// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity 0.8.9;

import "@openzeppelin/contracts/proxy/Clones.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "../interfaces/vaults/IERC20Vault.sol";
import "../interfaces/vaults/IVoltzVault.sol";
import "../utils/DefaultAccessControlLateInit.sol";
import "../interfaces/utils/ILpCallback.sol";
import "../libraries/external/FixedPoint96.sol";

contract LPOptimiserStrategy is DefaultAccessControlLateInit, ILpCallback {
    using SafeERC20 for IERC20;
    using PRBMathUD60x18 for uint256;

    // VAULT PARAMETERS
    struct VaultParams {
        int256 sigmaWad; // standard deviation parameter in wad 10^18
        int256 maxPossibleLowerBoundWad; // Maximum Possible Fixed Rate Lower bounds when initiating a rebalance
        uint256 proximityWad; // closeness parameter in wad 10^18
        uint256 weight; // weight parameter that decides how many funds are going to this vault
    }

    // IMMUTABLES
    address[] public tokens;
    IERC20Vault public erc20Vault;

    // INTERNAL STATE
    IVoltzVault[] internal _vaults;
    VaultParams[] internal _vaultParams;
    uint256 private _totalWeight; // sum of all vault weights

    // CONSTANTS
    int256 internal constant MINIMUM_FIXED_RATE = 1e16;
    uint256 internal constant LOG_BASE = 1000100000000000000;

    // GETTERS AND SETTERS

    /// @notice Get the addresses of all vaults
    function getVaults() public view returns (IVoltzVault[] memory) {
        return _vaults;
    }

    /// @notice Get the parameters of a vault
    /// @param index The index of the vault in _vaults
    function getVaultParams(uint256 index) public view returns (VaultParams memory) {
        return _vaultParams[index];
    }

    /// @notice Set the parameters of a vault
    /// @param index The index of the vault in _vaults
    /// @param vaultParams_ The new parameters of the vault
    function setVaultParams(uint256 index, VaultParams memory vaultParams_) external {
        _requireAdmin();
        require(index < _vaults.length, ExceptionsLibrary.INVALID_STATE);

        uint256 previousWeight = _vaultParams[index].weight;
        _vaultParams[index] = vaultParams_;
        _totalWeight = (_totalWeight + vaultParams_.weight) - previousWeight;
    }

    constructor(address admin_) {
        DefaultAccessControlLateInit.init(admin_);
    }

    /// @notice Constructor for a new contract
    /// @param erc20vault_ Reference to ERC20 Vault
    /// @param vaults_ Reference to Voltz Vaults
    /// @param vaultParams_ Rebalancing parameters of the voltz vaults
    /// @param admin_ Admin of the strategy
    function initialize(
        IERC20Vault erc20vault_,
        IVoltzVault[] memory vaults_,
        VaultParams[] memory vaultParams_,
        address admin_
    ) public {
        erc20Vault = erc20vault_;

        tokens = erc20vault_.vaultTokens();
        require(tokens.length == 1, ExceptionsLibrary.INVALID_TOKEN);

        require(vaults_.length == vaultParams_.length, ExceptionsLibrary.INVALID_LENGTH);
        for (uint256 i = 0; i < vaults_.length; i += 1) {
            _addVault(vaults_[i], vaultParams_[i]);
        }

        DefaultAccessControlLateInit.init(admin_);

        emit StrategyDeployment(erc20vault_, vaults_, vaultParams_, admin_);
    }

    function createStrategy(
        IERC20Vault erc20vault_,
        IVoltzVault[] memory vaults_,
        VaultParams[] memory vaultParams_,
        address admin_
    ) external returns (LPOptimiserStrategy strategy) {
        strategy = LPOptimiserStrategy(Clones.clone(address(this)));
        strategy.initialize(erc20vault_, vaults_, vaultParams_, admin_);
    }

    function _addVault(IVoltzVault vault_, VaultParams memory vaultParams_) internal {
        // 0. Set the local variables
        address[] memory vaultTokens = vault_.vaultTokens();

        // 1. Check if the tokens correspond
        require(vaultTokens.length == 1, ExceptionsLibrary.INVALID_TOKEN);
        require(vaultTokens[0] == tokens[0], ExceptionsLibrary.INVALID_TOKEN);

        // 2. Add the vault
        _vaults.push(vault_);
        _vaultParams.push(vaultParams_);
        _totalWeight += vaultParams_.weight;
    }

    /// @notice Get the current tick and position ticks and decide whether to rebalance
    /// @param index The index of the vault in _vaults
    /// @param currentFixedRateWad currentFixedRate which is passed in from a 7-day rolling avg. historical fixed rate
    /// @return bool True if rebalanceTicks should be called, false otherwise
    function rebalanceCheck(uint256 index, uint256 currentFixedRateWad) public view returns (bool) {
        require(index < _vaults.length, ExceptionsLibrary.INVALID_STATE);

        // 0. Set the local variables
        VaultParams memory vaultParams = _vaultParams[index];
        IVoltzVault vault = _vaults[index];

        // 1. Get current position, lower, and upper ticks form VoltzVault.sol
        IVoltzVault.TickRange memory currentPosition = vault.currentPosition();

        // 2. Convert the ticks into fixed rate
        uint256 lowFixedRateWad = convertTickToFixedRate(currentPosition.tickUpper);
        uint256 highFixedRateWad = convertTickToFixedRate(currentPosition.tickLower);

        if (
            lowFixedRateWad + vaultParams.proximityWad <= currentFixedRateWad &&
            currentFixedRateWad + vaultParams.proximityWad <= highFixedRateWad
        ) {
            // 3.1. If current fixed rate is within bounds, return false (don't rebalance)
            return false;
        } else {
            // 3.2. If current fixed rate is outside bounds, return true (do rebalance)
            return true;
        }
    }

    /// @notice Get the nearest tick multiple given a tick and tick spacing
    /// @param newTick The tick to be rounded to the closest multiple of tickSpacing
    /// @param tickSpacing The tick spacing of the vamm being used for this strategy
    /// @return int24 The nearest tick multiple for newTick
    function nearestTickMultiple(int24 newTick, int24 tickSpacing) public pure returns (int24) {
        return
            (newTick /
                tickSpacing +
                ((((newTick % tickSpacing) + tickSpacing) % tickSpacing) >= tickSpacing / 2 ? int24(1) : int24(0))) *
            tickSpacing;
    }

    /// @notice Convert a fixed rate to a tick in wad
    /// @param fixedRateWad The fixed rate to be converted to a tick in wad
    /// @return int256 The tick in wad
    function convertFixedRateToTick(int256 fixedRateWad) public pure returns (int256) {
        return -PRBMathSD59x18.div(PRBMathSD59x18.log2(int256(fixedRateWad)), PRBMathSD59x18.log2(int256(LOG_BASE)));
    }

    /// @notice Get the fixed rate corresponding to tick
    /// @param tick The tick to be converted into fixed rate
    /// @return uint256 The fixed rate in wad (1.0001 ^ -tick)
    function convertTickToFixedRate(int24 tick) public pure returns (uint256) {
        // 1. Convert the tick into X96 sqrt price (scaled by 2^96)
        uint160 sqrtPriceX96 = TickMath.getSqrtRatioAtTick(tick);

        // 2. Convert the X96 sqrt price (scaled by 2^96) to wad 1/sqrt price (scaled by 10^18)
        uint256 sqrtRatioWad = FullMath.mulDiv(1e18, FixedPoint96.Q96, sqrtPriceX96);

        // 3. Convert 1/sqrt price into fixed rate (1/price)
        uint256 fixedRateWad = sqrtRatioWad.mul(sqrtRatioWad);

        // 4. Return the fixed rate
        return fixedRateWad;
    }

    /// @notice Set new optimal tick range based on current twap tick given that we are using the offchain moving average of the fixed rate in the current iteration
    /// @param index The index of the vault in _vaults
    /// @param currentFixedRateWad currentFixedRate which is passed in from a 7-day rolling avg. historical fixed rate.
    /// @return newTickLower The new lower tick for the rebalanced position
    /// @return newTickUpper The new upper tick for the rebalanced position
    function rebalanceTicks(uint256 index, uint256 currentFixedRateWad)
        public
        returns (int24 newTickLower, int24 newTickUpper)
    {
        _requireAtLeastOperator();
        require(rebalanceCheck(index, currentFixedRateWad), ExceptionsLibrary.REBALANCE_NOT_NEEDED);

        VaultParams memory vaultParams = _vaultParams[index];
        IVoltzVault vault = _vaults[index];

        // 0. Get tickspacing from vamm
        int24 tickSpacing = vault.vamm().tickSpacing();

        // 1. Get the new tick lower
        int256 deltaWad = int256(currentFixedRateWad) - vaultParams.sigmaWad;
        int256 newFixedLowerWad;
        if (deltaWad > MINIMUM_FIXED_RATE) {
            // delta is greater than MINIMUM_FIXED_RATE (0.01) => choose delta
            if (deltaWad < vaultParams.maxPossibleLowerBoundWad) {
                newFixedLowerWad = deltaWad;
            } else {
                newFixedLowerWad = vaultParams.maxPossibleLowerBoundWad;
            }
        } else {
            // delta is less than or equal to MINIMUM_FIXED_RATE (0.01) => choose MINIMUM_FIXED_RATE (0.01)
            newFixedLowerWad = MINIMUM_FIXED_RATE;
        }
        // 2. Get the new tick upper
        int256 newFixedUpperWad = newFixedLowerWad + 2 * vaultParams.sigmaWad;

        // 3. Convert new fixed lower rate back to tick
        int256 newTickLowerWad = convertFixedRateToTick(newFixedUpperWad);

        // 4. Convert new fixed upper rate back to tick
        int256 newTickUpperWad = convertFixedRateToTick(newFixedLowerWad);

        // 5. Scale ticks from wad
        int256 newTickLowerExact = newTickLowerWad / 1e18;
        int256 newTickUpperExact = newTickUpperWad / 1e18;

        // 6. The underlying Voltz VAMM accepts only ticks multiple of tickSpacing
        // Hence, we get the nearest usable tick
        newTickLower = nearestTickMultiple(int24(newTickLowerExact), tickSpacing);
        newTickUpper = nearestTickMultiple(int24(newTickUpperExact), tickSpacing);

        // Call to VoltzVault contract to update the position lower and upper ticks
        vault.rebalance(IVoltzVault.TickRange(newTickLower, newTickUpper));

        emit RebalancedTicks(vault, newTickLower, newTickUpper);
        return (newTickLower, newTickUpper);
    }

    /// @notice This function grabs all funds from the buffer vault
    /// and distributed them to the voltz vaults according to their weights
    function _distributeTokens() internal {
        // 0. Set the local variables
        IERC20Vault localErc20Vault = erc20Vault;
        address[] memory localTokens = tokens;
        VaultParams[] memory vaultParams = _vaultParams;
        uint256 totalWeight = _totalWeight;

        uint256[] memory balances = new uint256[](1);
        balances[0] = IERC20(localTokens[0]).balanceOf(address(localErc20Vault));

        // 1. Distribute the funds
        uint256[] memory vaultShare = new uint256[](1);

        for (uint256 i = 0; i < _vaults.length; i++) {
            uint256 vaultWeight = vaultParams[i].weight;

            if (vaultWeight == 0) {
                continue;
            }

            // The share of i-th is vaultWeight / sum(vaultParams.weight)
            vaultShare[0] = FullMath.mulDiv(balances[0], vaultWeight, totalWeight);

            // Pull funds from the erc20 vault and push the share into the i-th voltz vault
            localErc20Vault.pull(address(_vaults[i]), localTokens, vaultShare, "");
        }
    }

    function transferPermissions(address newStrategy) external {
        _requireAdmin();
        IVaultRegistry vaultRegistry = erc20Vault.vaultGovernance().internalParams().registry;
        IVoltzVault[] memory voltzVaults = _vaults;
        for (uint256 i = 0; i < voltzVaults.length; ++i) {
            vaultRegistry.approve(newStrategy, voltzVaults[i].nft());
        }
        vaultRegistry.approve(newStrategy, erc20Vault.nft());
    }

    /// @notice Callback function called after for ERC20RootVault::deposit
    function depositCallback() external override {
        _distributeTokens();
    }

    /// @notice Callback function called after for ERC20RootVault::withdraw
    function withdrawCallback() external override {
        // Do nothing on withdraw
    }

    // EVENTS
    event StrategyDeployment(IERC20Vault erc20vault, IVoltzVault[] vaults, VaultParams[] vaultParams, address admin);

    event RebalancedTicks(IVoltzVault voltzVault, int24 tickLower, int24 tickUpper);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/AccessControl.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";
import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role, _msgSender());
        _;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControl).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/AccessControlEnumerable.sol)

pragma solidity ^0.8.0;

import "./IAccessControlEnumerable.sol";
import "./AccessControl.sol";
import "../utils/structs/EnumerableSet.sol";

/**
 * @dev Extension of {AccessControl} that allows enumerating the members of each role.
 */
abstract contract AccessControlEnumerable is IAccessControlEnumerable, AccessControl {
    using EnumerableSet for EnumerableSet.AddressSet;

    mapping(bytes32 => EnumerableSet.AddressSet) private _roleMembers;

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControlEnumerable).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns one of the accounts that have `role`. `index` must be a
     * value between 0 and {getRoleMemberCount}, non-inclusive.
     *
     * Role bearers are not sorted in any particular way, and their ordering may
     * change at any point.
     *
     * WARNING: When using {getRoleMember} and {getRoleMemberCount}, make sure
     * you perform all queries on the same block. See the following
     * https://forum.openzeppelin.com/t/iterating-over-elements-on-enumerableset-in-openzeppelin-contracts/2296[forum post]
     * for more information.
     */
    function getRoleMember(bytes32 role, uint256 index) public view override returns (address) {
        return _roleMembers[role].at(index);
    }

    /**
     * @dev Returns the number of accounts that have `role`. Can be used
     * together with {getRoleMember} to enumerate all bearers of a role.
     */
    function getRoleMemberCount(bytes32 role) public view override returns (uint256) {
        return _roleMembers[role].length();
    }

    /**
     * @dev Overload {_grantRole} to track enumerable memberships
     */
    function _grantRole(bytes32 role, address account) internal virtual override {
        super._grantRole(role, account);
        _roleMembers[role].add(account);
    }

    /**
     * @dev Overload {_revokeRole} to track enumerable memberships
     */
    function _revokeRole(bytes32 role, address account) internal virtual override {
        super._revokeRole(role, account);
        _roleMembers[role].remove(account);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (access/IAccessControlEnumerable.sol)

pragma solidity ^0.8.0;

import "./IAccessControl.sol";

/**
 * @dev External interface of AccessControlEnumerable declared to support ERC165 detection.
 */
interface IAccessControlEnumerable is IAccessControl {
    /**
     * @dev Returns one of the accounts that have `role`. `index` must be a
     * value between 0 and {getRoleMemberCount}, non-inclusive.
     *
     * Role bearers are not sorted in any particular way, and their ordering may
     * change at any point.
     *
     * WARNING: When using {getRoleMember} and {getRoleMemberCount}, make sure
     * you perform all queries on the same block. See the following
     * https://forum.openzeppelin.com/t/iterating-over-elements-on-enumerableset-in-openzeppelin-contracts/2296[forum post]
     * for more information.
     */
    function getRoleMember(bytes32 role, uint256 index) external view returns (address);

    /**
     * @dev Returns the number of accounts that have `role`. Can be used
     * together with {getRoleMember} to enumerate all bearers of a role.
     */
    function getRoleMemberCount(bytes32 role) external view returns (uint256);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (proxy/Clones.sol)

pragma solidity ^0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[EIP 1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * The library includes functions to deploy a proxy using either `create` (traditional deployment) or `create2`
 * (salted deterministic deployment). It also includes functions to predict the addresses of clones deployed using the
 * deterministic method.
 *
 * _Available since v3.4._
 */
library Clones {
    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create opcode, which should never revert.
     */
    function clone(address implementation) internal returns (address instance) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create(0, ptr, 0x37)
        }
        require(instance != address(0), "ERC1167: create failed");
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `implementation` and `salt` multiple time will revert, since
     * the clones cannot be deployed twice at the same address.
     */
    function cloneDeterministic(address implementation, bytes32 salt) internal returns (address instance) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
            instance := create2(0, ptr, 0x37, salt)
        }
        require(instance != address(0), "ERC1167: create2 failed");
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
            mstore(add(ptr, 0x14), shl(0x60, implementation))
            mstore(add(ptr, 0x28), 0x5af43d82803e903d91602b57fd5bf3ff00000000000000000000000000000000)
            mstore(add(ptr, 0x38), shl(0x60, deployer))
            mstore(add(ptr, 0x4c), salt)
            mstore(add(ptr, 0x6c), keccak256(ptr, 0x37))
            predicted := keccak256(add(ptr, 0x37), 0x55)
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(address implementation, bytes32 salt)
        internal
        view
        returns (address predicted)
    {
        return predictDeterministicAddress(implementation, salt, address(this));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) {
            // Return data is optional
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes calldata data
    ) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Address.sol)

pragma solidity ^0.8.0;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @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
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 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 functionCall(target, data, "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");
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason 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 {
            // 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

                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @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 Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/Strings.sol)

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @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] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/math/SafeCast.sol)

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= type(int128).min && value <= type(int128).max, "SafeCast: value doesn't fit in 128 bits");
        return int128(value);
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= type(int64).min && value <= type(int64).max, "SafeCast: value doesn't fit in 64 bits");
        return int64(value);
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= type(int32).min && value <= type(int32).max, "SafeCast: value doesn't fit in 32 bits");
        return int32(value);
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= type(int16).min && value <= type(int16).max, "SafeCast: value doesn't fit in 16 bits");
        return int16(value);
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits.
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= type(int8).min && value <= type(int8).max, "SafeCast: value doesn't fit in 8 bits");
        return int8(value);
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.0 (utils/structs/EnumerableSet.sol)

pragma solidity ^0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            if (lastIndex != toDeleteIndex) {
                bytes32 lastvalue = set._values[lastIndex];

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastvalue;
                // Update the index for the moved value
                set._indexes[lastvalue] = valueIndex; // Replace lastvalue's index to valueIndex
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        return _values(set._inner);
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        assembly {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        assembly {
            result := store
        }

        return result;
    }
}

// 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: 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: Unlicense
pragma solidity >=0.8.4;

import "./PRBMath.sol";

/// @title PRBMathUD60x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with uint256 numbers considered to have 18
/// trailing decimals. We call this number representation unsigned 60.18-decimal fixed-point, since there can be up to 60
/// 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 uint256.
library PRBMathUD60x18 {
    /// @dev Half the SCALE number.
    uint256 internal constant HALF_SCALE = 5e17;

    /// @dev log2(e) as an unsigned 60.18-decimal fixed-point number.
    uint256 internal constant LOG2_E = 1_442695040888963407;

    /// @dev The maximum value an unsigned 60.18-decimal fixed-point number can have.
    uint256 internal constant MAX_UD60x18 =
        115792089237316195423570985008687907853269984665640564039457_584007913129639935;

    /// @dev The maximum whole value an unsigned 60.18-decimal fixed-point number can have.
    uint256 internal constant MAX_WHOLE_UD60x18 =
        115792089237316195423570985008687907853269984665640564039457_000000000000000000;

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @notice Calculates the arithmetic average of x and y, rounding down.
    /// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
    /// @return result The arithmetic average as an unsigned 60.18-decimal fixed-point number.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 result) {
        // The operations can never overflow.
        unchecked {
            // The last operand checks if both x and y are odd and if that is the case, we add 1 to the result. We need
            // to do this because if both numbers are odd, the 0.5 remainder gets truncated twice.
            result = (x >> 1) + (y >> 1) + (x & y & 1);
        }
    }

    /// @notice Yields the least unsigned 60.18 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_UD60x18.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number to ceil.
    /// @param result The least integer greater than or equal to x, as an unsigned 60.18-decimal fixed-point number.
    function ceil(uint256 x) internal pure returns (uint256 result) {
        if (x > MAX_WHOLE_UD60x18) {
            revert PRBMathUD60x18__CeilOverflow(x);
        }
        assembly {
            // Equivalent to "x % SCALE" but faster.
            let remainder := mod(x, SCALE)

            // Equivalent to "SCALE - remainder" but faster.
            let delta := sub(SCALE, remainder)

            // Equivalent to "x + delta * (remainder > 0 ? 1 : 0)" but faster.
            result := add(x, mul(delta, gt(remainder, 0)))
        }
    }

    /// @notice Divides two unsigned 60.18-decimal fixed-point numbers, returning a new unsigned 60.18-decimal fixed-point number.
    ///
    /// @dev Uses mulDiv to enable overflow-safe multiplication and division.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    ///
    /// @param x The numerator as an unsigned 60.18-decimal fixed-point number.
    /// @param y The denominator as an unsigned 60.18-decimal fixed-point number.
    /// @param result The quotient as an unsigned 60.18-decimal fixed-point number.
    function div(uint256 x, uint256 y) internal pure returns (uint256 result) {
        result = PRBMath.mulDiv(x, SCALE, y);
    }

    /// @notice Returns Euler's number as an unsigned 60.18-decimal fixed-point number.
    /// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
    function e() internal pure returns (uint256 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.
    ///
    /// @param x The exponent as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp(uint256 x) internal pure returns (uint256 result) {
        // Without this check, the value passed to "exp2" would be greater than 192.
        if (x >= 133_084258667509499441) {
            revert PRBMathUD60x18__ExpInputTooBig(x);
        }

        // Do the fixed-point multiplication inline to save gas.
        unchecked {
            uint256 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_UD60x18.
    ///
    /// @param x The exponent as an unsigned 60.18-decimal 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) {
        // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
        if (x >= 192e18) {
            revert PRBMathUD60x18__Exp2InputTooBig(x);
        }

        unchecked {
            // Convert x to the 192.64-bit fixed-point format.
            uint256 x192x64 = (x << 64) / SCALE;

            // Pass x to the PRBMath.exp2 function, which uses the 192.64-bit fixed-point number representation.
            result = PRBMath.exp2(x192x64);
        }
    }

    /// @notice Yields the greatest unsigned 60.18 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.
    /// @param x The unsigned 60.18-decimal fixed-point number to floor.
    /// @param result The greatest integer less than or equal to x, as an unsigned 60.18-decimal fixed-point number.
    function floor(uint256 x) internal pure returns (uint256 result) {
        assembly {
            // Equivalent to "x % SCALE" but faster.
            let remainder := mod(x, SCALE)

            // Equivalent to "x - remainder * (remainder > 0 ? 1 : 0)" but faster.
            result := sub(x, mul(remainder, gt(remainder, 0)))
        }
    }

    /// @notice Yields the excess beyond the floor of x.
    /// @dev Based on the odd function definition https://en.wikipedia.org/wiki/Fractional_part.
    /// @param x The unsigned 60.18-decimal fixed-point number to get the fractional part of.
    /// @param result The fractional part of x as an unsigned 60.18-decimal fixed-point number.
    function frac(uint256 x) internal pure returns (uint256 result) {
        assembly {
            result := mod(x, SCALE)
        }
    }

    /// @notice Converts a number from basic integer form to unsigned 60.18-decimal fixed-point representation.
    ///
    /// @dev Requirements:
    /// - x must be less than or equal to MAX_UD60x18 divided by SCALE.
    ///
    /// @param x The basic integer to convert.
    /// @param result The same number in unsigned 60.18-decimal fixed-point representation.
    function fromUint(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            if (x > MAX_UD60x18 / SCALE) {
                revert PRBMathUD60x18__FromUintOverflow(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_UD60x18, lest it overflows.
    ///
    /// @param x The first operand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The second operand as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function gm(uint256 x, uint256 y) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        unchecked {
            // Checking for overflow this way is faster than letting Solidity do it.
            uint256 xy = x * y;
            if (xy / x != y) {
                revert PRBMathUD60x18__GmOverflow(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 = PRBMath.sqrt(xy);
        }
    }

    /// @notice Calculates 1 / x, rounding toward zero.
    ///
    /// @dev Requirements:
    /// - x cannot be zero.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the inverse.
    /// @return result The inverse as an unsigned 60.18-decimal fixed-point number.
    function inv(uint256 x) internal pure returns (uint256 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 2.718281828459045235, for that we would need more fine-grained precision.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the natural logarithm.
    /// @return result The natural logarithm as an unsigned 60.18-decimal fixed-point number.
    function ln(uint256 x) internal pure returns (uint256 result) {
        // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
        // can return is 196205294292027477728.
        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 unsigned 60.18-decimal fixed-point number for which to calculate the common logarithm.
    /// @return result The common logarithm as an unsigned 60.18-decimal fixed-point number.
    function log10(uint256 x) internal pure returns (uint256 result) {
        if (x < SCALE) {
            revert PRBMathUD60x18__LogInputTooSmall(x);
        }

        // Note that the "mul" in this block is the assembly multiplication 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) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 59) }
            default {
                result := MAX_UD60x18
            }
        }

        if (result == MAX_UD60x18) {
            // 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 or equal to SCALE, otherwise the result would be negative.
    ///
    /// Caveats:
    /// - The results are nor perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as an unsigned 60.18-decimal fixed-point number.
    function log2(uint256 x) internal pure returns (uint256 result) {
        if (x < SCALE) {
            revert PRBMathUD60x18__LogInputTooSmall(x);
        }
        unchecked {
            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = PRBMath.mostSignificantBit(x / SCALE);

            // The integer part of the logarithm as an unsigned 60.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255 and SCALE is 1e18.
            result = n * SCALE;

            // This is y = x * 2^(-n).
            uint256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == SCALE) {
                return result;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (uint256 delta = 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;
                }
            }
        }
    }

    /// @notice Multiplies two unsigned 60.18-decimal fixed-point numbers together, returning a new unsigned 60.18-decimal
    /// fixed-point number.
    /// @dev See the documentation for the "PRBMath.mulDivFixedPoint" function.
    /// @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 product as an unsigned 60.18-decimal fixed-point number.
    function mul(uint256 x, uint256 y) internal pure returns (uint256 result) {
        result = PRBMath.mulDivFixedPoint(x, y);
    }

    /// @notice Returns PI as an unsigned 60.18-decimal fixed-point number.
    function pi() internal pure returns (uint256 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".
    ///
    /// Caveats:
    /// - All from "exp2", "log2" and "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x Number to raise to given power y, as an unsigned 60.18-decimal fixed-point number.
    /// @param y Exponent to raise x to, as an unsigned 60.18-decimal fixed-point number.
    /// @return result x raised to power y, as an unsigned 60.18-decimal fixed-point number.
    function pow(uint256 x, uint256 y) internal pure returns (uint256 result) {
        if (x == 0) {
            result = y == 0 ? SCALE : uint256(0);
        } else {
            result = exp2(mul(log2(x), y));
        }
    }

    /// @notice Raises x (unsigned 60.18-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:
    /// - The result must fit within MAX_UD60x18.
    ///
    /// Caveats:
    /// - All from "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x The base as an unsigned 60.18-decimal fixed-point number.
    /// @param y The exponent as an uint256.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function powu(uint256 x, uint256 y) internal pure returns (uint256 result) {
        // Calculate the first iteration of the loop in advance.
        result = y & 1 > 0 ? x : SCALE;

        // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
        for (y >>= 1; y > 0; y >>= 1) {
            x = PRBMath.mulDivFixedPoint(x, x);

            // Equivalent to "y % 2 == 1" but faster.
            if (y & 1 > 0) {
                result = PRBMath.mulDivFixedPoint(result, x);
            }
        }
    }

    /// @notice Returns 1 as an unsigned 60.18-decimal fixed-point number.
    function scale() internal pure returns (uint256 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 must be less than MAX_UD60x18 / SCALE.
    ///
    /// @param x The unsigned 60.18-decimal fixed-point number for which to calculate the square root.
    /// @return result The result as an unsigned 60.18-decimal fixed-point .
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            if (x > MAX_UD60x18 / SCALE) {
                revert PRBMathUD60x18__SqrtOverflow(x);
            }
            // Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two unsigned
            // 60.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
            result = PRBMath.sqrt(x * SCALE);
        }
    }

    /// @notice Converts a unsigned 60.18-decimal fixed-point number to basic integer form, rounding down in the process.
    /// @param x The unsigned 60.18-decimal fixed-point number to convert.
    /// @return result The same number in basic integer form.
    function toUint(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            result = x / SCALE;
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "./utils/IDefaultAccessControl.sol";
import "./IUnitPricesGovernance.sol";

interface IProtocolGovernance is IDefaultAccessControl, IUnitPricesGovernance {
    /// @notice CommonLibrary protocol params.
    /// @param maxTokensPerVault Max different token addresses that could be managed by the vault
    /// @param governanceDelay The delay (in secs) that must pass before setting new pending params to commiting them
    /// @param protocolTreasury The address that collects protocolFees, if protocolFee is not zero
    /// @param forceAllowMask If a permission bit is set in this mask it forces all addresses to have this permission as true
    /// @param withdrawLimit Withdraw limit (in unit prices, i.e. usd)
    struct Params {
        uint256 maxTokensPerVault;
        uint256 governanceDelay;
        address protocolTreasury;
        uint256 forceAllowMask;
        uint256 withdrawLimit;
    }

    // -------------------  EXTERNAL, VIEW  -------------------

    /// @notice Timestamp after which staged granted permissions for the given address can be committed.
    /// @param target The given address
    /// @return Zero if there are no staged permission grants, timestamp otherwise
    function stagedPermissionGrantsTimestamps(address target) external view returns (uint256);

    /// @notice Staged granted permission bitmask for the given address.
    /// @param target The given address
    /// @return Bitmask
    function stagedPermissionGrantsMasks(address target) external view returns (uint256);

    /// @notice Permission bitmask for the given address.
    /// @param target The given address
    /// @return Bitmask
    function permissionMasks(address target) external view returns (uint256);

    /// @notice Timestamp after which staged pending protocol parameters can be committed
    /// @return Zero if there are no staged parameters, timestamp otherwise.
    function stagedParamsTimestamp() external view returns (uint256);

    /// @notice Staged pending protocol parameters.
    function stagedParams() external view returns (Params memory);

    /// @notice Current protocol parameters.
    function params() external view returns (Params memory);

    /// @notice Addresses for which non-zero permissions are set.
    function permissionAddresses() external view returns (address[] memory);

    /// @notice Permission addresses staged for commit.
    function stagedPermissionGrantsAddresses() external view returns (address[] memory);

    /// @notice Return all addresses where rawPermissionMask bit for permissionId is set to 1.
    /// @param permissionId Id of the permission to check.
    /// @return A list of dirty addresses.
    function addressesByPermission(uint8 permissionId) external view returns (address[] memory);

    /// @notice Checks if address has permission or given permission is force allowed for any address.
    /// @param addr Address to check
    /// @param permissionId Permission to check
    function hasPermission(address addr, uint8 permissionId) external view returns (bool);

    /// @notice Checks if address has all permissions.
    /// @param target Address to check
    /// @param permissionIds A list of permissions to check
    function hasAllPermissions(address target, uint8[] calldata permissionIds) external view returns (bool);

    /// @notice Max different ERC20 token addresses that could be managed by the protocol.
    function maxTokensPerVault() external view returns (uint256);

    /// @notice The delay for committing any governance params.
    function governanceDelay() external view returns (uint256);

    /// @notice The address of the protocol treasury.
    function protocolTreasury() external view returns (address);

    /// @notice Permissions mask which defines if ordinary permission should be reverted.
    /// This bitmask is xored with ordinary mask.
    function forceAllowMask() external view returns (uint256);

    /// @notice Withdraw limit per token per block.
    /// @param token Address of the token
    /// @return Withdraw limit per token per block
    function withdrawLimit(address token) external view returns (uint256);

    /// @notice Addresses that has staged validators.
    function stagedValidatorsAddresses() external view returns (address[] memory);

    /// @notice Timestamp after which staged granted permissions for the given address can be committed.
    /// @param target The given address
    /// @return Zero if there are no staged permission grants, timestamp otherwise
    function stagedValidatorsTimestamps(address target) external view returns (uint256);

    /// @notice Staged validator for the given address.
    /// @param target The given address
    /// @return Validator
    function stagedValidators(address target) external view returns (address);

    /// @notice Addresses that has validators.
    function validatorsAddresses() external view returns (address[] memory);

    /// @notice Address that has validators.
    /// @param i The number of address
    /// @return Validator address
    function validatorsAddress(uint256 i) external view returns (address);

    /// @notice Validator for the given address.
    /// @param target The given address
    /// @return Validator
    function validators(address target) external view returns (address);

    // -------------------  EXTERNAL, MUTATING, GOVERNANCE, IMMEDIATE  -------------------

    /// @notice Rollback all staged validators.
    function rollbackStagedValidators() external;

    /// @notice Revoke validator instantly from the given address.
    /// @param target The given address
    function revokeValidator(address target) external;

    /// @notice Stages a new validator for the given address
    /// @param target The given address
    /// @param validator The validator for the given address
    function stageValidator(address target, address validator) external;

    /// @notice Commits validator for the given address.
    /// @dev Reverts if governance delay has not passed yet.
    /// @param target The given address.
    function commitValidator(address target) external;

    /// @notice Commites all staged validators for which governance delay passed
    /// @return Addresses for which validators were committed
    function commitAllValidatorsSurpassedDelay() external returns (address[] memory);

    /// @notice Rollback all staged granted permission grant.
    function rollbackStagedPermissionGrants() external;

    /// @notice Commits permission grants for the given address.
    /// @dev Reverts if governance delay has not passed yet.
    /// @param target The given address.
    function commitPermissionGrants(address target) external;

    /// @notice Commites all staged permission grants for which governance delay passed.
    /// @return An array of addresses for which permission grants were committed.
    function commitAllPermissionGrantsSurpassedDelay() external returns (address[] memory);

    /// @notice Revoke permission instantly from the given address.
    /// @param target The given address.
    /// @param permissionIds A list of permission ids to revoke.
    function revokePermissions(address target, uint8[] memory permissionIds) external;

    /// @notice Commits staged protocol params.
    /// Reverts if governance delay has not passed yet.
    function commitParams() external;

    // -------------------  EXTERNAL, MUTATING, GOVERNANCE, DELAY  -------------------

    /// @notice Sets new pending params that could have been committed after governance delay expires.
    /// @param newParams New protocol parameters to set.
    function stageParams(Params memory newParams) external;

    /// @notice Stage granted permissions that could have been committed after governance delay expires.
    /// Resets commit delay and permissions if there are already staged permissions for this address.
    /// @param target Target address
    /// @param permissionIds A list of permission ids to grant
    function stagePermissionGrants(address target, uint8[] memory permissionIds) external;
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import "./utils/IDefaultAccessControl.sol";

interface IUnitPricesGovernance is IDefaultAccessControl, IERC165 {
    // -------------------  EXTERNAL, VIEW  -------------------

    /// @notice Estimated amount of token worth 1 USD staged for commit.
    /// @param token Address of the token
    /// @return The amount of token
    function stagedUnitPrices(address token) external view returns (uint256);

    /// @notice Timestamp after which staged unit prices for the given token can be committed.
    /// @param token Address of the token
    /// @return Timestamp
    function stagedUnitPricesTimestamps(address token) external view returns (uint256);

    /// @notice Estimated amount of token worth 1 USD.
    /// @param token Address of the token
    /// @return The amount of token
    function unitPrices(address token) external view returns (uint256);

    // -------------------  EXTERNAL, MUTATING  -------------------

    /// @notice Stage estimated amount of token worth 1 USD staged for commit.
    /// @param token Address of the token
    /// @param value The amount of token
    function stageUnitPrice(address token, uint256 value) external;

    /// @notice Reset staged value
    /// @param token Address of the token
    function rollbackUnitPrice(address token) external;

    /// @notice Commit staged unit price
    /// @param token Address of the token
    function commitUnitPrice(address token) external;
}

// SPDX-License-Identifier: MIT
pragma solidity =0.8.9;

import "@openzeppelin/contracts/token/ERC721/IERC721.sol";
import "./IProtocolGovernance.sol";

interface IVaultRegistry is IERC721 {
    /// @notice Get Vault for the giver NFT ID.
    /// @param nftId NFT ID
    /// @return vault Address of the Vault contract
    function vaultForNft(uint256 nftId) external view returns (address vault);

    /// @notice Get NFT ID for given Vault contract address.
    /// @param vault Address of the Vault contract
    /// @return nftId NFT ID
    function nftForVault(address vault) external view returns (uint256 nftId);

    /// @notice Checks if the nft is locked for all transfers
    /// @param nft NFT to check for lock
    /// @return `true` if locked, false otherwise
    function isLocked(uint256 nft) external view returns (bool);

    /// @notice Register new Vault and mint NFT.
    /// @param vault address of the vault
    /// @param owner owner of the NFT
    /// @return nft Nft minted for the given Vault
    function registerVault(address vault, address owner) external returns (uint256 nft);

    /// @notice Number of Vaults registered.
    function vaultsCount() external view returns (uint256);

    /// @notice All Vaults registered.
    function vaults() external view returns (address[] memory);

    /// @notice Address of the ProtocolGovernance.
    function protocolGovernance() external view returns (IProtocolGovernance);

    /// @notice Address of the staged ProtocolGovernance.
    function stagedProtocolGovernance() external view returns (IProtocolGovernance);

    /// @notice Minimal timestamp when staged ProtocolGovernance can be applied.
    function stagedProtocolGovernanceTimestamp() external view returns (uint256);

    /// @notice Stage new ProtocolGovernance.
    /// @param newProtocolGovernance new ProtocolGovernance
    function stageProtocolGovernance(IProtocolGovernance newProtocolGovernance) external;

    /// @notice Commit new ProtocolGovernance.
    function commitStagedProtocolGovernance() external;

    /// @notice Lock NFT for transfers
    /// @dev Use this method when vault structure is set up and should become immutable. Can be called by owner.
    /// @param nft - NFT to lock
    function lockNft(uint256 nft) external;
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

interface IERC1271 {
    /// @notice Verifies offchain signature.
    /// @dev Should return whether the signature provided is valid for the provided hash
    ///
    /// MUST return the bytes4 magic value 0x1626ba7e when function passes.
    ///
    /// MUST NOT modify state (using STATICCALL for solc < 0.5, view modifier for solc > 0.5)
    ///
    /// MUST allow external calls
    /// @param _hash Hash of the data to be signed
    /// @param _signature Signature byte array associated with _hash
    /// @return magicValue 0x1626ba7e if valid, 0xffffffff otherwise
    function isValidSignature(bytes32 _hash, bytes memory _signature) external view returns (bytes4 magicValue);
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;

/// @title Minimal ERC20 interface for Voltz
/// @notice Contains a subset of the full ERC20 interface that is used in Voltz
interface IERC20Minimal {
    /// @notice Returns the balance of a token
    /// @param account The account for which to look up the number of tokens it has, i.e. its balance
    /// @return The number of tokens held by the account
    function balanceOf(address account) external view returns (uint256);

    /// @notice Transfers the amount of token from the `msg.sender` to the recipient
    /// @param recipient The account that will receive the amount transferred
    /// @param amount The number of tokens to send from the sender to the recipient
    /// @return Returns true for a successful transfer, false for an unsuccessful transfer
    function transfer(address recipient, uint256 amount)
        external
        returns (bool);

    /// @notice Returns the current allowance given to a spender by an owner
    /// @param owner The account of the token owner
    /// @param spender The account of the token spender
    /// @return The current allowance granted by `owner` to `spender`
    function allowance(address owner, address spender)
        external
        view
        returns (uint256);

    /// @notice Sets the allowance of a spender from the `msg.sender` to the value `amount`
    /// @param spender The account which will be allowed to spend a given amount of the owners tokens
    /// @param amount The amount of tokens allowed to be used by `spender`
    /// @return Returns true for a successful approval, false for unsuccessful
    function approve(address spender, uint256 amount) external returns (bool);

    /// @notice Transfers `amount` tokens from `sender` to `recipient` up to the allowance given to the `msg.sender`
    /// @param sender The account from which the transfer will be initiated
    /// @param recipient The recipient of the transfer
    /// @param amount The amount of the transfer
    /// @return Returns true for a successful transfer, false for unsuccessful
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /// @dev Returns the number of decimals used to get its user representation.
    // For example, if decimals equals 2, a balance of 505 tokens should be displayed to a user as 5,05 (505 / 10 ** 2).
    // Tokens usually opt for a value of 18, imitating the relationship between Ether and Wei.
    function decimals() external view returns (uint8);

    /// @notice Event emitted when tokens are transferred from one address to another, either via `#transfer` or `#transferFrom`.
    /// @param from The account from which the tokens were sent, i.e. the balance decreased
    /// @param to The account to which the tokens were sent, i.e. the balance increased
    /// @param value The amount of tokens that were transferred
    event Transfer(address indexed from, address indexed to, uint256 value);

    /// @notice Event emitted when the approval amount for the spender of a given owner's tokens changes.
    /// @param owner The account that approved spending of its tokens
    /// @param spender The account for which the spending allowance was modified
    /// @param value The new allowance from the owner to the spender
    event Approval(
        address indexed owner,
        address indexed spender,
        uint256 value
    );
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

import "./utils/CustomErrors.sol";
import "./rate_oracles/IRateOracle.sol";
import "./IMarginEngine.sol";
import "./IVAMM.sol";
import "./fcms/IFCM.sol";
import "./IERC20Minimal.sol";
import "./IPeriphery.sol";

/// @title The interface for the Voltz AMM Factory
/// @notice The AMM Factory facilitates creation of Voltz AMMs
interface IFactory is CustomErrors {
    event IrsInstance(
        IERC20Minimal indexed underlyingToken,
        IRateOracle indexed rateOracle,
        uint256 termStartTimestampWad,
        uint256 termEndTimestampWad,
        int24 tickSpacing,
        IMarginEngine marginEngine,
        IVAMM vamm,
        IFCM fcm,
        uint8 yieldBearingProtocolID,
        uint8 underlyingTokenDecimals
    );

    event MasterFCM(IFCM masterFCMAddress, uint8 yieldBearingProtocolID);

    event Approval(
        address indexed owner,
        address indexed intAddress,
        bool indexed isApproved
    );

    event PeripheryUpdate(IPeriphery periphery);

    // view functions

    function isApproved(address _owner, address intAddress)
        external
        view
        returns (bool);

    function masterVAMM() external view returns (IVAMM);

    function masterMarginEngine() external view returns (IMarginEngine);

    function periphery() external view returns (IPeriphery);

    // settters

    function setApproval(address intAddress, bool allowIntegration) external;

    function setMasterFCM(IFCM masterFCM, uint8 yieldBearingProtocolID)
        external;

    function setMasterVAMM(IVAMM _masterVAMM) external;

    function setMasterMarginEngine(IMarginEngine _masterMarginEngine) external;

    function setPeriphery(IPeriphery _periphery) external;

    /// @notice Deploys the contracts required for a new Interest Rate Swap instance
    function deployIrsInstance(
        IERC20Minimal _underlyingToken,
        IRateOracle _rateOracle,
        uint256 _termStartTimestampWad,
        uint256 _termEndTimestampWad,
        int24 _tickSpacing
    )
        external
        returns (
            IMarginEngine marginEngineProxy,
            IVAMM vammProxy,
            IFCM fcmProxy
        );

    function masterFCMs(uint8 yieldBearingProtocolID)
        external
        view
        returns (IFCM masterFCM);
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;
import "./IVAMM.sol";
import "./IPositionStructs.sol";
import "./utils/Position.sol";
import "./rate_oracles/IRateOracle.sol";
import "./fcms/IFCM.sol";
import "./IFactory.sol";
import "./IERC20Minimal.sol";
import "./utils/CustomErrors.sol";

interface IMarginEngine is IPositionStructs, CustomErrors {
    // structs

    function setPausability(bool state) external;

    struct MarginCalculatorParameters {
        /// @dev Upper bound of the underlying pool (e.g. Aave v2 USDC lending pool) APY from the initiation of the IRS AMM and until its maturity (18 decimals fixed point number)
        uint256 apyUpperMultiplierWad;
        /// @dev Lower bound of the underlying pool (e.g. Aave v2 USDC lending pool) APY from the initiation of the IRS AMM and until its maturity (18 decimals)
        uint256 apyLowerMultiplierWad;
        /// @dev The volatility of the underlying pool APY (settable by the owner of the Margin Engine) (18 decimals)
        int256 sigmaSquaredWad;
        /// @dev Margin Engine Parameter estimated via CIR model calibration (for details refer to litepaper) (18 decimals)
        int256 alphaWad;
        /// @dev Margin Engine Parameter estimated via CIR model calibration (for details refer to litepaper) (18 decimals)
        int256 betaWad;
        /// @dev Standard normal critical value used in the computation of the Upper APY Bound of the underlying pool
        int256 xiUpperWad;
        /// @dev Standard normal critical value used in the computation of the Lower APY Bound of the underlying pool
        int256 xiLowerWad;
        /// @dev Max term possible for a Voltz IRS AMM in seconds (18 decimals)
        int256 tMaxWad;
        /// @dev multiplier of the starting fixed rate (refer to the litepaper) if simulating a counterfactual fixed taker unwind (moving to the left along the VAMM) for purposes of calculating liquidation margin requirement
        uint256 devMulLeftUnwindLMWad;
        /// @dev multiplier of the starting fixed rate (refer to the litepaper) if simulating a counterfactual variable taker unwind (moving to the right along the VAMM) for purposes of calculating liquidation margin requirement
        uint256 devMulRightUnwindLMWad;
        /// @dev same as devMulLeftUnwindLMWad but for purposes of calculating the initial margin requirement
        uint256 devMulLeftUnwindIMWad;
        /// @dev same as devMulRightUnwindLMWad but for purposes of calculating the initial margin requirement
        uint256 devMulRightUnwindIMWad;
        /// @dev r_min from the litepaper eq. 11 for a scenario where counterfactual is a simulated fixed taker unwind (left unwind along the VAMM), used for liquidation margin calculation
        uint256 fixedRateDeviationMinLeftUnwindLMWad;
        /// @dev r_min from the litepaper eq. 11 for a scenario where counterfactual is a simulated variable taker unwind (right unwind along the VAMM), used for liquidation margin calculation
        uint256 fixedRateDeviationMinRightUnwindLMWad;
        /// @dev same as fixedRateDeviationMinLeftUnwindLMWad but for Initial Margin Requirement
        uint256 fixedRateDeviationMinLeftUnwindIMWad;
        /// @dev same as fixedRateDeviationMinRightUnwindLMWad but for Initial Margin Requirement
        uint256 fixedRateDeviationMinRightUnwindIMWad;
        /// @dev gamma from eqn. 12 [append this logic to the litepaper] from the litepaper, gamma is an adjustable parameter necessary to calculate scaled deviations to the fixed rate in counterfactual unwinds for minimum margin requirement calculations
        uint256 gammaWad;
        /// @dev settable parameter that ensures that minimumMarginRequirement is always above or equal to the minMarginToIncentiviseLiquidators which ensures there is always sufficient incentive for liquidators to liquidate positions given the fact their income is a proportion of position margin
        uint256 minMarginToIncentiviseLiquidators;
    }

    // Events
    event HistoricalApyWindowSetting(uint256 secondsAgo);
    event CacheMaxAgeSetting(uint256 cacheMaxAgeInSeconds);
    event RateOracle(uint256 cacheMaxAgeInSeconds);

    event ProtocolCollection(
        address sender,
        address indexed recipient,
        uint256 amount
    );
    event LiquidatorRewardSetting(uint256 liquidatorRewardWad);

    event VAMMSetting(IVAMM indexed vamm);

    event RateOracleSetting(IRateOracle indexed rateOracle);

    event FCMSetting(IFCM indexed fcm);

    event MarginCalculatorParametersSetting(
        MarginCalculatorParameters marginCalculatorParameters
    );

    event PositionMarginUpdate(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        int256 marginDelta
    );

    event HistoricalApy(uint256 value);

    event PositionSettlement(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        int256 settlementCashflow
    );

    event PositionLiquidation(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        address liquidator,
        int256 notionalUnwound,
        uint256 liquidatorReward
    );

    event PositionUpdate(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 _liquidity,
        int256 margin,
        int256 fixedTokenBalance,
        int256 variableTokenBalance,
        uint256 accumulatedFees
    );

    /// @dev emitted after the _isAlpha boolean is updated by the owner of the Margin Engine
    /// @dev _isAlpha boolean dictates whether the Margin Engine is in the Alpha State, i.e. margin updates can only be done via the periphery
    /// @dev additionally, the periphery has the logic to take care of lp margin caps in the Alpha State phase of the Margin Engine
    /// @dev __isAlpha is the newly set value for the _isAlpha boolean
    event IsAlpha(bool __isAlpha);

    // immutables

    /// @notice The Full Collateralisation Module (FCM)
    /// @dev The FCM is a smart contract that acts as an intermediary Position between the Voltz Core and traders who wish to take fully collateralised fixed taker positions
    /// @dev An example FCM is the AaveFCM.sol module which inherits from the IFCM interface, it lets fixed takers deposit underlying yield bearing tokens (e.g.) aUSDC as margin to enter into a fixed taker swap without the need to worry about liquidations
    /// @dev since the MarginEngine is confident the FCM is always fully collateralised, it does not let liquidators liquidate the FCM Position
    /// @return The Full Collateralisation Module linked to the MarginEngine
    function fcm() external view returns (IFCM);

    /// @notice The Factory
    /// @dev the factory that deployed the master Margin Engine
    function factory() external view returns (IFactory);

    /// @notice The address of the underlying (non-yield bearing) token - e.g. USDC
    /// @return The underlying ERC20 token (e.g. USDC)
    function underlyingToken() external view returns (IERC20Minimal);

    /// @notice The rateOracle contract which lets the protocol access historical apys in the yield bearing pools it is built on top of
    /// @return The underlying ERC20 token (e.g. USDC)
    function rateOracle() external view returns (IRateOracle);

    /// @notice The unix termStartTimestamp of the MarginEngine in Wad
    /// @return Term Start Timestamp in Wad
    function termStartTimestampWad() external view returns (uint256);

    /// @notice The unix termEndTimestamp of the MarginEngine in Wad
    /// @return Term End Timestamp in Wad
    function termEndTimestampWad() external view returns (uint256);

    /// @dev "constructor" for proxy instances
    function initialize(
        IERC20Minimal __underlyingToken,
        IRateOracle __rateOracle,
        uint256 __termStartTimestampWad,
        uint256 __termEndTimestampWad
    ) external;

    // view functions

    /// @notice The liquidator Reward Percentage (in Wad)
    /// @dev liquidatorReward (in wad) is the percentage of the margin (of a liquidated position) that is sent to the liquidator
    /// @dev following a successful liquidation that results in a trader/position unwind; example value:  2 * 10**16 => 2% of position margin is used to cover liquidator reward
    /// @return Liquidator Reward in Wad
    function liquidatorRewardWad() external view returns (uint256);

    /// @notice VAMM (Virtual Automated Market Maker) linked to the MarginEngine
    /// @dev The VAMM is responsible for pricing only (determining the effective fixed rate at which a given Interest Rate Swap notional will be executed)
    /// @return The VAMM
    function vamm() external view returns (IVAMM);

    /// @return If true, the Margin Engine Proxy is currently in alpha state, hence margin updates of LPs can only be done via the periphery. If false, lps can directly update their margin via Margin Engine.
    function isAlpha() external view returns (bool);

    /// @notice Returns the information about a position by the position's key
    /// @param _owner The address of the position owner
    /// @param _tickLower The lower tick boundary of the position
    /// @param _tickUpper The upper tick boundary of the position
    /// Returns position The Position.Info corresponding to the requested position
    function getPosition(
        address _owner,
        int24 _tickLower,
        int24 _tickUpper
    ) external returns (Position.Info memory position);

    /// @notice Gets the look-back window size that's used to request the historical APY from the rate Oracle
    /// @dev The historical APY of the Rate Oracle is necessary for MarginEngine computations
    /// @dev The look-back window is seconds from the current timestamp
    /// @dev This value is only settable by the the Factory owner and may be unique for each MarginEngine
    /// @dev When setting secondAgo, the setter needs to take into consideration the underlying volatility of the APYs in the reference yield-bearing pool (e.g. Aave v2 USDC)
    function lookbackWindowInSeconds() external view returns (uint256);

    // non-view functions

    /// @notice Sets secondsAgo: The look-back window size used to calculate the historical APY for margin purposes
    /// @param _secondsAgo the duration of the lookback window in seconds
    /// @dev Can only be set by the Factory Owner
    function setLookbackWindowInSeconds(uint256 _secondsAgo) external;

    /// @notice Set the MarginCalculatorParameters (each margin engine can have its own custom set of margin calculator parameters)
    /// @param _marginCalculatorParameters the MarginCalculatorParameters to set
    /// @dev marginCalculatorParameteres is of type MarginCalculatorParameters (refer to the definition of the struct for elaboration on what each parameter means)
    function setMarginCalculatorParameters(
        MarginCalculatorParameters memory _marginCalculatorParameters
    ) external;

    /// @notice Sets the liquidator reward: proportion of liquidated position's margin paid as a reward to the liquidator
    function setLiquidatorReward(uint256 _liquidatorRewardWad) external;

    /// @notice Function that sets the _isAlpha state variable, if it is set to true the protocol is in the Alpha State
    /// @dev if the Margin Engine is at the alpha state, lp margin updates can only be done via the periphery which in turn takes care of margin caps for the LPs
    /// @dev this function can only be called by the owner of the VAMM
    function setIsAlpha(bool __isAlpha) external;

    /// @notice updates the margin account of a position which can be uniquily identified with its _owner, tickLower, tickUpper
    /// @dev if the position has positive liquidity then before the margin update, we call the updatePositionTokenBalancesAndAccountForFees functon that calculates up to date
    /// @dev margin, fixed and variable token balances by taking into account the fee income from their tick range and fixed and variable deltas settled along their tick range
    /// @dev marginDelta is the delta applied to the current margin of a position, if the marginDelta is negative, the position is withdrawing margin, if the marginDelta is positive, the position is depositing funds in terms of the underlying tokens
    /// @dev if marginDelta is negative, we need to check if the msg.sender is either the _owner of the position or the msg.sender is apporved by the _owner to act on their behalf in Voltz Protocol
    /// @dev the approval logic is implemented in the Factory.sol
    /// @dev if marginDelta is negative, we additionally need to check if post the initial margin requirement is still satisfied post withdrawal
    /// @dev if marginDelta is positive, the depositor of the margin is either the msg.sender or the owner who interacted through an approved peripheral contract
    function updatePositionMargin(
        address _owner,
        int24 _tickLower,
        int24 _tickUpper,
        int256 marginDelta
    ) external;

    /// @notice Settles a Position
    /// @dev Can be called by anyone
    /// @dev A position cannot be settled before maturity
    /// @dev Steps to settle a position:
    /// @dev 1. Retrieve the current fixed and variable token growth inside the tick range of a position
    /// @dev 2. Calculate accumulated fixed and variable balances of the position since the last mint/poke/burn
    /// @dev 3. Update the postion's fixed and variable token balances
    /// @dev 4. Update the postion's fixed and varaible token growth inside last to enable future updates
    /// @dev 5. Calculates the settlement cashflow from all of the IRS contracts the position has entered since entering the AMM
    /// @dev 6. Updates the fixed and variable token balances of the position to be zero, adds the settlement cashflow to the position's current margin
    function settlePosition(
        address _owner,
        int24 _tickLower,
        int24 _tickUpper
    ) external;

    /// @notice Liquidate a Position
    /// @dev Steps to liquidate: update position's fixed and variable token balances to account for balances accumulated throughout the trades made since the last mint/burn/poke,
    /// @dev Check if the position is liquidatable by calling the isLiquidatablePosition function of the calculator, revert if that is not the case,
    /// @dev Calculate the liquidation reward = current margin of the position * liquidatorReward, subtract the liquidator reward from the position margin,
    /// @dev Burn the position's liquidity, unwind unnetted fixed and variable balances of a position, transfer the reward to the liquidator
    function liquidatePosition(
        address _owner,
        int24 _tickLower,
        int24 _tickUpper
    ) external returns (uint256);

    /// @notice Update a Position post VAMM induced mint or burn
    /// @dev Steps taken:
    /// @dev 1. Update position liquidity based on params.liquidityDelta
    /// @dev 2. Update fixed and variable token balances of the position based on how much has been accumulated since the last mint/burn/poke
    /// @dev 3. Update position's margin by taking into account the position accumulated fees since the last mint/burn/poke
    /// @dev 4. Update fixed and variable token growth + fee growth in the position info struct for future interactions with the position
    /// @param _params necessary for the purposes of referencing the position being updated (owner, tickLower, tickUpper, _) and the liquidity delta that needs to be applied to position._liquidity
    function updatePositionPostVAMMInducedMintBurn(
        IPositionStructs.ModifyPositionParams memory _params
    ) external returns (int256 _positionMarginRequirement);

    // @notive Update a position post VAMM induced swap
    /// @dev Since every position can also engage in swaps with the VAMM, this function needs to be invoked after non-external calls are made to the VAMM's swap function
    /// @dev This purpose of this function is to:
    /// @dev 1. updatePositionTokenBalancesAndAccountForFees
    /// @dev 2. update position margin to account for fees paid to execute the swap
    /// @dev 3. calculate the position margin requrement given the swap, check if the position marigin satisfies the most up to date requirement
    /// @dev 4. if all the requirements are satisfied then position gets updated to take into account the swap that it just entered, if the minimum margin requirement is not satisfied then the transaction will revert
    function updatePositionPostVAMMInducedSwap(
        address _owner,
        int24 _tickLower,
        int24 _tickUpper,
        int256 _fixedTokenDelta,
        int256 _variableTokenDelta,
        uint256 _cumulativeFeeIncurred,
        int256 _fixedTokenDeltaUnbalanced
    ) external returns (int256 _positionMarginRequirement);

    /// @notice function that can only be called by the owner enables collection of protocol generated fees from any give margin engine
    /// @param _recipient the address which collects the protocol generated fees
    /// @param _amount the amount in terms of underlying tokens collected from the protocol's earnings
    function collectProtocol(address _recipient, uint256 _amount) external;

    /// @notice sets the Virtual Automated Market Maker (VAMM) attached to the MarginEngine
    /// @dev the VAMM is responsible for price discovery, whereas the management of the underlying collateral and liquidations are handled by the Margin Engine
    function setVAMM(IVAMM _vAMM) external;

    /// @notice sets the Virtual Automated Market Maker (VAMM) attached to the MarginEngine
    /// @dev the VAMM is responsible for price discovery, whereas the management of the underlying collateral and liquidations are handled by the Margin Engine
    function setRateOracle(IRateOracle __rateOracle) external;

    /// @notice sets the Full Collateralisation Module
    function setFCM(IFCM _newFCM) external;

    /// @notice transfers margin in terms of underlying tokens to a trader from the Full Collateralisation Module
    /// @dev post maturity date of the MarginEngine, the traders from the Full Collateralisation module will be able to settle with the MarginEngine
    /// @dev to ensure their fixed yield is guaranteed, in order to collect the funds from the MarginEngine, the FCM needs to invoke the transferMarginToFCMTrader function whcih is only callable by the FCM attached to a particular Margin Engine
    function transferMarginToFCMTrader(address _account, uint256 _marginDelta)
        external;

    /// @notice Gets the maximum age of the cached historical APY value can be without being refreshed
    function cacheMaxAgeInSeconds() external view returns (uint256);

    /// @notice Sets the maximum age that the cached historical APY value
    /// @param _cacheMaxAgeInSeconds The new maximum age that the historical APY cache can be before being considered stale
    function setCacheMaxAgeInSeconds(uint256 _cacheMaxAgeInSeconds) external;

    /// @notice Get Historical APY
    /// @dev The lookback window used by this function is determined by `lookbackWindowInSeconds`
    /// @dev refresh the historical apy cache if necessary
    /// @return historicalAPY (Wad)
    function getHistoricalApy() external returns (uint256);

    /// @notice Computes the historical APY value of the RateOracle, without updating the cached value
    /// @dev The lookback window used by this function is determined by `lookbackWindowInSeconds`
    function getHistoricalApyReadOnly() external view returns (uint256);

    function getPositionMarginRequirement(
        address _recipient,
        int24 _tickLower,
        int24 _tickUpper,
        bool _isLM
    ) external returns (uint256);
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

import "./IMarginEngine.sol";
import "./IVAMM.sol";
import "./utils/CustomErrors.sol";

interface IPeriphery is CustomErrors {
    // events

    /// @dev emitted after new lp margin cap is set
    event MarginCap(IVAMM _vamm, int256 _lpMarginCapNew);

    // structs

    struct MintOrBurnParams {
        IMarginEngine marginEngine;
        int24 tickLower;
        int24 tickUpper;
        uint256 notional;
        bool isMint;
        int256 marginDelta;
    }

    struct SwapPeripheryParams {
        IMarginEngine marginEngine;
        bool isFT;
        uint256 notional;
        uint160 sqrtPriceLimitX96;
        int24 tickLower;
        int24 tickUpper;
        uint256 marginDelta;
    }

    // view functions

    function getCurrentTick(IMarginEngine marginEngine)
        external
        view
        returns (int24 currentTick);

    /// @param _vamm VAMM for which to get the lp cap in underlying tokens
    /// @return Notional Cap for liquidity providers that mint or burn via periphery (enforced in the core if isAlpha is set to true)
    function lpMarginCaps(IVAMM _vamm) external returns (int256);

    /// @param _vamm VAMM for which to get the lp notional cumulative in underlying tokens
    /// @return Total amount of notional supplied by the LPs to a given VAMM via the periphery
    function lpMarginCumulatives(IVAMM _vamm) external returns (int256);

    // non-view functions

    function mintOrBurn(MintOrBurnParams memory params)
        external
        returns (int256 positionMarginRequirement);

    function swap(SwapPeripheryParams memory params)
        external
        returns (
            int256 _fixedTokenDelta,
            int256 _variableTokenDelta,
            uint256 _cumulativeFeeIncurred,
            int256 _fixedTokenDeltaUnbalanced,
            int256 _marginRequirement,
            int24 _tickAfter
        );

    function updatePositionMargin(
        IMarginEngine _marginEngine,
        int24 _tickLower,
        int24 _tickUpper,
        int256 _marginDelta,
        bool _fullyWithdraw
    ) external;

    function setLPMarginCap(IVAMM _vamm, int256 _lpMarginCapNew) external;

    function settlePositionAndWithdrawMargin(
        IMarginEngine _marginEngine,
        address _owner,
        int24 _tickLower,
        int24 _tickUpper
    ) external;
    
    function getLiquidityForNotional(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 notionalAmount
    ) external pure returns (uint128 liquidity);
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;

interface IPositionStructs {
    struct ModifyPositionParams {
        // the address that owns the position
        address owner;
        // the lower and upper tick of the position
        int24 tickLower;
        int24 tickUpper;
        // any change in liquidity
        int128 liquidityDelta;
    }
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;
import "./IMarginEngine.sol";
import "./IFactory.sol";
import "./IPositionStructs.sol";
import "./utils/Tick.sol";
import "./utils/CustomErrors.sol";

interface IVAMM is IPositionStructs, CustomErrors {
    function setPausability(bool state) external;

    // events
    event Swap(
        address sender,
        address indexed recipient,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        int256 desiredNotional,
        uint160 sqrtPriceLimitX96,
        uint256 cumulativeFeeIncurred,
        int256 fixedTokenDelta,
        int256 variableTokenDelta,
        int256 fixedTokenDeltaUnbalanced
    );

    /// @dev emitted after a given vamm is successfully initialized
    event VAMMInitialization(uint160 sqrtPriceX96, int24 tick);

    /// @dev emitted after a successful minting of a given LP position
    event Mint(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount
    );

    /// @dev emitted after a successful burning of a given LP position
    event Burn(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount
    );

    /// @dev emitted after setting feeProtocol
    event FeeProtocol(uint8 feeProtocol);

    /// @dev emitted after fee is set
    event Fee(uint256 feeWad);

    /// @dev emitted after the _isAlpha boolean is updated by the owner of the VAMM
    /// @dev _isAlpha boolean dictates whether the VAMM is in the Alpha State, i.e. mints can only be done via the periphery
    /// @dev additionally, the periphery has the logic to take care of lp notional caps in the Alpha State phase of VAMM
    /// @dev __isAlpha is the newly set value for the _isAlpha boolean
    event IsAlpha(bool __isAlpha);

    event VAMMPriceChange(int24 tick);

    // structs

    struct VAMMVars {
        /// @dev The current price of the pool as a sqrt(variableToken/fixedToken) Q64.96 value
        uint160 sqrtPriceX96;
        /// @dev The current tick of the vamm, i.e. according to the last tick transition that was run.
        int24 tick;
        // the current protocol fee as a percentage of the swap fee taken on withdrawal
        // represented as an integer denominator (1/x)
        uint8 feeProtocol;
    }

    struct SwapParams {
        /// @dev Address of the trader initiating the swap
        address recipient;
        /// @dev The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
        int256 amountSpecified;
        /// @dev The Q64.96 sqrt price limit. If !isFT, the price cannot be less than this
        uint160 sqrtPriceLimitX96;
        /// @dev lower tick of the position
        int24 tickLower;
        /// @dev upper tick of the position
        int24 tickUpper;
    }

    struct SwapCache {
        /// @dev liquidity at the beginning of the swap
        uint128 liquidityStart;
        // the current protocol fee as a percentage of the swap fee taken on withdrawal
        // represented as an integer denominator (1/x)%
        uint8 feeProtocol;
    }

    /// @dev the top level state of the swap, the results of which are recorded in storage at the end
    struct SwapState {
        /// @dev the amount remaining to be swapped in/out of the input/output asset
        int256 amountSpecifiedRemaining;
        /// @dev the amount already swapped out/in of the output/input asset
        int256 amountCalculated;
        /// @dev current sqrt(price)
        uint160 sqrtPriceX96;
        /// @dev the tick associated with the current price
        int24 tick;
        /// @dev the global fixed token growth
        int256 fixedTokenGrowthGlobalX128;
        /// @dev the global variable token growth
        int256 variableTokenGrowthGlobalX128;
        /// @dev the current liquidity in range
        uint128 liquidity;
        /// @dev the global fee growth of the underlying token
        uint256 feeGrowthGlobalX128;
        /// @dev amount of underlying token paid as protocol fee
        uint256 protocolFee;
        /// @dev cumulative fee incurred while initiating a swap
        uint256 cumulativeFeeIncurred;
        /// @dev fixedTokenDelta that will be applied to the fixed token balance of the position executing the swap (recipient)
        int256 fixedTokenDeltaCumulative;
        /// @dev variableTokenDelta that will be applied to the variable token balance of the position executing the swap (recipient)
        int256 variableTokenDeltaCumulative;
        /// @dev fixed token delta cumulative but without rebalancings applied
        int256 fixedTokenDeltaUnbalancedCumulative;
    }

    struct StepComputations {
        /// @dev the price at the beginning of the step
        uint160 sqrtPriceStartX96;
        /// @dev the next tick to swap to from the current tick in the swap direction
        int24 tickNext;
        /// @dev whether tickNext is initialized or not
        bool initialized;
        /// @dev sqrt(price) for the next tick (1/0)
        uint160 sqrtPriceNextX96;
        /// @dev how much is being swapped in in this step
        uint256 amountIn;
        /// @dev how much is being swapped out
        uint256 amountOut;
        /// @dev how much fee is being paid in (underlying token)
        uint256 feeAmount;
        /// @dev ...
        uint256 feeProtocolDelta;
        /// @dev ...
        int256 fixedTokenDeltaUnbalanced; // for LP
        /// @dev ...
        int256 fixedTokenDelta; // for LP
        /// @dev ...
        int256 variableTokenDelta; // for LP
    }

    /// @dev "constructor" for proxy instances
    function initialize(IMarginEngine __marginEngine, int24 __tickSpacing)
        external;

    // immutables

    /// @notice The vamm's fee (proportion) in wad
    /// @return The fee in wad
    function feeWad() external view returns (uint256);

    /// @notice The vamm tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);

    /// @notice The maximum amount of position liquidity that can use any tick in the range
    /// @dev This parameter should be enforced per tick (when setting) to prevent liquidity from overflowing a uint128 at any point, and
    /// also prevents out-of-range liquidity from being used to prevent adding in-range liquidity to the vamm
    /// @return The max amount of liquidity per tick
    function maxLiquidityPerTick() external view returns (uint128);

    // state variables

    /// @return The current VAMM Vars (see struct definition for semantics)
    function vammVars() external view returns (VAMMVars memory);

    /// @return If true, the VAMM Proxy is currently in alpha state, hence minting can only be done via the periphery. If false, minting can be done directly via VAMM.
    function isAlpha() external view returns (bool);

    /// @notice The fixed token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @dev This value can overflow the uint256
    function fixedTokenGrowthGlobalX128() external view returns (int256);

    /// @notice The variable token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @dev This value can overflow the uint256
    function variableTokenGrowthGlobalX128() external view returns (int256);

    /// @notice The fee growth collected per unit of liquidity for the entire life of the vamm
    /// @dev This value can overflow the uint256
    function feeGrowthGlobalX128() external view returns (uint256);

    /// @notice The currently in range liquidity available to the vamm
    function liquidity() external view returns (uint128);

    /// @notice The amount underlying token that are owed to the protocol
    /// @dev Protocol fees will never exceed uint256
    function protocolFees() external view returns (uint256);

    function marginEngine() external view returns (IMarginEngine);

    function factory() external view returns (IFactory);

    /// @notice Function that sets the feeProtocol of the vamm
    /// @dev the current protocol fee as a percentage of the swap fee taken on withdrawal
    // represented as an integer denominator (1/x)
    function setFeeProtocol(uint8 feeProtocol) external;

    /// @notice Function that sets the _isAlpha state variable, if it is set to true the protocol is in the Alpha State
    /// @dev if the VAMM is at the alpha state, mints can only be done via the periphery which in turn takes care of notional caps for the LPs
    /// @dev this function can only be called by the owner of the VAMM
    function setIsAlpha(bool __isAlpha) external;

    /// @notice Function that sets fee of the vamm
    /// @dev The vamm's fee (proportion) in wad
    function setFee(uint256 _fee) external;

    /// @notice Updates internal accounting to reflect a collection of protocol fees. The actual transfer of fees must happen separately in the AMM
    /// @dev can only be done via the collectProtocol function of the parent AMM of the vamm
    function updateProtocolFees(uint256 protocolFeesCollected) external;

    /// @notice Sets the initial price for the vamm
    /// @dev Price is represented as a sqrt(amountVariableToken/amountFixedToken) Q64.96 value
    /// @param sqrtPriceX96 the initial sqrt price of the vamm as a Q64.96
    function initializeVAMM(uint160 sqrtPriceX96) external;

    /// @notice removes liquidity given recipient/tickLower/tickUpper of the position
    /// @param recipient The address for which the liquidity will be removed
    /// @param tickLower The lower tick of the position in which to remove liquidity
    /// @param tickUpper The upper tick of the position in which to remove liqudiity
    /// @param amount The amount of liquidity to burn
    function burn(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (int256 positionMarginRequirement);

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (int256 positionMarginRequirement);

    /// @notice Initiate an Interest Rate Swap
    /// @param params SwapParams necessary to initiate an Interest Rate Swap
    /// @return fixedTokenDelta Fixed Token Delta
    /// @return variableTokenDelta Variable Token Delta
    /// @return cumulativeFeeIncurred Cumulative Fee Incurred
    function swap(SwapParams memory params)
        external
        returns (
            int256 fixedTokenDelta,
            int256 variableTokenDelta,
            uint256 cumulativeFeeIncurred,
            int256 fixedTokenDeltaUnbalanced,
            int256 marginRequirement
        );

    /// @notice Look up information about a specific tick in the amm
    /// @param tick The tick to look up
    /// @return liquidityGross: the total amount of position liquidity that uses the vamm either as tick lower or tick upper,
    /// liquidityNet: how much liquidity changes when the vamm price crosses the tick,
    /// feeGrowthOutsideX128: the fee growth on the other side of the tick from the current tick in underlying token. i.e. if liquidityGross is greater than 0. In addition, these values are only relative.
    function ticks(int24 tick) external view returns (Tick.Info memory);

    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information
    function tickBitmap(int16 wordPosition) external view returns (uint256);

    /// @notice Computes the current fixed and variable token growth inside a given tick range given the current tick in the vamm
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @return fixedTokenGrowthInsideX128 Fixed Token Growth inside the given tick range
    /// @return variableTokenGrowthInsideX128 Variable Token Growth inside the given tick range
    /// @return feeGrowthInsideX128 Fee Growth Inside given tick range
    function computeGrowthInside(int24 tickLower, int24 tickUpper)
        external
        view
        returns (
            int256 fixedTokenGrowthInsideX128,
            int256 variableTokenGrowthInsideX128,
            uint256 feeGrowthInsideX128
        );
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

import "../IMarginEngine.sol";
import "../utils/CustomErrors.sol";
import "../IERC20Minimal.sol";
import "./TraderWithYieldBearingAssets.sol";
import "../IVAMM.sol";
import "../rate_oracles/IRateOracle.sol";

interface IFCM is CustomErrors {
    function setPausability(bool state) external;

    function getTraderWithYieldBearingAssets(address trader)
        external
        view
        returns (TraderWithYieldBearingAssets.Info memory traderInfo);

    /// @notice Initiate a Fully Collateralised Fixed Taker Swap
    /// @param notional amount of notional (in terms of the underlying token) to trade
    /// @param sqrtPriceLimitX96 the sqrtPriceLimit (in binary fixed point math notation) beyond which swaps won't be executed
    /// @dev An example of an initiated fully collateralised fixed taker swap is a scenario where a trader with 100 aTokens wishes to get a fixed return on them
    /// @dev they can choose to deposit their 100aTokens into the FCM (enter into a fixed taker position with a notional of 100) to swap variable cashflows from the aTokens
    /// @dev with the fixed cashflows from the variable takers
    function initiateFullyCollateralisedFixedTakerSwap(
        uint256 notional,
        uint160 sqrtPriceLimitX96
    ) external returns (int256 fixedTokenDelta, int256 variableTokenDelta, uint256 cumulativeFeeIncurred, int256 fixedTokenDeltaUnbalanced);

    /// @notice Unwind a Fully Collateralised Fixed Taker Swap
    /// @param notionalToUnwind The amount of notional of the original Fully Collateralised Fixed Taker swap to be unwound at the current VAMM fixed rates
    /// @param sqrtPriceLimitX96 the sqrtPriceLimit (in binary fixed point math notation) beyond which the unwind swaps won't be executed
    /// @dev The purpose of this function is to let fully collateralised fixed takers to exist their swaps by entering into variable taker positions against the VAMM
    /// @dev thus effectively releasing the margin in yield bearing tokens from the fixed swap contract
    function unwindFullyCollateralisedFixedTakerSwap(
        uint256 notionalToUnwind,
        uint160 sqrtPriceLimitX96
    ) external returns (int256 fixedTokenDelta, int256 variableTokenDelta, uint256 cumulativeFeeIncurred, int256 fixedTokenDeltaUnbalanced);

    /// @notice Settle Trader
    /// @dev this function in the fcm let's traders settle with the MarginEngine based on their settlement cashflows which is a functon of their fixed and variable token balances
    function settleTrader() external returns (int256);

    /// @notice
    /// @param account address of the position owner from the MarginEngine who wishes to settle with the FCM in underlying tokens
    /// @param marginDeltaInUnderlyingTokens amount in terms of underlying tokens that needs to be settled with the trader from the MarginEngine
    function transferMarginToMarginEngineTrader(
        address account,
        uint256 marginDeltaInUnderlyingTokens
    ) external;

    /// @notice initialize is the constructor for the proxy instances of the FCM
    /// @dev "constructor" for proxy instances
    /// @dev in the initialize function we set the vamm and the margiEngine associated with the fcm
    /// @dev different FCM implementations are free to have different implementations for the initialisation logic
    function initialize(IVAMM __vamm, IMarginEngine __marginEngine)
        external;

    /// @notice Margine Engine linked to the Full Collateralisation Module
    /// @return marginEngine Margine Engine linked to the Full Collateralisation Module
    function marginEngine() external view returns (IMarginEngine);

    /// @notice VAMM linked to the Full Collateralisation Module
    /// @return VAMM linked to the Full Collateralisation Module
    function vamm() external view returns (IVAMM);

    /// @notice Rate Oracle linked to the Full Collateralisation Module
    /// @return Rate Oracle linked to the Full Collateralisation Module
    function rateOracle() external view returns (IRateOracle);

    event FullyCollateralisedSwap(
        address indexed trader,
        uint256 desiredNotional,
        uint160 sqrtPriceLimitX96,
        uint256 cumulativeFeeIncurred,
        int256 fixedTokenDelta,
        int256 variableTokenDelta,
        int256 fixedTokenDeltaUnbalanced
    );

    event FullyCollateralisedUnwind(
        address indexed trader,
        uint256 desiredNotional,
        uint160 sqrtPriceLimitX96,
        uint256 cumulativeFeeIncurred,
        int256 fixedTokenDelta,
        int256 variableTokenDelta,
        int256 fixedTokenDeltaUnbalanced
    );

    event fcmPositionSettlement(
        address indexed trader,
        int256 settlementCashflow
    );

    event FCMTraderUpdate(
        address indexed trader,
        uint256 marginInScaledYieldBearingTokens,
        int256 fixedTokenBalance,
        int256 variableTokenBalance
    );
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

/// @title Trader
library TraderWithYieldBearingAssets {
    // info stored for each user's position
    struct Info {
        // For Aave v2 The scaled balance is the sum of all the updated stored balances in the
        // underlying token, divided by the reserve's liquidity index at the moment of the update
        //
        // For componund, the scaled balance is the sum of all the updated stored balances in the
        // underlying token, divided by the cToken exchange rate at the moment of the update.
        // This is simply the number of cTokens!
        uint256 marginInScaledYieldBearingTokens;
        int256 fixedTokenBalance;
        int256 variableTokenBalance;
        bool isSettled;
    }

    function updateMarginInScaledYieldBearingTokens(
        Info storage self,
        uint256 _marginInScaledYieldBearingTokens
    ) internal {
        self
            .marginInScaledYieldBearingTokens = _marginInScaledYieldBearingTokens;
    }

    function settleTrader(Info storage self) internal {
        require(!self.isSettled, "already settled");
        self.isSettled = true;
    }

    function updateBalancesViaDeltas(
        Info storage self,
        int256 fixedTokenBalanceDelta,
        int256 variableTokenBalanceDelta
    )
        internal
        returns (int256 _fixedTokenBalance, int256 _variableTokenBalance)
    {
        _fixedTokenBalance = self.fixedTokenBalance + fixedTokenBalanceDelta;
        _variableTokenBalance =
            self.variableTokenBalance +
            variableTokenBalanceDelta;

        self.fixedTokenBalance = _fixedTokenBalance;
        self.variableTokenBalance = _variableTokenBalance;
    }
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

import "../utils/CustomErrors.sol";
import "../IERC20Minimal.sol";

/// @dev The RateOracle is used for two purposes on the Voltz Protocol
/// @dev Settlement: in order to be able to settle IRS positions after the termEndTimestamp of a given AMM
/// @dev Margin Engine Computations: getApyFromTo is used by the MarginCalculator and MarginEngine
/// @dev It is necessary to produce margin requirements for Trader and Liquidity Providers
interface IRateOracle is CustomErrors {

    // events
    event MinSecondsSinceLastUpdate(uint256 _minSecondsSinceLastUpdate);
    event OracleBufferUpdate(
        uint256 blockTimestampScaled,
        address source,
        uint16 index,
        uint32 blockTimestamp,
        uint256 observedValue,
        uint16 cardinality,
        uint16 cardinalityNext
    );

    /// @notice Emitted by the rate oracle for increases to the number of observations that can be stored
    /// @param observationCardinalityNextNew The updated value of the next observation cardinality
    event RateCardinalityNext(
        uint16 observationCardinalityNextNew
    );

    // view functions

    /// @notice Gets minimum number of seconds that need to pass since the last update to the rates array
    /// @dev This is a throttling mechanic that needs to ensure we don't run out of space in the rates array
    /// @dev The maximum size of the rates array is 65535 entries
    // AB: as long as this doesn't affect the termEndTimestamp rateValue too much
    // AB: can have a different minSecondsSinceLastUpdate close to termEndTimestamp to have more granularity for settlement purposes
    /// @return minSecondsSinceLastUpdate in seconds
    function minSecondsSinceLastUpdate() external view returns (uint256);

    /// @notice Gets the address of the underlying token of the RateOracle
    /// @return underlying The address of the underlying token
    function underlying() external view returns (IERC20Minimal);

    /// @notice Gets the variable factor between termStartTimestamp and termEndTimestamp
    /// @return result The variable factor
    /// @dev If the current block timestamp is beyond the maturity of the AMM, then the variableFactor is getRateFromTo(termStartTimestamp, termEndTimestamp). Term end timestamps are cached for quick retrieval later.
    /// @dev If the current block timestamp is before the maturity of the AMM, then the variableFactor is getRateFromTo(termStartTimestamp,Time.blockTimestampScaled());
    /// @dev if queried before maturity then returns the rate of return between pool initiation and current timestamp (in wad)
    /// @dev if queried after maturity then returns the rate of return between pool initiation and maturity timestamp (in wad)
    function variableFactor(uint256 termStartTimestamp, uint256 termEndTimestamp) external returns(uint256 result);

    /// @notice Gets the variable factor between termStartTimestamp and termEndTimestamp
    /// @return result The variable factor
    /// @dev If the current block timestamp is beyond the maturity of the AMM, then the variableFactor is getRateFromTo(termStartTimestamp, termEndTimestamp). No caching takes place.
    /// @dev If the current block timestamp is before the maturity of the AMM, then the variableFactor is getRateFromTo(termStartTimestamp,Time.blockTimestampScaled());
    function variableFactorNoCache(uint256 termStartTimestamp, uint256 termEndTimestamp) external view returns(uint256 result);

    
    /// @notice Calculates the observed interest returned by the underlying in a given period
    /// @dev Reverts if we have no data point for either timestamp
    /// @param from The timestamp of the start of the period, in seconds
    /// @param to The timestamp of the end of the period, in seconds
    /// @return The "floating rate" expressed in Wad, e.g. 4% is encoded as 0.04*10**18 = 4*10*16
    function getRateFromTo(uint256 from, uint256 to)
        external
        view
        returns (uint256);

    /// @notice Calculates the observed APY returned by the rate oracle in a given period
    /// @param from The timestamp of the start of the period, in seconds
    /// @param to The timestamp of the end of the period, in seconds
    /// @dev Reverts if we have no data point for either timestamp
    //  how is the returned rate encoded? Floating rate?
    function getApyFromTo(uint256 from, uint256 to)
        external
        view
        returns (uint256 apyFromTo);

    // non-view functions

    /// @notice Sets minSecondsSinceLastUpdate: The minimum number of seconds that need to pass since the last update to the rates array
    /// @dev Can only be set by the Factory Owner
    function setMinSecondsSinceLastUpdate(uint256 _minSecondsSinceLastUpdate) external;

    /// @notice Increase the maximum number of rates observations that this RateOracle will store
    /// @dev This method is no-op if the RateOracle already has an observationCardinalityNext greater than or equal to
    /// the input observationCardinalityNext.
    /// @param rateCardinalityNext The desired minimum number of observations for the pool to store
    function increaseObservationCardinalityNext(uint16 rateCardinalityNext) external;

    /// @notice Writes a rate observation to the rates array given the current rate cardinality, rate index and rate cardinality next
    /// Write oracle entry is called whenever a new position is minted via the vamm or when a swap is initiated via the vamm
    /// That way the gas costs of Rate Oracle updates can be distributed across organic interactions with the protocol
    function writeOracleEntry() external;

    /// @notice unique ID of the underlying yield bearing protocol (e.g. Aave v2 has id 1)
    /// @return yieldBearingProtocolID unique id of the underlying yield bearing protocol
    function UNDERLYING_YIELD_BEARING_PROTOCOL_ID() external view returns(uint8 yieldBearingProtocolID);
}

// SPDX-License-Identifier: Apache-2.0

pragma solidity =0.8.9;

interface CustomErrors {
    /// @dev No need to unwind a net zero position
    error PositionNetZero();

    error DebugError(uint256 x, uint256 y);

    /// @dev Cannot have less margin than the minimum requirement
    error MarginLessThanMinimum(int256 marginRequirement);

    /// @dev We can't withdraw more margin than we have
    error WithdrawalExceedsCurrentMargin();

    /// @dev Position must be settled after AMM has reached maturity
    error PositionNotSettled();

    /// The resulting margin does not meet minimum requirements
    error MarginRequirementNotMet(
        int256 marginRequirement,
        int24 tick,
        int256 fixedTokenDelta,
        int256 variableTokenDelta,
        uint256 cumulativeFeeIncurred,
        int256 fixedTokenDeltaUnbalanced
    );

    /// The position/trader needs to be below the liquidation threshold to be liquidated
    error CannotLiquidate();

    /// Only the position/trade owner can update the LP/Trader margin
    error OnlyOwnerCanUpdatePosition();

    error OnlyVAMM();

    error OnlyFCM();

    /// Margin delta must not equal zero
    error InvalidMarginDelta();

    /// Positions and Traders cannot be settled before the applicable interest rate swap has matured
    error CannotSettleBeforeMaturity();

    error closeToOrBeyondMaturity();

    /// @dev There are not enough funds available for the requested operation
    error NotEnoughFunds(uint256 requested, uint256 available);

    /// @dev The two values were expected to have oppostite sigs, but do not
    error ExpectedOppositeSigns(int256 amount0, int256 amount1);

    /// @dev Error which is reverted if the sqrt price of the vamm is non-zero before a vamm is initialized
    error ExpectedSqrtPriceZeroBeforeInit(uint160 sqrtPriceX96);

    /// @dev Error which ensures the liquidity delta is positive if a given LP wishes to mint further liquidity in the vamm
    error LiquidityDeltaMustBePositiveInMint(uint128 amount);

    /// @dev Error which ensures the liquidity delta is positive if a given LP wishes to burn liquidity in the vamm
    error LiquidityDeltaMustBePositiveInBurn(uint128 amount);

    /// @dev Error which ensures the amount of notional specified when initiating an IRS contract (via the swap function in the vamm) is non-zero
    error IRSNotionalAmountSpecifiedMustBeNonZero();

    /// @dev Error which ensures the VAMM is unlocked
    error CanOnlyTradeIfUnlocked(bool unlocked);

    /// @dev only the margin engine can run a certain function
    error OnlyMarginEngine();

    /// The resulting margin does not meet minimum requirements
    error MarginRequirementNotMetFCM(int256 marginRequirement);

    /// @dev getReserveNormalizedIncome() returned zero for underlying asset. Oracle only supports active Aave-V2 assets.
    error AavePoolGetReserveNormalizedIncomeReturnedZero();

    /// @dev ctoken.exchangeRateStored() returned zero for a given Compound ctoken. Oracle only supports active Compound assets.
    error CTokenExchangeRateReturnedZero();

    /// @dev currentTime < queriedTime
    error OOO();
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;

/// @title FixedPoint128
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
library FixedPoint128 {
    uint256 internal constant Q128 = 0x100000000000000000000000000000000;
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;

/// @title Math library for liquidity
library LiquidityMath {
    /// @notice Add a signed liquidity delta to liquidity and revert if it overflows or underflows
    /// @param x The liquidity before change
    /// @param y The delta by which liquidity should be changed
    /// @return z The liquidity delta
    function addDelta(uint128 x, int128 y) internal pure returns (uint128 z) {
        if (y < 0) {
            uint128 yAbsolute;

            unchecked {
                yAbsolute = uint128(-y);
            }

            z = x - yAbsolute;
        } else {
            z = x + uint128(y);
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;

import "./LiquidityMath.sol";
import "./FixedPoint128.sol";
import "./Tick.sol";
import "@prb/math/contracts/PRBMathSD59x18.sol";
import "@prb/math/contracts/PRBMathUD60x18.sol";
import "@openzeppelin/contracts/utils/math/SafeCast.sol";
import "contracts/libraries/external/FullMath.sol";

/// @title Position
/// @notice Positions represent an owner address' liquidity between a lower and upper tick boundary
/// @dev Positions store additional state for tracking fees owed to the position as well as their fixed and variable token balances
library Position {
    using Position for Info;

    // info stored for each user's position
    struct Info {
        // has the position been already burned
        // a burned position can no longer support new IRS contracts but still needs to cover settlement cash-flows of on-going IRS contracts it entered
        // bool isBurned;, equivalent to having zero liquidity
        // is position settled
        bool isSettled;
        // the amount of liquidity owned by this position
        uint128 _liquidity;
        // current margin of the position in terms of the underlyingToken
        int256 margin;
        // fixed token growth per unit of liquidity as of the last update to liquidity or fixed/variable token balance
        int256 fixedTokenGrowthInsideLastX128;
        // variable token growth per unit of liquidity as of the last update to liquidity or fixed/variable token balance
        int256 variableTokenGrowthInsideLastX128;
        // current Fixed Token balance of the position, 1 fixed token can be redeemed for 1% APY * (annualised amm term) at the maturity of the amm
        // assuming 1 token worth of notional "deposited" in the underlying pool at the inception of the amm
        // can be negative/positive/zero
        int256 fixedTokenBalance;
        // current Variable Token Balance of the position, 1 variable token can be redeemed for underlyingPoolAPY*(annualised amm term) at the maturity of the amm
        // assuming 1 token worth of notional "deposited" in the underlying pool at the inception of the amm
        // can be negative/positive/zero
        int256 variableTokenBalance;
        // fee growth per unit of liquidity as of the last update to liquidity or fees owed (via the margin)
        uint256 feeGrowthInsideLastX128;
        // amount of variable tokens at the initiation of liquidity
        uint256 rewardPerAmount;
        // amount of fees accumulated
        uint256 accumulatedFees;
    }

    /// @notice Returns the Info struct of a position, given an owner and position boundaries
    /// @param self The mapping containing all user positions
    /// @param owner The address of the position owner
    /// @param tickLower The lower tick boundary of the position
    /// @param tickUpper The upper tick boundary of the position
    /// @return position The position info struct of the given owners' position
    function get(
        mapping(bytes32 => Info) storage self,
        address owner,
        int24 tickLower,
        int24 tickUpper
    ) internal view returns (Position.Info storage position) {
        Tick.checkTicks(tickLower, tickUpper);

        position = self[
            keccak256(abi.encodePacked(owner, tickLower, tickUpper))
        ];
    }

    function settlePosition(Info storage self) internal {
        require(!self.isSettled, "already settled");
        self.isSettled = true;
    }

    /// @notice Updates the Info struct of a position by changing the amount of margin according to marginDelta
    /// @param self Position Info Struct of the Liquidity Provider
    /// @param marginDelta Change in the margin account of the position (in wei)
    function updateMarginViaDelta(Info storage self, int256 marginDelta)
        internal
    {
        self.margin += marginDelta;
    }

    /// @notice Updates the Info struct of a position by changing the fixed and variable token balances of the position
    /// @param self Position Info struct of the liquidity provider
    /// @param fixedTokenBalanceDelta Change in the number of fixed tokens in the position's fixed token balance
    /// @param variableTokenBalanceDelta Change in the number of variable tokens in the position's variable token balance
    function updateBalancesViaDeltas(
        Info storage self,
        int256 fixedTokenBalanceDelta,
        int256 variableTokenBalanceDelta
    ) internal {
        if (fixedTokenBalanceDelta | variableTokenBalanceDelta != 0) {
            self.fixedTokenBalance += fixedTokenBalanceDelta;
            self.variableTokenBalance += variableTokenBalanceDelta;
        }
    }

    /// @notice Returns Fee Delta = (feeGrowthInside-feeGrowthInsideLast) * liquidity of the position
    /// @param self position info struct represeting a liquidity provider
    /// @param feeGrowthInsideX128 fee growth per unit of liquidity as of now
    /// @return _feeDelta Fee Delta
    function calculateFeeDelta(Info storage self, uint256 feeGrowthInsideX128)
        internal
        pure
        returns (uint256 _feeDelta)
    {
        Info memory _self = self;

        /// @dev 0xZenus: The multiplication overflows, need to wrap the below expression in an unchecked block.
        unchecked {
            _feeDelta = FullMath.mulDiv(
                feeGrowthInsideX128 - _self.feeGrowthInsideLastX128,
                _self._liquidity,
                FixedPoint128.Q128
            );
        }
    }

    /// @notice Returns Fixed and Variable Token Deltas
    /// @param self position info struct represeting a liquidity provider
    /// @param fixedTokenGrowthInsideX128 fixed token growth per unit of liquidity as of now (in wei)
    /// @param variableTokenGrowthInsideX128 variable token growth per unit of liquidity as of now (in wei)
    /// @return _fixedTokenDelta = (fixedTokenGrowthInside-fixedTokenGrowthInsideLast) * liquidity of a position
    /// @return _variableTokenDelta = (variableTokenGrowthInside-variableTokenGrowthInsideLast) * liquidity of a position
    function calculateFixedAndVariableDelta(
        Info storage self,
        int256 fixedTokenGrowthInsideX128,
        int256 variableTokenGrowthInsideX128
    )
        internal
        pure
        returns (int256 _fixedTokenDelta, int256 _variableTokenDelta)
    {
        Info memory _self = self;

        int256 fixedTokenGrowthInsideDeltaX128 = fixedTokenGrowthInsideX128 -
            _self.fixedTokenGrowthInsideLastX128;

        _fixedTokenDelta = FullMath.mulDivSigned(
            fixedTokenGrowthInsideDeltaX128,
            _self._liquidity,
            FixedPoint128.Q128
        );

        int256 variableTokenGrowthInsideDeltaX128 = variableTokenGrowthInsideX128 -
                _self.variableTokenGrowthInsideLastX128;

        _variableTokenDelta = FullMath.mulDivSigned(
            variableTokenGrowthInsideDeltaX128,
            _self._liquidity,
            FixedPoint128.Q128
        );
    }

    /// @notice Updates fixedTokenGrowthInsideLast and variableTokenGrowthInsideLast to the current values
    /// @param self position info struct represeting a liquidity provider
    /// @param fixedTokenGrowthInsideX128 fixed token growth per unit of liquidity as of now
    /// @param variableTokenGrowthInsideX128 variable token growth per unit of liquidity as of now
    function updateFixedAndVariableTokenGrowthInside(
        Info storage self,
        int256 fixedTokenGrowthInsideX128,
        int256 variableTokenGrowthInsideX128
    ) internal {
        self.fixedTokenGrowthInsideLastX128 = fixedTokenGrowthInsideX128;
        self.variableTokenGrowthInsideLastX128 = variableTokenGrowthInsideX128;
    }

    /// @notice Updates feeGrowthInsideLast to the current value
    /// @param self position info struct represeting a liquidity provider
    /// @param feeGrowthInsideX128 fee growth per unit of liquidity as of now
    function updateFeeGrowthInside(
        Info storage self,
        uint256 feeGrowthInsideX128
    ) internal {
        self.feeGrowthInsideLastX128 = feeGrowthInsideX128;
    }

    /// @notice Updates position's liqudity following either mint or a burn
    /// @param self The individual position to update
    /// @param liquidityDelta The change in pool liquidity as a result of the position update
    function updateLiquidity(Info storage self, int128 liquidityDelta)
        internal
    {
        Info memory _self = self;

        if (liquidityDelta == 0) {
            require(_self._liquidity > 0, "NP"); // disallow pokes for 0 liquidity positions
        } else {
            self._liquidity = LiquidityMath.addDelta(
                _self._liquidity,
                liquidityDelta
            );
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1
// With contributions from OpenZeppelin Contracts v4.4.0 (utils/math/SafeCast.sol)

pragma solidity =0.8.9;

/// @title Safe casting methods
/// @notice Contains methods for safely casting between types
library SafeCastUni {
    /// @notice Cast a uint256 to a uint160, revert on overflow
    /// @param y The uint256 to be downcasted
    /// @return z The downcasted integer, now type uint160
    function toUint160(uint256 y) internal pure returns (uint160 z) {
        require((z = uint160(y)) == y, "toUint160 oflo");
    }

    /// @notice Cast a int256 to a int128, revert on overflow or underflow
    /// @param y The int256 to be downcasted
    /// @return z The downcasted integer, now type int128
    function toInt128(int256 y) internal pure returns (int128 z) {
        require((z = int128(y)) == y, "toInt128 oflo");
    }

    /// @notice Cast a uint256 to a int256, revert on overflow
    /// @param y The uint256 to be casted
    /// @return z The casted integer, now type int256
    function toInt256(uint256 y) internal pure returns (int256 z) {
        require(y < 2**255, "toInt256 oflo");
        z = int256(y);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "toUint256 < 0");
        return uint256(value);
    }

    /**
     * @dev Converts a signed int128 into an unsigned uint128.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint128(int128 value) internal pure returns (uint128) {
        require(value >= 0, "toUint128 < 0");
        return uint128(value);
    }

    /**
     * @dev Converts a signed uint256 into an unsigned uint128.
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "toUint128 > max(uint128)");
        return uint128(value);
    }
}

// SPDX-License-Identifier: BUSL-1.1

pragma solidity =0.8.9;
import "./LiquidityMath.sol";
import "./TickMath.sol";
import "./SafeCastUni.sol";

/// @title Tick
/// @notice Contains functions for managing tick processes and relevant calculations
library Tick {
    using SafeCastUni for int256;
    using SafeCastUni for uint256;

    int24 public constant MAXIMUM_TICK_SPACING = 16384;

    // info stored for each initialized individual tick
    struct Info {
        /// @dev the total position liquidity that references this tick (either as tick lower or tick upper)
        uint128 liquidityGross;
        /// @dev amount of net liquidity added (subtracted) when tick is crossed from left to right (right to left),
        int128 liquidityNet;
        /// @dev fee growth per unit of liquidity on the _other_ side of this tick (relative to the current tick)
        /// @dev only has relative meaning, not absolute — the value depends on when the tick is initialized
        int256 fixedTokenGrowthOutsideX128;
        int256 variableTokenGrowthOutsideX128;
        uint256 feeGrowthOutsideX128;
        /// @dev true iff the tick is initialized, i.e. the value is exactly equivalent to the expression liquidityGross != 0
        /// @dev these 8 bits are set to prevent fresh sstores when crossing newly initialized ticks
        bool initialized;
    }

    /// @notice Derives max liquidity per tick from given tick spacing
    /// @dev Executed within the pool constructor
    /// @param tickSpacing The amount of required tick separation, realized in multiples of `tickSpacing`
    ///     e.g., a tickSpacing of 3 requires ticks to be initialized every 3rd tick i.e., ..., -6, -3, 0, 3, 6, ...
    /// @return The max liquidity per tick
    function tickSpacingToMaxLiquidityPerTick(int24 tickSpacing)
        internal
        pure
        returns (uint128)
    {
        int24 minTick = TickMath.MIN_TICK - (TickMath.MIN_TICK % tickSpacing);
        int24 maxTick = -minTick;
        uint24 numTicks = uint24((maxTick - minTick) / tickSpacing) + 1;
        return type(uint128).max / numTicks;
    }

    /// @dev Common checks for valid tick inputs.
    function checkTicks(int24 tickLower, int24 tickUpper) internal pure {
        require(tickLower < tickUpper, "TLU");
        require(tickLower >= TickMath.MIN_TICK, "TLM");
        require(tickUpper <= TickMath.MAX_TICK, "TUM");
    }

    struct FeeGrowthInsideParams {
        int24 tickLower;
        int24 tickUpper;
        int24 tickCurrent;
        uint256 feeGrowthGlobalX128;
    }

    function _getGrowthInside(
        int24 _tickLower,
        int24 _tickUpper,
        int24 _tickCurrent,
        int256 _growthGlobalX128,
        int256 _lowerGrowthOutsideX128,
        int256 _upperGrowthOutsideX128
) private pure returns (int256) {
        // calculate the growth below
        int256 _growthBelowX128;

        if (_tickCurrent >= _tickLower) {
            _growthBelowX128 = _lowerGrowthOutsideX128;
        } else {
            _growthBelowX128 = _growthGlobalX128 - _lowerGrowthOutsideX128;
        }

        // calculate the growth above
        int256 _growthAboveX128;

        if (_tickCurrent < _tickUpper) {
            _growthAboveX128 = _upperGrowthOutsideX128;
        } else {
            _growthAboveX128 = _growthGlobalX128 - _upperGrowthOutsideX128;
        }

        int256 _growthInsideX128;

        _growthInsideX128 =
            _growthGlobalX128 -
            (_growthBelowX128 + _growthAboveX128);

        return _growthInsideX128;
    }

    function getFeeGrowthInside(
        mapping(int24 => Tick.Info) storage self,
        FeeGrowthInsideParams memory params
    ) internal view returns (uint256 feeGrowthInsideX128) {
        unchecked {
            Info storage lower = self[params.tickLower];
            Info storage upper = self[params.tickUpper];

            feeGrowthInsideX128 = uint256(
                _getGrowthInside(
                    params.tickLower,
                    params.tickUpper,
                    params.tickCurrent,
                    params.feeGrowthGlobalX128.toInt256(),
                    lower.feeGrowthOutsideX128.toInt256(),
                    upper.feeGrowthOutsideX128.toInt256()
                )
            );
        }
    }

    struct VariableTokenGrowthInsideParams {
        int24 tickLower;
        int24 tickUpper;
        int24 tickCurrent;
        int256 variableTokenGrowthGlobalX128;
    }

    function getVariableTokenGrowthInside(
        mapping(int24 => Tick.Info) storage self,
        VariableTokenGrowthInsideParams memory params
    ) internal view returns (int256 variableTokenGrowthInsideX128) {
        Info storage lower = self[params.tickLower];
        Info storage upper = self[params.tickUpper];

        variableTokenGrowthInsideX128 = _getGrowthInside(
            params.tickLower,
            params.tickUpper,
            params.tickCurrent,
            params.variableTokenGrowthGlobalX128,
            lower.variableTokenGrowthOutsideX128,
            upper.variableTokenGrowthOutsideX128
        );
    }

    struct FixedTokenGrowthInsideParams {
        int24 tickLower;
        int24 tickUpper;
        int24 tickCurrent;
        int256 fixedTokenGrowthGlobalX128;
    }

    function getFixedTokenGrowthInside(
        mapping(int24 => Tick.Info) storage self,
        FixedTokenGrowthInsideParams memory params
    ) internal view returns (int256 fixedTokenGrowthInsideX128) {
        Info storage lower = self[params.tickLower];
        Info storage upper = self[params.tickUpper];

        // do we need an unchecked block in here (given we are dealing with an int256)?
        fixedTokenGrowthInsideX128 = _getGrowthInside(
            params.tickLower,
            params.tickUpper,
            params.tickCurrent,
            params.fixedTokenGrowthGlobalX128,
            lower.fixedTokenGrowthOutsideX128,
            upper.fixedTokenGrowthOutsideX128
        );
    }

    /// @notice Updates a tick and returns true if the tick was flipped from initialized to uninitialized, or vice versa
    /// @param self The mapping containing all tick information for initialized ticks
    /// @param tick The tick that will be updated
    /// @param tickCurrent The current tick
    /// @param liquidityDelta A new amount of liquidity to be added (subtracted) when tick is crossed from left to right (right to left)
    /// @param fixedTokenGrowthGlobalX128 The fixed token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @param variableTokenGrowthGlobalX128 The variable token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @param upper true for updating a position's upper tick, or false for updating a position's lower tick
    /// @param maxLiquidity The maximum liquidity allocation for a single tick
    /// @return flipped Whether the tick was flipped from initialized to uninitialized, or vice versa
    function update(
        mapping(int24 => Tick.Info) storage self,
        int24 tick,
        int24 tickCurrent,
        int128 liquidityDelta,
        int256 fixedTokenGrowthGlobalX128,
        int256 variableTokenGrowthGlobalX128,
        uint256 feeGrowthGlobalX128,
        bool upper,
        uint128 maxLiquidity
    ) internal returns (bool flipped) {
        Tick.Info storage info = self[tick];

        uint128 liquidityGrossBefore = info.liquidityGross;
        require(
            int128(info.liquidityGross) + liquidityDelta >= 0,
            "not enough liquidity to burn"
        );
        uint128 liquidityGrossAfter = LiquidityMath.addDelta(
            liquidityGrossBefore,
            liquidityDelta
        );

        require(liquidityGrossAfter <= maxLiquidity, "LO");

        flipped = (liquidityGrossAfter == 0) != (liquidityGrossBefore == 0);

        if (liquidityGrossBefore == 0) {
            // by convention, we assume that all growth before a tick was initialized happened _below_ the tick
            if (tick <= tickCurrent) {
                info.feeGrowthOutsideX128 = feeGrowthGlobalX128;

                info.fixedTokenGrowthOutsideX128 = fixedTokenGrowthGlobalX128;

                info
                    .variableTokenGrowthOutsideX128 = variableTokenGrowthGlobalX128;
            }

            info.initialized = true;
        }

        /// check shouldn't we unintialize the tick if liquidityGrossAfter = 0?

        info.liquidityGross = liquidityGrossAfter;

        /// add comments
        // when the lower (upper) tick is crossed left to right (right to left), liquidity must be added (removed)
        info.liquidityNet = upper
            ? info.liquidityNet - liquidityDelta
            : info.liquidityNet + liquidityDelta;
    }

    /// @notice Clears tick data
    /// @param self The mapping containing all initialized tick information for initialized ticks
    /// @param tick The tick that will be cleared
    function clear(mapping(int24 => Tick.Info) storage self, int24 tick)
        internal
    {
        delete self[tick];
    }

    /// @notice Transitions to next tick as needed by price movement
    /// @param self The mapping containing all tick information for initialized ticks
    /// @param tick The destination tick of the transition
    /// @param fixedTokenGrowthGlobalX128 The fixed token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @param variableTokenGrowthGlobalX128 The variable token growth accumulated per unit of liquidity for the entire life of the vamm
    /// @param feeGrowthGlobalX128 The fee growth collected per unit of liquidity for the entire life of the vamm
    /// @return liquidityNet The amount of liquidity added (subtracted) when tick is crossed from left to right (right to left)
    function cross(
        mapping(int24 => Tick.Info) storage self,
        int24 tick,
        int256 fixedTokenGrowthGlobalX128,
        int256 variableTokenGrowthGlobalX128,
        uint256 feeGrowthGlobalX128
    ) internal returns (int128 liquidityNet) {
        Tick.Info storage info = self[tick];

        info.feeGrowthOutsideX128 =
            feeGrowthGlobalX128 -
            info.feeGrowthOutsideX128;

        info.fixedTokenGrowthOutsideX128 =
            fixedTokenGrowthGlobalX128 -
            info.fixedTokenGrowthOutsideX128;

        info.variableTokenGrowthOutsideX128 =
            variableTokenGrowthGlobalX128 -
            info.variableTokenGrowthOutsideX128;

        liquidityNet = info.liquidityNet;
    }
}

// SPDX-License-Identifier: BUSL-1.1

// solhint-disable no-inline-assembly

pragma solidity =0.8.9;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
library TickMath {
    /// @dev MIN_TICK corresponds to an annualized fixed rate of 1000%
    /// @dev MAX_TICK corresponds to an annualized fixed rate of 0.001%
    /// @dev MIN and MAX TICKs can't be safely changed without reinstating getSqrtRatioAtTick removed lines of code from original
    /// TickMath.sol implementation in uniswap v3

    /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
    int24 internal constant MIN_TICK = -69100;
    /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
    int24 internal constant MAX_TICK = -MIN_TICK;

    /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
    uint160 internal constant MIN_SQRT_RATIO = 2503036416286949174936592462;
    /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
    uint160 internal constant MAX_SQRT_RATIO = 2507794810551837817144115957740;

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick)
        internal
        pure
        returns (uint160 sqrtPriceX96)
    {
        uint256 absTick = tick < 0
            ? uint256(-int256(tick))
            : uint256(int256(tick));
        require(absTick <= uint256(int256(MAX_TICK)), "T");

        uint256 ratio = absTick & 0x1 != 0
            ? 0xfffcb933bd6fad37aa2d162d1a594001
            : 0x100000000000000000000000000000000;
        if (absTick & 0x2 != 0)
            ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
        if (absTick & 0x4 != 0)
            ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
        if (absTick & 0x8 != 0)
            ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
        if (absTick & 0x10 != 0)
            ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
        if (absTick & 0x20 != 0)
            ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
        if (absTick & 0x40 != 0)
            ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
        if (absTick & 0x80 != 0)
            ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
        if (absTick & 0x100 != 0)
            ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
        if (absTick & 0x200 != 0)
            ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
        if (absTick & 0x400 != 0)
            ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
        if (absTick & 0x800 != 0)
            ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
        if (absTick & 0x1000 != 0)
            ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
        if (absTick & 0x2000 != 0)
            ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
        if (absTick & 0x4000 != 0)
            ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
        if (absTick & 0x8000 != 0)
            ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
        if (absTick & 0x10000 != 0)
            ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
        if (tick > 0) ratio = type(uint256).max / ratio;

        // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
        // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
        // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
        sqrtPriceX96 = uint160(
            (ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1)
        );
    }

    /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
    /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
    /// ever return.
    /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96
    /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
    function getTickAtSqrtRatio(uint160 sqrtPriceX96)
        internal
        pure
        returns (int24 tick)
    {
        // second inequality must be < because the price can never reach the price at the max tick
        require(
            sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO,
            "R"
        );
        uint256 ratio = uint256(sqrtPriceX96) << 32;

        uint256 r = ratio;
        uint256 msb = 0;

        assembly {
            let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(5, gt(r, 0xFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(4, gt(r, 0xFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(3, gt(r, 0xFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(2, gt(r, 0xF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(1, gt(r, 0x3))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := gt(r, 0x1)
            msb := or(msb, f)
        }

        if (msb >= 128) r = ratio >> (msb - 127);
        else r = ratio << (127 - msb);

        // solhint-disable-next-line var-name-mixedcase
        int256 log_2 = (int256(msb) - 128) << 64;

        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(63, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(62, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(61, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(60, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(59, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(58, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(57, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(56, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(55, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(54, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(53, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(52, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(51, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(50, f))
        }

        // solhint-disable-next-line var-name-mixedcase
        int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

        int24 tickLow = int24(
            (log_sqrt10001 - 3402992956809132418596140100660247210) >> 128
        );
        int24 tickHi = int24(
            (log_sqrt10001 + 291339464771989622907027621153398088495) >> 128
        );

        tick = tickLow == tickHi
            ? tickLow
            : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96
            ? tickHi
            : tickLow;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "@openzeppelin/contracts/access/IAccessControlEnumerable.sol";

interface IDefaultAccessControl is IAccessControlEnumerable {
    /// @notice Checks that the address is contract admin.
    /// @param who Address to check
    /// @return `true` if who is admin, `false` otherwise
    function isAdmin(address who) external view returns (bool);

    /// @notice Checks that the address is contract admin.
    /// @param who Address to check
    /// @return `true` if who is operator, `false` otherwise
    function isOperator(address who) external view returns (bool);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

interface ILpCallback {
    /// @notice Function, that ERC20RootVault calling after deposit
    function depositCallback() external;

    /// @notice Function, that ERC20RootVault calling after withdraw
    function withdrawCallback() external;
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "./IIntegrationVault.sol";

interface IERC20Vault is IIntegrationVault {
    /// @notice Initialized a new contract.
    /// @dev Can only be initialized by vault governance
    /// @param nft_ NFT of the vault in the VaultRegistry
    /// @param vaultTokens_ ERC20 tokens that will be managed by this Vault
    function initialize(uint256 nft_, address[] memory vaultTokens_) external;
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "../external/erc/IERC1271.sol";
import "./IVault.sol";

interface IIntegrationVault is IVault, IERC1271 {
    /// @notice Pushes tokens on the vault balance to the underlying protocol. For example, for Yearn this operation will take USDC from
    /// the contract balance and convert it to yUSDC.
    /// @dev Tokens **must** be a subset of Vault Tokens. However, the convention is that if tokenAmount == 0 it is the same as token is missing.
    ///
    /// Also notice that this operation doesn't guarantee that tokenAmounts will be invested in full.
    /// @param tokens Tokens to push
    /// @param tokenAmounts Amounts of tokens to push
    /// @param options Additional options that could be needed for some vaults. E.g. for Uniswap this could be `deadline` param. For the exact bytes structure see concrete vault descriptions
    /// @return actualTokenAmounts The amounts actually invested. It could be less than tokenAmounts (but not higher)
    function push(
        address[] memory tokens,
        uint256[] memory tokenAmounts,
        bytes memory options
    ) external returns (uint256[] memory actualTokenAmounts);

    /// @notice The same as `push` method above but transfers tokens to vault balance prior to calling push.
    /// After the `push` it returns all the leftover tokens back (`push` method doesn't guarantee that tokenAmounts will be invested in full).
    /// @param tokens Tokens to push
    /// @param tokenAmounts Amounts of tokens to push
    /// @param options Additional options that could be needed for some vaults. E.g. for Uniswap this could be `deadline` param. For the exact bytes structure see concrete vault descriptions
    /// @return actualTokenAmounts The amounts actually invested. It could be less than tokenAmounts (but not higher)
    function transferAndPush(
        address from,
        address[] memory tokens,
        uint256[] memory tokenAmounts,
        bytes memory options
    ) external returns (uint256[] memory actualTokenAmounts);

    /// @notice Pulls tokens from the underlying protocol to the `to` address.
    /// @dev Can only be called but Vault Owner or Strategy. Vault owner is the owner of NFT for this vault in VaultManager.
    /// Strategy is approved address for the vault NFT.
    /// When called by vault owner this method just pulls the tokens from the protocol to the `to` address
    /// When called by strategy on vault other than zero vault it pulls the tokens to zero vault (required `to` == zero vault)
    /// When called by strategy on zero vault it pulls the tokens to zero vault, pushes tokens on the `to` vault, and reclaims everything that's left.
    /// Thus any vault other than zero vault cannot have any tokens on it
    ///
    /// Tokens **must** be a subset of Vault Tokens. However, the convention is that if tokenAmount == 0 it is the same as token is missing.
    ///
    /// Pull is fulfilled on the best effort basis, i.e. if the tokenAmounts overflows available funds it withdraws all the funds.
    /// @param to Address to receive the tokens
    /// @param tokens Tokens to pull
    /// @param tokenAmounts Amounts of tokens to pull
    /// @param options Additional options that could be needed for some vaults. E.g. for Uniswap this could be `deadline` param. For the exact bytes structure see concrete vault descriptions
    /// @return actualTokenAmounts The amounts actually withdrawn. It could be less than tokenAmounts (but not higher)
    function pull(
        address to,
        address[] memory tokens,
        uint256[] memory tokenAmounts,
        bytes memory options
    ) external returns (uint256[] memory actualTokenAmounts);

    /// @notice Claim ERC20 tokens from vault balance to zero vault.
    /// @dev Cannot be called from zero vault.
    /// @param tokens Tokens to claim
    /// @return actualTokenAmounts Amounts reclaimed
    function reclaimTokens(address[] memory tokens) external returns (uint256[] memory actualTokenAmounts);

    /// @notice Execute one of whitelisted calls.
    /// @dev Can only be called by Vault Owner or Strategy. Vault owner is the owner of NFT for this vault in VaultManager.
    /// Strategy is approved address for the vault NFT.
    ///
    /// Since this method allows sending arbitrary transactions, the destinations of the calls
    /// are whitelisted by Protocol Governance.
    /// @param to Address of the reward pool
    /// @param selector Selector of the call
    /// @param data Abi encoded parameters to `to::selector`
    /// @return result Result of execution of the call
    function externalCall(
        address to,
        bytes4 selector,
        bytes memory data
    ) external payable returns (bytes memory result);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "./IVaultGovernance.sol";

interface IVault is IERC165 {
    /// @notice Checks if the vault is initialized

    function initialized() external view returns (bool);

    /// @notice VaultRegistry NFT for this vault
    function nft() external view returns (uint256);

    /// @notice Address of the Vault Governance for this contract.
    function vaultGovernance() external view returns (IVaultGovernance);

    /// @notice ERC20 tokens under Vault management.
    function vaultTokens() external view returns (address[] memory);

    /// @notice Checks if a token is vault token
    /// @param token Address of the token to check
    /// @return `true` if this token is managed by Vault
    function isVaultToken(address token) external view returns (bool);

    /// @notice Total value locked for this contract.
    /// @dev Generally it is the underlying token value of this contract in some
    /// other DeFi protocol. For example, for USDC Yearn Vault this would be total USDC balance that could be withdrawn for Yearn to this contract.
    /// The tvl itself is estimated in some range. Sometimes the range is exact, sometimes it's not
    /// @return minTokenAmounts Lower bound for total available balances estimation (nth tokenAmount corresponds to nth token in vaultTokens)
    /// @return maxTokenAmounts Upper bound for total available balances estimation (nth tokenAmount corresponds to nth token in vaultTokens)
    function tvl() external view returns (uint256[] memory minTokenAmounts, uint256[] memory maxTokenAmounts);

    /// @notice Existential amounts for each token
    function pullExistentials() external view returns (uint256[] memory);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "../IProtocolGovernance.sol";
import "../IVaultRegistry.sol";
import "./IVault.sol";

interface IVaultGovernance {
    /// @notice Internal references of the contract.
    /// @param protocolGovernance Reference to Protocol Governance
    /// @param registry Reference to Vault Registry
    struct InternalParams {
        IProtocolGovernance protocolGovernance;
        IVaultRegistry registry;
        IVault singleton;
    }

    // -------------------  EXTERNAL, VIEW  -------------------

    /// @notice Timestamp in unix time seconds after which staged Delayed Strategy Params could be committed.
    /// @param nft Nft of the vault
    function delayedStrategyParamsTimestamp(uint256 nft) external view returns (uint256);

    /// @notice Timestamp in unix time seconds after which staged Delayed Protocol Params could be committed.
    function delayedProtocolParamsTimestamp() external view returns (uint256);

    /// @notice Timestamp in unix time seconds after which staged Delayed Protocol Params Per Vault could be committed.
    /// @param nft Nft of the vault
    function delayedProtocolPerVaultParamsTimestamp(uint256 nft) external view returns (uint256);

    /// @notice Timestamp in unix time seconds after which staged Internal Params could be committed.
    function internalParamsTimestamp() external view returns (uint256);

    /// @notice Internal Params of the contract.
    function internalParams() external view returns (InternalParams memory);

    /// @notice Staged new Internal Params.
    /// @dev The Internal Params could be committed after internalParamsTimestamp
    function stagedInternalParams() external view returns (InternalParams memory);

    // -------------------  EXTERNAL, MUTATING  -------------------

    /// @notice Stage new Internal Params.
    /// @param newParams New Internal Params
    function stageInternalParams(InternalParams memory newParams) external;

    /// @notice Commit staged Internal Params.
    function commitInternalParams() external;
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

import "./IIntegrationVault.sol";
import "../external/voltz/IMarginEngine.sol";
import "../external/voltz/IPeriphery.sol";
import "../external/voltz/IVAMM.sol";
import "../external/voltz/rate_oracles/IRateOracle.sol";

interface IVoltzVault is IIntegrationVault {
    /// @dev LP Position on Voltz
    struct TickRange {
        /// @dev Lower tick of LP position on Voltz
        int24 tickLower;
        /// @dev Upper tick of LP position on Voltz
        int24 tickUpper;
    }

    struct InitializeParams {
        /// @dev Lower tick of initial LP position on Voltz
        int24 tickLower;
        /// @dev Upper tick of initial LP position on Voltz
        int24 tickUpper;
        /// @dev Leverage used for LP positions on Voltz (in wad)
        uint256 leverageWad; 
        /// @dev Multiplier used to decide how much margin is left in partially unwound positions on Voltz (in wad)
        uint256 marginMultiplierPostUnwindWad;
    }

    // -------------------  EXTERNAL, VIEW  -------------------

    /// @notice Returns the leverage used for LP positions on Voltz (in wad)
    function leverageWad() external view returns (uint256);

    /// @notice Returns the multiplier used to decide how much margin is 
    /// @notice left in partially unwound positions on Voltz (in wad)
    function marginMultiplierPostUnwindWad() external view returns (uint256);

    /// @notice Reference to the margin engine of Voltz Protocol
    function marginEngine() external view returns (IMarginEngine);

    /// @notice Reference to the vamm of Voltz Protocol
    function vamm() external view returns (IVAMM);

    /// @notice Reference to the rate oracle of Voltz Protocol
    function rateOracle() external view returns (IRateOracle);

    /// @notice Reference to the periphery of Voltz Protocol
    function periphery() external view returns (IPeriphery);

    /// @notice Returns the currently active LP position of the Vault
    function currentPosition() external view returns (TickRange memory);

    /// @notice Returns the address of the associated Voltz Vault Helper
    function voltzVaultHelper() external view returns (address);

    // -------------------  EXTERNAL, MUTATING  -------------------

    /// @notice Initializes a new vault
    /// @dev Can only be initialized by vault governance
    /// @param nft_ NFT of the vault in the VaultRegistry
    /// @param vaultTokens_ ERC20 tokens that will be managed by this Vault
    /// @param marginEngine_ the underlying margin engine of the Voltz pool
    /// @param initializeParams the InitializeParams used to initiate the vault
    function initialize(
        uint256 nft_,
        address[] memory vaultTokens_,
        address marginEngine_,
        address periphery_,
        address voltzHelper_,
        InitializeParams memory initializeParams
    ) external;

    /// @notice Vault's available funds are moved to a new LP position
    /// @dev Unwinds existing active position and funnels 
    /// @dev available funds into a new LP position on Voltz
    /// @param position The new LP position on Voltz
    function rebalance(TickRange memory position) external;

    /// @notice Settles Vault-owned position on Voltz and withdraws margin
    /// @dev The function settles position only if not settled before and
    /// @dev withdraws all available funds
    /// @param position The LP position to be settled and withdrawn from
    function settleVaultPositionAndWithdrawMargin(TickRange memory position) external;

    /// @notice Settles up to batchSize Vault-owned positions on Voltz and withdraws margin
    /// @dev Only positions with strictly positive cashflows are settled
    /// @dev and withdrawn from
    /// @param batchSize Limit on the number of positions to be settled (settles all positions if 0)
    /// @return settledBatchSize Number of positions which were settled and withdrawn from
    function settleVault(uint256 batchSize) external returns (uint256 settledBatchSize);

    /// @notice Updates estimated tvl values
    function updateTvl() external returns (
        uint256[] memory minTokenAmounts, 
        uint256[] memory maxTokenAmounts
    ); 

    /// @notice Sets the leverage used for LP positions on Voltz (in wad)
    function setLeverageWad(uint256 leverageWad) external;

    /// @notice Sets the multiplier used to decide how much margin is 
    /// @notice left in partially unwound positions on Voltz (in wad)
    function setMarginMultiplierPostUnwindWad(uint256 marginMultiplierPostUnwindWad) external;

    // -------------------  EVENTS  -------------------

    /// @notice Emitted when active LP position is changed
    /// @param oldPosition the previous active position
    /// @param marginLeftInOldPosition margin left in previous unwound position
    /// @param newPosition the new active position
    /// @param marginDepositedInNewPosition margin deposited in the new active position
    /// @param notionalLiquidityMintedInNewPosition the amount of notional that was minted as liquidity in the new position
    event PositionRebalance(
        TickRange oldPosition,
        int256 marginLeftInOldPosition,
        TickRange newPosition,
        uint256 marginDepositedInNewPosition,
        uint256 notionalLiquidityMintedInNewPosition
    );

    /// @notice Emitted when Vault is initialised
    /// @param marginEngine The address of the Voltz margin engine
    /// @param periphery The address of the Voltz periphery
    /// @param voltzVaultHelper The address of the Voltz Vault helper
    /// @param tickLower Lower tick of initial LP position on Voltz
    /// @param tickUpper Upper tick of initial LP position on Voltz
    /// @param leverageWad Leverage used for LP positions on Voltz (in wad)
    /// @param marginMultiplierPostUnwindWad Multiplier used to decide how much margin is left in partially unwound positions on Voltz (in wad)
    event VaultInitialized(
        address indexed marginEngine,
        address indexed periphery,
        address indexed voltzVaultHelper,
        int24 tickLower,
        int24 tickUpper,
        uint256 leverageWad,
        uint256 marginMultiplierPostUnwindWad
    );

    /// @notice Emitted when tokens are deposited into the Vault
    /// @param amountDeposited The amount depositied
    /// @param notionalLiquidityMinted The amount of liquidity minted on deposit
    event PushDeposit(
        uint256 amountDeposited,
        uint256 notionalLiquidityMinted
    );

    /// @notice Emitted when tokens are withdrawn from the Vault
    /// @param to Address of recipient
    /// @param amountRequestedToWithdraw The amount requested to be withdrawn
    /// @param amountWithdrawn The amount sent to the recipient
    event PullWithdraw(
        address to,
        uint256 amountRequestedToWithdraw,
        uint256 amountWithdrawn
    );

    /// @notice Emitted when TVL is updated
    /// @param tvl The estimated TVL
    event TvlUpdate(
        int256 tvl
    );

    /// @notice Emitted when a single Vault-owned position is settled and withdrawn from
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param margin The margin withdrawn
    event PositionSettledAndMarginWithdrawn(
        int24 tickLower,
        int24 tickUpper,
        int256 margin
    );

    /// @notice Emitted when multilpe Vault-owned positions are settled and withdrawn from
    /// @param batchSizeRequested The number of positions requested to be settled and withdrawn from
    /// @param fromIndex The index of the first position from the trackedPositions array to be settled and withdrawn from
    /// @param toIndex The index of the last position from the trackedPositions array to be settled and withdrawn from
    event VaultSettle(
        uint256 batchSizeRequested,
        uint256 fromIndex,
        uint256 toIndex
    );

    /// @notice Emitted when unwind fails
    /// @param reason Reason of failure
    event UnwindFail(
        string reason
    );
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.9;

/// @notice Exceptions stores project`s smart-contracts exceptions
library ExceptionsLibrary {
    string constant ADDRESS_ZERO = "AZ";
    string constant VALUE_ZERO = "VZ";
    string constant EMPTY_LIST = "EMPL";
    string constant NOT_FOUND = "NF";
    string constant INIT = "INIT";
    string constant DUPLICATE = "DUP";
    string constant NULL = "NULL";
    string constant TIMESTAMP = "TS";
    string constant FORBIDDEN = "FRB";
    string constant ALLOWLIST = "ALL";
    string constant LIMIT_OVERFLOW = "LIMO";
    string constant LIMIT_UNDERFLOW = "LIMU";
    string constant INVALID_VALUE = "INV";
    string constant INVARIANT = "INVA";
    string constant INVALID_TARGET = "INVTR";
    string constant INVALID_TOKEN = "INVTO";
    string constant INVALID_INTERFACE = "INVI";
    string constant INVALID_SELECTOR = "INVS";
    string constant INVALID_STATE = "INVST";
    string constant INVALID_LENGTH = "INVL";
    string constant LOCK = "LCKD";
    string constant DISABLED = "DIS";
    string constant REBALANCE_NOT_NEEDED = "RNN";
}

// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.8.9;

/// @title FixedPoint96
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
/// @dev Used in SqrtPriceMath.sol
library FixedPoint96 {
    uint8 internal constant RESOLUTION = 96;
    uint256 internal constant Q96 = 0x1000000000000000000000000;
}

// SPDX-License-Identifier: MIT
pragma solidity =0.8.9;

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // diff: original lib works under 0.7.6 with overflows enabled
        unchecked {
            // 512-bit multiply [prod1 prod0] = a * b
            // Compute the product mod 2**256 and mod 2**256 - 1
            // then 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(a, b, not(0))
                prod0 := mul(a, b)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division
            if (prod1 == 0) {
                require(denominator > 0);
                assembly {
                    result := div(prod0, denominator)
                }
                return result;
            }

            // 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]
            // Compute remainder using mulmod
            uint256 remainder;
            assembly {
                remainder := mulmod(a, b, denominator)
            }
            // Subtract 256 bit number from 512 bit number
            assembly {
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator
            // Compute largest power of two divisor of denominator.
            // Always >= 1.
            // diff: original uint256 twos = -denominator & denominator;
            uint256 twos = uint256(-int256(denominator)) & denominator;
            // Divide denominator by power of two
            assembly {
                denominator := div(denominator, twos)
            }

            // Divide [prod1 prod0] by the factors of two
            assembly {
                prod0 := div(prod0, twos)
            }
            // Shift in bits from prod1 into prod0. For this we need
            // to flip `twos` such that it is 2**256 / twos.
            // If twos is zero, then it becomes one
            assembly {
                twos := add(div(sub(0, twos), twos), 1)
            }
            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
            // correct for four bits. That is, denominator * inv = 1 mod 2**4
            uint256 inv = (3 * denominator) ^ 2;
            // Now use 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.
            inv *= 2 - denominator * inv; // inverse mod 2**8
            inv *= 2 - denominator * inv; // inverse mod 2**16
            inv *= 2 - denominator * inv; // inverse mod 2**32
            inv *= 2 - denominator * inv; // inverse mod 2**64
            inv *= 2 - denominator * inv; // inverse mod 2**128
            inv *= 2 - denominator * inv; // 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 precoditions 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 * inv;
            return result;
        }
    }

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // diff: original lib works under 0.7.6 with overflows enabled
        unchecked {
            result = mulDiv(a, b, denominator);
            if (mulmod(a, b, denominator) > 0) {
                require(result < type(uint256).max);
                result++;
            }
        }
    }

    function mulDivSigned(
        int256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (int256 result) {
        if (a < 0) return -int256(mulDiv(uint256(-a), b, denominator));
        return int256(mulDiv(uint256(a), b, denominator));
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.9;

import "@openzeppelin/contracts/access/AccessControlEnumerable.sol";
import "../interfaces/utils/IDefaultAccessControl.sol";
import "../libraries/ExceptionsLibrary.sol";

/// @notice This is a default access control with 3 roles:
///
/// - ADMIN: allowed to do anything
/// - ADMIN_DELEGATE: allowed to do anything except assigning ADMIN and ADMIN_DELEGATE roles
/// - OPERATOR: low-privileged role, generally keeper or some other bot
contract DefaultAccessControlLateInit is IDefaultAccessControl, AccessControlEnumerable {
    bool public initialized;

    bytes32 public constant OPERATOR = keccak256("operator");
    bytes32 public constant ADMIN_ROLE = keccak256("admin");
    bytes32 public constant ADMIN_DELEGATE_ROLE = keccak256("admin_delegate");

    // -------------------------  EXTERNAL, VIEW  ------------------------------

    /// @inheritdoc IDefaultAccessControl
    function isAdmin(address sender) public view returns (bool) {
        return hasRole(ADMIN_ROLE, sender) || hasRole(ADMIN_DELEGATE_ROLE, sender);
    }

    /// @inheritdoc IDefaultAccessControl
    function isOperator(address sender) public view returns (bool) {
        return hasRole(OPERATOR, sender);
    }

    // -------------------------  EXTERNAL, MUTATING  ------------------------------

    /// @notice Initializes a new contract with roles and single ADMIN.
    /// @param admin Admin of the contract
    function init(address admin) public {
        require(admin != address(0), ExceptionsLibrary.ADDRESS_ZERO);
        require(!initialized, ExceptionsLibrary.INIT);

        _setupRole(OPERATOR, admin);
        _setupRole(ADMIN_ROLE, admin);

        _setRoleAdmin(ADMIN_ROLE, ADMIN_ROLE);
        _setRoleAdmin(ADMIN_DELEGATE_ROLE, ADMIN_ROLE);
        _setRoleAdmin(OPERATOR, ADMIN_DELEGATE_ROLE);

        initialized = true;
    }

    // -------------------------  INTERNAL, VIEW  ------------------------------

    function _requireAdmin() internal view {
        require(isAdmin(msg.sender), ExceptionsLibrary.FORBIDDEN);
    }

    function _requireAtLeastOperator() internal view {
        require(isAdmin(msg.sender) || isOperator(msg.sender), ExceptionsLibrary.FORBIDDEN);
    }
}

{
  "evmVersion": "istanbul",
  "libraries": {},
  "metadata": {
    "bytecodeHash": "ipfs",
    "useLiteralContent": true
  },
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "remappings": [],
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  }
}

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