - 1));
            // otherwise it means the product is a spot.
            if (productId % 2 == 0) {
                (
                    int128 canSettle,
                    LpState memory lpState,
                    LpBalance memory lpBalance,
                    State memory state,
                    Balance memory balance
                ) = getSettlementState(productId, subaccount);

                state.availableSettle -= canSettle;
                balance.vQuoteBalance -= canSettle;

                totalSettled += canSettle;

                lpStates[productId] = lpState;
                states[productId] = state;
                lpBalances[productId][subaccount] = lpBalance;
                balances[productId][subaccount] = balance;
                _balanceUpdate(productId, subaccount);
            }
            productIds >>= 32;
        }
        return totalSettled;
    }

    function calculatePositionPnl(
        LpState memory lpState,
        LpBalance memory lpBalance,
        Balance memory balance,
        uint32 productId
    ) internal view returns (int128 positionPnl) {
        int128 priceX18 = _risk(productId).priceX18;

        (int128 ammBase, int128 ammQuote) = MathHelper.ammEquilibrium(
            lpState.base,
            lpState.quote,
            priceX18
        );

        if (lpBalance.amount == 0) {
            positionPnl = priceX18.mul(balance.amount) + balance.vQuoteBalance;
        } else {
            positionPnl =
                priceX18.mul(
                    balance.amount +
                        ammBase.mul(lpBalance.amount).div(lpState.supply)
                ) +
                balance.vQuoteBalance +
                ammQuote.mul(lpBalance.amount).div(lpState.supply);
        }
    }

    function getPositionPnl(uint32 productId, bytes32 subaccount)
        external
        view
        returns (int128)
    {
        (
            LpState memory lpState,
            LpBalance memory lpBalance,
            ,
            Balance memory balance
        ) = getStatesAndBalances(productId, subaccount);

        return calculatePositionPnl(lpState, lpBalance, balance, productId);
    }

    function getSettlementState(uint32 productId, bytes32 subaccount)
        public
        view
        returns (
            int128 availableSettle,
            LpState memory lpState,
            LpBalance memory lpBalance,
            State memory state,
            Balance memory balance
        )
    {
        (lpState, lpBalance, state, balance) = getStatesAndBalances(
            productId,
            subaccount
        );

        availableSettle = MathHelper.min(
            calculatePositionPnl(lpState, lpBalance, balance, productId),
            state.availableSettle
        );
    }

    function socializeSubaccount(bytes32 subaccount, int128 insurance)
        external
        returns (int128)
    {
        require(msg.sender == address(_clearinghouse), ERR_UNAUTHORIZED);

        uint32[] memory _productIds = getProductIds();
        for (uint128 i = 0; i < _productIds.length; ++i) {
            uint32 productId = _productIds[i];
            (State memory state, Balance memory balance) = getStateAndBalance(
                productId,
                subaccount
            );
            if (balance.vQuoteBalance < 0) {
                int128 insuranceCover = MathHelper.min(
                    insurance,
                    -balance.vQuoteBalance
                );
                insurance -= insuranceCover;
                balance.vQuoteBalance += insuranceCover;
                state.availableSettle += insuranceCover;

                // actually socialize if still not enough
                if (balance.vQuoteBalance < 0) {
                    // socialize across all other participants
                    int128 fundingPerShare = -balance.vQuoteBalance.div(
                        state.openInterest
                    ) / 2;
                    state.cumulativeFundingLongX18 += fundingPerShare;
                    state.cumulativeFundingShortX18 -= fundingPerShare;

                    LpState memory lpState = lpStates[productId];
                    Balance memory tmp = Balance({
                        amount: lpState.base,
                        vQuoteBalance: 0,
                        lastCumulativeFundingX18: lpState
                            .lastCumulativeFundingX18
                    });
                    _updateBalance(state, tmp, 0, 0);
                    if (lpState.supply != 0) {
                        lpState.cumulativeFundingPerLpX18 += tmp
                            .vQuoteBalance
                            .div(lpState.supply);
                    }
                    lpState.lastCumulativeFundingX18 = state
                        .cumulativeFundingLongX18;

                    lpStates[productId] = lpState;
                    balance.vQuoteBalance = 0;
                }
                states[productId] = state;
                balances[productId][subaccount] = balance;
                _balanceUpdate(productId, subaccount);
            }
        }
        return insurance;
    }

    function manualAssert(int128[] calldata openInterests) external view {
        for (uint128 i = 0; i < openInterests.length; ++i) {
            uint32 productId = productIds[i];
            require(
                states[productId].openInterest == openInterests[i],
                ERR_DSYNC
            );
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./clearinghouse/IClearinghouse.sol";

interface IEndpoint {
    event SubmitTransactions();

    // events that we parse transactions into
    enum TransactionType {
        LiquidateSubaccount,
        DepositCollateral,
        WithdrawCollateral,
        SpotTick,
        UpdatePrice,
        SettlePnl,
        MatchOrders,
        DepositInsurance,
        ExecuteSlowMode,
        MintLp,
        BurnLp,
        SwapAMM,
        MatchOrderAMM,
        DumpFees,
        ClaimSequencerFees,
        PerpTick,
        ManualAssert,
        Rebate, // deprecated
        UpdateProduct,
        LinkSigner,
        UpdateFeeRates,
        BurnLpAndTransfer,
        MatchOrdersRFQ,
        TransferQuote,
        RebalanceXWithdraw,
        UpdateMinDepositRate,
        AssertCode,
        WithdrawInsurance,
        CreateIsolatedSubaccount
    }

    struct UpdateProduct {
        address engine;
        bytes tx;
    }

    /// requires signature from sender
    enum LiquidationMode {
        SPREAD,
        SPOT,
        PERP
    }

    struct LegacyLiquidateSubaccount {
        bytes32 sender;
        bytes32 liquidatee;
        uint8 mode;
        uint32 healthGroup;
        int128 amount;
        uint64 nonce;
    }

    struct LiquidateSubaccount {
        bytes32 sender;
        bytes32 liquidatee;
        uint32 productId;
        bool isEncodedSpread;
        int128 amount;
        uint64 nonce;
    }

    struct LegacySignedLiquidateSubaccount {
        LegacyLiquidateSubaccount tx;
        bytes signature;
    }

    struct SignedLiquidateSubaccount {
        LiquidateSubaccount tx;
        bytes signature;
    }

    struct DepositCollateral {
        bytes32 sender;
        uint32 productId;
        uint128 amount;
    }

    struct SignedDepositCollateral {
        DepositCollateral tx;
        bytes signature;
    }

    struct WithdrawCollateral {
        bytes32 sender;
        uint32 productId;
        uint128 amount;
        uint64 nonce;
    }

    struct SignedWithdrawCollateral {
        WithdrawCollateral tx;
        bytes signature;
    }

    struct MintLp {
        bytes32 sender;
        uint32 productId;
        uint128 amountBase;
        uint128 quoteAmountLow;
        uint128 quoteAmountHigh;
        uint64 nonce;
    }

    struct SignedMintLp {
        MintLp tx;
        bytes signature;
    }

    struct BurnLp {
        bytes32 sender;
        uint32 productId;
        uint128 amount;
        uint64 nonce;
    }

    struct SignedBurnLp {
        BurnLp tx;
        bytes signature;
    }

    struct LinkSigner {
        bytes32 sender;
        bytes32 signer;
        uint64 nonce;
    }

    struct SignedLinkSigner {
        LinkSigner tx;
        bytes signature;
    }

    /// callable by endpoint; no signature verifications needed
    struct PerpTick {
        uint128 time;
        int128[] avgPriceDiffs;
    }

    struct LegacySpotTick {
        uint128 time;
    }

    struct SpotTick {
        uint128 time;
        // utilization ratio across all chains
        int128[] utilizationRatiosX18;
    }

    struct ManualAssert {
        int128[] openInterests;
        int128[] totalDeposits;
        int128[] totalBorrows;
    }

    struct AssertCode {
        string[] contractNames;
        bytes32[] codeHashes;
    }

    struct WithdrawInsurance {
        uint128 amount;
        address sendTo;
    }

    struct Rebate {
        bytes32[] subaccounts;
        int128[] amounts;
    }

    struct UpdateFeeRates {
        address user;
        uint32 productId;
        // the absolute value of fee rates can't be larger than 100%,
        // so their X18 values are in the range [-1e18, 1e18], which
        // can be stored by using int64.
        int64 makerRateX18;
        int64 takerRateX18;
    }

    struct ClaimSequencerFees {
        bytes32 subaccount;
    }

    struct RebalanceXWithdraw {
        uint32 productId;
        uint128 amount;
        address sendTo;
    }

    struct UpdateMinDepositRate {
        uint32 productId;
        int128 minDepositRateX18;
    }

    struct UpdatePrice {
        uint32 productId;
        int128 priceX18;
    }

    struct SettlePnl {
        bytes32[] subaccounts;
        uint256[] productIds;
    }

    /// matching
    struct Order {
        bytes32 sender;
        int128 priceX18;
        int128 amount;
        uint64 expiration;
        uint64 nonce;
    }

    struct SignedOrder {
        Order order;
        bytes signature;
    }

    struct LegacyMatchOrders {
        uint32 productId;
        bool amm;
        SignedOrder taker;
        SignedOrder maker;
    }

    struct MatchOrders {
        uint32 productId;
        SignedOrder taker;
        SignedOrder maker;
    }

    struct MatchOrdersWithSigner {
        MatchOrders matchOrders;
        address takerLinkedSigner;
        address makerLinkedSigner;
    }

    // just swap against AMM -- theres no maker order
    struct MatchOrderAMM {
        uint32 productId;
        int128 baseDelta;
        int128 quoteDelta;
        SignedOrder taker;
    }

    struct SwapAMM {
        bytes32 sender;
        uint32 productId;
        int128 amount;
        int128 priceX18;
    }

    struct DepositInsurance {
        uint128 amount;
    }

    struct SlowModeTx {
        uint64 executableAt;
        address sender;
        bytes tx;
    }

    struct SlowModeConfig {
        uint64 timeout;
        uint64 txCount;
        uint64 txUpTo;
    }

    // legacy :(
    struct Prices {
        int128 spotPriceX18;
        int128 perpPriceX18;
    }

    struct BurnLpAndTransfer {
        bytes32 sender;
        uint32 productId;
        uint128 amount;
        bytes32 recipient;
    }

    struct TransferQuote {
        bytes32 sender;
        bytes32 recipient;
        uint128 amount;
        uint64 nonce;
    }

    struct SignedTransferQuote {
        TransferQuote tx;
        bytes signature;
    }

    struct IsolatedOrder {
        bytes32 sender;
        int128 priceX18;
        int128 amount;
        uint64 expiration;
        uint64 nonce;
        int128 margin;
    }

    struct CreateIsolatedSubaccount {
        IsolatedOrder order;
        uint32 productId;
        bytes signature;
    }

    function depositCollateral(
        bytes12 subaccountName,
        uint32 productId,
        uint128 amount
    ) external;

    function depositCollateralWithReferral(
        bytes12 subaccountName,
        uint32 productId,
        uint128 amount,
        string calldata referralCode
    ) external;

    function depositCollateralWithReferral(
        bytes32 subaccount,
        uint32 productId,
        uint128 amount,
        string calldata referralCode
    ) external;

    function submitSlowModeTransaction(bytes calldata transaction) external;

    function getTime() external view returns (uint128);

    function getSequencer() external view returns (address);

    function getNonce(address sender) external view returns (uint64);

    function getOffchainExchange() external view returns (address);

    function getPriceX18(uint32 productId) external view returns (int128);
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./IProductEngine.sol";
import "../../libraries/RiskHelper.sol";

interface IPerpEngine is IProductEngine {
    event FundingPayment(
        uint32 productId,
        uint128 dt,
        int128 openInterest,
        int128 payment
    );

    struct State {
        int128 cumulativeFundingLongX18;
        int128 cumulativeFundingShortX18;
        int128 availableSettle;
        int128 openInterest;
    }

    struct Balance {
        int128 amount;
        int128 vQuoteBalance;
        int128 lastCumulativeFundingX18;
    }

    struct LpState {
        int128 supply;
        // TODO: this should be removed; we can just get it from State.cumulativeFundingLongX18
        int128 lastCumulativeFundingX18;
        int128 cumulativeFundingPerLpX18;
        int128 base;
        int128 quote;
    }

    struct LpBalance {
        int128 amount;
        // NOTE: funding payments should be rolled
        // into Balance.vQuoteBalance;
        int128 lastCumulativeFundingX18;
    }

    struct UpdateProductTx {
        uint32 productId;
        int128 sizeIncrement;
        int128 minSize;
        int128 lpSpreadX18;
        RiskHelper.RiskStore riskStore;
    }

    function getStateAndBalance(uint32 productId, bytes32 subaccount)
        external
        view
        returns (State memory, Balance memory);

    function getBalance(uint32 productId, bytes32 subaccount)
        external
        view
        returns (Balance memory);

    function getStatesAndBalances(uint32 productId, bytes32 subaccount)
        external
        view
        returns (
            LpState memory,
            LpBalance memory,
            State memory,
            Balance memory
        );

    /// @dev Returns amount settled and emits SettlePnl events for each product
    function settlePnl(bytes32 subaccount, uint256 productIds)
        external
        returns (int128);

    function getSettlementState(uint32 productId, bytes32 subaccount)
        external
        view
        returns (
            int128 availableSettle,
            LpState memory lpState,
            LpBalance memory lpBalance,
            State memory state,
            Balance memory balance
        );

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta,
        int128 vQuoteDelta
    ) external;

    function updateStates(uint128 dt, int128[] calldata avgPriceDiffs) external;

    function manualAssert(int128[] calldata openInterests) external view;

    function getPositionPnl(uint32 productId, bytes32 subaccount)
        external
        view
        returns (int128);

    function socializeSubaccount(bytes32 subaccount, int128 insurance)
        external
        returns (int128);
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./IProductEngine.sol";
import "../../libraries/RiskHelper.sol";

interface ISpotEngine is IProductEngine {
    event SpotBalance(
        bytes32 indexed subaccount,
        uint32 indexed productId,
        int128 amount,
        int128 lastCumulativeMultiplierX18
    );

    event InterestPayment(
        uint32 productId,
        uint128 dt,
        int128 depositRateMultiplierX18,
        int128 borrowRateMultiplierX18,
        int128 feeAmount
    );

    struct Config {
        address token;
        int128 interestInflectionUtilX18;
        int128 interestFloorX18;
        int128 interestSmallCapX18;
        int128 interestLargeCapX18;
    }

    struct State {
        int128 cumulativeDepositsMultiplierX18;
        int128 cumulativeBorrowsMultiplierX18;
        int128 totalDepositsNormalized;
        int128 totalBorrowsNormalized;
    }

    struct Balance {
        int128 amount;
        int128 lastCumulativeMultiplierX18;
    }

    struct BalanceNormalized {
        int128 amountNormalized;
    }

    struct LpState {
        int128 supply;
        Balance quote;
        Balance base;
    }

    struct LpBalance {
        int128 amount;
    }

    struct Balances {
        BalanceNormalized balance;
        LpBalance lpBalance;
    }

    struct UpdateProductTx {
        uint32 productId;
        int128 sizeIncrement;
        int128 minSize;
        int128 lpSpreadX18;
        Config config;
        RiskHelper.RiskStore riskStore;
    }

    function getStateAndBalance(uint32 productId, bytes32 subaccount)
        external
        view
        returns (State memory, Balance memory);

    function getBalance(uint32 productId, bytes32 subaccount)
        external
        view
        returns (Balance memory);

    function getStatesAndBalances(uint32 productId, bytes32 subaccount)
        external
        view
        returns (
            LpState memory,
            LpBalance memory,
            State memory,
            Balance memory
        );

    function getConfig(uint32 productId) external view returns (Config memory);

    function getToken(uint32 productId) external view returns (address);

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta
    ) external;

    function updateBalance(
        uint32 productId,
        bytes32 subaccount,
        int128 amountDelta,
        int128 quoteDelta
    ) external;

    function updateQuoteFromInsurance(bytes32 subaccount, int128 insurance)
        external
        returns (int128);

    function updateStates(uint128 dt) external;

    function updateMinDepositRate(uint32 productId, int128 minDepositRateX18)
        external;

    function manualAssert(
        int128[] calldata totalDeposits,
        int128[] calldata totalBorrows
    ) external view;

    function socializeSubaccount(bytes32 subaccount) external;

    function assertUtilization(uint32 productId) external view;
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "../clearinghouse/IClearinghouse.sol";
import "../../libraries/RiskHelper.sol";

interface IProductEngine {
    event AddProduct(uint32 productId);

    enum EngineType {
        SPOT,
        PERP
    }

    enum HealthType {
        INITIAL,
        MAINTENANCE,
        PNL
    }

    struct ProductDelta {
        uint32 productId;
        bytes32 subaccount;
        int128 amountDelta;
        int128 vQuoteDelta;
    }

    struct CoreRisk {
        int128 amount;
        int128 price;
        int128 longWeight;
    }

    /// @notice Initializes the engine
    function initialize(
        address _clearinghouse,
        address _offchainExchange,
        address _quote,
        address _endpoint,
        address _admin
    ) external;

    function getHealthContribution(
        bytes32 subaccount,
        IProductEngine.HealthType healthType
    ) external view returns (int128);

    function getCoreRisk(
        bytes32 subaccount,
        uint32 productId,
        IProductEngine.HealthType healthType
    ) external view returns (IProductEngine.CoreRisk memory);

    function updateProduct(bytes calldata txn) external;

    function swapLp(
        uint32 productId,
        int128 baseDelta,
        int128 quoteDelta
    ) external returns (int128, int128);

    function mintLp(
        uint32 productId,
        bytes32 subaccount,
        int128 amountBase,
        int128 quoteAmountLow,
        int128 quoteAmountHigh
    ) external;

    function burnLp(
        uint32 productId,
        bytes32 subaccount,
        // passing 0 here means to burn all
        int128 amountLp
    ) external returns (int128, int128);

    function decomposeLps(bytes32 liquidatee, bytes32 liquidator)
        external
        returns (int128);

    /// @notice return clearinghouse addr
    function getClearinghouse() external view returns (address);

    /// @notice return productIds associated with engine
    function getProductIds() external view returns (uint32[] memory);

    function getRisk(uint32 productId)
        external
        view
        returns (RiskHelper.Risk memory);

    /// @notice return the type of engine
    function getEngineType() external pure returns (IProductEngine.EngineType);

    function updatePrice(uint32 productId, int128 priceX18) external;
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;
import "./MathSD21x18.sol";
import "../interfaces/engine/IProductEngine.sol";
import "../common/Constants.sol";
import "../common/Errors.sol";
import "./MathHelper.sol";

/// @title RiskHelper
/// @dev Provides basic math functions
library RiskHelper {
    using MathSD21x18 for int128;

    struct RiskStore {
        // these weights are all
        // between 0 and 2
        // these integers are the real
        // weights times 1e9
        int32 longWeightInitial;
        int32 shortWeightInitial;
        int32 longWeightMaintenance;
        int32 shortWeightMaintenance;
        int128 priceX18;
    }

    struct Risk {
        int128 longWeightInitialX18;
        int128 shortWeightInitialX18;
        int128 longWeightMaintenanceX18;
        int128 shortWeightMaintenanceX18;
        int128 priceX18;
    }

    function _getSpreadHealthRebateAmount(
        Risk memory perpRisk,
        int128 basisAmount,
        int128 priceSumX18,
        IProductEngine.HealthType healthType
    ) internal pure returns (int128) {
        // 5x more leverage than the standard perp
        // by refunding 4/5 of the health penalty
        int128 rebateRateX18 = ((ONE - _getWeightX18(perpRisk, 1, healthType)) *
            4) / 5;
        return rebateRateX18.mul(priceSumX18).mul(basisAmount);
    }

    function _getLpRawValue(
        int128 baseAmount,
        int128 quoteAmount,
        int128 priceX18
    ) internal pure returns (int128) {
        // naive way: value an LP token by value of the raw components 2 * arithmetic mean of base value and quote value
        // price manipulation proof way: use the geometric mean
        return
            2 *
            int128(
                MathHelper.sqrt256(
                    int256(baseAmount.mul(priceX18)) * quoteAmount
                )
            );
    }

    function _getWeightX18(
        Risk memory risk,
        int128 amount,
        IProductEngine.HealthType healthType
    ) internal pure returns (int128) {
        // (1 + imf * sqrt(amount))
        if (healthType == IProductEngine.HealthType.PNL) {
            return ONE;
        }

        int128 weight;
        if (amount >= 0) {
            weight = healthType == IProductEngine.HealthType.INITIAL
                ? risk.longWeightInitialX18
                : risk.longWeightMaintenanceX18;
        } else {
            weight = healthType == IProductEngine.HealthType.INITIAL
                ? risk.shortWeightInitialX18
                : risk.shortWeightMaintenanceX18;
        }

        return weight;
    }

    function isIsolatedSubaccount(bytes32 subaccount)
        internal
        pure
        returns (bool)
    {
        return uint256(subaccount) & 0xFFFFFF == 6910831;
    }

    function getIsolatedProductId(bytes32 subaccount)
        internal
        pure
        returns (uint32)
    {
        if (!isIsolatedSubaccount(subaccount)) {
            return 0;
        }
        return uint32((uint256(subaccount) >> 32) & 0xFFFF);
    }

    function getIsolatedId(bytes32 subaccount) internal pure returns (uint8) {
        if (!isIsolatedSubaccount(subaccount)) {
            return 0;
        }
        return uint8((uint256(subaccount) >> 24) & 0xFF);
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "hardhat/console.sol";

import "./common/Constants.sol";
import "./common/Errors.sol";
import "./libraries/MathHelper.sol";
import "./libraries/MathSD21x18.sol";
import "./interfaces/clearinghouse/IClearinghouse.sol";
import "./interfaces/engine/IProductEngine.sol";
import "./interfaces/IOffchainExchange.sol";
import "./interfaces/IEndpoint.sol";
import "./EndpointGated.sol";
import "./libraries/Logger.sol";

abstract contract BaseEngine is IProductEngine, EndpointGated {
    using MathSD21x18 for int128;

    IClearinghouse internal _clearinghouse;
    address internal _fees; // deprecated
    uint32[] internal productIds;

    mapping(uint32 => address) internal markets; // deprecated

    // Whether an address can apply deltas - all orderbooks and clearinghouse is whitelisted
    mapping(address => bool) internal canApplyDeltas;

    bytes32 internal constant RISK_STORAGE = keccak256("vertex.protocol.risk");

    event BalanceUpdate(uint32 productId, bytes32 subaccount);
    event ProductUpdate(uint32 productId);

    function _productUpdate(uint32 productId) internal virtual {}

    struct Uint256Slot {
        uint256 value;
    }

    struct RiskStoreMappingSlot {
        mapping(uint32 => RiskHelper.RiskStore) value;
    }

    function _risk() internal pure returns (RiskStoreMappingSlot storage r) {
        bytes32 slot = RISK_STORAGE;
        assembly {
            r.slot := slot
        }
    }

    function _risk(uint32 productId, RiskStoreMappingSlot storage rmap)
        internal
        view
        returns (RiskHelper.Risk memory r)
    {
        RiskHelper.RiskStore memory s = rmap.value[productId];
        r.longWeightInitialX18 = int128(s.longWeightInitial) * 1e9;
        r.shortWeightInitialX18 = int128(s.shortWeightInitial) * 1e9;
        r.longWeightMaintenanceX18 = int128(s.longWeightMaintenance) * 1e9;
        r.shortWeightMaintenanceX18 = int128(s.shortWeightMaintenance) * 1e9;
        r.priceX18 = s.priceX18;
    }

    function _risk(uint32 productId)
        internal
        view
        returns (RiskHelper.Risk memory)
    {
        return _risk(productId, _risk());
    }

    function getRisk(uint32 productId)
        external
        view
        returns (RiskHelper.Risk memory)
    {
        return _risk(productId);
    }

    function _getInLpBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        virtual
        returns (
            // baseAmount, quoteAmount, quoteDeltaAmount (funding)
            int128,
            int128,
            int128
        );

    function _getBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        virtual
        returns (int128, int128);

    function getHealthContribution(
        bytes32 subaccount,
        IProductEngine.HealthType healthType
    ) public view returns (int128 health) {
        uint32[] memory _productIds = getProductIds();
        RiskStoreMappingSlot storage r = _risk();

        for (uint32 i = 0; i < _productIds.length; i++) {
            uint32 productId = _productIds[i];
            RiskHelper.Risk memory risk = _risk(productId, r);
            {
                (int128 amount, int128 quoteAmount) = _getBalance(
                    productId,
                    subaccount
                );
                int128 weight = RiskHelper._getWeightX18(
                    risk,
                    amount,
                    healthType
                );
                health += quoteAmount;
                if (amount != 0) {
                    // anything with a short weight of 2 is a spot that
                    // should not count towards health and exists out of the risk system
                    // if we're getting a weight of 2 it means this is attempting to short
                    // the spot, so we should error out
                    if (weight == 2 * ONE) {
                        return type(int128).min;
                    }

                    health += amount.mul(weight).mul(risk.priceX18);
                }
            }

            {
                (
                    int128 baseAmount,
                    int128 quoteAmount,
                    int128 quoteDeltaAmount
                ) = _getInLpBalance(productId, subaccount);
                if (baseAmount != 0) {
                    int128 lpValue = RiskHelper._getLpRawValue(
                        baseAmount,
                        quoteAmount,
                        risk.priceX18
                    );
                    health +=
                        lpValue.mul(
                            RiskHelper._getWeightX18(risk, 1, healthType)
                        ) +
                        quoteDeltaAmount;
                }
            }
        }
    }

    function getCoreRisk(
        bytes32 subaccount,
        uint32 productId,
        IProductEngine.HealthType healthType
    ) external view returns (IProductEngine.CoreRisk memory) {
        RiskHelper.Risk memory risk = _risk(productId);
        (int128 amount, ) = _getBalance(productId, subaccount);
        return
            IProductEngine.CoreRisk(
                amount,
                risk.priceX18,
                RiskHelper._getWeightX18(risk, 1, healthType)
            );
    }

    function _balanceUpdate(uint32 productId, bytes32 subaccount)
        internal
        virtual
    {}

    function _assertInternal() internal view virtual {
        require(canApplyDeltas[msg.sender], ERR_UNAUTHORIZED);
    }

    function _initialize(
        address _clearinghouseAddr,
        address _offchainExchangeAddr,
        address _endpointAddr,
        address _admin
    ) internal initializer {
        __Ownable_init();
        setEndpoint(_endpointAddr);
        transferOwnership(_admin);

        _clearinghouse = IClearinghouse(_clearinghouseAddr);

        canApplyDeltas[_endpointAddr] = true;
        canApplyDeltas[_clearinghouseAddr] = true;
        canApplyDeltas[_offchainExchangeAddr] = true;
    }

    function getClearinghouse() external view returns (address) {
        return address(_clearinghouse);
    }

    function getProductIds() public view returns (uint32[] memory) {
        return productIds;
    }

    function _addProductForId(
        uint32 productId,
        uint32 quoteId,
        address virtualBook,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18,
        RiskHelper.RiskStore memory riskStore
    ) internal {
        require(virtualBook != address(0));
        require(
            riskStore.longWeightInitial <= riskStore.longWeightMaintenance &&
                riskStore.longWeightMaintenance <= 10**9 &&
                riskStore.shortWeightInitial >=
                riskStore.shortWeightMaintenance &&
                riskStore.shortWeightMaintenance >= 10**9,
            ERR_BAD_PRODUCT_CONFIG
        );

        _risk().value[productId] = riskStore;

        // register product with clearinghouse
        _clearinghouse.registerProduct(productId);

        productIds.push(productId);
        // product ids are in ascending order
        for (uint256 i = productIds.length - 1; i > 0; i--) {
            if (productIds[i] < productIds[i - 1]) {
                uint32 t = productIds[i];
                productIds[i] = productIds[i - 1];
                productIds[i - 1] = t;
            } else {
                break;
            }
        }

        _exchange().updateMarket(
            productId,
            quoteId,
            virtualBook,
            sizeIncrement,
            minSize,
            lpSpreadX18
        );

        emit AddProduct(productId);
    }

    function _exchange() internal view returns (IOffchainExchange) {
        return
            IOffchainExchange(IEndpoint(getEndpoint()).getOffchainExchange());
    }

    function updatePrice(uint32 productId, int128 priceX18)
        external
        onlyEndpoint
    {
        _risk().value[productId].priceX18 = priceX18;
    }

    function updateRisk(uint32 productId, RiskHelper.RiskStore memory riskStore)
        external
        onlyOwner
    {
        require(
            riskStore.longWeightInitial <= riskStore.longWeightMaintenance &&
                riskStore.shortWeightInitial >=
                riskStore.shortWeightMaintenance,
            ERR_BAD_PRODUCT_CONFIG
        );

        _risk().value[productId] = riskStore;
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./interfaces/engine/ISpotEngine.sol";
import "./libraries/Logger.sol";
import "./BaseEngine.sol";

abstract contract SpotEngineState is ISpotEngine, BaseEngine {
    using MathSD21x18 for int128;

    mapping(uint32 => Config) internal configs;
    mapping(uint32 => State) internal states;
    mapping(uint32 => mapping(bytes32 => Balances)) internal balances;

    mapping(uint32 => LpState) internal lpStates;

    mapping(uint32 => int128) internal withdrawFees;

    uint64 public migrationFlag; // deprecated

    mapping(uint32 => int128) internal minDepositRatesX18;

    function _updateBalanceWithoutDelta(
        State memory state,
        Balance memory balance
    ) internal pure {
        if (balance.amount == 0) {
            balance.lastCumulativeMultiplierX18 = state
                .cumulativeDepositsMultiplierX18;
            return;
        }

        // Current cumulative multiplier associated with product
        int128 cumulativeMultiplierX18;
        if (balance.amount > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        if (balance.lastCumulativeMultiplierX18 == cumulativeMultiplierX18) {
            return;
        }

        balance.amount = balance.amount.mul(cumulativeMultiplierX18).div(
            balance.lastCumulativeMultiplierX18
        );

        balance.lastCumulativeMultiplierX18 = cumulativeMultiplierX18;
    }

    function _updateBalance(
        State memory state,
        Balance memory balance,
        int128 balanceDelta
    ) internal pure {
        if (balance.amount == 0 && balance.lastCumulativeMultiplierX18 == 0) {
            balance.lastCumulativeMultiplierX18 = ONE;
        }

        if (balance.amount > 0) {
            state.totalDepositsNormalized -= balance.amount.div(
                balance.lastCumulativeMultiplierX18
            );
        } else {
            state.totalBorrowsNormalized += balance.amount.div(
                balance.lastCumulativeMultiplierX18
            );
        }

        // Current cumulative multiplier associated with product
        int128 cumulativeMultiplierX18;
        if (balance.amount > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        // Apply balance delta and interest rate
        balance.amount =
            balance.amount.mul(
                cumulativeMultiplierX18.div(balance.lastCumulativeMultiplierX18)
            ) +
            balanceDelta;

        if (balance.amount > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        balance.lastCumulativeMultiplierX18 = cumulativeMultiplierX18;

        // Update the product given balanceDelta
        if (balance.amount > 0) {
            state.totalDepositsNormalized += balance.amount.div(
                balance.lastCumulativeMultiplierX18
            );
        } else {
            state.totalBorrowsNormalized -= balance.amount.div(
                balance.lastCumulativeMultiplierX18
            );
        }
    }

    function _updateBalanceNormalizedNoTotals(
        State memory state,
        BalanceNormalized memory balance,
        int128 balanceDelta
    ) internal pure {
        // dont count X balances in total deposits / borrows
        // Current cumulative multiplier associated with product
        int128 cumulativeMultiplierX18;
        if (balance.amountNormalized > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        int128 newAmount = balance.amountNormalized.mul(
            cumulativeMultiplierX18
        ) + balanceDelta;

        if (newAmount > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        balance.amountNormalized = newAmount.div(cumulativeMultiplierX18);
    }

    function _updateBalanceNormalized(
        State memory state,
        BalanceNormalized memory balance,
        int128 balanceDelta
    ) internal pure {
        if (balance.amountNormalized > 0) {
            state.totalDepositsNormalized -= balance.amountNormalized;
        } else {
            state.totalBorrowsNormalized += balance.amountNormalized;
        }

        _updateBalanceNormalizedNoTotals(state, balance, balanceDelta);
        // Update the product given balanceDelta
        if (balance.amountNormalized > 0) {
            state.totalDepositsNormalized += balance.amountNormalized;
        } else {
            state.totalBorrowsNormalized -= balance.amountNormalized;
        }
    }

    function _updateState(
        uint32 productId,
        State memory state,
        uint128 dt
    ) internal {
        int128 borrowRateMultiplierX18;
        int128 totalDeposits = state.totalDepositsNormalized.mul(
            state.cumulativeDepositsMultiplierX18
        );
        int128 totalBorrows = state.totalBorrowsNormalized.mul(
            state.cumulativeBorrowsMultiplierX18
        );
        int128 utilizationRatioX18 = totalBorrows.div(totalDeposits);
        {
            Config memory config = configs[productId];

            // annualized borrower rate
            int128 borrowerRateX18 = config.interestFloorX18;
            if (utilizationRatioX18 == 0) {
                // setting borrowerRateX18 to 0 here has the property that
                // adding a product at the beginning of time and not using it until time T
                // results in the same state as adding the product at time T
                borrowerRateX18 = 0;
            } else if (utilizationRatioX18 < config.interestInflectionUtilX18) {
                borrowerRateX18 += config
                    .interestSmallCapX18
                    .mul(utilizationRatioX18)
                    .div(config.interestInflectionUtilX18);
            } else {
                borrowerRateX18 +=
                    config.interestSmallCapX18 +
                    config.interestLargeCapX18.mul(
                        (
                            (utilizationRatioX18 -
                                config.interestInflectionUtilX18).div(
                                    ONE - config.interestInflectionUtilX18
                                )
                        )
                    );
            }

            // convert to per second
            borrowerRateX18 = borrowerRateX18.div(
                MathSD21x18.fromInt(31536000)
            );
            borrowRateMultiplierX18 = (ONE + borrowerRateX18).pow(int128(dt));
        }

        // if we don't take fees into account, the liquidity, which is
        // (deposits - borrows) should remain the same after updating state.

        // For simplicity, we use `tb`, `cbm`, `td`, and `cdm` for
        // `totalBorrowsNormalized`, `cumulativeBorrowsMultiplier`,
        // `totalDepositsNormalized`, and `cumulativeDepositsMultiplier`

        // before the updating, the liquidity is (td * cdm - tb * cbm)
        // after the updating, the liquidity is
        // (td * cdm * depositRateMultiplier - tb * cbm * borrowRateMultiplier)
        // so we can get
        // depositRateMultiplier = utilization * (borrowRateMultiplier - 1) + 1

        int128 totalDepositRateX18 = utilizationRatioX18.mul(
            borrowRateMultiplierX18 - ONE
        );

        // deduct protocol fees
        int128 realizedDepositRateX18 = totalDepositRateX18.mul(
            ONE - INTEREST_FEE_FRACTION
        );

        // pass fees balance change
        int128 feesAmt = totalDeposits.mul(
            totalDepositRateX18 - realizedDepositRateX18
        );

        state.cumulativeBorrowsMultiplierX18 = state
            .cumulativeBorrowsMultiplierX18
            .mul(borrowRateMultiplierX18);

        int128 depositRateMultiplierX18 = ONE + realizedDepositRateX18;

        state.cumulativeDepositsMultiplierX18 = state
            .cumulativeDepositsMultiplierX18
            .mul(depositRateMultiplierX18);

        if (feesAmt != 0) {
            BalanceNormalized memory feesAccBalance = balances[productId][
                FEES_ACCOUNT
            ].balance;
            _updateBalanceNormalized(state, feesAccBalance, feesAmt);
            balances[productId][FEES_ACCOUNT].balance = feesAccBalance;
            _balanceUpdate(productId, FEES_ACCOUNT);
        }

        // apply the min deposit rate
        if (minDepositRatesX18[productId] != 0) {
            int128 minDepositRatePerSecondX18 = minDepositRatesX18[productId]
                .div(MathSD21x18.fromInt(31536000));
            int128 minDepositRateMultiplierX18 = (ONE +
                minDepositRatePerSecondX18).pow(int128(dt));

            state.cumulativeBorrowsMultiplierX18 = state
                .cumulativeBorrowsMultiplierX18
                .mul(minDepositRateMultiplierX18);

            state.cumulativeDepositsMultiplierX18 = state
                .cumulativeDepositsMultiplierX18
                .mul(minDepositRateMultiplierX18);

            depositRateMultiplierX18 = depositRateMultiplierX18.mul(
                minDepositRateMultiplierX18
            );
            borrowRateMultiplierX18 = borrowRateMultiplierX18.mul(
                minDepositRateMultiplierX18
            );
        }

        emit InterestPayment(
            productId,
            dt,
            depositRateMultiplierX18,
            borrowRateMultiplierX18,
            feesAmt
        );
    }

    function balanceNormalizedToBalance(
        State memory state,
        BalanceNormalized memory balance
    ) internal pure returns (Balance memory) {
        int128 cumulativeMultiplierX18;
        if (balance.amountNormalized > 0) {
            cumulativeMultiplierX18 = state.cumulativeDepositsMultiplierX18;
        } else {
            cumulativeMultiplierX18 = state.cumulativeBorrowsMultiplierX18;
        }

        return
            Balance(
                balance.amountNormalized.mul(cumulativeMultiplierX18),
                cumulativeMultiplierX18
            );
    }

    function _balanceUpdate(uint32 productId, bytes32 subaccount)
        internal
        virtual
        override
    {
        Balance memory balance = getBalance(productId, subaccount);
        emit SpotBalance(
            subaccount,
            productId,
            balance.amount,
            balance.lastCumulativeMultiplierX18
        );
    }

    // TODO: maybe combine the next two functions
    // probably also need some protection where quote state must
    // be fetched through getQuoteState
    function getStateAndBalance(uint32 productId, bytes32 subaccount)
        public
        view
        returns (State memory, Balance memory)
    {
        State memory state = states[productId];
        BalanceNormalized memory balance = balances[productId][subaccount]
            .balance;
        return (state, balanceNormalizedToBalance(state, balance));
    }

    function getBalance(uint32 productId, bytes32 subaccount)
        public
        view
        returns (Balance memory)
    {
        State memory state = states[productId];
        BalanceNormalized memory balance = balances[productId][subaccount]
            .balance;
        return balanceNormalizedToBalance(state, balance);
    }

    function _getBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        override
        returns (int128, int128)
    {
        return (getBalance(productId, subaccount).amount, 0);
    }

    function _getInLpBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        virtual
        override
        returns (
            // baseAmount, quoteAmount, deltaQuoteAmount (funding)
            int128,
            int128,
            int128
        )
    {
        LpBalance memory lpBalance = balances[productId][subaccount].lpBalance;
        if (lpBalance.amount == 0) {
            return (0, 0, 0);
        }
        LpState memory lpState = lpStates[productId];
        int128 ratio = lpBalance.amount.div(lpState.supply);
        int128 baseAmount = lpState.base.amount.mul(ratio);
        int128 quoteAmount = lpState.quote.amount.mul(ratio);

        return (baseAmount, quoteAmount, 0);
    }

    function getStatesAndBalances(uint32 productId, bytes32 subaccount)
        external
        view
        returns (
            LpState memory,
            LpBalance memory,
            State memory,
            Balance memory
        )
    {
        LpState memory lpState = lpStates[productId];
        State memory state = states[productId];

        Balances memory bal = balances[productId][subaccount];

        LpBalance memory lpBalance = bal.lpBalance;
        BalanceNormalized memory balance = bal.balance;

        return (
            lpState,
            lpBalance,
            state,
            balanceNormalizedToBalance(state, balance)
        );
    }

    function updateStates(uint128 dt) external onlyEndpoint {
        State memory quoteState;
        require(dt < 7 * SECONDS_PER_DAY, ERR_INVALID_TIME);
        for (uint32 i = 0; i < productIds.length; i++) {
            uint32 productId = productIds[i];
            State memory state = states[productId];
            if (productId == QUOTE_PRODUCT_ID) {
                quoteState = state;
            }
            if (state.totalDepositsNormalized == 0) {
                continue;
            }
            LpState memory lpState = lpStates[productId];
            _updateState(productId, state, dt);
            _updateBalanceWithoutDelta(state, lpState.base);
            _updateBalanceWithoutDelta(quoteState, lpState.quote);
            lpStates[productId] = lpState;
            states[productId] = state;
            _productUpdate(productId);
        }
    }

    function updateMinDepositRate(uint32 productId, int128 minDepositRateX18)
        external
        onlyEndpoint
    {
        // deposit rate can't be larger than 100% so that when the rate is incorrectly
        // set, we still can rescue it without having too much damage.
        require(
            minDepositRateX18 >= 0 && minDepositRateX18 <= ONE,
            ERR_BAD_PRODUCT_CONFIG
        );
        minDepositRatesX18[productId] = minDepositRateX18;
    }

    function getMinDepositRate(uint32 productId)
        external
        view
        returns (int128)
    {
        return minDepositRatesX18[productId];
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./SpotEngineState.sol";
import "./libraries/Logger.sol";

abstract contract SpotEngineLP is SpotEngineState {
    using MathSD21x18 for int128;

    function mintLp(
        uint32 productId,
        bytes32 subaccount,
        int128 amountBase,
        int128 quoteAmountLow,
        int128 quoteAmountHigh
    ) external {
        _assertInternal();
        require(
            amountBase > 0 && quoteAmountLow > 0 && quoteAmountHigh > 0,
            ERR_INVALID_LP_AMOUNT
        );

        require(
            _exchange().getMarketInfo(productId).quoteId == QUOTE_PRODUCT_ID,
            ERR_INVALID_PRODUCT
        );

        LpState memory lpState = lpStates[productId];
        State memory base = states[productId];
        State memory quote = states[QUOTE_PRODUCT_ID];

        int128 amountQuote = (lpState.base.amount == 0)
            ? amountBase.mul(_risk(productId).priceX18)
            : amountBase.mul(lpState.quote.amount.div(lpState.base.amount));
        require(amountQuote >= quoteAmountLow, ERR_SLIPPAGE_TOO_HIGH);
        require(amountQuote <= quoteAmountHigh, ERR_SLIPPAGE_TOO_HIGH);

        int128 toMint;
        if (lpState.supply == 0) {
            toMint = amountBase + amountQuote;
        } else {
            toMint = amountBase.div(lpState.base.amount).mul(lpState.supply);
        }

        _updateBalance(base, lpState.base, amountBase);
        _updateBalance(quote, lpState.quote, amountQuote);
        lpState.supply += toMint;

        balances[productId][subaccount].lpBalance.amount += toMint;

        lpStates[productId] = lpState;

        BalanceNormalized memory baseBalance = balances[productId][subaccount]
            .balance;
        BalanceNormalized memory quoteBalance = balances[QUOTE_PRODUCT_ID][
            subaccount
        ].balance;

        _updateBalanceNormalized(base, baseBalance, -amountBase);
        _updateBalanceNormalized(quote, quoteBalance, -amountQuote);

        balances[productId][subaccount].balance = baseBalance;
        balances[QUOTE_PRODUCT_ID][subaccount].balance = quoteBalance;
        states[productId] = base;
        states[QUOTE_PRODUCT_ID] = quote;

        _balanceUpdate(productId, subaccount);
        _balanceUpdate(QUOTE_PRODUCT_ID, subaccount);
    }

    function burnLp(
        uint32 productId,
        bytes32 subaccount,
        int128 amountLp
    ) public returns (int128 amountBase, int128 amountQuote) {
        _assertInternal();
        require(amountLp > 0, ERR_INVALID_LP_AMOUNT);

        LpState memory lpState = lpStates[productId];
        LpBalance memory lpBalance = balances[productId][subaccount].lpBalance;
        State memory base = states[productId];
        State memory quote = states[QUOTE_PRODUCT_ID];

        if (amountLp == type(int128).max) {
            amountLp = lpBalance.amount;
        }
        if (amountLp == 0) {
            return (0, 0);
        }

        require(lpBalance.amount >= amountLp, ERR_INSUFFICIENT_LP);
        lpBalance.amount -= amountLp;

        amountBase = int128(
            (int256(amountLp) * lpState.base.amount) / lpState.supply
        );
        amountQuote = int128(
            (int256(amountLp) * lpState.quote.amount) / lpState.supply
        );

        _updateBalance(base, lpState.base, -amountBase);
        _updateBalance(quote, lpState.quote, -amountQuote);
        lpState.supply -= amountLp;

        lpStates[productId] = lpState;
        balances[productId][subaccount].lpBalance = lpBalance;

        BalanceNormalized memory baseBalance = balances[productId][subaccount]
            .balance;
        BalanceNormalized memory quoteBalance = balances[QUOTE_PRODUCT_ID][
            subaccount
        ].balance;

        _updateBalanceNormalized(base, baseBalance, amountBase);
        _updateBalanceNormalized(quote, quoteBalance, amountQuote);

        balances[productId][subaccount].balance = baseBalance;
        balances[QUOTE_PRODUCT_ID][subaccount].balance = quoteBalance;
        states[productId] = base;
        states[QUOTE_PRODUCT_ID] = quote;

        _balanceUpdate(productId, subaccount);
        _balanceUpdate(QUOTE_PRODUCT_ID, subaccount);
    }

    function swapLp(
        uint32 productId,
        int128 baseDelta,
        int128 quoteDelta
    ) external returns (int128, int128) {
        _assertInternal();
        LpState memory lpState = lpStates[productId];
        require(
            MathHelper.isSwapValid(
                baseDelta,
                quoteDelta,
                lpState.base.amount,
                lpState.quote.amount
            ),
            ERR_INVALID_MAKER
        );

        int128 baseDepositsMultiplierX18 = states[productId]
            .cumulativeDepositsMultiplierX18;
        int128 quoteDepositsMultiplierX18 = states[QUOTE_PRODUCT_ID]
            .cumulativeDepositsMultiplierX18;

        lpState.base.amount += baseDelta;
        lpState.quote.amount += quoteDelta;
        lpStates[productId] = lpState;

        states[productId].totalDepositsNormalized += baseDelta.div(
            baseDepositsMultiplierX18
        );
        states[QUOTE_PRODUCT_ID].totalDepositsNormalized += quoteDelta.div(
            quoteDepositsMultiplierX18
        );
        _productUpdate(productId);
        return (baseDelta, quoteDelta);
    }

    function decomposeLps(bytes32 liquidatee, bytes32 liquidator)
        external
        returns (int128 liquidationFees)
    {
        uint32[] memory _productIds = getProductIds();
        for (uint128 i = 0; i < _productIds.length; ++i) {
            uint32 productId = _productIds[i];
            (, int128 amountQuote) = burnLp(
                productId,
                liquidatee,
                type(int128).max
            );
            if (amountQuote != 0) {
                int128 rewards = amountQuote.mul(
                    (ONE -
                        RiskHelper._getWeightX18(
                            _risk(productId),
                            amountQuote,
                            IProductEngine.HealthType.MAINTENANCE
                        )) / 50
                );
                int128 fees = rewards.mul(LIQUIDATION_FEE_FRACTION);
                rewards -= fees;
                liquidationFees += fees;

                State memory quote = states[QUOTE_PRODUCT_ID];
                BalanceNormalized memory liquidateeQuote = balances[
                    QUOTE_PRODUCT_ID
                ][liquidatee].balance;
                BalanceNormalized memory liquidatorQuote = balances[
                    QUOTE_PRODUCT_ID
                ][liquidator].balance;

                _updateBalanceNormalized(
                    quote,
                    liquidateeQuote,
                    -rewards - fees
                );
                _updateBalanceNormalized(quote, liquidatorQuote, rewards);

                balances[QUOTE_PRODUCT_ID][liquidatee]
                    .balance = liquidateeQuote;
                balances[QUOTE_PRODUCT_ID][liquidator]
                    .balance = liquidatorQuote;
                states[QUOTE_PRODUCT_ID] = quote;
                _balanceUpdate(QUOTE_PRODUCT_ID, liquidator);
                _balanceUpdate(QUOTE_PRODUCT_ID, liquidatee);
            }
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import "./interfaces/IEndpoint.sol";
import "./interfaces/IEndpointGated.sol";
import "./libraries/MathSD21x18.sol";
import "./common/Constants.sol";
import "hardhat/console.sol";

abstract contract EndpointGated is OwnableUpgradeable, IEndpointGated {
    address private endpoint;

    function setEndpoint(address _endpoint) internal onlyOwner {
        endpoint = _endpoint;
    }

    function getEndpoint() public view returns (address) {
        return endpoint;
    }

    function getOracleTime() internal view returns (uint128) {
        return IEndpoint(endpoint).getTime();
    }

    modifier onlyEndpoint() {
        require(
            msg.sender == endpoint,
            "SequencerGated: caller is not the endpoint"
        );
        _;
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

/// @dev Each clearinghouse has a unique quote product
uint32 constant QUOTE_PRODUCT_ID = 0;

/// @dev Fees account
bytes32 constant FEES_ACCOUNT = bytes32(0);
bytes32 constant X_ACCOUNT = 0x0000000000000000000000000000000000000000000000000000000000000001;

string constant DEFAULT_REFERRAL_CODE = "-1";

uint128 constant MINIMUM_LIQUIDITY = 10**3;

int128 constant ONE = 10**18;

uint8 constant MAX_DECIMALS = 18;

int128 constant TAKER_SEQUENCER_FEE = 0; // $0.00

int128 constant SLOW_MODE_FEE = 1000000; // $1

int128 constant FAST_WITHDRAWAL_FEE_RATE = 1_000_000_000_000_000; // 0.1%

int128 constant LIQUIDATION_FEE = 1e18; // $1
int128 constant HEALTHCHECK_FEE = 1e18; // $1

uint128 constant INT128_MAX = uint128(type(int128).max);

uint64 constant SECONDS_PER_DAY = 3600 * 24;

uint32 constant VRTX_PRODUCT_ID = 41;

int128 constant LIQUIDATION_FEE_FRACTION = 500_000_000_000_000_000; // 50%

int128 constant INTEREST_FEE_FRACTION = 200_000_000_000_000_000; // 20%

int256 constant MIN_DEPOSIT_AMOUNT = 5 * ONE;

uint32 constant MAX_ISOLATED_SUBACCOUNTS_PER_ADDRESS = 10;

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./PerpEngineState.sol";
import "./libraries/Logger.sol";

abstract contract PerpEngineLp is PerpEngineState {
    using MathSD21x18 for int128;

    function mintLp(
        uint32 productId,
        bytes32 subaccount,
        int128 amountBase,
        int128 quoteAmountLow,
        int128 quoteAmountHigh
    ) external {
        _assertInternal();

        int128 sizeIncrement = _exchange().getSizeIncrement(productId);

        require(
            amountBase > 0 &&
                quoteAmountLow > 0 &&
                quoteAmountHigh > 0 &&
                amountBase % sizeIncrement == 0,
            ERR_INVALID_LP_AMOUNT
        );

        (
            LpState memory lpState,
            LpBalance memory lpBalance,
            State memory state,
            Balance memory balance
        ) = getStatesAndBalances(productId, subaccount);

        int128 amountQuote = (lpState.base == 0)
            ? amountBase.mul(_risk(productId).priceX18)
            : amountBase.mul(lpState.quote.div(lpState.base));
        require(amountQuote >= quoteAmountLow, ERR_SLIPPAGE_TOO_HIGH);
        require(amountQuote <= quoteAmountHigh, ERR_SLIPPAGE_TOO_HIGH);

        int128 toMint;
        if (lpState.supply == 0) {
            toMint = amountBase + amountQuote;
        } else {
            toMint = amountBase.div(lpState.base).mul(lpState.supply);
        }

        state.openInterest += amountBase;

        lpState.base += amountBase;
        lpState.quote += amountQuote;
        lpBalance.amount += toMint;
        _updateBalance(state, balance, -amountBase, -amountQuote);
        lpState.supply += toMint;

        lpBalances[productId][subaccount] = lpBalance;
        states[productId] = state;
        lpStates[productId] = lpState;
        balances[productId][subaccount] = balance;

        _balanceUpdate(productId, subaccount);
    }

    function burnLp(
        uint32 productId,
        bytes32 subaccount,
        int128 amountLp
    ) public returns (int128 amountBase, int128 amountQuote) {
        _assertInternal();
        require(amountLp > 0, ERR_INVALID_LP_AMOUNT);
        int128 sizeIncrement = _exchange().getSizeIncrement(productId);

        (
            LpState memory lpState,
            LpBalance memory lpBalance,
            State memory state,
            Balance memory balance
        ) = getStatesAndBalances(productId, subaccount);

        if (amountLp == type(int128).max) {
            amountLp = lpBalance.amount;
        }
        if (amountLp == 0) {
            return (0, 0);
        }

        require(lpBalance.amount >= amountLp, ERR_INSUFFICIENT_LP);
        lpBalance.amount -= amountLp;

        amountBase = MathHelper.floor(
            int128((int256(amountLp) * lpState.base) / lpState.supply),
            sizeIncrement
        );

        amountQuote = int128(
            (int256(amountLp) * lpState.quote) / lpState.supply
        );

        state.openInterest -= amountBase;

        _updateBalance(state, balance, amountBase, amountQuote);
        lpState.base -= amountBase;
        lpState.quote -= amountQuote;
        lpState.supply -= amountLp;

        lpStates[productId] = lpState;
        lpBalances[productId][subaccount] = lpBalance;
        states[productId] = state;
        balances[productId][subaccount] = balance;

        _balanceUpdate(productId, subaccount);
    }

    function swapLp(
        uint32 productId,
        int128 baseDelta,
        int128 quoteDelta
    ) external returns (int128, int128) {
        _assertInternal();
        LpState memory lpState = lpStates[productId];
        require(
            MathHelper.isSwapValid(
                baseDelta,
                quoteDelta,
                lpState.base,
                lpState.quote
            ),
            ERR_INVALID_MAKER
        );

        states[productId].openInterest += baseDelta;

        lpState.base += baseDelta;
        lpState.quote += quoteDelta;
        lpStates[productId] = lpState;
        _productUpdate(productId);
        return (baseDelta, quoteDelta);
    }

    function decomposeLps(bytes32 liquidatee, bytes32 liquidator)
        external
        returns (int128 liquidationFees)
    {
        uint32[] memory _productIds = getProductIds();
        for (uint128 i = 0; i < _productIds.length; ++i) {
            uint32 productId = _productIds[i];
            (, int128 amountQuote) = burnLp(
                productId,
                liquidatee,
                type(int128).max
            );
            if (amountQuote != 0) {
                int128 rewards = amountQuote.mul(
                    (ONE -
                        RiskHelper._getWeightX18(
                            _risk(productId),
                            amountQuote,
                            IProductEngine.HealthType.MAINTENANCE
                        )) / 50
                );

                int128 fees = rewards.mul(LIQUIDATION_FEE_FRACTION);
                rewards -= fees;
                liquidationFees += fees;

                // transfer some of the burned proceeds to liquidator
                State memory state = states[productId];
                Balance memory liquidateeBalance = balances[productId][
                    liquidatee
                ];
                Balance memory liquidatorBalance = balances[productId][
                    liquidator
                ];
                _updateBalance(state, liquidateeBalance, 0, -rewards - fees);
                _updateBalance(state, liquidatorBalance, 0, rewards);

                states[productId] = state;
                balances[productId][liquidatee] = liquidateeBalance;
                balances[productId][liquidator] = liquidatorBalance;
                _balanceUpdate(productId, liquidator);
                _balanceUpdate(productId, liquidatee);
            }
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./IClearinghouseEventEmitter.sol";
import "../engine/IProductEngine.sol";
import "../IEndpoint.sol";
import "../IEndpointGated.sol";
import "../../libraries/RiskHelper.sol";

interface IClearinghouse is IClearinghouseEventEmitter, IEndpointGated {
    function addEngine(
        address engine,
        address offchainExchange,
        IProductEngine.EngineType engineType
    ) external;

    function registerProduct(uint32 productId) external;

    function transferQuote(IEndpoint.TransferQuote calldata tx) external;

    function depositCollateral(IEndpoint.DepositCollateral calldata tx)
        external;

    function withdrawCollateral(
        bytes32 sender,
        uint32 productId,
        uint128 amount,
        address sendTo,
        uint64 idx
    ) external;

    function mintLp(IEndpoint.MintLp calldata tx) external;

    function burnLp(IEndpoint.BurnLp calldata tx) external;

    function liquidateSubaccount(IEndpoint.LiquidateSubaccount calldata tx)
        external;

    function depositInsurance(bytes calldata transaction) external;

    function withdrawInsurance(bytes calldata transaction, uint64 idx) external;

    function settlePnl(bytes calldata transaction) external;

    function claimSequencerFees(
        IEndpoint.ClaimSequencerFees calldata tx,
        int128[] calldata fees
    ) external;

    /// @notice Retrieve quote ERC20 address
    function getQuote() external view returns (address);

    /// @notice Returns the registered engine address by type
    function getEngineByType(IProductEngine.EngineType engineType)
        external
        view
        returns (address);

    /// @notice Returns the engine associated with a product ID
    function getEngineByProduct(uint32 productId)
        external
        view
        returns (address);

    /// @notice Returns health for the subaccount across all engines
    function getHealth(bytes32 subaccount, IProductEngine.HealthType healthType)
        external
        view
        returns (int128);

    /// @notice Returns the amount of insurance remaining in this clearinghouse
    function getInsurance() external view returns (int128);

    function getSpreads() external view returns (uint256);

    function upgradeClearinghouseLiq(address _clearinghouseLiq) external;

    function getClearinghouseLiq() external view returns (address);

    function burnLpAndTransfer(IEndpoint.BurnLpAndTransfer calldata txn)
        external;

    function requireMinDeposit(uint32 productId, uint128 amount) external;

    function assertCode(bytes calldata tx) external;

    function manualAssert(bytes calldata tx) external;

    function getWithdrawPool() external view returns (address);

    function getSlowModeFee() external view returns (uint256);

    function getWithdrawFee(uint32 productId) external view returns (int128);

    function setWithdrawPool(address _withdrawPool) external;
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "prb-math/contracts/PRBMathSD59x18.sol";

library MathSD21x18 {
    using PRBMathSD59x18 for int256;

    int128 private constant ONE_X18 = 1000000000000000000;
    int128 private constant MIN_X18 = -0x80000000000000000000000000000000;
    int128 private constant MAX_X18 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
    string private constant ERR_OVERFLOW = "OF";
    string private constant ERR_DIV_BY_ZERO = "DBZ";

    function fromInt(int128 x) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) * ONE_X18;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function mulDiv(
        int128 x,
        int128 y,
        int128 z
    ) internal pure returns (int128) {
        unchecked {
            require(z != 0, ERR_DIV_BY_ZERO);
            int256 result = (int256(x) * y) / z;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function toInt(int128 x) internal pure returns (int128) {
        unchecked {
            return int128(x / ONE_X18);
        }
    }

    function add(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) + y;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function sub(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) - y;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function mul(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = (int256(x) * y) / ONE_X18;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function div(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            require(y != 0, ERR_DIV_BY_ZERO);
            int256 result = (int256(x) * ONE_X18) / y;
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    function abs(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != MIN_X18, ERR_OVERFLOW);
            return x < 0 ? -x : x;
        }
    }

    function sqrt(int128 x) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x).sqrt();
            require(result >= MIN_X18 && result <= MAX_X18, ERR_OVERFLOW);
            return int128(result);
        }
    }

    // note that y is not X18
    function pow(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            require(y >= 0, ERR_OVERFLOW);
            int128 result = ONE_X18;
            for (int128 i = 1; i <= y; i *= 2) {
                if (i & y != 0) {
                    result = mul(result, x);
                }
                x = mul(x, x);
            }
            return result;
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

// Trying to take an action on vertex when
string constant ERR_REQUIRES_DEPOSIT = "RS";

// ERC20 Transfer failed
string constant ERR_TRANSFER_FAILED = "TF";

// Unauthorized
string constant ERR_UNAUTHORIZED = "U";

// Invalid product
string constant ERR_INVALID_PRODUCT = "IP";

// Subaccount health too low
string constant ERR_SUBACCT_HEALTH = "SH";

// Not liquidatable
string constant ERR_NOT_LIQUIDATABLE = "NL";

// Liquidator health too low
string constant ERR_NOT_LIQUIDATABLE_INITIAL = "NLI";

// Liquidatee has positive initial health
string constant ERR_LIQUIDATED_TOO_MUCH = "LTM";

// Trying to liquidate quote, or
string constant ERR_INVALID_LIQUIDATION_PARAMS = "NILP";

// Trying to liquidate perp but the amount is not divisible by sizeIncrement
string constant ERR_INVALID_LIQUIDATION_AMOUNT = "NILA";

// Tried to liquidate too little, too much or signs are different
string constant ERR_NOT_LIQUIDATABLE_AMT = "NLA";

// Tried to liquidate liabilities before perps
string constant ERR_NOT_LIQUIDATABLE_LIABILITIES = "NLL";

// Tried to finalize subaccount that cannot be finalized
string constant ERR_NOT_FINALIZABLE_SUBACCOUNT = "NFS";

// Not enough quote to settle
string constant ERR_CANNOT_SETTLE = "CS";

// Not enough insurance to settle
string constant ERR_NO_INSURANCE = "NI";

// Above reserve ratio
string constant ERR_RESERVE_RATIO = "RR";

// Invalid socialize amount
string constant ERR_INVALID_SOCIALIZE_AMT = "ISA";

// Socializing product with no open interest
string constant ERR_NO_OPEN_INTEREST = "NOI";

// FOK not filled, this isn't rly an error so this is jank
string constant ERR_FOK_NOT_FILLED = "ENF";

// bad product config via weights
string constant ERR_BAD_PRODUCT_CONFIG = "BPC";

// subacct name too long
string constant ERR_LONG_NAME = "LN";

// already registered in health group
string constant ERR_ALREADY_REGISTERED = "AR";

// invalid health group provided
string constant ERR_INVALID_HEALTH_GROUP = "IHG";

string constant ERR_GETTING_ZERO_HEALTH_GROUP = "GZHG";

// trying to burn more LP than owned
string constant ERR_INSUFFICIENT_LP = "ILP";

// taker order subaccount fails risk or is invalid
string constant ERR_INVALID_TAKER = "IT";

// maker order subaccount fails risk or is invalid
string constant ERR_INVALID_MAKER = "IM";

string constant ERR_INVALID_SIGNATURE = "IS";

string constant ERR_ORDERS_CANNOT_BE_MATCHED = "OCBM";

string constant ERR_INVALID_LP_AMOUNT = "ILA";

string constant ERR_SLIPPAGE_TOO_HIGH = "STH";

string constant ERR_SUBACCOUNT_NOT_FOUND = "SNF";

string constant ERR_INVALID_PRICE = "IPR";

string constant ERR_INVALID_TIME = "ITI";

// states on node and engine are not same
string constant ERR_DSYNC = "DSYNC";

string constant ERR_INVALID_SWAP_PARAMS = "ISP";

string constant ERR_CONVERSION_OVERFLOW = "CO";

string constant ERR_ONLY_CLEARINGHOUSE_CAN_SET_BOOK = "OCCSB";

// we match on containing these strings in sequencer
string constant ERR_INVALID_SUBMISSION_INDEX = "IX";
string constant ERR_NO_SLOW_MODE_TXS_REMAINING = "no slow mode transactions remaining";
string constant ERR_INVALID_COUNT = "IC";
string constant ERR_SLOW_TX_TOO_RECENT = "STTR";
string constant ERR_WALLET_NOT_TRANSFERABLE = "WNT";

string constant ERR_WALLET_SANCTIONED = "WS";

string constant ERR_SLOW_MODE_WRONG_SENDER = "SMWS";
string constant ERR_WRONG_NONCE = "WN";

// initially wanted to call this
// ERR_FULL_UTILIZATION but the shortened
// error string may make people mad on the frontend
string constant ERR_MAX_UTILIZATION = "MU";

string constant ERR_INVALID_RISK_GROUP = "IRG";

string constant ERR_VERIFY_SCHNORR = "VSR";

string constant ERR_DEPOSIT_TOO_SMALL = "DTS";

string constant ERR_CODE_NOT_MATCH = "CNM";

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;
import "./MathSD21x18.sol";

/// @title MathHelper
/// @dev Provides basic math functions
library MathHelper {
    using MathSD21x18 for int128;

    /// @notice Returns market id for two given product ids
    function max(int128 a, int128 b) internal pure returns (int128) {
        return a > b ? a : b;
    }

    function min(int128 a, int128 b) internal pure returns (int128) {
        return a < b ? a : b;
    }

    function abs(int128 val) internal pure returns (int128) {
        return val < 0 ? -val : val;
    }

    // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
    function sqrt(int128 y) internal pure returns (int128 z) {
        require(y >= 0, "ds-math-sqrt-non-positive");
        if (y > 3) {
            z = y;
            int128 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }

    function sqrt256(int256 y) internal pure returns (int256 z) {
        require(y >= 0, "ds-math-sqrt-non-positive");
        if (y > 3) {
            z = y;
            int256 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }

    function int2str(int128 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0";
        }

        bool negative = value < 0;
        uint128 absval = uint128(negative ? -value : value);
        string memory out = uint2str(absval);
        if (negative) {
            out = string.concat("-", out);
        }
        return out;
    }

    function uint2str(uint128 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0";
        }
        uint128 temp = value;
        uint128 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint128(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    // https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v3.1.0/contracts/math/SignedSafeMath.sol#L86
    function add(int128 x, int128 y) internal pure returns (int128) {
        int128 z = x + y;
        require((y >= 0 && z >= x) || (y < 0 && z < x), "ds-math-add-overflow");
        return z;
    }

    // https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v3.1.0/contracts/math/SignedSafeMath.sol#L69
    function sub(int128 x, int128 y) internal pure returns (int128) {
        int128 z = x - y;
        require(
            (y >= 0 && z <= x) || (y < 0 && z > x),
            "ds-math-sub-underflow"
        );
        return z;
    }

    function mul(int128 x, int128 y) internal pure returns (int128 z) {
        require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
    }

    function floor(int128 x, int128 y) internal pure returns (int128 z) {
        require(y > 0, "ds-math-floor-neg-mod");
        int128 r = x % y;
        if (r == 0) {
            z = x;
        } else {
            z = (x >= 0 ? x - r : x - r - y);
        }
    }

    function ceil(int128 x, int128 y) internal pure returns (int128 z) {
        require(y > 0, "ds-math-ceil-neg-mod");
        int128 r = x % y;
        if (r == 0) {
            z = x;
        } else {
            z = (x >= 0 ? x + y - r : x - r);
        }
    }

    // we don't need to floor base with sizeIncrement in this function
    // because this function is only used by `view` functions, which means
    // the returned values will not be written into storage.
    function ammEquilibrium(
        int128 base,
        int128 quote,
        int128 priceX18
    ) internal pure returns (int128, int128) {
        if (base == 0 || quote == 0) {
            return (0, 0);
        }
        int256 k = int256(base) * quote;
        // base * price * base == k
        // base = sqrt(k / price);
        base = int128(MathHelper.sqrt256((k * 1e18) / priceX18));
        quote = (base == 0) ? int128(0) : int128(k / base);
        return (base, quote);
    }

    function isSwapValid(
        int128 baseDelta,
        int128 quoteDelta,
        int128 base,
        int128 quote
    ) internal pure returns (bool) {
        if (
            base == 0 ||
            quote == 0 ||
            base + baseDelta <= 0 ||
            quote + quoteDelta <= 0
        ) {
            return false;
        }
        int256 kPrev = int256(base) * quote;
        int256 kNew = int256(base + baseDelta) * (quote + quoteDelta);
        return kNew > kPrev;
    }

    function swap(
        int128 amountSwap,
        int128 base,
        int128 quote,
        int128 priceX18,
        int128 sizeIncrement,
        int128 lpSpreadX18
    ) internal pure returns (int128, int128) {
        // (amountSwap % sizeIncrement) is guaranteed to be 0
        if (base == 0 || quote == 0) {
            return (0, 0);
        }
        int128 currentPriceX18 = quote.div(base);

        int128 keepRateX18 = 1e18 - lpSpreadX18;

        // selling
        if (amountSwap > 0) {
            priceX18 = priceX18.div(keepRateX18);
            if (priceX18 >= currentPriceX18) {
                return (0, 0);
            }
        } else {
            priceX18 = priceX18.mul(keepRateX18);
            if (priceX18 <= currentPriceX18) {
                return (0, 0);
            }
        }

        int256 k = int256(base) * quote;
        int128 baseAtPrice = int128(
            (MathHelper.sqrt256(k) * 1e9) / MathHelper.sqrt(priceX18)
        );
        // base -> base + amountSwap

        int128 baseSwapped;

        if (
            (amountSwap > 0 && base + amountSwap > baseAtPrice) ||
            (amountSwap < 0 && base + amountSwap < baseAtPrice)
        ) {
            // we hit price limits before we exhaust amountSwap
            if (baseAtPrice >= base) {
                baseSwapped = MathHelper.floor(
                    baseAtPrice - base,
                    sizeIncrement
                );
            } else {
                baseSwapped = MathHelper.ceil(
                    baseAtPrice - base,
                    sizeIncrement
                );
            }
        } else {
            // just swap it all
            // amountSwap is already guaranteed to adhere to sizeIncrement
            baseSwapped = amountSwap;
        }

        int128 quoteSwapped = int128(k / (base + baseSwapped) - quote);
        if (amountSwap > 0) {
            quoteSwapped = quoteSwapped.mul(keepRateX18);
        } else {
            quoteSwapped = quoteSwapped.div(keepRateX18);
        }
        return (baseSwapped, quoteSwapped);
    }
}

// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;

interface IVerifier {
    function requireValidSignature(
        bytes32 message,
        bytes32 e,
        bytes32 s,
        uint8 signerBitmask
    ) external;

    function revertGasInfo(uint256 i, uint256 gasUsed) external pure;

    function validateSignature(
        bytes32 sender,
        address linkedSigner,
        bytes32 digest,
        bytes memory signature
    ) external pure;
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./clearinghouse/IClearinghouse.sol";

interface IOffchainExchange {
    event FillOrder(
        uint32 indexed productId,
        // original order information
        bytes32 indexed digest,
        bytes32 indexed subaccount,
        int128 priceX18,
        int128 amount,
        uint64 expiration,
        uint64 nonce,
        // whether this order is taking or making
        bool isTaker,
        // amount paid in fees (in quote)
        int128 feeAmount,
        // change in this subaccount's base balance from this fill
        int128 baseDelta,
        // change in this subaccount's quote balance from this fill
        int128 quoteDelta
    );

    event CloseIsolatedSubaccount(
        bytes32 indexed isolatedSubaccount,
        bytes32 indexed parentSubaccount
    );

    struct FeeRates {
        int64 makerRateX18;
        int64 takerRateX18;
        uint8 isNonDefault; // 1: non-default, 0: default
    }

    struct LpParams {
        int128 lpSpreadX18;
    }

    struct MarketInfoStore {
        int64 minSize;
        int64 sizeIncrement;
        int128 collectedFees;
    }

    struct MarketInfo {
        uint32 quoteId;
        int128 minSize;
        int128 sizeIncrement;
        int128 collectedFees;
    }

    function initialize(address _clearinghouse, address _endpoint) external;

    function updateFeeRates(
        address user,
        uint32 productId,
        int64 makerRateX18,
        int64 takerRateX18
    ) external;

    function updateMarket(
        uint32 productId,
        uint32 quoteId,
        address virtualBook,
        int128 sizeIncrement,
        int128 minSize,
        int128 lpSpreadX18
    ) external;

    function getMinSize(uint32 productId) external view returns (int128);

    function getDigest(uint32 productId, IEndpoint.Order memory order)
        external
        view
        returns (bytes32);

    function getSizeIncrement(uint32 productId) external view returns (int128);

    function getMarketInfo(uint32 productId)
        external
        view
        returns (MarketInfo memory);

    function getLpParams(uint32 productId)
        external
        view
        returns (LpParams memory);

    function swapAMM(IEndpoint.SwapAMM calldata tx) external;

    function matchOrderAMM(
        IEndpoint.MatchOrderAMM calldata tx,
        address takerLinkedSigner
    ) external;

    function matchOrders(IEndpoint.MatchOrdersWithSigner calldata tx) external;

    function dumpFees() external;

    function createIsolatedSubaccount(
        IEndpoint.CreateIsolatedSubaccount memory tx,
        address linkedSigner
    ) external returns (bytes32);

    function isIsolatedSubaccountActive(bytes32 parent, bytes32 subaccount)
        external
        view
        returns (bool);

    function getParentSubaccount(bytes32 subaccount)
        external
        view
        returns (bytes32);

    function tryCloseIsolatedSubaccount(bytes32 subaccount) external;
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "../interfaces/IERC20Base.sol";
import "../common/Errors.sol";
import "hardhat/console.sol";

// @dev Adapted from https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/TransferHelper.sol
library ERC20Helper {
    function safeTransfer(
        IERC20Base self,
        address to,
        uint256 amount
    ) internal {
        (bool success, bytes memory data) = address(self).call(
            abi.encodeWithSelector(IERC20Base.transfer.selector, to, amount)
        );
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            ERR_TRANSFER_FAILED
        );
    }

    function safeTransferFrom(
        IERC20Base self,
        address from,
        address to,
        uint256 amount
    ) internal {
        (bool success, bytes memory data) = address(self).call(
            abi.encodeWithSelector(
                IERC20Base.transferFrom.selector,
                from,
                to,
                amount
            )
        );

        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            ERR_TRANSFER_FAILED
        );
    }
}

// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;
import "@openzeppelin/contracts/utils/Strings.sol";
import "./MathHelper.sol";

library Logger {
    event VertexEVMLog(string message);

    function log(string memory message) internal {
        emit VertexEVMLog(message);
    }

    function log(int128 value) internal {
        log(MathHelper.int2str(value));
    }

    function log(string memory message, int128 value) internal {
        log(string.concat(message, " ", MathHelper.int2str(value)));
    }

    function log(string memory message, uint128 value) internal {
        log(string.concat(message, " ", MathHelper.uint2str(value)));
    }

    //    function log(string memory message, uint32 value) internal {
    //        log(message, uint128(value));
    //    }

    function log(string memory message, address value) internal {
        log(
            string.concat(message, " ", Strings.toHexString(uint160(value), 20))
        );
    }

    function log(string memory messages, bytes32 value) internal {
        log(string.concat(messages, " ", string(abi.encodePacked(value))));
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

interface IERC20Base {
    function decimals() external view returns (uint8);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);

    function increaseAllowance(address spender, uint256 addedValue)
        external
        returns (bool);

    function decreaseAllowance(address spender, uint256 subtractedValue)
        external
        returns (bool);

    function balanceOf(address account) external view returns (uint256);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }

    function __Ownable_init_unchained() internal onlyInitializing {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.0;

import "./ECDSAUpgradeable.sol";
import "../../proxy/utils/Initializable.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 *
 * @custom:storage-size 52
 */
abstract contract EIP712Upgradeable is Initializable {
    /* solhint-disable var-name-mixedcase */
    bytes32 private _HASHED_NAME;
    bytes32 private _HASHED_VERSION;
    bytes32 private constant _TYPE_HASH = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    function __EIP712_init(string memory name, string memory version) internal onlyInitializing {
        __EIP712_init_unchained(name, version);
    }

    function __EIP712_init_unchained(string memory name, string memory version) internal onlyInitializing {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        return _buildDomainSeparator(_TYPE_HASH, _EIP712NameHash(), _EIP712VersionHash());
    }

    function _buildDomainSeparator(
        bytes32 typeHash,
        bytes32 nameHash,
        bytes32 versionHash
    ) private view returns (bytes32) {
        return keccak256(abi.encode(typeHash, nameHash, versionHash, block.chainid, address(this)));
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSAUpgradeable.toTypedDataHash(_domainSeparatorV4(), structHash);
    }

    /**
     * @dev The hash of the name parameter for the EIP712 domain.
     *
     * NOTE: This function reads from storage by default, but can be redefined to return a constant value if gas costs
     * are a concern.
     */
    function _EIP712NameHash() internal virtual view returns (bytes32) {
        return _HASHED_NAME;
    }

    /**
     * @dev The hash of the version parameter for the EIP712 domain.
     *
     * NOTE: This function reads from storage by default, but can be redefined to return a constant value if gas costs
     * are a concern.
     */
    function _EIP712VersionHash() internal virtual view returns (bytes32) {
        return _HASHED_VERSION;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.4.22 <0.9.0;

library console {
    address constant CONSOLE_ADDRESS =
        0x000000000000000000636F6e736F6c652e6c6f67;

    function _sendLogPayloadImplementation(bytes memory payload) internal view {
        address consoleAddress = CONSOLE_ADDRESS;
        /// @solidity memory-safe-assembly
        assembly {
            pop(
                staticcall(
                    gas(),
                    consoleAddress,
                    add(payload, 32),
                    mload(payload),
                    0,
                    0
                )
            )
        }
    }

    function _castToPure(
      function(bytes memory) internal view fnIn
    ) internal pure returns (function(bytes memory) pure fnOut) {
        assembly {
            fnOut := fnIn
        }
    }

    function _sendLogPayload(bytes memory payload) internal pure {
        _castToPure(_sendLogPayloadImplementation)(payload);
    }

    function log() internal pure {
        _sendLogPayload(abi.encodeWithSignature("log()"));
    }

    function logInt(int256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(int256)", p0));
    }

    function logUint(uint256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256)", p0));
    }

    function logString(string memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function logBool(bool p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function logAddress(address p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function logBytes(bytes memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes)", p0));
    }

    function logBytes1(bytes1 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes1)", p0));
    }

    function logBytes2(bytes2 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes2)", p0));
    }

    function logBytes3(bytes3 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes3)", p0));
    }

    function logBytes4(bytes4 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes4)", p0));
    }

    function logBytes5(bytes5 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes5)", p0));
    }

    function logBytes6(bytes6 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes6)", p0));
    }

    function logBytes7(bytes7 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes7)", p0));
    }

    function logBytes8(bytes8 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes8)", p0));
    }

    function logBytes9(bytes9 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes9)", p0));
    }

    function logBytes10(bytes10 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes10)", p0));
    }

    function logBytes11(bytes11 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes11)", p0));
    }

    function logBytes12(bytes12 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes12)", p0));
    }

    function logBytes13(bytes13 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes13)", p0));
    }

    function logBytes14(bytes14 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes14)", p0));
    }

    function logBytes15(bytes15 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes15)", p0));
    }

    function logBytes16(bytes16 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes16)", p0));
    }

    function logBytes17(bytes17 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes17)", p0));
    }

    function logBytes18(bytes18 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes18)", p0));
    }

    function logBytes19(bytes19 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes19)", p0));
    }

    function logBytes20(bytes20 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes20)", p0));
    }

    function logBytes21(bytes21 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes21)", p0));
    }

    function logBytes22(bytes22 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes22)", p0));
    }

    function logBytes23(bytes23 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes23)", p0));
    }

    function logBytes24(bytes24 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes24)", p0));
    }

    function logBytes25(bytes25 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes25)", p0));
    }

    function logBytes26(bytes26 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes26)", p0));
    }

    function logBytes27(bytes27 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes27)", p0));
    }

    function logBytes28(bytes28 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes28)", p0));
    }

    function logBytes29(bytes29 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes29)", p0));
    }

    function logBytes30(bytes30 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes30)", p0));
    }

    function logBytes31(bytes31 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes31)", p0));
    }

    function logBytes32(bytes32 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes32)", p0));
    }

    function log(uint256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256)", p0));
    }

    function log(string memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function log(bool p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function log(address p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function log(uint256 p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256)", p0, p1));
    }

    function log(uint256 p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string)", p0, p1));
    }

    function log(uint256 p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool)", p0, p1));
    }

    function log(uint256 p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address)", p0, p1));
    }

    function log(string memory p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256)", p0, p1));
    }

    function log(string memory p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string)", p0, p1));
    }

    function log(string memory p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool)", p0, p1));
    }

    function log(string memory p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address)", p0, p1));
    }

    function log(bool p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256)", p0, p1));
    }

    function log(bool p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string)", p0, p1));
    }

    function log(bool p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool)", p0, p1));
    }

    function log(bool p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address)", p0, p1));
    }

    function log(address p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256)", p0, p1));
    }

    function log(address p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string)", p0, p1));
    }

    function log(address p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool)", p0, p1));
    }

    function log(address p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address)", p0, p1));
    }

    function log(uint256 p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,uint256)", p0, p1, p2));
    }

    function log(uint256 p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,string)", p0, p1, p2));
    }

    function log(uint256 p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,bool)", p0, p1, p2));
    }

    function log(uint256 p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,address)", p0, p1, p2));
    }

    function log(uint256 p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,uint256)", p0, p1, p2));
    }

    function log(uint256 p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,string)", p0, p1, p2));
    }

    function log(uint256 p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,bool)", p0, p1, p2));
    }

    function log(uint256 p0, string memory p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,address)", p0, p1, p2));
    }

    function log(uint256 p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,uint256)", p0, p1, p2));
    }

    function log(uint256 p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,string)", p0, p1, p2));
    }

    function log(uint256 p0, bool p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,bool)", p0, p1, p2));
    }

    function log(uint256 p0, bool p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,address)", p0, p1, p2));
    }

    function log(uint256 p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,uint256)", p0, p1, p2));
    }

    function log(uint256 p0, address p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,string)", p0, p1, p2));
    }

    function log(uint256 p0, address p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,bool)", p0, p1, p2));
    }

    function log(uint256 p0, address p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,address)", p0, p1, p2));
    }

    function log(string memory p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,uint256)", p0, p1, p2));
    }

    function log(string memory p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,string)", p0, p1, p2));
    }

    function log(string memory p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,bool)", p0, p1, p2));
    }

    function log(string memory p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,address)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint256)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool)", p0, p1, p2));
    }

    function log(string memory p0, string memory p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint256)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool)", p0, p1, p2));
    }

    function log(string memory p0, bool p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address)", p0, p1, p2));
    }

    function log(string memory p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint256)", p0, p1, p2));
    }

    function log(string memory p0, address p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string)", p0, p1, p2));
    }

    function log(string memory p0, address p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool)", p0, p1, p2));
    }

    function log(string memory p0, address p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address)", p0, p1, p2));
    }

    function log(bool p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,uint256)", p0, p1, p2));
    }

    function log(bool p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,string)", p0, p1, p2));
    }

    function log(bool p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,bool)", p0, p1, p2));
    }

    function log(bool p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,address)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint256)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool)", p0, p1, p2));
    }

    function log(bool p0, string memory p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address)", p0, p1, p2));
    }

    function log(bool p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint256)", p0, p1, p2));
    }

    function log(bool p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string)", p0, p1, p2));
    }

    function log(bool p0, bool p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool)", p0, p1, p2));
    }

    function log(bool p0, bool p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address)", p0, p1, p2));
    }

    function log(bool p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint256)", p0, p1, p2));
    }

    function log(bool p0, address p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string)", p0, p1, p2));
    }

    function log(bool p0, address p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool)", p0, p1, p2));
    }

    function log(bool p0, address p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address)", p0, p1, p2));
    }

    function log(address p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,uint256)", p0, p1, p2));
    }

    function log(address p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,string)", p0, p1, p2));
    }

    function log(address p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,bool)", p0, p1, p2));
    }

    function log(address p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,address)", p0, p1, p2));
    }

    function log(address p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint256)", p0, p1, p2));
    }

    function log(address p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string)", p0, p1, p2));
    }

    function log(address p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool)", p0, p1, p2));
    }

    function log(address p0, string memory p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address)", p0, p1, p2));
    }

    function log(address p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint256)", p0, p1, p2));
    }

    function log(address p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string)", p0, p1, p2));
    }

    function log(address p0, bool p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool)", p0, p1, p2));
    }

    function log(address p0, bool p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address)", p0, p1, p2));
    }

    function log(address p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint256)", p0, p1, p2));
    }

    function log(address p0, address p1, string memory p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string)", p0, p1, p2));
    }

    function log(address p0, address p1, bool p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool)", p0, p1, p2));
    }

    function log(address p0, address p1, address p2) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address)", p0, p1, p2));
    }

    function log(uint256 p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,uint256,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,uint256,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,uint256,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,string,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,string,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,string,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,string,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,bool,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,bool,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,bool,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,address,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,address,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,address,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,uint256,address,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,uint256,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,uint256,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,uint256,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,string,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,string,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,string,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,string,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,bool,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,bool,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,bool,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,address,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,address,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,address,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, string memory p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string,address,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,uint256,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,uint256,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,uint256,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,string,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,string,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,string,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,bool,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,address,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,address,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool,address,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,uint256,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,uint256,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,uint256,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,string,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,string,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,string,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,string,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,bool,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,bool,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,bool,address)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,address,uint256)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,address,string)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,address,bool)", p0, p1, p2, p3));
    }

    function log(uint256 p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,address,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,uint256,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,uint256,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,uint256,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,string,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,bool,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,address,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint256,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint256,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,uint256,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, string memory p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint256,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint256,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,uint256,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool,address,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint256,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint256,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,uint256,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,string,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,bool,address)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,uint256)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,string)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,bool)", p0, p1, p2, p3));
    }

    function log(string memory p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,uint256,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,uint256,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,uint256,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,string,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,bool,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,address,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint256,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint256,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,uint256,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, string memory p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint256,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint256,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,uint256,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool,address,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint256,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint256,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,uint256,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,string,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,bool,address)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,uint256)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,string)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,bool)", p0, p1, p2, p3));
    }

    function log(bool p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,uint256,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,uint256,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,uint256,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,string,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,bool,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,address,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,uint256,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint256,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint256,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,uint256,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, string memory p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint256,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint256,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,uint256,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool,address,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint256,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint256,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint256,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,uint256,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, string memory p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,string,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,bool,address)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,uint256)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, string memory p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,string)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,bool)", p0, p1, p2, p3));
    }

    function log(address p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,address,address,address)", p0, p1, p2, p3));
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.13;

import "./IEndpoint.sol";

interface IEndpointGated {
    function getEndpoint() external view returns (address endpoint);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/cryptography/draft-EIP712.sol)

pragma solidity ^0.8.0;

// EIP-712 is Final as of 2022-08-11. This file is deprecated.

import "./EIP712Upgradeable.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./interfaces/engine/IPerpEngine.sol";
import "./BaseEngine.sol";

int128 constant EMA_TIME_CONSTANT_X18 = 998334721450938752;
int128 constant ONE_DAY_X18 = 86400_000000000000000000; // 24 hours

// we will want to config this later, but for now this is global and a percentage
int128 constant MAX_DAILY_FUNDING_RATE = 20000000000000000; // 0.02

abstract contract PerpEngineState is IPerpEngine, BaseEngine {
    using MathSD21x18 for int128;

    mapping(uint32 => State) public states;
    mapping(uint32 => mapping(bytes32 => Balance)) public balances;

    mapping(uint32 => LpState) public lpStates;
    mapping(uint32 => mapping(bytes32 => LpBalance)) public lpBalances;

    function _updateBalance(
        State memory state,
        Balance memory balance,
        int128 balanceDelta,
        int128 vQuoteDelta
    ) internal pure {
        // pre update
        state.openInterest -= (balance.amount > 0) ? balance.amount : int128(0);
        int128 cumulativeFundingAmountX18 = (balance.amount > 0)
            ? state.cumulativeFundingLongX18
            : state.cumulativeFundingShortX18;
        int128 diffX18 = cumulativeFundingAmountX18 -
            balance.lastCumulativeFundingX18;
        int128 deltaQuote = vQuoteDelta - diffX18.mul(balance.amount);

        // apply delta
        balance.amount += balanceDelta;

        // apply vquote
        balance.vQuoteBalance += deltaQuote;

        // post update
        if (balance.amount > 0) {
            state.openInterest += balance.amount;
            balance.lastCumulativeFundingX18 = state.cumulativeFundingLongX18;
        } else {
            balance.lastCumulativeFundingX18 = state.cumulativeFundingShortX18;
        }
    }

    function _applyLpBalanceFunding(
        LpState memory lpState,
        LpBalance memory lpBalance,
        Balance memory balance
    ) internal pure {
        int128 vQuoteDelta = (lpState.cumulativeFundingPerLpX18 -
            lpBalance.lastCumulativeFundingX18).mul(lpBalance.amount);
        balance.vQuoteBalance += vQuoteDelta;
        lpBalance.lastCumulativeFundingX18 = lpState.cumulativeFundingPerLpX18;
    }

    function getStateAndBalance(uint32 productId, bytes32 subaccount)
        public
        view
        returns (State memory, Balance memory)
    {
        State memory state = states[productId];
        Balance memory balance = balances[productId][subaccount];
        _updateBalance(state, balance, 0, 0);
        return (state, balance);
    }

    function getBalance(uint32 productId, bytes32 subaccount)
        public
        view
        returns (Balance memory)
    {
        State memory state = states[productId];
        Balance memory balance = balances[productId][subaccount];
        _updateBalance(state, balance, 0, 0);
        return balance;
    }

    function _getBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        virtual
        override
        returns (int128, int128)
    {
        State memory state = states[productId];
        Balance memory balance = balances[productId][subaccount];
        _updateBalance(state, balance, 0, 0);
        return (balance.amount, balance.vQuoteBalance);
    }

    function _getInLpBalance(uint32 productId, bytes32 subaccount)
        internal
        view
        virtual
        override
        returns (
            // baseAmount, quoteAmount, deltaQuoteAmount (funding)
            int128,
            int128,
            int128
        )
    {
        LpBalance memory lpBalance = lpBalances[productId][subaccount];
        if (lpBalance.amount == 0) {
            return (0, 0, 0);
        }
        LpState memory lpState = lpStates[productId];
        int128 ratio = lpBalance.amount.div(lpState.supply);
        int128 baseAmount = lpState.base.mul(ratio);
        int128 quoteAmount = lpState.quote.mul(ratio);

        int128 quoteDeltaAmount = lpState
            .cumulativeFundingPerLpX18
            .sub(lpBalance.lastCumulativeFundingX18)
            .mul(lpBalance.amount);
        return (baseAmount, quoteAmount, quoteDeltaAmount);
    }

    function getStatesAndBalances(uint32 productId, bytes32 subaccount)
        public
        view
        returns (
            LpState memory,
            LpBalance memory,
            State memory,
            Balance memory
        )
    {
        LpState memory lpState = lpStates[productId];
        State memory state = states[productId];
        LpBalance memory lpBalance = lpBalances[productId][subaccount];
        Balance memory balance = balances[productId][subaccount];

        _updateBalance(state, balance, 0, 0);
        _applyLpBalanceFunding(lpState, lpBalance, balance);
        return (lpState, lpBalance, state, balance);
    }

    function updateStates(uint128 dt, int128[] calldata avgPriceDiffs)
        external
        onlyEndpoint
    {
        int128 dtX18 = int128(dt).fromInt();
        for (uint32 i = 0; i < avgPriceDiffs.length; i++) {
            uint32 productId = productIds[i];
            State memory state = states[productId];
            if (state.openInterest == 0) {
                continue;
            }
            require(dt < 7 * SECONDS_PER_DAY, ERR_INVALID_TIME);

            LpState memory lpState = lpStates[productId];

            {
                int128 indexPriceX18 = _risk(productId).priceX18;

                // cap this price diff
                int128 priceDiffX18 = avgPriceDiffs[i];

                int128 maxPriceDiff = MAX_DAILY_FUNDING_RATE.mul(indexPriceX18);

                if (priceDiffX18.abs() > maxPriceDiff) {
                    // Proper sign
                    priceDiffX18 = (priceDiffX18 > 0)
                        ? maxPriceDiff
                        : -maxPriceDiff;
                }

                int128 paymentAmount = priceDiffX18.mul(dtX18).div(ONE_DAY_X18);
                state.cumulativeFundingLongX18 += paymentAmount;
                state.cumulativeFundingShortX18 += paymentAmount;

                emit FundingPayment(
                    productId,
                    dt,
                    state.openInterest,
                    paymentAmount
                );
            }

            {
                Balance memory balance = Balance({
                    amount: lpState.base,
                    vQuoteBalance: 0,
                    lastCumulativeFundingX18: lpState.lastCumulativeFundingX18
                });
                _updateBalance(state, balance, 0, 0);
                if (lpState.supply != 0) {
                    lpState.cumulativeFundingPerLpX18 += balance
                        .vQuoteBalance
                        .div(lpState.supply);
                }
                lpState.lastCumulativeFundingX18 = state
                    .cumulativeFundingLongX18;
            }
            lpStates[productId] = lpState;
            states[productId] = state;
            _productUpdate(productId);
        }
    }
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

interface IClearinghouseEventEmitter {
    /// @notice Emitted during initialization
    event ClearinghouseInitialized(address endpoint, address quote);

    /// @notice Emitted when collateral is modified for a subaccount
    event ModifyCollateral(
        int128 amount,
        bytes32 indexed subaccount,
        uint32 productId
    );

    event Liquidation(
        bytes32 indexed liquidatorSubaccount,
        bytes32 indexed liquidateeSubaccount,
        uint32 productId,
        bool isEncodedSpread,
        int128 amount,
        int128 amountQuote
    );
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}

// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;

import "./PRBMath.sol";

/// @title PRBMathSD59x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with int256 numbers considered to have 18
/// trailing decimals. We call this number representation signed 59.18-decimal fixed-point, since the numbers can have
/// a sign and there can be up to 59 digits in the integer part and up to 18 decimals in the fractional part. The numbers
/// are bound by the minimum and the maximum values permitted by the Solidity type int256.
library PRBMathSD59x18 {
    /// @dev log2(e) as a signed 59.18-decimal fixed-point number.
    int256 internal constant LOG2_E = 1_442695040888963407;

    /// @dev Half the SCALE number.
    int256 internal constant HALF_SCALE = 5e17;

    /// @dev The maximum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_792003956564819967;

    /// @dev The maximum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_WHOLE_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev The minimum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_792003956564819968;

    /// @dev The minimum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_WHOLE_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev How many trailing decimals can be represented.
    int256 internal constant SCALE = 1e18;

    /// INTERNAL FUNCTIONS ///

    /// @notice Calculate the absolute value of x.
    ///
    /// @dev Requirements:
    /// - x must be greater than MIN_SD59x18.
    ///
    /// @param x The number to calculate the absolute value for.
    /// @param result The absolute value of x.
    function abs(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x == MIN_SD59x18) {
                revert PRBMathSD59x18__AbsInputTooSmall();
            }
            result = x < 0 ? -x : x;
        }
    }

    /// @notice Calculates the arithmetic average of x and y, rounding down.
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The arithmetic average as a signed 59.18-decimal fixed-point number.
    function avg(int256 x, int256 y) internal pure returns (int256 result) {
        // The operations can never overflow.
        unchecked {
            int256 sum = (x >> 1) + (y >> 1);
            if (sum < 0) {
                // If at least one of x and y is odd, we add 1 to the result. This is because shifting negative numbers to the
                // right rounds down to infinity.
                assembly {
                    result := add(sum, and(or(x, y), 1))
                }
            } else {
                // If both x and y are odd, we add 1 to the result. This is because if both numbers are odd, the 0.5
                // remainder gets truncated twice.
                result = sum + (x & y & 1);
            }
        }
    }

    /// @notice Yields the least greatest signed 59.18 decimal fixed-point number greater than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be less than or equal to MAX_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to ceil.
    /// @param result The least integer greater than or equal to x, as a signed 58.18-decimal fixed-point number.
    function ceil(int256 x) internal pure returns (int256 result) {
        if (x > MAX_WHOLE_SD59x18) {
            revert PRBMathSD59x18__CeilOverflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x > 0) {
                    result += SCALE;
                }
            }
        }
    }

    /// @notice Divides two signed 59.18-decimal fixed-point numbers, returning a new signed 59.18-decimal fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDiv".
    /// - None of the inputs can be MIN_SD59x18.
    /// - The denominator cannot be zero.
    /// - The result must fit within int256.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDiv".
    ///
    /// @param x The numerator as a signed 59.18-decimal fixed-point number.
    /// @param y The denominator as a signed 59.18-decimal fixed-point number.
    /// @param result The quotient as a signed 59.18-decimal fixed-point number.
    function div(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__DivInputTooSmall();
        }

        // Get hold of the absolute values of x and y.
        uint256 ax;
        uint256 ay;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
        }

        // Compute the absolute value of (x*SCALE)÷y. The result must fit within int256.
        uint256 rAbs = PRBMath.mulDiv(ax, uint256(SCALE), ay);
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__DivOverflow(rAbs);
        }

        // Get the signs of x and y.
        uint256 sx;
        uint256 sy;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
        }

        // XOR over sx and sy. This is basically checking whether the inputs have the same sign. If yes, the result
        // should be positive. Otherwise, it should be negative.
        result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns Euler's number as a signed 59.18-decimal fixed-point number.
    /// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
    function e() internal pure returns (int256 result) {
        result = 2_718281828459045235;
    }

    /// @notice Calculates the natural exponent of x.
    ///
    /// @dev Based on the insight that e^x = 2^(x * log2(e)).
    ///
    /// Requirements:
    /// - All from "log2".
    /// - x must be less than 133.084258667509499441.
    ///
    /// Caveats:
    /// - All from "exp2".
    /// - For any x less than -41.446531673892822322, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp(int256 x) internal pure returns (int256 result) {
        // Without this check, the value passed to "exp2" would be less than -59.794705707972522261.
        if (x < -41_446531673892822322) {
            return 0;
        }

        // Without this check, the value passed to "exp2" would be greater than 192.
        if (x >= 133_084258667509499441) {
            revert PRBMathSD59x18__ExpInputTooBig(x);
        }

        // Do the fixed-point multiplication inline to save gas.
        unchecked {
            int256 doubleScaleProduct = x * LOG2_E;
            result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
        }
    }

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    ///
    /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
    ///
    /// Requirements:
    /// - x must be 192 or less.
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - For any x less than -59.794705707972522261, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp2(int256 x) internal pure returns (int256 result) {
        // This works because 2^(-x) = 1/2^x.
        if (x < 0) {
            // 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
            if (x < -59_794705707972522261) {
                return 0;
            }

            // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
            unchecked {
                result = 1e36 / exp2(-x);
            }
        } else {
            // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
            if (x >= 192e18) {
                revert PRBMathSD59x18__Exp2InputTooBig(x);
            }

            unchecked {
                // Convert x to the 192.64-bit fixed-point format.
                uint256 x192x64 = (uint256(x) << 64) / uint256(SCALE);

                // Safe to convert the result to int256 directly because the maximum input allowed is 192.
                result = int256(PRBMath.exp2(x192x64));
            }
        }
    }

    /// @notice Yields the greatest signed 59.18 decimal fixed-point number less than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be greater than or equal to MIN_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to floor.
    /// @param result The greatest integer less than or equal to x, as a signed 58.18-decimal fixed-point number.
    function floor(int256 x) internal pure returns (int256 result) {
        if (x < MIN_WHOLE_SD59x18) {
            revert PRBMathSD59x18__FloorUnderflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x < 0) {
                    result -= SCALE;
                }
            }
        }
    }

    /// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right
    /// of the radix point for negative numbers.
    /// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
    /// @param x The signed 59.18-decimal fixed-point number to get the fractional part of.
    /// @param result The fractional part of x as a signed 59.18-decimal fixed-point number.
    function frac(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x % SCALE;
        }
    }

    /// @notice Converts a number from basic integer form to signed 59.18-decimal fixed-point representation.
    ///
    /// @dev Requirements:
    /// - x must be greater than or equal to MIN_SD59x18 divided by SCALE.
    /// - x must be less than or equal to MAX_SD59x18 divided by SCALE.
    ///
    /// @param x The basic integer to convert.
    /// @param result The same number in signed 59.18-decimal fixed-point representation.
    function fromInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < MIN_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntUnderflow(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntOverflow(x);
            }
            result = x * SCALE;
        }
    }

    /// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
    ///
    /// @dev Requirements:
    /// - x * y must fit within MAX_SD59x18, lest it overflows.
    /// - x * y cannot be negative.
    ///
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function gm(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            return 0;
        }

        unchecked {
            // Checking for overflow this way is faster than letting Solidity do it.
            int256 xy = x * y;
            if (xy / x != y) {
                revert PRBMathSD59x18__GmOverflow(x, y);
            }

            // The product cannot be negative.
            if (xy < 0) {
                revert PRBMathSD59x18__GmNegativeProduct(x, y);
            }

            // We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
            // during multiplication. See the comments within the "sqrt" function.
            result = int256(PRBMath.sqrt(uint256(xy)));
        }
    }

    /// @notice Calculates 1 / x, rounding toward zero.
    ///
    /// @dev Requirements:
    /// - x cannot be zero.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the inverse.
    /// @return result The inverse as a signed 59.18-decimal fixed-point number.
    function inv(int256 x) internal pure returns (int256 result) {
        unchecked {
            // 1e36 is SCALE * SCALE.
            result = 1e36 / x;
        }
    }

    /// @notice Calculates the natural logarithm of x.
    ///
    /// @dev Based on the insight that ln(x) = log2(x) / log2(e).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    /// - This doesn't return exactly 1 for 2718281828459045235, for that we would need more fine-grained precision.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the natural logarithm.
    /// @return result The natural logarithm as a signed 59.18-decimal fixed-point number.
    function ln(int256 x) internal pure returns (int256 result) {
        // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
        // can return is 195205294292027477728.
        unchecked {
            result = (log2(x) * SCALE) / LOG2_E;
        }
    }

    /// @notice Calculates the common logarithm of x.
    ///
    /// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
    /// logarithm based on the insight that log10(x) = log2(x) / log2(10).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the common logarithm.
    /// @return result The common logarithm as a signed 59.18-decimal fixed-point number.
    function log10(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }

        // Note that the "mul" in this block is the assembly mul operation, not the "mul" function defined in this contract.
        // prettier-ignore
        assembly {
            switch x
            case 1 { result := mul(SCALE, sub(0, 18)) }
            case 10 { result := mul(SCALE, sub(1, 18)) }
            case 100 { result := mul(SCALE, sub(2, 18)) }
            case 1000 { result := mul(SCALE, sub(3, 18)) }
            case 10000 { result := mul(SCALE, sub(4, 18)) }
            case 100000 { result := mul(SCALE, sub(5, 18)) }
            case 1000000 { result := mul(SCALE, sub(6, 18)) }
            case 10000000 { result := mul(SCALE, sub(7, 18)) }
            case 100000000 { result := mul(SCALE, sub(8, 18)) }
            case 1000000000 { result := mul(SCALE, sub(9, 18)) }
            case 10000000000 { result := mul(SCALE, sub(10, 18)) }
            case 100000000000 { result := mul(SCALE, sub(11, 18)) }
            case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
            case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
            case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
            case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
            case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
            case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
            case 1000000000000000000 { result := 0 }
            case 10000000000000000000 { result := SCALE }
            case 100000000000000000000 { result := mul(SCALE, 2) }
            case 1000000000000000000000 { result := mul(SCALE, 3) }
            case 10000000000000000000000 { result := mul(SCALE, 4) }
            case 100000000000000000000000 { result := mul(SCALE, 5) }
            case 1000000000000000000000000 { result := mul(SCALE, 6) }
            case 10000000000000000000000000 { result := mul(SCALE, 7) }
            case 100000000000000000000000000 { result := mul(SCALE, 8) }
            case 1000000000000000000000000000 { result := mul(SCALE, 9) }
            case 10000000000000000000000000000 { result := mul(SCALE, 10) }
            case 100000000000000000000000000000 { result := mul(SCALE, 11) }
            case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
            case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
            case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
            case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
            case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
            case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
            case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
            case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
            case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
            case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
            case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
            case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
            case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
            case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
            case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
            case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
            case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
            case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
            case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
            case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
            case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
            case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
            case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
            case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
            case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
            case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
            case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
            case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
            case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
            case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
            case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
            case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
            case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
            case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
            case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
            case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
            case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
            case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
            case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
            default {
                result := MAX_SD59x18
            }
        }

        if (result == MAX_SD59x18) {
            // Do the fixed-point division inline to save gas. The denominator is log2(10).
            unchecked {
                result = (log2(x) * SCALE) / 3_321928094887362347;
            }
        }
    }

    /// @notice Calculates the binary logarithm of x.
    ///
    /// @dev Based on the iterative approximation algorithm.
    /// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
    ///
    /// Requirements:
    /// - x must be greater than zero.
    ///
    /// Caveats:
    /// - The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as a signed 59.18-decimal fixed-point number.
    function log2(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }
        unchecked {
            // This works because log2(x) = -log2(1/x).
            int256 sign;
            if (x >= SCALE) {
                sign = 1;
            } else {
                sign = -1;
                // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
                assembly {
                    x := div(1000000000000000000000000000000000000, x)
                }
            }

            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = PRBMath.mostSignificantBit(uint256(x / SCALE));

            // The integer part of the logarithm as a signed 59.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255, SCALE is 1e18 and sign is either 1 or -1.
            result = int256(n) * SCALE;

            // This is y = x * 2^(-n).
            int256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == SCALE) {
                return result * sign;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (int256 delta = int256(HALF_SCALE); delta > 0; delta >>= 1) {
                y = (y * y) / SCALE;

                // Is y^2 > 2 and so in the range [2,4)?
                if (y >= 2 * SCALE) {
                    // Add the 2^(-m) factor to the logarithm.
                    result += delta;

                    // Corresponds to z/2 on Wikipedia.
                    y >>= 1;
                }
            }
            result *= sign;
        }
    }

    /// @notice Multiplies two signed 59.18-decimal fixed-point numbers together, returning a new signed 59.18-decimal
    /// fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers and employs constant folding, i.e. the denominator is
    /// always 1e18.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - None of the inputs can be MIN_SD59x18
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    ///
    /// @param x The multiplicand as a signed 59.18-decimal fixed-point number.
    /// @param y The multiplier as a signed 59.18-decimal fixed-point number.
    /// @return result The product as a signed 59.18-decimal fixed-point number.
    function mul(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__MulInputTooSmall();
        }

        unchecked {
            uint256 ax;
            uint256 ay;
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);

            uint256 rAbs = PRBMath.mulDivFixedPoint(ax, ay);
            if (rAbs > uint256(MAX_SD59x18)) {
                revert PRBMathSD59x18__MulOverflow(rAbs);
            }

            uint256 sx;
            uint256 sy;
            assembly {
                sx := sgt(x, sub(0, 1))
                sy := sgt(y, sub(0, 1))
            }
            result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
        }
    }

    /// @notice Returns PI as a signed 59.18-decimal fixed-point number.
    function pi() internal pure returns (int256 result) {
        result = 3_141592653589793238;
    }

    /// @notice Raises x to the power of y.
    ///
    /// @dev Based on the insight that x^y = 2^(log2(x) * y).
    ///
    /// Requirements:
    /// - All from "exp2", "log2" and "mul".
    /// - z cannot be zero.
    ///
    /// Caveats:
    /// - All from "exp2", "log2" and "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x Number to raise to given power y, as a signed 59.18-decimal fixed-point number.
    /// @param y Exponent to raise x to, as a signed 59.18-decimal fixed-point number.
    /// @return result x raised to power y, as a signed 59.18-decimal fixed-point number.
    function pow(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            result = y == 0 ? SCALE : int256(0);
        } else {
            result = exp2(mul(log2(x), y));
        }
    }

    /// @notice Raises x (signed 59.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
    /// famous algorithm "exponentiation by squaring".
    ///
    /// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
    ///
    /// Requirements:
    /// - All from "abs" and "PRBMath.mulDivFixedPoint".
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x The base as a signed 59.18-decimal fixed-point number.
    /// @param y The exponent as an uint256.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function powu(int256 x, uint256 y) internal pure returns (int256 result) {
        uint256 xAbs = uint256(abs(x));

        // Calculate the first iteration of the loop in advance.
        uint256 rAbs = y & 1 > 0 ? xAbs : uint256(SCALE);

        // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
        uint256 yAux = y;
        for (yAux >>= 1; yAux > 0; yAux >>= 1) {
            xAbs = PRBMath.mulDivFixedPoint(xAbs, xAbs);

            // Equivalent to "y % 2 == 1" but faster.
            if (yAux & 1 > 0) {
                rAbs = PRBMath.mulDivFixedPoint(rAbs, xAbs);
            }
        }

        // The result must fit within the 59.18-decimal fixed-point representation.
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__PowuOverflow(rAbs);
        }

        // Is the base negative and the exponent an odd number?
        bool isNegative = x < 0 && y & 1 == 1;
        result = isNegative ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns 1 as a signed 59.18-decimal fixed-point number.
    function scale() internal pure returns (int256 result) {
        result = SCALE;
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Requirements:
    /// - x cannot be negative.
    /// - x must be less than MAX_SD59x18 / SCALE.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the square root.
    /// @return result The result as a signed 59.18-decimal fixed-point .
    function sqrt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < 0) {
                revert PRBMathSD59x18__SqrtNegativeInput(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__SqrtOverflow(x);
            }
            // Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two signed
            // 59.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
            result = int256(PRBMath.sqrt(uint256(x * SCALE)));
        }
    }

    /// @notice Converts a signed 59.18-decimal fixed-point number to basic integer form, rounding down in the process.
    /// @param x The signed 59.18-decimal fixed-point number to convert.
    /// @return result The same number in basic integer form.
    function toInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x / SCALE;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Internal function that returns the initialized version. Returns `_initialized`
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

    /**
     * @dev Internal function that returns the initialized version. Returns `_initializing`
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../StringsUpgradeable.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSAUpgradeable {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(
        bytes32 hash,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", StringsUpgradeable.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

// SPDX-License-Identifier: Unlicense
pragma solidity >=0.8.4;

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);

/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);

/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();

/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();

/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);

/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);

/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);

/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);

/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);

/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);

/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);

/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);

/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);

/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);

/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);

/// @notice Emitted when the calculating the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);

/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);

/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
library PRBMath {
    /// STRUCTS ///

    struct SD59x18 {
        int256 value;
    }

    struct UD60x18 {
        uint256 value;
    }

    /// STORAGE ///

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @dev Largest power of two divisor of SCALE.
    uint256 internal constant SCALE_LPOTD = 262144;

    /// @dev SCALE inverted mod 2^256.
    uint256 internal constant SCALE_INVERSE =
        78156646155174841979727994598816262306175212592076161876661_508869554232690281;

    /// FUNCTIONS ///

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    /// @dev Has to use 192.64-bit fixed-point numbers.
    /// See https://ethereum.stackexchange.com/a/96594/24693.
    /// @param x The exponent as an unsigned 192.64-bit fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp2(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            // Start from 0.5 in the 192.64-bit fixed-point format.
            result = 0x800000000000000000000000000000000000000000000000;

            // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
            // because the initial result is 2^191 and all magic factors are less than 2^65.
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }

            // We're doing two things at the same time:
            //
            //   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
            //      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
            //      rather than 192.
            //   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
            //
            // This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
            result *= SCALE;
            result >>= (191 - (x >> 64));
        }
    }

    /// @notice Finds the zero-based index of the first one in the binary representation of x.
    /// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
    /// @param x The uint256 number for which to find the index of the most significant bit.
    /// @return msb The index of the most significant bit as an uint256.
    function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
        if (x >= 2**128) {
            x >>= 128;
            msb += 128;
        }
        if (x >= 2**64) {
            x >>= 64;
            msb += 64;
        }
        if (x >= 2**32) {
            x >>= 32;
            msb += 32;
        }
        if (x >= 2**16) {
            x >>= 16;
            msb += 16;
        }
        if (x >= 2**8) {
            x >>= 8;
            msb += 8;
        }
        if (x >= 2**4) {
            x >>= 4;
            msb += 4;
        }
        if (x >= 2**2) {
            x >>= 2;
            msb += 2;
        }
        if (x >= 2**1) {
            // No need to shift x any more.
            msb += 1;
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The multiplicand as an uint256.
    /// @param y The multiplier as an uint256.
    /// @param denominator The divisor as an uint256.
    /// @return result The result as an uint256.
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
        // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
        // variables such that product = prod1 * 2^256 + prod0.
        uint256 prod0; // Least significant 256 bits of the product
        uint256 prod1; // Most significant 256 bits of the product
        assembly {
            let mm := mulmod(x, y, not(0))
            prod0 := mul(x, y)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        // Handle non-overflow cases, 256 by 256 division.
        if (prod1 == 0) {
            unchecked {
                result = prod0 / denominator;
            }
            return result;
        }

        // Make sure the result is less than 2^256. Also prevents denominator == 0.
        if (prod1 >= denominator) {
            revert PRBMath__MulDivOverflow(prod1, denominator);
        }

        ///////////////////////////////////////////////
        // 512 by 256 division.
        ///////////////////////////////////////////////

        // Make division exact by subtracting the remainder from [prod1 prod0].
        uint256 remainder;
        assembly {
            // Compute remainder using mulmod.
            remainder := mulmod(x, y, denominator)

            // Subtract 256 bit number from 512 bit number.
            prod1 := sub(prod1, gt(remainder, prod0))
            prod0 := sub(prod0, remainder)
        }

        // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
        // See https://cs.stackexchange.com/q/138556/92363.
        unchecked {
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 lpotdod = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by lpotdod.
                denominator := div(denominator, lpotdod)

                // Divide [prod1 prod0] by lpotdod.
                prod0 := div(prod0, lpotdod)

                // Flip lpotdod such that it is 2^256 / lpotdod. If lpotdod is zero, then it becomes one.
                lpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * lpotdod;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /// @notice Calculates floor(x*y÷1e18) with full precision.
    ///
    /// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
    /// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
    /// being rounded to 1e-18.  See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
    ///
    /// Requirements:
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    /// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
    ///     1. x * y = type(uint256).max * SCALE
    ///     2. (x * y) % SCALE >= SCALE / 2
    ///
    /// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
        uint256 prod0;
        uint256 prod1;
        assembly {
            let mm := mulmod(x, y, not(0))
            prod0 := mul(x, y)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        if (prod1 >= SCALE) {
            revert PRBMath__MulDivFixedPointOverflow(prod1);
        }

        uint256 remainder;
        uint256 roundUpUnit;
        assembly {
            remainder := mulmod(x, y, SCALE)
            roundUpUnit := gt(remainder, 499999999999999999)
        }

        if (prod1 == 0) {
            unchecked {
                result = (prod0 / SCALE) + roundUpUnit;
                return result;
            }
        }

        assembly {
            result := add(
                mul(
                    or(
                        div(sub(prod0, remainder), SCALE_LPOTD),
                        mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
                    ),
                    SCALE_INVERSE
                ),
                roundUpUnit
            )
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - None of the inputs can be type(int256).min.
    /// - The result must fit within int256.
    ///
    /// @param x The multiplicand as an int256.
    /// @param y The multiplier as an int256.
    /// @param denominator The divisor as an int256.
    /// @return result The result as an int256.
    function mulDivSigned(
        int256 x,
        int256 y,
        int256 denominator
    ) internal pure returns (int256 result) {
        if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
            revert PRBMath__MulDivSignedInputTooSmall();
        }

        // Get hold of the absolute values of x, y and the denominator.
        uint256 ax;
        uint256 ay;
        uint256 ad;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
            ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
        }

        // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
        uint256 rAbs = mulDiv(ax, ay, ad);
        if (rAbs > uint256(type(int256).max)) {
            revert PRBMath__MulDivSignedOverflow(rAbs);
        }

        // Get the signs of x, y and the denominator.
        uint256 sx;
        uint256 sy;
        uint256 sd;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
            sd := sgt(denominator, sub(0, 1))
        }

        // XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
        // If yes, the result should be negative.
        result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The uint256 number for which to calculate the square root.
    /// @return result The result as an uint256.
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        // Set the initial guess to the least power of two that is greater than or equal to sqrt(x).
        uint256 xAux = uint256(x);
        result = 1;
        if (xAux >= 0x100000000000000000000000000000000) {
            xAux >>= 128;
            result <<= 64;
        }
        if (xAux >= 0x10000000000000000) {
            xAux >>= 64;
            result <<= 32;
        }
        if (xAux >= 0x100000000) {
            xAux >>= 32;
            result <<= 16;
        }
        if (xAux >= 0x10000) {
            xAux >>= 16;
            result <<= 8;
        }
        if (xAux >= 0x100) {
            xAux >>= 8;
            result <<= 4;
        }
        if (xAux >= 0x10) {
            xAux >>= 4;
            result <<= 2;
        }
        if (xAux >= 0x8) {
            result <<= 1;
        }

        // The operations can never overflow because the result is max 2^127 when it enters this block.
        unchecked {
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1; // Seven iterations should be enough
            uint256 roundedDownResult = x / result;
            return result >= roundedDownResult ? roundedDownResult : result;
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10**64) {
                value /= 10**64;
                result += 64;
            }
            if (value >= 10**32) {
                value /= 10**32;
                result += 32;
            }
            if (value >= 10**16) {
                value /= 10**16;
                result += 16;
            }
            if (value >= 10**8) {
                value /= 10**8;
                result += 8;
            }
            if (value >= 10**4) {
                value /= 10**4;
                result += 4;
            }
            if (value >= 10**2) {
                value /= 10**2;
                result += 2;
            }
            if (value >= 10**1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/MathUpgradeable.sol";

/**
 * @dev String operations.
 */
library StringsUpgradeable {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = MathUpgradeable.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, MathUpgradeable.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0-rc.2) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library MathUpgradeable {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10**64) {
                value /= 10**64;
                result += 64;
            }
            if (value >= 10**32) {
                value /= 10**32;
                result += 32;
            }
            if (value >= 10**16) {
                value /= 10**16;
                result += 16;
            }
            if (value >= 10**8) {
                value /= 10**8;
                result += 8;
            }
            if (value >= 10**4) {
                value /= 10**4;
                result += 4;
            }
            if (value >= 10**2) {
                value /= 10**2;
                result += 2;
            }
            if (value >= 10**1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10**result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
        }
    }
}