Cryo Explorer Ethereum Mainnet

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.26;

import { Ownable } from "@openzeppelin/contracts/access/Ownable.sol";
import { Ownable2Step } from "@openzeppelin/contracts/access/Ownable2Step.sol";
import { FixedPointMathLib } from "solady/src/utils/FixedPointMathLib.sol";

import { IWstETH } from "../interfaces/IWstETH.sol";
import { IBaseLiquidationRewardsManager } from
    "../interfaces/LiquidationRewardsManager/IBaseLiquidationRewardsManager.sol";
import { ILiquidationRewardsManager } from "../interfaces/LiquidationRewardsManager/ILiquidationRewardsManager.sol";
import { IUsdnProtocolTypes as Types } from "../interfaces/UsdnProtocol/IUsdnProtocolTypes.sol";

/**
 * @title Liquidation Rewards Manager
 * @notice This contract calculates rewards for liquidators within the USDN protocol.
 * @dev Rewards are computed based on gas costs, position size, and other parameters.
 */
contract LiquidationRewardsManager is ILiquidationRewardsManager, Ownable2Step {
    /* -------------------------------------------------------------------------- */
    /*                                  Constants                                 */
    /* -------------------------------------------------------------------------- */

    /// @inheritdoc ILiquidationRewardsManager
    uint32 public constant BPS_DIVISOR = 10_000;

    /// @inheritdoc ILiquidationRewardsManager
    uint256 public constant BASE_GAS_COST = 21_000;

    /// @inheritdoc ILiquidationRewardsManager
    uint256 public constant MAX_GAS_USED_PER_TICK = 500_000;

    /// @inheritdoc ILiquidationRewardsManager
    uint256 public constant MAX_OTHER_GAS_USED = 1_000_000;

    /// @inheritdoc ILiquidationRewardsManager
    uint256 public constant MAX_REBASE_GAS_USED = 200_000;

    /// @inheritdoc ILiquidationRewardsManager
    uint256 public constant MAX_REBALANCER_GAS_USED = 300_000;

    /* -------------------------------------------------------------------------- */
    /*                              Storage Variables                             */
    /* -------------------------------------------------------------------------- */

    /// @notice The address of the wrapped stETH (wstETH) token contract.
    IWstETH private immutable _wstEth;

    /**
     * @notice Holds the parameters used for rewards calculation.
     * @dev Parameters should be updated to reflect changes in gas costs or protocol adjustments.
     */
    RewardsParameters private _rewardsParameters;

    /// @param wstETH The address of the wstETH token.
    constructor(IWstETH wstETH) Ownable(msg.sender) {
        _wstEth = wstETH;
        _rewardsParameters = RewardsParameters({
            gasUsedPerTick: 44_666,
            otherGasUsed: 245_021,
            rebaseGasUsed: 6955,
            rebalancerGasUsed: 252_471,
            baseFeeOffset: 2 gwei,
            gasMultiplierBps: 10_500, // 1.05
            positionBonusMultiplierBps: 200, // 0.02
            fixedReward: 0.001 ether,
            maxReward: 0.5 ether
        });
    }

    /// @inheritdoc IBaseLiquidationRewardsManager
    function getLiquidationRewards(
        Types.LiqTickInfo[] calldata liquidatedTicks,
        uint256 currentPrice,
        bool rebased,
        Types.RebalancerAction rebalancerAction,
        Types.ProtocolAction,
        bytes calldata,
        bytes calldata
    ) external view returns (uint256 wstETHRewards_) {
        if (liquidatedTicks.length == 0) {
            return 0;
        }

        RewardsParameters memory rewardsParameters = _rewardsParameters;
        // calculate the amount of gas spent during the liquidation
        uint256 gasUsed = rewardsParameters.otherGasUsed + BASE_GAS_COST
            + uint256(rewardsParameters.gasUsedPerTick) * liquidatedTicks.length;
        if (rebased) {
            gasUsed += rewardsParameters.rebaseGasUsed;
        }
        if (uint8(rebalancerAction) > uint8(Types.RebalancerAction.NoCloseNoOpen)) {
            gasUsed += rewardsParameters.rebalancerGasUsed;
        }

        uint256 totalRewardETH = rewardsParameters.fixedReward
            + _calcGasPrice(rewardsParameters.baseFeeOffset) * gasUsed * rewardsParameters.gasMultiplierBps / BPS_DIVISOR;

        uint256 wstEthBonus =
            _calcPositionSizeBonus(liquidatedTicks, currentPrice, rewardsParameters.positionBonusMultiplierBps);

        totalRewardETH += _wstEth.getStETHByWstETH(wstEthBonus);

        if (totalRewardETH > rewardsParameters.maxReward) {
            totalRewardETH = rewardsParameters.maxReward;
        }

        // convert to wstETH
        wstETHRewards_ = _wstEth.getWstETHByStETH(totalRewardETH);
    }

    /// @inheritdoc ILiquidationRewardsManager
    function getRewardsParameters() external view returns (RewardsParameters memory) {
        return _rewardsParameters;
    }

    /// @inheritdoc ILiquidationRewardsManager
    function setRewardsParameters(
        uint32 gasUsedPerTick,
        uint32 otherGasUsed,
        uint32 rebaseGasUsed,
        uint32 rebalancerGasUsed,
        uint64 baseFeeOffset,
        uint16 gasMultiplierBps,
        uint16 positionBonusMultiplierBps,
        uint128 fixedReward,
        uint128 maxReward
    ) external onlyOwner {
        if (gasUsedPerTick > MAX_GAS_USED_PER_TICK) {
            revert LiquidationRewardsManagerGasUsedPerTickTooHigh(gasUsedPerTick);
        } else if (otherGasUsed > MAX_OTHER_GAS_USED) {
            revert LiquidationRewardsManagerOtherGasUsedTooHigh(otherGasUsed);
        } else if (rebaseGasUsed > MAX_REBASE_GAS_USED) {
            revert LiquidationRewardsManagerRebaseGasUsedTooHigh(rebaseGasUsed);
        } else if (rebalancerGasUsed > MAX_REBALANCER_GAS_USED) {
            revert LiquidationRewardsManagerRebalancerGasUsedTooHigh(rebalancerGasUsed);
        }

        _rewardsParameters = RewardsParameters({
            gasUsedPerTick: gasUsedPerTick,
            otherGasUsed: otherGasUsed,
            rebaseGasUsed: rebaseGasUsed,
            rebalancerGasUsed: rebalancerGasUsed,
            baseFeeOffset: baseFeeOffset,
            gasMultiplierBps: gasMultiplierBps,
            positionBonusMultiplierBps: positionBonusMultiplierBps,
            fixedReward: fixedReward,
            maxReward: maxReward
        });

        emit RewardsParametersUpdated(
            gasUsedPerTick,
            otherGasUsed,
            rebaseGasUsed,
            rebalancerGasUsed,
            baseFeeOffset,
            gasMultiplierBps,
            positionBonusMultiplierBps,
            fixedReward,
            maxReward
        );
    }

    /**
     * @notice Calculates the gas price used for rewards calculations.
     * @param baseFeeOffset An offset added to the block's base gas fee.
     * @return gasPrice_ The gas price used for reward calculation.
     */
    function _calcGasPrice(uint64 baseFeeOffset) internal view returns (uint256 gasPrice_) {
        gasPrice_ = block.basefee + baseFeeOffset;
        if (gasPrice_ > tx.gasprice) {
            gasPrice_ = tx.gasprice;
        }
    }

    /**
     * @notice Computes the size and price-dependent bonus given for liquidating the ticks.
     * @param liquidatedTicks Information about the liquidated ticks.
     * @param currentPrice The current asset price.
     * @param multiplier The bonus multiplier (in BPS).
     * @return bonus_ The calculated bonus (in wstETH).
     */
    function _calcPositionSizeBonus(
        Types.LiqTickInfo[] calldata liquidatedTicks,
        uint256 currentPrice,
        uint16 multiplier
    ) internal pure returns (uint256 bonus_) {
        uint256 length = liquidatedTicks.length;
        uint256 i;
        do {
            if (currentPrice >= liquidatedTicks[i].tickPrice) {
                // the currentPrice should never exceed the tick price, as a tick cannot be liquidated when the current
                // price is greater than the tick price
                // if this condition occurs, the bonus is clamped to 0
                // additionally, when the `currentPrice` equals the tick price, the bonus is 0 by definition of the
                // formula, so the calculation can be skipped
                unchecked {
                    i++;
                }
                continue;
            }
            uint256 priceDiff;
            unchecked {
                priceDiff = liquidatedTicks[i].tickPrice - currentPrice;
            }
            bonus_ += FixedPointMathLib.fullMulDiv(liquidatedTicks[i].totalExpo, priceDiff, currentPrice);
            unchecked {
                i++;
            }
        } while (i < length);
        bonus_ = bonus_ * multiplier / BPS_DIVISOR;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)

pragma solidity ^0.8.20;

import {Context} from "../utils/Context.sol";

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

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

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

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    constructor(address initialOwner) {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

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

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.20;

import {Ownable} from "./Ownable.sol";

/**
 * @dev Contract module which provides access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * This extension of the {Ownable} contract includes a two-step mechanism to transfer
 * ownership, where the new owner must call {acceptOwnership} in order to replace the
 * old one. This can help prevent common mistakes, such as transfers of ownership to
 * incorrect accounts, or to contracts that are unable to interact with the
 * permission system.
 *
 * The initial owner is specified at deployment time in the constructor for `Ownable`. This
 * can later be changed with {transferOwnership} and {acceptOwnership}.
 *
 * This module is used through inheritance. It will make available all functions
 * from parent (Ownable).
 */
abstract contract Ownable2Step is Ownable {
    address private _pendingOwner;

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

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

    /**
     * @dev Starts the ownership transfer of the contract to a new account. Replaces the pending transfer if there is one.
     * Can only be called by the current owner.
     *
     * Setting `newOwner` to the zero address is allowed; this can be used to cancel an initiated ownership transfer.
     */
    function transferOwnership(address newOwner) public virtual override onlyOwner {
        _pendingOwner = newOwner;
        emit OwnershipTransferStarted(owner(), newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`) and deletes any pending owner.
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual override {
        delete _pendingOwner;
        super._transferOwnership(newOwner);
    }

    /**
     * @dev The new owner accepts the ownership transfer.
     */
    function acceptOwnership() public virtual {
        address sender = _msgSender();
        if (pendingOwner() != sender) {
            revert OwnableUnauthorizedAccount(sender);
        }
        _transferOwnership(sender);
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error ExpOverflow();

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error FactorialOverflow();

    /// @dev The operation failed, due to an overflow.
    error RPowOverflow();

    /// @dev The mantissa is too big to fit.
    error MantissaOverflow();

    /// @dev The operation failed, due to an multiplication overflow.
    error MulWadFailed();

    /// @dev The operation failed, due to an multiplication overflow.
    error SMulWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error DivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error SDivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error MulDivFailed();

    /// @dev The division failed, as the denominator is zero.
    error DivFailed();

    /// @dev The full precision multiply-divide operation failed, either due
    /// to the result being larger than 256 bits, or a division by a zero.
    error FullMulDivFailed();

    /// @dev The output is undefined, as the input is less-than-or-equal to zero.
    error LnWadUndefined();

    /// @dev The input outside the acceptable domain.
    error OutOfDomain();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The scalar of ETH and most ERC20s.
    uint256 internal constant WAD = 1e18;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              SIMPLIFIED FIXED POINT OPERATIONS             */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if mul(y, gt(x, div(not(0), y))) {
                mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
            if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
                mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up.
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if mul(y, gt(x, div(not(0), y))) {
                mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
    function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
            if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, WAD)
            // Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
            if iszero(and(iszero(iszero(y)), eq(sdiv(z, WAD), x))) {
                mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up.
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
            if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
    function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `x` to the power of `y`.
    /// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
    /// Note: This function is an approximation.
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Using `ln(x)` means `x` must be greater than 0.
        return expWad((lnWad(x) * y) / int256(WAD));
    }

    /// @dev Returns `exp(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is less than 0.5 we return zero.
            // This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
            if (x <= -41446531673892822313) return r;

            /// @solidity memory-safe-assembly
            assembly {
                // When the result is greater than `(2**255 - 1) / 1e18` we can not represent it as
                // an int. This happens when `x >= floor(log((2**255 - 1) / 1e18) * 1e18) ≈ 135`.
                if iszero(slt(x, 135305999368893231589)) {
                    mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
                    revert(0x1c, 0x04)
                }
            }

            // `x` is now in the range `(-42, 136) * 1e18`. Convert to `(-42, 136) * 2**96`
            // for more intermediate precision and a binary basis. This base conversion
            // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
            x = (x << 78) / 5 ** 18;

            // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
            // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
            // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
            int256 k = ((x << 96) / 54916777467707473351141471128 + 2 ** 95) >> 96;
            x = x - k * 54916777467707473351141471128;

            // `k` is in the range `[-61, 195]`.

            // Evaluate using a (6, 7)-term rational approximation.
            // `p` is made monic, we'll multiply by a scale factor later.
            int256 y = x + 1346386616545796478920950773328;
            y = ((y * x) >> 96) + 57155421227552351082224309758442;
            int256 p = y + x - 94201549194550492254356042504812;
            p = ((p * y) >> 96) + 28719021644029726153956944680412240;
            p = p * x + (4385272521454847904659076985693276 << 96);

            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
            int256 q = x - 2855989394907223263936484059900;
            q = ((q * x) >> 96) + 50020603652535783019961831881945;
            q = ((q * x) >> 96) - 533845033583426703283633433725380;
            q = ((q * x) >> 96) + 3604857256930695427073651918091429;
            q = ((q * x) >> 96) - 14423608567350463180887372962807573;
            q = ((q * x) >> 96) + 26449188498355588339934803723976023;

            /// @solidity memory-safe-assembly
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial won't have zeros in the domain as all its roots are complex.
                // No scaling is necessary because p is already `2**96` too large.
                r := sdiv(p, q)
            }

            // r should be in the range `(0.09, 0.25) * 2**96`.

            // We now need to multiply r by:
            // - The scale factor `s ≈ 6.031367120`.
            // - The `2**k` factor from the range reduction.
            // - The `1e18 / 2**96` factor for base conversion.
            // We do this all at once, with an intermediate result in `2**213`
            // basis, so the final right shift is always by a positive amount.
            r = int256(
                (uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)
            );
        }
    }

    /// @dev Returns `ln(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function lnWad(int256 x) internal pure returns (int256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // We want to convert `x` from `10**18` fixed point to `2**96` fixed point.
            // We do this by multiplying by `2**96 / 10**18`. But since
            // `ln(x * C) = ln(x) + ln(C)`, we can simply do nothing here
            // and add `ln(2**96 / 10**18)` at the end.

            // Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // We place the check here for more optimal stack operations.
            if iszero(sgt(x, 0)) {
                mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
                revert(0x1c, 0x04)
            }
            // forgefmt: disable-next-item
            r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            x := shr(159, shl(r, x))

            // Evaluate using a (8, 8)-term rational approximation.
            // `p` is made monic, we will multiply by a scale factor later.
            // forgefmt: disable-next-item
            let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
                sar(96, mul(add(43456485725739037958740375743393,
                sar(96, mul(add(24828157081833163892658089445524,
                sar(96, mul(add(3273285459638523848632254066296,
                    x), x))), x))), x)), 11111509109440967052023855526967)
            p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
            p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
            p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.

            // `q` is monic by convention.
            let q := add(5573035233440673466300451813936, x)
            q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
            q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
            q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
            q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
            q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
            q := add(909429971244387300277376558375, sar(96, mul(x, q)))

            // `p / q` is in the range `(0, 0.125) * 2**96`.

            // Finalization, we need to:
            // - Multiply by the scale factor `s = 5.549…`.
            // - Add `ln(2**96 / 10**18)`.
            // - Add `k * ln(2)`.
            // - Multiply by `10**18 / 2**96 = 5**18 >> 78`.

            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already `2**96` too large.
            p := sdiv(p, q)
            // Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
            p := mul(1677202110996718588342820967067443963516166, p)
            // Add `ln(2) * k * 5**18 * 2**192`.
            // forgefmt: disable-next-item
            p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
            // Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
            p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
            // Base conversion: mul `2**18 / 2**192`.
            r := sar(174, p)
        }
    }

    /// @dev Returns `W_0(x)`, denominated in `WAD`.
    /// See: https://en.wikipedia.org/wiki/Lambert_W_function
    /// a.k.a. Product log function. This is an approximation of the principal branch.
    /// Note: This function is an approximation. Monotonically increasing.
    function lambertW0Wad(int256 x) internal pure returns (int256 w) {
        // forgefmt: disable-next-item
        unchecked {
            if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
            int256 wad = int256(WAD);
            int256 p = x;
            uint256 c; // Whether we need to avoid catastrophic cancellation.
            uint256 i = 4; // Number of iterations.
            if (w <= 0x1ffffffffffff) {
                if (-0x4000000000000 <= w) {
                    i = 1; // Inputs near zero only take one step to converge.
                } else if (w <= -0x3ffffffffffffff) {
                    i = 32; // Inputs near `-1/e` take very long to converge.
                }
            } else if (uint256(w >> 63) == uint256(0)) {
                /// @solidity memory-safe-assembly
                assembly {
                    // Inline log2 for more performance, since the range is small.
                    let v := shr(49, w)
                    let l := shl(3, lt(0xff, v))
                    l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
                        0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
                    w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
                    c := gt(l, 60)
                    i := add(2, add(gt(l, 53), c))
                }
            } else {
                int256 ll = lnWad(w = lnWad(w));
                /// @solidity memory-safe-assembly
                assembly {
                    // `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
                    w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
                    i := add(3, iszero(shr(68, x)))
                    c := iszero(shr(143, x))
                }
                if (c == uint256(0)) {
                    do { // If `x` is big, use Newton's so that intermediate values won't overflow.
                        int256 e = expWad(w);
                        /// @solidity memory-safe-assembly
                        assembly {
                            let t := mul(w, div(e, wad))
                            w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
                        }
                        if (p <= w) break;
                        p = w;
                    } while (--i != uint256(0));
                    /// @solidity memory-safe-assembly
                    assembly {
                        w := sub(w, sgt(w, 2))
                    }
                    return w;
                }
            }
            do { // Otherwise, use Halley's for faster convergence.
                int256 e = expWad(w);
                /// @solidity memory-safe-assembly
                assembly {
                    let t := add(w, wad)
                    let s := sub(mul(w, e), mul(x, wad))
                    w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
                }
                if (p <= w) break;
                p = w;
            } while (--i != c);
            /// @solidity memory-safe-assembly
            assembly {
                w := sub(w, sgt(w, 2))
            }
            // For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
            // R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
            if (c == uint256(0)) return w;
            int256 t = w | 1;
            /// @solidity memory-safe-assembly
            assembly {
                x := sdiv(mul(x, wad), t)
            }
            x = (t * (wad + lnWad(x)));
            /// @solidity memory-safe-assembly
            assembly {
                w := sdiv(x, add(wad, t))
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  GENERAL NUMBER UTILITIES                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
    function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // 512-bit multiply `[p1 p0] = x * y`.
            // 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 = p1 * 2**256 + p0`.

            // Temporarily use `result` as `p0` to save gas.
            result := mul(x, y) // Lower 256 bits of `x * y`.
            for {} 1 {} {
                // If overflows.
                if iszero(mul(or(iszero(x), eq(div(result, x), y)), d)) {
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(result, lt(mm, result))) // Upper 256 bits of `x * y`.

                    /*------------------- 512 by 256 division --------------------*/

                    // Make division exact by subtracting the remainder from `[p1 p0]`.
                    let r := mulmod(x, y, d) // Compute remainder using mulmod.
                    let t := and(d, sub(0, d)) // The least significant bit of `d`. `t >= 1`.
                    // Make sure the result is less than `2**256`. Also prevents `d == 0`.
                    // Placing the check here seems to give more optimal stack operations.
                    if iszero(gt(d, p1)) {
                        mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                        revert(0x1c, 0x04)
                    }
                    d := div(d, t) // Divide `d` by `t`, which is a power of two.
                    // Invert `d mod 2**256`
                    // Now that `d` is an odd number, it has an inverse
                    // modulo `2**256` such that `d * inv = 1 mod 2**256`.
                    // Compute the inverse by starting with a seed that is correct
                    // correct for four bits. That is, `d * inv = 1 mod 2**4`.
                    let inv := xor(2, mul(3, d))
                    // 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 := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
                    result :=
                        mul(
                            // Divide [p1 p0] by the factors of two.
                            // Shift in bits from `p1` into `p0`. For this we need
                            // to flip `t` such that it is `2**256 / t`.
                            or(
                                mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)),
                                div(sub(result, r), t)
                            ),
                            mul(sub(2, mul(d, inv)), inv) // inverse mod 2**256
                        )
                    break
                }
                result := div(result, d)
                break
            }
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Behavior is undefined if `d` is zero or the final result cannot fit in 256 bits.
    /// Performs the full 512 bit calculation regardless.
    function fullMulDivUnchecked(uint256 x, uint256 y, uint256 d)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := mul(x, y)
            let mm := mulmod(x, y, not(0))
            let p1 := sub(mm, add(result, lt(mm, result)))
            let t := and(d, sub(0, d))
            let r := mulmod(x, y, d)
            d := div(d, t)
            let inv := xor(2, mul(3, d))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            result :=
                mul(
                    or(mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)), div(sub(result, r), t)),
                    mul(sub(2, mul(d, inv)), inv)
                )
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Uniswap-v3-core under MIT license:
    /// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
    function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
        result = fullMulDiv(x, y, d);
        /// @solidity memory-safe-assembly
        assembly {
            if mulmod(x, y, d) {
                result := add(result, 1)
                if iszero(result) {
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
            }
        }
    }

    /// @dev Returns `floor(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(z, d)
        }
    }

    /// @dev Returns `ceil(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(z, d))), div(z, d))
        }
    }

    /// @dev Returns `ceil(x / d)`.
    /// Reverts if `d` is zero.
    function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(d) {
                mstore(0x00, 0x65244e4e) // `DivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(x, d))), div(x, d))
        }
    }

    /// @dev Returns `max(0, x - y)`.
    function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(gt(x, y), sub(x, y))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, uint256 x, uint256 y) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
    /// Reverts if the computation overflows.
    function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
            if x {
                z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
                let half := shr(1, b) // Divide `b` by 2.
                // Divide `y` by 2 every iteration.
                for { y := shr(1, y) } y { y := shr(1, y) } {
                    let xx := mul(x, x) // Store x squared.
                    let xxRound := add(xx, half) // Round to the nearest number.
                    // Revert if `xx + half` overflowed, or if `x ** 2` overflows.
                    if or(lt(xxRound, xx), shr(128, x)) {
                        mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                        revert(0x1c, 0x04)
                    }
                    x := div(xxRound, b) // Set `x` to scaled `xxRound`.
                    // If `y` is odd:
                    if and(y, 1) {
                        let zx := mul(z, x) // Compute `z * x`.
                        let zxRound := add(zx, half) // Round to the nearest number.
                        // If `z * x` overflowed or `zx + half` overflowed:
                        if or(xor(div(zx, x), z), lt(zxRound, zx)) {
                            // Revert if `x` is non-zero.
                            if x {
                                mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                                revert(0x1c, 0x04)
                            }
                        }
                        z := div(zxRound, b) // Return properly scaled `zxRound`.
                    }
                }
            }
        }
    }

    /// @dev Returns the square root of `x`, rounded down.
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
            // but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffffff, shr(r, x))))
            z := shl(shr(1, r), z)

            // Goal was to get `z*z*y` within a small factor of `x`. More iterations could
            // get y in a tighter range. Currently, we will have y in `[256, 256*(2**16))`.
            // We ensured `y >= 256` so that the relative difference between `y` and `y+1` is small.
            // That's not possible if `x < 256` but we can just verify those cases exhaustively.

            // Now, `z*z*y <= x < z*z*(y+1)`, and `y <= 2**(16+8)`, and either `y >= 256`, or `x < 256`.
            // Correctness can be checked exhaustively for `x < 256`, so we assume `y >= 256`.
            // Then `z*sqrt(y)` is within `sqrt(257)/sqrt(256)` of `sqrt(x)`, or about 20bps.

            // For `s` in the range `[1/256, 256]`, the estimate `f(s) = (181/1024) * (s+1)`
            // is in the range `(1/2.84 * sqrt(s), 2.84 * sqrt(s))`,
            // with largest error when `s = 1` and when `s = 256` or `1/256`.

            // Since `y` is in `[256, 256*(2**16))`, let `a = y/65536`, so that `a` is in `[1/256, 256)`.
            // Then we can estimate `sqrt(y)` using
            // `sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2**18`.

            // There is no overflow risk here since `y < 2**136` after the first branch above.
            z := shr(18, mul(z, add(shr(r, x), 65536))) // A `mul()` is saved from starting `z` at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If `x+1` is a perfect square, the Babylonian method cycles between
            // `floor(sqrt(x))` and `ceil(sqrt(x))`. This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            z := sub(z, lt(div(x, z), z))
        }
    }

    /// @dev Returns the cube root of `x`, rounded down.
    /// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
    /// https://github.com/pcaversaccio/snekmate/blob/main/src/utils/Math.vy
    function cbrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))

            z := div(shl(div(r, 3), shl(lt(0xf, shr(r, x)), 0xf)), xor(7, mod(r, 3)))

            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)

            z := sub(z, lt(div(x, mul(z, z)), z))
        }
    }

    /// @dev Returns the square root of `x`, denominated in `WAD`, rounded down.
    function sqrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 18) return sqrt(x * 10 ** 18);
            z = (1 + sqrt(x)) * 10 ** 9;
            z = (fullMulDivUnchecked(x, 10 ** 18, z) + z) >> 1;
        }
        /// @solidity memory-safe-assembly
        assembly {
            z := sub(z, gt(999999999999999999, sub(mulmod(z, z, x), 1)))
        }
    }

    /// @dev Returns the cube root of `x`, denominated in `WAD`, rounded down.
    function cbrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 36) return cbrt(x * 10 ** 36);
            z = (1 + cbrt(x)) * 10 ** 12;
            z = (fullMulDivUnchecked(x, 10 ** 36, z * z) + z + z) / 3;
            x = fullMulDivUnchecked(x, 10 ** 36, z * z);
        }
        /// @solidity memory-safe-assembly
        assembly {
            z := sub(z, lt(x, z))
        }
    }

    /// @dev Returns the factorial of `x`.
    function factorial(uint256 x) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := 1
            if iszero(lt(x, 58)) {
                mstore(0x00, 0xaba0f2a2) // `FactorialOverflow()`.
                revert(0x1c, 0x04)
            }
            for {} x { x := sub(x, 1) } { result := mul(result, x) }
        }
    }

    /// @dev Returns the log2 of `x`.
    /// Equivalent to computing the index of the most significant bit (MSB) of `x`.
    /// Returns 0 if `x` is zero.
    function log2(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0x0706060506020504060203020504030106050205030304010505030400000000))
        }
    }

    /// @dev Returns the log2 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log2Up(uint256 x) internal pure returns (uint256 r) {
        r = log2(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(r, 1), x))
        }
    }

    /// @dev Returns the log10 of `x`.
    /// Returns 0 if `x` is zero.
    function log10(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(x, 100000000000000000000000000000000000000)) {
                x := div(x, 100000000000000000000000000000000000000)
                r := 38
            }
            if iszero(lt(x, 100000000000000000000)) {
                x := div(x, 100000000000000000000)
                r := add(r, 20)
            }
            if iszero(lt(x, 10000000000)) {
                x := div(x, 10000000000)
                r := add(r, 10)
            }
            if iszero(lt(x, 100000)) {
                x := div(x, 100000)
                r := add(r, 5)
            }
            r := add(r, add(gt(x, 9), add(gt(x, 99), add(gt(x, 999), gt(x, 9999)))))
        }
    }

    /// @dev Returns the log10 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log10Up(uint256 x) internal pure returns (uint256 r) {
        r = log10(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(exp(10, r), x))
        }
    }

    /// @dev Returns the log256 of `x`.
    /// Returns 0 if `x` is zero.
    function log256(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(shr(3, r), lt(0xff, shr(r, x)))
        }
    }

    /// @dev Returns the log256 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log256Up(uint256 x) internal pure returns (uint256 r) {
        r = log256(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(shl(3, r), 1), x))
        }
    }

    /// @dev Returns the scientific notation format `mantissa * 10 ** exponent` of `x`.
    /// Useful for compressing prices (e.g. using 25 bit mantissa and 7 bit exponent).
    function sci(uint256 x) internal pure returns (uint256 mantissa, uint256 exponent) {
        /// @solidity memory-safe-assembly
        assembly {
            mantissa := x
            if mantissa {
                if iszero(mod(mantissa, 1000000000000000000000000000000000)) {
                    mantissa := div(mantissa, 1000000000000000000000000000000000)
                    exponent := 33
                }
                if iszero(mod(mantissa, 10000000000000000000)) {
                    mantissa := div(mantissa, 10000000000000000000)
                    exponent := add(exponent, 19)
                }
                if iszero(mod(mantissa, 1000000000000)) {
                    mantissa := div(mantissa, 1000000000000)
                    exponent := add(exponent, 12)
                }
                if iszero(mod(mantissa, 1000000)) {
                    mantissa := div(mantissa, 1000000)
                    exponent := add(exponent, 6)
                }
                if iszero(mod(mantissa, 10000)) {
                    mantissa := div(mantissa, 10000)
                    exponent := add(exponent, 4)
                }
                if iszero(mod(mantissa, 100)) {
                    mantissa := div(mantissa, 100)
                    exponent := add(exponent, 2)
                }
                if iszero(mod(mantissa, 10)) {
                    mantissa := div(mantissa, 10)
                    exponent := add(exponent, 1)
                }
            }
        }
    }

    /// @dev Convenience function for packing `x` into a smaller number using `sci`.
    /// The `mantissa` will be in bits [7..255] (the upper 249 bits).
    /// The `exponent` will be in bits [0..6] (the lower 7 bits).
    /// Use `SafeCastLib` to safely ensure that the `packed` number is small
    /// enough to fit in the desired unsigned integer type:
    /// ```
    ///     uint32 packed = SafeCastLib.toUint32(FixedPointMathLib.packSci(777 ether));
    /// ```
    function packSci(uint256 x) internal pure returns (uint256 packed) {
        (x, packed) = sci(x); // Reuse for `mantissa` and `exponent`.
        /// @solidity memory-safe-assembly
        assembly {
            if shr(249, x) {
                mstore(0x00, 0xce30380c) // `MantissaOverflow()`.
                revert(0x1c, 0x04)
            }
            packed := or(shl(7, x), packed)
        }
    }

    /// @dev Convenience function for unpacking a packed number from `packSci`.
    function unpackSci(uint256 packed) internal pure returns (uint256 unpacked) {
        unchecked {
            unpacked = (packed >> 7) * 10 ** (packed & 0x7f);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards zero.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = (x & y) + ((x ^ y) >> 1);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards negative infinity.
    function avg(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = (x >> 1) + (y >> 1) + (x & y & 1);
        }
    }

    /// @dev Returns the absolute value of `x`.
    function abs(int256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(sar(255, x), add(sar(255, x), x))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(mul(xor(sub(y, x), sub(x, y)), gt(x, y)), sub(y, x))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(int256 x, int256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(mul(xor(sub(y, x), sub(x, y)), sgt(x, y)), sub(y, x))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), lt(y, x)))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), slt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), gt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), sgt(y, x)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(uint256 x, uint256 minValue, uint256 maxValue)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), gt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), lt(maxValue, z)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), sgt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), slt(maxValue, z)))
        }
    }

    /// @dev Returns greatest common divisor of `x` and `y`.
    function gcd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            for { z := x } y {} {
                let t := y
                y := mod(z, y)
                z := t
            }
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`,
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(uint256 a, uint256 b, uint256 t, uint256 begin, uint256 end)
        internal
        pure
        returns (uint256)
    {
        if (begin > end) {
            t = ~t;
            begin = ~begin;
            end = ~end;
        }
        if (t <= begin) return a;
        if (t >= end) return b;
        unchecked {
            if (b >= a) return a + fullMulDiv(b - a, t - begin, end - begin);
            return a - fullMulDiv(a - b, t - begin, end - begin);
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`.
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(int256 a, int256 b, int256 t, int256 begin, int256 end)
        internal
        pure
        returns (int256)
    {
        if (begin > end) {
            t = int256(~uint256(t));
            begin = int256(~uint256(begin));
            end = int256(~uint256(end));
        }
        if (t <= begin) return a;
        if (t >= end) return b;
        // forgefmt: disable-next-item
        unchecked {
            if (b >= a) return int256(uint256(a) + fullMulDiv(uint256(b) - uint256(a),
                uint256(t) - uint256(begin), uint256(end) - uint256(begin)));
            return int256(uint256(a) - fullMulDiv(uint256(a) - uint256(b),
                uint256(t) - uint256(begin), uint256(end) - uint256(begin)));
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RAW NUMBER OPERATIONS                    */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(x, y)
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawSDiv(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mod(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawSMod(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := smod(x, y)
        }
    }

    /// @dev Returns `(x + y) % d`, return 0 if `d` if zero.
    function rawAddMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := addmod(x, y, d)
        }
    }

    /// @dev Returns `(x * y) % d`, return 0 if `d` if zero.
    function rawMulMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mulmod(x, y, d)
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { IERC20Permit } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Permit.sol";

interface IWstETH is IERC20Metadata, IERC20Permit {
    /**
     * @notice Exchanges stETH to wstETH
     * @param _stETHAmount The amount of stETH to wrap in exchange for wstETH
     * @dev Requirements:
     *  - `_stETHAmount` must be non-zero
     *  - msg.sender must approve at least `_stETHAmount` stETH to this contract
     *  - msg.sender must have at least `_stETHAmount` of stETH
     * User should first approve `_stETHAmount` to the WstETH contract
     * @return Amount of wstETH user receives after wrap
     */
    function wrap(uint256 _stETHAmount) external returns (uint256);

    /**
     * @notice Exchanges wstETH to stETH
     * @param _wstETHAmount The amount of wstETH to unwrap in exchange for stETH
     * @dev Requirements:
     *  - `_wstETHAmount` must be non-zero
     *  - msg.sender must have at least `_wstETHAmount` wstETH
     * @return The amount of stETH user receives after unwrap
     */
    function unwrap(uint256 _wstETHAmount) external returns (uint256);

    /**
     * @notice Get the amount of wstETH for a given amount of stETH
     * @param _stETHAmount The amount of stETH
     * @return The amount of wstETH for a given stETH amount
     */
    function getWstETHByStETH(uint256 _stETHAmount) external view returns (uint256);

    /**
     * @notice Get the amount of stETH for a given amount of wstETH
     * @param _wstETHAmount The amount of wstETH
     * @return The amount of stETH for a given wstETH amount
     */
    function getStETHByWstETH(uint256 _wstETHAmount) external view returns (uint256);

    /**
     * @notice Get the amount of stETH for a one wstETH
     * @return The amount of stETH for 1 wstETH
     */
    function stEthPerToken() external view returns (uint256);

    /**
     * @notice Get the amount of wstETH for a one stETH
     * @return The amount of wstETH for a 1 stETH
     */
    function tokensPerStEth() external view returns (uint256);

    /**
     * @notice Get the address of stETH
     * @return The address of stETH
     */
    function stETH() external view returns (address);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IUsdnProtocolTypes as Types } from "../UsdnProtocol/IUsdnProtocolTypes.sol";

/**
 * @title IBaseLiquidationRewardsManager
 * @notice This interface exposes the only function used by the UsdnProtocol.
 * @dev Future implementations of the rewards manager must implement this interface without modifications.
 */
interface IBaseLiquidationRewardsManager {
    /**
     * @notice Computes the amount of assets to reward a liquidator.
     * @param liquidatedTicks Information about the liquidated ticks.
     * @param currentPrice The current price of the asset.
     * @param rebased Indicates whether a USDN rebase was performed.
     * @param rebalancerAction The action performed by the {UsdnProtocolLongLibrary._triggerRebalancer} function.
     * @param action The type of protocol action that triggered the liquidation.
     * @param rebaseCallbackResult The result of the rebase callback, if any.
     * @param priceData The oracle price data, if any. This can be used to differentiate rewards based on the oracle
     * used to provide the liquidation price.
     * @return assetRewards_ The amount of asset tokens to reward the liquidator.
     */
    function getLiquidationRewards(
        Types.LiqTickInfo[] calldata liquidatedTicks,
        uint256 currentPrice,
        bool rebased,
        Types.RebalancerAction rebalancerAction,
        Types.ProtocolAction action,
        bytes calldata rebaseCallbackResult,
        bytes calldata priceData
    ) external view returns (uint256 assetRewards_);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IBaseLiquidationRewardsManager } from "./IBaseLiquidationRewardsManager.sol";
import { ILiquidationRewardsManagerErrorsEventsTypes } from "./ILiquidationRewardsManagerErrorsEventsTypes.sol";

/**
 * @title ILiquidationRewardsManager
 * @notice Interface for managing liquidation rewards within the protocol.
 */
interface ILiquidationRewardsManager is IBaseLiquidationRewardsManager, ILiquidationRewardsManagerErrorsEventsTypes {
    /**
     * @notice Gets the denominator used for the reward multipliers.
     * @return The BPS divisor.
     */
    function BPS_DIVISOR() external pure returns (uint32);

    /**
     * @notice Gets the fixed gas amount used as a base for transaction cost computations.
     * @dev Stored as a uint256 to prevent overflow during gas usage computations.
     * @return The base gas cost.
     */
    function BASE_GAS_COST() external pure returns (uint256);

    /**
     * @notice Gets the maximum allowable gas usage per liquidated tick.
     * @return The maximum gas used per tick.
     */
    function MAX_GAS_USED_PER_TICK() external pure returns (uint256);

    /**
     * @notice Gets the maximum allowable gas usage for all other computations.
     * @return The maximum gas used for additional computations.
     */
    function MAX_OTHER_GAS_USED() external pure returns (uint256);

    /**
     * @notice Gets the maximum allowable gas usage for rebase operations.
     * @return The maximum gas used for rebase operations.
     */
    function MAX_REBASE_GAS_USED() external pure returns (uint256);

    /**
     * @notice Gets the maximum allowable gas usage for triggering the optional rebalancer.
     * @return The maximum gas used for the optional rebalancer trigger.
     */
    function MAX_REBALANCER_GAS_USED() external pure returns (uint256);

    /**
     * @notice Retrieves the current parameters used for reward calculations.
     * @return rewardsParameters_ A struct containing the rewards parameters.
     */
    function getRewardsParameters() external view returns (RewardsParameters memory);

    /**
     * @notice Updates the parameters used for calculating liquidation rewards.
     * @param gasUsedPerTick The gas consumed per tick for liquidation.
     * @param otherGasUsed The gas consumed for all additional computations.
     * @param rebaseGasUsed The gas consumed for optional USDN rebase operation.
     * @param rebalancerGasUsed The gas consumed for the optional rebalancer trigger.
     * @param baseFeeOffset An offset added to the block's base gas fee.
     * @param gasMultiplierBps The multiplier for the gas usage (in BPS).
     * @param positionBonusMultiplierBps Multiplier for position size bonus (in BPS).
     * @param fixedReward A fixed reward amount (in native currency, converted to wstETH).
     * @param maxReward The maximum allowable reward amount (in native currency, converted to wstETH).
     */
    function setRewardsParameters(
        uint32 gasUsedPerTick,
        uint32 otherGasUsed,
        uint32 rebaseGasUsed,
        uint32 rebalancerGasUsed,
        uint64 baseFeeOffset,
        uint16 gasMultiplierBps,
        uint16 positionBonusMultiplierBps,
        uint128 fixedReward,
        uint128 maxReward
    ) external;
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { HugeUint } from "@smardex-solidity-libraries-1/HugeUint.sol";
import { LibBitmap } from "solady/src/utils/LibBitmap.sol";

import { DoubleEndedQueue } from "../../libraries/DoubleEndedQueue.sol";
import { IBaseLiquidationRewardsManager } from "../LiquidationRewardsManager/IBaseLiquidationRewardsManager.sol";
import { IBaseOracleMiddleware } from "../OracleMiddleware/IBaseOracleMiddleware.sol";
import { IBaseRebalancer } from "../Rebalancer/IBaseRebalancer.sol";
import { IUsdn } from "../Usdn/IUsdn.sol";

interface IUsdnProtocolTypes {
    /**
     * @notice All possible action types for the protocol.
     * @dev This is used for pending actions and to interact with the oracle middleware.
     * @param None No particular action.
     * @param Initialize The contract is being initialized.
     * @param InitiateDeposit Initiating a `deposit` action.
     * @param ValidateDeposit Validating a `deposit` action.
     * @param InitiateWithdrawal Initiating a `withdraw` action.
     * @param ValidateWithdrawal Validating a `withdraw` action.
     * @param InitiateOpenPosition Initiating an `open` position action.
     * @param ValidateOpenPosition Validating an `open` position action.
     * @param InitiateClosePosition Initiating a `close` position action.
     * @param ValidateClosePosition Validating a `close` position action.
     * @param Liquidation The price is requested for a liquidation action.
     */
    enum ProtocolAction {
        None,
        Initialize,
        InitiateDeposit,
        ValidateDeposit,
        InitiateWithdrawal,
        ValidateWithdrawal,
        InitiateOpenPosition,
        ValidateOpenPosition,
        InitiateClosePosition,
        ValidateClosePosition,
        Liquidation
    }

    /**
     * @notice The outcome of the call targeting a long position.
     * @param Processed The call did what it was supposed to do.
     * An initiate close has been completed / a pending action was validated.
     * @param Liquidated The position has been liquidated by this call.
     * @param PendingLiquidations The call cannot be completed because of pending liquidations.
     * Try calling the {IUsdnProtocolActions.liquidate} function with a fresh price to unblock the situation.
     */
    enum LongActionOutcome {
        Processed,
        Liquidated,
        PendingLiquidations
    }

    /**
     * @notice Classifies how far in its logic the {UsdnProtocolLongLibrary._triggerRebalancer} function made it to.
     * @dev Used to estimate the gas spent by the function call to more accurately calculate liquidation rewards.
     * @param None The rebalancer is not set.
     * @param NoImbalance The protocol imbalance is not reached.
     * @param PendingLiquidation The rebalancer position should be liquidated.
     * @param NoCloseNoOpen The action neither closes nor opens a position.
     * @param Closed The action only closes a position.
     * @param Opened The action only opens a position.
     * @param ClosedOpened The action closes and opens a position.
     */
    enum RebalancerAction {
        None,
        NoImbalance,
        PendingLiquidation,
        NoCloseNoOpen,
        Closed,
        Opened,
        ClosedOpened
    }

    /**
     * @notice Information about a long user position.
     * @param validated Whether the position was validated.
     * @param timestamp The timestamp of the position start.
     * @param user The user's address.
     * @param totalExpo The total exposure of the position (0 for vault deposits). The product of the initial
     * collateral and the initial leverage.
     * @param amount The amount of initial collateral in the position.
     */
    struct Position {
        bool validated; // 1 byte
        uint40 timestamp; // 5 bytes. Max 1_099_511_627_775 (36812-02-20 01:36:15)
        address user; // 20 bytes
        uint128 totalExpo; // 16 bytes. Max 340_282_366_920_938_463_463.374_607_431_768_211_455 ether
        uint128 amount; // 16 bytes
    }

    /**
     * @notice A pending action in the queue.
     * @param action The action type.
     * @param timestamp The timestamp of the initiate action.
     * @param var0 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param to The target of the action.
     * @param validator The address that is supposed to validate the action.
     * @param securityDepositValue The security deposit of the pending action.
     * @param var1 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var2 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var3 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var4 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var5 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var6 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     * @param var7 See {DepositPendingAction}, {WithdrawalPendingAction} and {LongPendingAction}.
     */
    struct PendingAction {
        ProtocolAction action; // 1 byte
        uint40 timestamp; // 5 bytes
        uint24 var0; // 3 bytes
        address to; // 20 bytes
        address validator; // 20 bytes
        uint64 securityDepositValue; // 8 bytes
        int24 var1; // 3 bytes
        uint128 var2; // 16 bytes
        uint128 var3; // 16 bytes
        uint256 var4; // 32 bytes
        uint256 var5; // 32 bytes
        uint256 var6; // 32 bytes
        uint256 var7; // 32 bytes
    }

    /**
     * @notice A pending action in the queue for a vault deposit.
     * @param action The action type.
     * @param timestamp The timestamp of the initiate action.
     * @param feeBps Fee for the deposit, in BPS.
     * @param to The recipient of the funds.
     * @param validator The address that is supposed to validate the action.
     * @param securityDepositValue The security deposit of the pending action.
     * @param _unused Unused field to align the struct to `PendingAction`.
     * @param amount The amount of assets of the pending deposit.
     * @param assetPrice The price of the asset at the time of the last update.
     * @param totalExpo The total exposure at the time of the last update.
     * @param balanceVault The balance of the vault at the time of the last update.
     * @param balanceLong The balance of the long position at the time of the last update.
     * @param usdnTotalShares The total supply of USDN shares at the time of the action.
     */
    struct DepositPendingAction {
        ProtocolAction action; // 1 byte
        uint40 timestamp; // 5 bytes
        uint24 feeBps; // 3 bytes
        address to; // 20 bytes
        address validator; // 20 bytes
        uint64 securityDepositValue; // 8 bytes
        uint24 _unused; // 3 bytes
        uint128 amount; // 16 bytes
        uint128 assetPrice; // 16 bytes
        uint256 totalExpo; // 32 bytes
        uint256 balanceVault; // 32 bytes
        uint256 balanceLong; // 32 bytes
        uint256 usdnTotalShares; // 32 bytes
    }

    /**
     * @notice A pending action in the queue for a vault withdrawal.
     * @param action The action type.
     * @param timestamp The timestamp of the initiate action.
     * @param feeBps Fee for the withdrawal, in BPS.
     * @param to The recipient of the funds.
     * @param validator The address that is supposed to validate the action.
     * @param securityDepositValue The security deposit of the pending action.
     * @param sharesLSB 3 least significant bytes of the withdrawal shares amount (uint152).
     * @param sharesMSB 16 most significant bytes of the withdrawal shares amount (uint152).
     * @param assetPrice The price of the asset at the time of the last update.
     * @param totalExpo The total exposure at the time of the last update.
     * @param balanceVault The balance of the vault at the time of the last update.
     * @param balanceLong The balance of the long position at the time of the last update.
     * @param usdnTotalShares The total shares supply of USDN at the time of the action.
     */
    struct WithdrawalPendingAction {
        ProtocolAction action; // 1 byte
        uint40 timestamp; // 5 bytes
        uint24 feeBps; // 3 bytes
        address to; // 20 bytes
        address validator; // 20 bytes
        uint64 securityDepositValue; // 8 bytes
        uint24 sharesLSB; // 3 bytes
        uint128 sharesMSB; // 16 bytes
        uint128 assetPrice; // 16 bytes
        uint256 totalExpo; // 32 bytes
        uint256 balanceVault; // 32 bytes
        uint256 balanceLong; // 32 bytes
        uint256 usdnTotalShares; // 32 bytes
    }

    /**
     * @notice A pending action in the queue for a long position.
     * @param action The action type.
     * @param timestamp The timestamp of the initiate action.
     * @param closeLiqPenalty The liquidation penalty of the tick (only used when closing a position).
     * @param to The recipient of the position.
     * @param validator The address that is supposed to validate the action.
     * @param securityDepositValue The security deposit of the pending action.
     * @param tick The tick of the position.
     * @param closeAmount The portion of the initial position amount to close (only used when closing a position).
     * @param closePosTotalExpo The total expo of the position (only used when closing a position).
     * @param tickVersion The version of the tick.
     * @param index The index of the position in the tick list.
     * @param liqMultiplier A fixed precision representation of the liquidation multiplier (with
     * `LIQUIDATION_MULTIPLIER_DECIMALS` decimals) used to calculate the effective price for a given tick number.
     * @param closeBoundedPositionValue The amount that was removed from the long balance on
     * {IUsdnProtocolActions.initiateClosePosition} (only used when closing a position).
     */
    struct LongPendingAction {
        ProtocolAction action; // 1 byte
        uint40 timestamp; // 5 bytes
        uint24 closeLiqPenalty; // 3 bytes
        address to; // 20 bytes
        address validator; // 20 bytes
        uint64 securityDepositValue; // 8 bytes
        int24 tick; // 3 bytes
        uint128 closeAmount; // 16 bytes
        uint128 closePosTotalExpo; // 16 bytes
        uint256 tickVersion; // 32 bytes
        uint256 index; // 32 bytes
        uint256 liqMultiplier; // 32 bytes
        uint256 closeBoundedPositionValue; // 32 bytes
    }

    /**
     * @notice The data allowing to validate an actionable pending action.
     * @param priceData An array of bytes, each representing the data to be forwarded to the oracle middleware to
     * validate a pending action in the queue.
     * @param rawIndices An array of raw indices in the pending actions queue, in the same order as the corresponding
     * priceData.
     */
    struct PreviousActionsData {
        bytes[] priceData;
        uint128[] rawIndices;
    }

    /**
     * @notice Information of a liquidated tick.
     * @param totalPositions The total number of positions in the tick.
     * @param totalExpo The total expo of the tick.
     * @param remainingCollateral The remaining collateral after liquidation.
     * @param tickPrice The corresponding price.
     * @param priceWithoutPenalty The price without the liquidation penalty.
     */
    struct LiqTickInfo {
        uint256 totalPositions;
        uint256 totalExpo;
        int256 remainingCollateral;
        uint128 tickPrice;
        uint128 priceWithoutPenalty;
    }

    /**
     * @notice The effects of executed liquidations on the protocol.
     * @param liquidatedPositions The total number of liquidated positions.
     * @param remainingCollateral The remaining collateral after liquidation.
     * @param newLongBalance The new balance of the long side.
     * @param newVaultBalance The new balance of the vault side.
     * @param isLiquidationPending Whether some ticks are still populated above the current price (left to liquidate).
     * @param liquidatedTicks Information about the liquidated ticks.
     */
    struct LiquidationsEffects {
        uint256 liquidatedPositions;
        int256 remainingCollateral;
        uint256 newLongBalance;
        uint256 newVaultBalance;
        bool isLiquidationPending;
        LiqTickInfo[] liquidatedTicks;
    }

    /**
     * @notice Accumulator for tick data.
     * @param totalExpo The sum of the total expo of each position in the tick.
     * @param totalPos The number of positions in the tick.
     * @param liquidationPenalty The liquidation penalty for the positions in the tick.
     * @dev Since the liquidation penalty is a parameter that can be updated, we need to ensure that positions that get
     * created with a given penalty, use this penalty throughout their lifecycle. As such, once a tick gets populated by
     * a first position, it gets assigned the current liquidation penalty parameter value and can't use another value
     * until it gets liquidated or all positions exit the tick.
     */
    struct TickData {
        uint256 totalExpo;
        uint248 totalPos;
        uint24 liquidationPenalty;
    }

    /**
     * @notice The unique identifier for a long position.
     * @param tick The tick of the position.
     * @param tickVersion The version of the tick.
     * @param index The index of the position in the tick list.
     */
    struct PositionId {
        int24 tick;
        uint256 tickVersion;
        uint256 index;
    }

    /**
     * @notice Parameters for the internal {UsdnProtocolActionsLongLibrary._initiateOpenPosition} function.
     * @param user The address of the user initiating the open position.
     * @param to The address that will be the owner of the position.
     * @param validator The address that is supposed to validate the action.
     * @param amount The amount of assets to deposit.
     * @param desiredLiqPrice The desired liquidation price, including the liquidation penalty.
     * @param userMaxPrice The maximum price at which the position can be opened. The userMaxPrice is compared with the
     * price after confidence interval, penalty, etc...
     * @param userMaxLeverage The maximum leverage for the newly created position.
     * @param deadline The deadline of the open position to be initiated.
     * @param securityDepositValue The value of the security deposit for the newly created pending action.
     * @param currentPriceData The current price data (used to calculate the temporary leverage and entry price,
     * pending validation).
     */
    struct InitiateOpenPositionParams {
        address user;
        address to;
        address validator;
        uint128 amount;
        uint128 desiredLiqPrice;
        uint128 userMaxPrice;
        uint256 userMaxLeverage;
        uint256 deadline;
        uint64 securityDepositValue;
    }

    /**
     * @notice Parameters for the internal {UsdnProtocolLongLibrary._prepareInitiateOpenPosition} function.
     * @param validator The address that is supposed to validate the action.
     * @param amount The amount of assets to deposit.
     * @param desiredLiqPrice The desired liquidation price, including the liquidation penalty.
     * @param userMaxPrice The maximum price at which the position can be opened. The userMaxPrice is compared with the
     * price after confidence interval, penalty, etc...
     * @param userMaxLeverage The maximum leverage for the newly created position.
     * @param currentPriceData The current price data.
     */
    struct PrepareInitiateOpenPositionParams {
        address validator;
        uint128 amount;
        uint128 desiredLiqPrice;
        uint256 userMaxPrice;
        uint256 userMaxLeverage;
        bytes currentPriceData;
    }

    /**
     * @notice Parameters for the internal {UsdnProtocolActionsUtilsLibrary._prepareClosePositionData} function.
     * @param to The recipient of the funds.
     * @param validator The address that is supposed to validate the action.
     * @param posId The unique identifier of the position.
     * @param amountToClose The amount of collateral to remove from the position's amount.
     * @param userMinPrice The minimum price at which the position can be closed.
     * @param deadline The deadline until the position can be closed.
     * @param currentPriceData The current price data.
     * @param delegationSignature An EIP712 signature that proves the caller is authorized by the owner of the position
     * to close it on their behalf.
     * @param domainSeparatorV4 The domain separator v4.
     */
    struct PrepareInitiateClosePositionParams {
        address to;
        address validator;
        PositionId posId;
        uint128 amountToClose;
        uint256 userMinPrice;
        uint256 deadline;
        bytes currentPriceData;
        bytes delegationSignature;
        bytes32 domainSeparatorV4;
    }

    /**
     * @notice Parameters for the internal {UsdnProtocolActionsLongLibrary._initiateClosePosition} function.
     * @param to The recipient of the funds.
     * @param validator The address that is supposed to validate the action.
     * @param posId The unique identifier of the position.
     * @param amountToClose The amount to close.
     * @param userMinPrice The minimum price at which the position can be closed.
     * @param deadline The deadline of the close position to be initiated.
     * @param securityDepositValue The value of the security deposit for the newly created pending action.
     * @param domainSeparatorV4 The domain separator v4 for EIP712 signature.
     */
    struct InitiateClosePositionParams {
        address to;
        address payable validator;
        uint256 deadline;
        PositionId posId;
        uint128 amountToClose;
        uint256 userMinPrice;
        uint64 securityDepositValue;
        bytes32 domainSeparatorV4;
    }

    /**
     * @dev Structure to hold the transient data during {UsdnProtocolActionsLongLibrary._initiateClosePosition}
     * @param pos The position to close.
     * @param liquidationPenalty The liquidation penalty.
     * @param totalExpoToClose The total expo to close.
     * @param lastPrice The price after the last balances update.
     * @param tempPositionValue The bounded value of the position that was removed from the long balance.
     * @param longTradingExpo The long trading expo.
     * @param liqMulAcc The liquidation multiplier accumulator.
     * @param isLiquidationPending Whether some ticks are still populated above the current price (left to liquidate).
     */
    struct ClosePositionData {
        Position pos;
        uint24 liquidationPenalty;
        uint128 totalExpoToClose;
        uint128 lastPrice;
        uint256 tempPositionValue;
        uint256 longTradingExpo;
        HugeUint.Uint512 liqMulAcc;
        bool isLiquidationPending;
    }

    /**
     * @dev Structure to hold the transient data during {UsdnProtocolActionsLongLibrary._validateOpenPosition}.
     * @param action The long pending action.
     * @param startPrice The new entry price of the position.
     * @param lastPrice The price of the last balances update.
     * @param tickHash The tick hash.
     * @param pos The position object.
     * @param liqPriceWithoutPenaltyNorFunding The liquidation price without penalty nor funding used to calculate the
     * user leverage and the new total expo.
     * @param liqPriceWithoutPenalty The new liquidation price without penalty.
     * @param leverage The new leverage.
     * @param oldPosValue The value of the position according to the old entry price and the _lastPrice.
     * @param liquidationPenalty The liquidation penalty for the position's tick.
     * @param isLiquidationPending Whether some ticks are still populated above the current price (left to liquidate).
     */
    struct ValidateOpenPositionData {
        LongPendingAction action;
        uint128 startPrice;
        uint128 lastPrice;
        bytes32 tickHash;
        Position pos;
        uint128 liqPriceWithoutPenaltyNorFunding;
        uint128 liqPriceWithoutPenalty;
        uint256 leverage;
        uint256 oldPosValue;
        uint24 liquidationPenalty;
        bool isLiquidationPending;
    }

    /**
     * @dev Structure to hold the transient data during {UsdnProtocolActionsLongLibrary._initiateOpenPosition}.
     * @param adjustedPrice The adjusted price with position fees applied.
     * @param posId The unique identifier of the position.
     * @param liquidationPenalty The liquidation penalty.
     * @param positionTotalExpo The total expo of the position. The product of the initial collateral and the initial
     * leverage.
     * @param positionValue The value of the position, taking into account the position fee.
     * @param liqMultiplier The liquidation multiplier represented with fixed precision.
     * @param isLiquidationPending Whether some ticks are still populated above the current price (left to liquidate).
     */
    struct InitiateOpenPositionData {
        uint128 adjustedPrice;
        PositionId posId;
        uint24 liquidationPenalty;
        uint128 positionTotalExpo;
        uint256 positionValue;
        uint256 liqMultiplier;
        bool isLiquidationPending;
    }

    /**
     * @notice Structure to hold the state of the protocol.
     * @param totalExpo The long total expo.
     * @param tradingExpo The long trading expo.
     * @param longBalance The long balance.
     * @param vaultBalance The vault balance.
     * @param liqMultiplierAccumulator The liquidation multiplier accumulator.
     */
    struct CachedProtocolState {
        uint256 totalExpo;
        uint256 tradingExpo;
        uint256 longBalance;
        uint256 vaultBalance;
        HugeUint.Uint512 liqMultiplierAccumulator;
    }

    /**
     * @notice Structure to hold transient data during the {UsdnProtocolActionsLongLibrary._calcRebalancerPositionTick}
     * function.
     * @param protocolMaxLeverage The protocol maximum leverage.
     * @param longImbalanceTargetBps The long imbalance target in basis points.
     * @param tradingExpoToFill The trading expo to fill.
     * @param highestUsableTradingExpo The highest usable trading expo.
     * @param currentLiqPenalty The current liquidation penalty.
     * @param liqPriceWithoutPenalty The liquidation price without penalty.
     */
    struct CalcRebalancerPositionTickData {
        uint256 protocolMaxLeverage;
        int256 longImbalanceTargetBps;
        uint256 tradingExpoToFill;
        uint256 highestUsableTradingExpo;
        uint24 currentLiqPenalty;
        uint128 liqPriceWithoutPenalty;
    }

    /**
     * @notice Structure to hold the return values of the {UsdnProtocolActionsLongLibrary._calcRebalancerPositionTick}
     * function.
     * @param tick The tick of the rebalancer position, includes liquidation penalty.
     * @param totalExpo The total expo of the rebalancer position.
     * @param liquidationPenalty The liquidation penalty of the tick.
     */
    struct RebalancerPositionData {
        int24 tick;
        uint128 totalExpo;
        uint24 liquidationPenalty;
    }

    /**
     * @notice Data structure for the {UsdnProtocolCoreLibrary._applyPnlAndFunding} function.
     * @param tempLongBalance The new balance of the long side, could be negative (temporarily).
     * @param tempVaultBalance The new balance of the vault side, could be negative (temporarily).
     * @param lastPrice The last price.
     */
    struct ApplyPnlAndFundingData {
        int256 tempLongBalance;
        int256 tempVaultBalance;
        uint128 lastPrice;
    }

    /**
     * @notice Data structure for tick to price conversion functions.
     * @param tradingExpo The long side trading expo.
     * @param accumulator The liquidation multiplier accumulator.
     * @param tickSpacing The tick spacing.
     */
    struct TickPriceConversionData {
        uint256 tradingExpo;
        HugeUint.Uint512 accumulator;
        int24 tickSpacing;
    }

    /**
     * @custom:storage-location erc7201:UsdnProtocol.storage.main.
     * @notice Structure to hold the state of the protocol.
     * @param _tickSpacing The liquidation tick spacing for storing long positions.
     * A tick spacing of 1 is equivalent to a 0.01% increase in liquidation price between ticks. A tick spacing of
     * 100 is equivalent to a ~1.005% increase in liquidation price between ticks.
     * @param _asset The asset ERC20 contract.
     * Assets with a blacklist are not supported because the protocol would be DoS if transfers revert.
     * @param _assetDecimals The number of decimals used by the `_asset`.
     * @param _priceFeedDecimals The price feed decimals (18).
     * @param _usdn The USDN ERC20 contract.
     * @param _sdex The SDEX ERC20 contract.
     * @param _usdnMinDivisor The minimum divisor for USDN.
     * @param _oracleMiddleware The oracle middleware contract.
     * @param _liquidationRewardsManager The liquidation rewards manager contract.
     * @param _rebalancer The rebalancer contract.
     * @param _isRebalancer Whether an address is or has been a rebalancer.
     * @param _minLeverage The minimum leverage for a position.
     * @param _maxLeverage The maximum leverage for a position.
     * @param _lowLatencyValidatorDeadline The deadline for a user to confirm their action with a low-latency oracle.
     * After this deadline, any user can validate the action with the low-latency oracle until the
     * OracleMiddleware's _lowLatencyDelay. This is an offset compared to the timestamp of the initiate action.
     * @param _onChainValidatorDeadline The deadline for a user to confirm their action with an on-chain oracle.
     * After this deadline, any user can validate the action with the on-chain oracle. This is an offset compared
     * to the timestamp of the initiate action + the oracle middleware's _lowLatencyDelay.
     * @param _safetyMarginBps Safety margin for the liquidation price of newly open positions, in basis points.
     * @param _liquidationIteration The number of iterations to perform during the user's action (in tick).
     * @param _protocolFeeBps The protocol fee in basis points.
     * @param _rebalancerBonusBps Part of the remaining collateral that is given as a bonus to the Rebalancer upon
     * liquidation of a tick, in basis points. The rest is sent to the Vault balance.
     * @param _liquidationPenalty The liquidation penalty (in ticks).
     * @param _EMAPeriod The moving average period of the funding rate.
     * @param _fundingSF The scaling factor (SF) of the funding rate.
     * @param _feeThreshold The threshold above which the fee will be sent.
     * @param _openExpoImbalanceLimitBps The imbalance limit of the long expo for open actions (in basis points).
     * As soon as the difference between the vault expo and the long expo exceeds this basis point limit in favor
     * of long the open rebalancing mechanism is triggered, preventing the opening of a new long position.
     * @param _withdrawalExpoImbalanceLimitBps The imbalance limit of the long expo for withdrawal actions (in basis
     * points). As soon as the difference between vault expo and long expo exceeds this basis point limit in favor of
     * long, the withdrawal rebalancing mechanism is triggered, preventing the withdrawal of the existing vault
     * position.
     * @param _depositExpoImbalanceLimitBps The imbalance limit of the vault expo for deposit actions (in basis points).
     * As soon as the difference between the vault expo and the long expo exceeds this basis point limit in favor
     * of the vault, the deposit vault rebalancing mechanism is triggered, preventing the opening of a new vault
     * position.
     * @param _closeExpoImbalanceLimitBps The imbalance limit of the vault expo for close actions (in basis points).
     * As soon as the difference between the vault expo and the long expo exceeds this basis point limit in favor
     * of the vault, the close rebalancing mechanism is triggered, preventing the close of an existing long position.
     * @param _rebalancerCloseExpoImbalanceLimitBps The imbalance limit of the vault expo for close actions from the
     * rebalancer (in basis points). As soon as the difference between the vault expo and the long expo exceeds this
     * basis point limit in favor of the vault, the close rebalancing mechanism is triggered, preventing the close of an
     * existing long position from the rebalancer contract.
     * @param _longImbalanceTargetBps The target imbalance on the long side (in basis points)
     * This value will be used to calculate how much of the missing trading expo the rebalancer position will try
     * to compensate. A negative value means the rebalancer will compensate enough to go above the equilibrium. A
     * positive value means the rebalancer will compensate but stay below the equilibrium.
     * @param _positionFeeBps The position fee in basis points.
     * @param _vaultFeeBps The fee for vault deposits and withdrawals, in basis points.
     * @param _sdexRewardsRatioBps The ratio of SDEX rewards to send to the user (in basis points).
     * @param _sdexBurnOnDepositRatio The ratio of USDN to SDEX tokens to burn on deposit.
     * @param _feeCollector The fee collector's address.
     * @param _securityDepositValue The deposit required for a new position.
     * @param _targetUsdnPrice The nominal (target) price of USDN (with _priceFeedDecimals).
     * @param _usdnRebaseThreshold The USDN price threshold to trigger a rebase (with _priceFeedDecimals).
     * @param _minLongPosition The minimum long position size (with `_assetDecimals`).
     * @param _lastFundingPerDay The funding rate calculated at the last update timestamp.
     * @param _lastPrice The price of the asset during the last balances update (with price feed decimals).
     * @param _lastUpdateTimestamp The timestamp of the last balances update.
     * @param _pendingProtocolFee The pending protocol fee accumulator.
     * @param _pendingActions The pending actions by the user (1 per user max).
     * The value stored is an index into the `pendingActionsQueue` deque, shifted by one. A value of 0 means no
     * pending action. Since the deque uses uint128 indices, the highest index will not overflow when adding one.
     * @param _pendingActionsQueue The queue of pending actions.
     * @param _balanceVault The balance of deposits (with `_assetDecimals`).
     * @param _pendingBalanceVault The unreflected balance change due to pending vault actions (with `_assetDecimals`).
     * @param _EMA The exponential moving average of the funding (0.0003 at initialization).
     * @param _balanceLong The balance of long positions (with `_assetDecimals`).
     * @param _totalExpo The total exposure of the long positions (with `_assetDecimals`).
     * @param _liqMultiplierAccumulator The accumulator used to calculate the liquidation multiplier.
     * This is the sum, for all ticks, of the total expo of positions inside the tick, multiplied by the
     * unadjusted price of the tick which is `_tickData[tickHash].liquidationPenalty` below
     * The unadjusted price is obtained with `TickMath.getPriceAtTick.
     * @param _tickVersion The liquidation tick version.
     * @param _longPositions The long positions per versioned tick (liquidation price).
     * @param _tickData Accumulated data for a given tick and tick version.
     * @param _highestPopulatedTick The highest tick with a position.
     * @param _totalLongPositions Cache of the total long positions count.
     * @param _tickBitmap The bitmap used to quickly find populated ticks.
     * @param _protocolFallbackAddr The address of the fallback contract.
     * @param _nonce The user EIP712 nonce.
     */
    struct Storage {
        // immutable
        int24 _tickSpacing;
        IERC20Metadata _asset;
        uint8 _assetDecimals;
        uint8 _priceFeedDecimals;
        IUsdn _usdn;
        IERC20Metadata _sdex;
        uint256 _usdnMinDivisor;
        // parameters
        IBaseOracleMiddleware _oracleMiddleware;
        IBaseLiquidationRewardsManager _liquidationRewardsManager;
        IBaseRebalancer _rebalancer;
        mapping(address => bool) _isRebalancer;
        uint256 _minLeverage;
        uint256 _maxLeverage;
        uint128 _lowLatencyValidatorDeadline;
        uint128 _onChainValidatorDeadline;
        uint256 _safetyMarginBps;
        uint16 _liquidationIteration;
        uint16 _protocolFeeBps;
        uint16 _rebalancerBonusBps;
        uint24 _liquidationPenalty;
        uint128 _EMAPeriod;
        uint256 _fundingSF;
        uint256 _feeThreshold;
        int256 _openExpoImbalanceLimitBps;
        int256 _withdrawalExpoImbalanceLimitBps;
        int256 _depositExpoImbalanceLimitBps;
        int256 _closeExpoImbalanceLimitBps;
        int256 _rebalancerCloseExpoImbalanceLimitBps;
        int256 _longImbalanceTargetBps;
        uint16 _positionFeeBps;
        uint16 _vaultFeeBps;
        uint16 _sdexRewardsRatioBps;
        uint32 _sdexBurnOnDepositRatio;
        address _feeCollector;
        uint64 _securityDepositValue;
        uint128 _targetUsdnPrice;
        uint128 _usdnRebaseThreshold;
        uint256 _minLongPosition;
        // state
        int256 _lastFundingPerDay;
        uint128 _lastPrice;
        uint128 _lastUpdateTimestamp;
        uint256 _pendingProtocolFee;
        // pending actions queue
        mapping(address => uint256) _pendingActions;
        DoubleEndedQueue.Deque _pendingActionsQueue;
        // vault
        uint256 _balanceVault;
        int256 _pendingBalanceVault;
        // long positions
        int256 _EMA;
        uint256 _balanceLong;
        uint256 _totalExpo;
        HugeUint.Uint512 _liqMultiplierAccumulator;
        mapping(int24 => uint256) _tickVersion;
        mapping(bytes32 => Position[]) _longPositions;
        mapping(bytes32 => TickData) _tickData;
        int24 _highestPopulatedTick;
        uint256 _totalLongPositions;
        LibBitmap.Bitmap _tickBitmap;
        // fallback
        address _protocolFallbackAddr;
        // EIP712
        mapping(address => uint256) _nonce;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;

/**
 * @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;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC-20 standard.
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[ERC-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC-20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * ==== Security Considerations
 *
 * There are two important considerations concerning the use of `permit`. The first is that a valid permit signature
 * expresses an allowance, and it should not be assumed to convey additional meaning. In particular, it should not be
 * considered as an intention to spend the allowance in any specific way. The second is that because permits have
 * built-in replay protection and can be submitted by anyone, they can be frontrun. A protocol that uses permits should
 * take this into consideration and allow a `permit` call to fail. Combining these two aspects, a pattern that may be
 * generally recommended is:
 *
 * ```solidity
 * function doThingWithPermit(..., uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public {
 *     try token.permit(msg.sender, address(this), value, deadline, v, r, s) {} catch {}
 *     doThing(..., value);
 * }
 *
 * function doThing(..., uint256 value) public {
 *     token.safeTransferFrom(msg.sender, address(this), value);
 *     ...
 * }
 * ```
 *
 * Observe that: 1) `msg.sender` is used as the owner, leaving no ambiguity as to the signer intent, and 2) the use of
 * `try/catch` allows the permit to fail and makes the code tolerant to frontrunning. (See also
 * {SafeERC20-safeTransferFrom}).
 *
 * Additionally, note that smart contract wallets (such as Argent or Safe) are not able to produce permit signatures, so
 * contracts should have entry points that don't rely on permit.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     *
     * CAUTION: See Security Considerations above.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/**
 * @title ILiquidationRewardsManagerErrorsEventsTypes
 * @notice Interface defining events, structs, and errors for the {LiquidationRewardsManager}.
 */
interface ILiquidationRewardsManagerErrorsEventsTypes {
    /* -------------------------------------------------------------------------- */
    /*                                   Events                                   */
    /* -------------------------------------------------------------------------- */

    /**
     * @notice The rewards parameters are updated.
     * @param gasUsedPerTick The amount of gas consumed per tick for liquidation.
     * @param otherGasUsed The gas consumed for all additional computations.
     * @param rebaseGasUsed The gas consumed for optional USDN rebase operation.
     * @param rebalancerGasUsed The gas consumed for the optional rebalancer trigger.
     * @param baseFeeOffset An offset added to the block's base gas fee.
     * @param gasMultiplierBps The multiplier for the gas usage (in BPS).
     * @param positionBonusMultiplierBps The multiplier for position size bonus (in BPS).
     * @param fixedReward A fixed reward amount (in native currency, converted to wstETH).
     * @param maxReward The maximum allowable reward amount (in native currency, converted to wstETH).
     */
    event RewardsParametersUpdated(
        uint32 gasUsedPerTick,
        uint32 otherGasUsed,
        uint32 rebaseGasUsed,
        uint32 rebalancerGasUsed,
        uint64 baseFeeOffset,
        uint16 gasMultiplierBps,
        uint16 positionBonusMultiplierBps,
        uint128 fixedReward,
        uint128 maxReward
    );

    /* -------------------------------------------------------------------------- */
    /*                                    Structs                                 */
    /* -------------------------------------------------------------------------- */

    /**
     * @notice The parameters used for calculating rewards.
     * @param gasUsedPerTick The gas consumed per tick for liquidation.
     * @param otherGasUsed The gas consumed for all additional computations.
     * @param rebaseGasUsed The gas consumed for optional USDN rebase operation.
     * @param rebalancerGasUsed The gas consumed for the optional rebalancer trigger.
     * @param baseFeeOffset An offset added to the block's base gas fee.
     * @param gasMultiplierBps The multiplier for the gas usage (in BPS).
     * @param positionBonusMultiplierBps The multiplier for position size bonus (in BPS).
     * @param fixedReward A fixed reward amount (in native currency, converted to wstETH).
     * @param maxReward The maximum allowable reward amount (in native currency, converted to wstETH).
     */
    struct RewardsParameters {
        uint32 gasUsedPerTick;
        uint32 otherGasUsed;
        uint32 rebaseGasUsed;
        uint32 rebalancerGasUsed;
        uint64 baseFeeOffset;
        uint16 gasMultiplierBps;
        uint16 positionBonusMultiplierBps;
        uint128 fixedReward;
        uint128 maxReward;
    }

    /* -------------------------------------------------------------------------- */
    /*                                   Errors                                   */
    /* -------------------------------------------------------------------------- */

    /**
     * @notice The `gasUsedPerTick` parameter exceeds the allowable limit.
     * @param value The given value.
     */
    error LiquidationRewardsManagerGasUsedPerTickTooHigh(uint256 value);

    /**
     * @notice The `otherGasUsed` parameter exceeds the allowable limit.
     * @param value The given value.
     */
    error LiquidationRewardsManagerOtherGasUsedTooHigh(uint256 value);

    /**
     * @notice The `rebaseGasUsed` parameter exceeds the allowable limit.
     * @param value The given value.
     */
    error LiquidationRewardsManagerRebaseGasUsedTooHigh(uint256 value);

    /**
     * @notice The `rebalancerGasUsed` parameter exceeds the allowable limit.
     * @param value The given value.
     */
    error LiquidationRewardsManagerRebalancerGasUsedTooHigh(uint256 value);

    /**
     * @notice The `maxReward` parameter is below the allowable minimum.
     * @param value The given value.
     */
    error LiquidationRewardsManagerMaxRewardTooLow(uint256 value);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.20;

/**
 * @notice A library for manipulating uint512 quantities.
 * @dev The 512-bit unsigned integers are represented as two uint256 "limbs", a `hi` limb for the most significant bits,
 * and a `lo` limb for the least-significant bits. The resulting uint512 quantity is obtained with `hi * 2^256 + lo`.
 */
library HugeUint {
    /// @notice Indicates that the division failed because the divisor is zero or the result overflows a uint256.
    error HugeUintDivisionFailed();

    /// @notice Indicates that the addition overflowed a uint512.
    error HugeUintAddOverflow();

    /// @notice Indicates that the subtraction underflowed.
    error HugeUintSubUnderflow();

    /// @notice Indicates that the multiplication overflowed a uint512.
    error HugeUintMulOverflow();

    /**
     * @notice A 512-bit integer represented as two 256-bit limbs.
     * @dev The integer value can be reconstructed as `hi * 2^256 + lo`.
     * @param hi The most-significant bits (higher limb) of the integer.
     * @param lo The least-significant bits (lower limb) of the integer.
     */
    struct Uint512 {
        uint256 hi;
        uint256 lo;
    }

    /**
     * @notice Wraps a uint256 into a {Uint512} integer.
     * @param x A uint256 integer.
     * @return The same value as a 512-bit integer.
     */
    function wrap(uint256 x) internal pure returns (Uint512 memory) {
        return Uint512({ hi: 0, lo: x });
    }

    /**
     * @notice Calculates the sum `a + b` of two 512-bit unsigned integers.
     * @dev This function will revert if the result overflows a uint512.
     * @param a The first operand.
     * @param b The second operand.
     * @return res_ The sum of `a` and `b`.
     */
    function add(Uint512 memory a, Uint512 memory b) internal pure returns (Uint512 memory res_) {
        (res_.lo, res_.hi) = _add(a.lo, a.hi, b.lo, b.hi);
        // check for overflow, i.e. if the result is less than b
        if (res_.hi < b.hi || (res_.hi == b.hi && res_.lo < b.lo)) {
            revert HugeUintAddOverflow();
        }
    }

    /**
     * @notice Calculates the difference `a - b` of two 512-bit unsigned integers.
     * @dev This function will revert if `b > a`.
     * @param a The first operand.
     * @param b The second operand.
     * @return res_ The difference `a - b`.
     */
    function sub(Uint512 memory a, Uint512 memory b) internal pure returns (Uint512 memory res_) {
        // check for underflow
        if (a.hi < b.hi || (a.hi == b.hi && a.lo < b.lo)) {
            revert HugeUintSubUnderflow();
        }
        (res_.lo, res_.hi) = _sub(a.lo, a.hi, b.lo, b.hi);
    }

    /**
     * @notice Calculates the product `a * b` of two 256-bit unsigned integers using the Chinese remainder theorem.
     * @param a The first operand.
     * @param b The second operand.
     * @return res_ The product `a * b` of the operands as an unsigned 512-bit integer.
     */
    function mul(uint256 a, uint256 b) internal pure returns (Uint512 memory res_) {
        (res_.lo, res_.hi) = _mul256(a, b);
    }

    /**
     * @notice Calculates the product `a * b` of a 512-bit unsigned integer and a 256-bit unsigned integer.
     * @dev This function reverts if the result overflows a uint512.
     * @param a The first operand.
     * @param b The second operand.
     * @return res_ The product `a * b` of the operands as an unsigned 512-bit integer.
     */
    function mul(Uint512 memory a, uint256 b) internal pure returns (Uint512 memory res_) {
        if ((a.hi == 0 && a.lo == 0) || b == 0) {
            return res_;
        }
        (res_.lo, res_.hi) = _mul256(a.lo, b);
        unchecked {
            uint256 p = a.hi * b;
            if (p / b != a.hi) {
                revert HugeUintMulOverflow();
            }
            res_.hi += p;
            if (res_.hi < p) {
                revert HugeUintMulOverflow();
            }
        }
    }

    /**
     * @notice Calculates the division `floor(a / b)` of a 512-bit unsigned integer by an unsigned 256-bit integer.
     * @dev The call will revert if the result doesn't fit inside a uint256 or if the denominator is zero.
     * @param a The numerator as a 512-bit unsigned integer.
     * @param b The denominator as a 256-bit unsigned integer.
     * @return res_ The division `floor(a / b)` of the operands as an unsigned 256-bit integer.
     */
    function div(Uint512 memory a, uint256 b) internal pure returns (uint256 res_) {
        // make sure the output fits inside a uint256, also prevents b == 0
        if (b <= a.hi) {
            revert HugeUintDivisionFailed();
        }
        // if the numerator is smaller than the denominator, the result is zero
        if (a.hi == 0 && a.lo < b) {
            return 0;
        }
        // the first operand fits in 256 bits, we can use the Solidity division operator
        if (a.hi == 0) {
            unchecked {
                return a.lo / b;
            }
        }
        res_ = _div256(a.lo, a.hi, b);
    }

    /**
     * @notice Computes the division `floor(a/b)` of two 512-bit integers, knowing the result fits inside a uint256.
     * @dev Credits chfast (Apache 2.0 License): <https://github.com/chfast/intx>.
     * This function will revert if the second operand is zero or if the result doesn't fit inside a uint256.
     * @param a The numerator as a 512-bit integer.
     * @param b The denominator as a 512-bit integer.
     * @return res_ The quotient floor(a/b).
     */
    function div(Uint512 memory a, Uint512 memory b) internal pure returns (uint256 res_) {
        res_ = _div(a.lo, a.hi, b.lo, b.hi);
    }

    /**
     * @notice Calculates the sum `a + b` of two 512-bit unsigned integers.
     * @dev Credits Remco Bloemen (MIT license): <https://2π.com/17/512-bit-division>.
     * The result is not checked for overflow, the caller must ensure that the result fits inside a uint512.
     * @param a0 The low limb of the first operand.
     * @param a1 The high limb of the first operand.
     * @param b0 The low limb of the second operand.
     * @param b1 The high limb of the second operand.
     * @return lo_ The low limb of the result of `a + b`.
     * @return hi_ The high limb of the result of `a + b`.
     */
    function _add(uint256 a0, uint256 a1, uint256 b0, uint256 b1) internal pure returns (uint256 lo_, uint256 hi_) {
        assembly {
            lo_ := add(a0, b0)
            hi_ := add(add(a1, b1), lt(lo_, a0))
        }
    }

    /**
     * @notice Calculates the difference `a - b` of two 512-bit unsigned integers.
     * @dev Credits Remco Bloemen (MIT license): <https://2π.com/17/512-bit-division>.
     * The result is not checked for underflow, the caller must ensure that the second operand is less than or equal to
     * the first operand.
     * @param a0 The low limb of the first operand.
     * @param a1 The high limb of the first operand.
     * @param b0 The low limb of the second operand.
     * @param b1 The high limb of the second operand.
     * @return lo_ The low limb of the result of `a - b`.
     * @return hi_ The high limb of the result of `a - b`.
     */
    function _sub(uint256 a0, uint256 a1, uint256 b0, uint256 b1) internal pure returns (uint256 lo_, uint256 hi_) {
        assembly {
            lo_ := sub(a0, b0)
            hi_ := sub(sub(a1, b1), lt(a0, b0))
        }
    }

    /**
     * @notice Calculates the product `a * b` of two 256-bit unsigned integers using the Chinese remainder theorem.
     * @dev Credits Remco Bloemen (MIT license): <https://2π.com/17/chinese-remainder-theorem>
     * and Solady (MIT license): <https://github.com/Vectorized/solady>.
     * @param a The first operand.
     * @param b The second operand.
     * @return lo_ The low limb of the result of `a * b`.
     * @return hi_ The high limb of the result of `a * b`.
     */
    function _mul256(uint256 a, uint256 b) internal pure returns (uint256 lo_, uint256 hi_) {
        assembly {
            lo_ := mul(a, b)
            let mm := mulmod(a, b, not(0)) // (a * b) % uint256.max
            hi_ := sub(mm, add(lo_, lt(mm, lo_)))
        }
    }

    /**
     * @notice Calculates the division `floor(a / b)` of a 512-bit unsigned integer by an unsigned 256-bit integer.
     * @dev Credits Solady (MIT license): <https://github.com/Vectorized/solady>.
     * The caller must ensure that the result fits inside a uint256 and that the division is non-zero.
     * For performance reasons, the caller should ensure that the numerator high limb (hi) is non-zero.
     * @param a0 The low limb of the numerator.
     * @param a1 The high limb of the  numerator.
     * @param b The denominator as a 256-bit unsigned integer.
     * @return res_ The division `floor(a / b)` of the operands as an unsigned 256-bit integer.
     */
    function _div256(uint256 a0, uint256 a1, uint256 b) internal pure returns (uint256 res_) {
        uint256 r;
        assembly {
            // to make the division exact, we find out the remainder of the division of a by b
            r := mulmod(a1, not(0), b) // (a1 * uint256.max) % b
            r := addmod(r, a1, b) // (r + a1) % b
            r := addmod(r, a0, b) // (r + a0) % b

            // `t` is the least significant bit of `b`
            // always greater or equal to 1
            let t := and(b, sub(0, b))
            // divide `b` by `t`, which is a power of two
            b := div(b, t)
            // invert `b mod 2**256`
            // now that `b` is an odd number, it has an inverse
            // modulo `2**256` such that `b * inv = 1 mod 2**256`
            // compute the inverse by starting with a seed that is
            // correct for four bits. That is, `b * inv = 1 mod 2**4`
            let inv := xor(2, mul(3, b))
            // 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 := mul(inv, sub(2, mul(b, inv))) // inverse mod 2**8
            inv := mul(inv, sub(2, mul(b, inv))) // inverse mod 2**16
            inv := mul(inv, sub(2, mul(b, inv))) // inverse mod 2**32
            inv := mul(inv, sub(2, mul(b, inv))) // inverse mod 2**64
            inv := mul(inv, sub(2, mul(b, inv))) // inverse mod 2**128
            res_ :=
                mul(
                    // divide [a1 a0] by the factors of two
                    // shift in bits from `a1` into `a0`
                    // for this we need to flip `t` such that it is `2**256 / t`
                    or(mul(sub(a1, gt(r, a0)), add(div(sub(0, t), t), 1)), div(sub(a0, r), t)),
                    // inverse mod 2**256
                    mul(inv, sub(2, mul(b, inv)))
                )
        }
    }

    /**
     * @notice Computes the division of a 768-bit integer `a` by a 512-bit integer `b`, knowing the reciprocal of `b`.
     * @dev Credits chfast (Apache 2.0 License): <https://github.com/chfast/intx>.
     * @param a0 The LSB of the numerator.
     * @param a1 The middle limb of the numerator.
     * @param a2 The MSB of the numerator.
     * @param b0 The low limb of the divisor.
     * @param b1 The high limb of the divisor.
     * @param v The reciprocal `v` as defined in `_reciprocal_2`.
     * @return The quotient floor(a/b).
     */
    function _div_2(uint256 a0, uint256 a1, uint256 a2, uint256 b0, uint256 b1, uint256 v)
        internal
        pure
        returns (uint256)
    {
        (uint256 q0, uint256 q1) = _mul256(v, a2);
        (q0, q1) = _add(q0, q1, a1, a2);
        (uint256 t0, uint256 t1) = _mul256(b0, q1);
        uint256 r1;
        assembly {
            r1 := sub(a1, mul(q1, b1))
        }
        uint256 r0;
        (r0, r1) = _sub(a0, r1, t0, t1);
        (r0, r1) = _sub(r0, r1, b0, b1);
        assembly {
            q1 := add(q1, 1)
        }
        if (r1 >= q0) {
            assembly {
                q1 := sub(q1, 1)
            }
            (r0, r1) = _add(r0, r1, b0, b1);
        }
        if (r1 > b1 || (r1 == b1 && r0 >= b0)) {
            assembly {
                q1 := add(q1, 1)
            }
            // we don't care about the remainder
            // (r0, r1) = _sub(r0, r1, b0, b1);
        }
        return q1;
    }

    /**
     * @notice Computes the division floor(a/b) of two 512-bit integers, knowing the result fits inside a uint256.
     * @dev Credits chfast (Apache 2.0 License): <https://github.com/chfast/intx>.
     * @param a0 LSB of the numerator.
     * @param a1 MSB of the numerator.
     * @param b0 LSB of the divisor.
     * @param b1 MSB of the divisor.
     * @return res_ The quotient floor(a/b).
     */
    function _div(uint256 a0, uint256 a1, uint256 b0, uint256 b1) internal pure returns (uint256 res_) {
        if (b1 == 0) {
            // prevent division by zero
            if (b0 == 0) {
                revert HugeUintDivisionFailed();
            }
            // if both operands fit inside a uint256, we can use the Solidity division operator
            if (a1 == 0) {
                unchecked {
                    return a0 / b0;
                }
            }
            // if the result fits inside a uint256, we can use the `div(Uint512,uint256)` function
            if (b0 > a1) {
                return _div256(a0, a1, b0);
            }
            revert HugeUintDivisionFailed();
        }

        // if the numerator is smaller than the denominator, the result is zero
        if (a1 < b1 || (a1 == b1 && a0 < b0)) {
            return 0;
        }

        // division algo
        uint256 lsh = _clz(b1);
        if (lsh == 0) {
            // numerator is equal or larger than the denominator, and the denominator is at least 0b1000...
            // the result is necessarily 1
            return 1;
        }

        uint256 bn_lo;
        uint256 bn_hi;
        uint256 an_lo;
        uint256 an_hi;
        uint256 an_ex;
        assembly {
            let rsh := sub(256, lsh)
            bn_lo := shl(lsh, b0)
            bn_hi := or(shl(lsh, b1), shr(rsh, b0))
            an_lo := shl(lsh, a0)
            an_hi := or(shl(lsh, a1), shr(rsh, a0))
            an_ex := shr(rsh, a1)
        }
        uint256 v = _reciprocal_2(bn_lo, bn_hi);
        res_ = _div_2(an_lo, an_hi, an_ex, bn_lo, bn_hi, v);
    }

    /**
     * @notice Computes the reciprocal `v = floor((2^512-1) / d) - 2^256`.
     * @dev The input must be normalized (d >= 2^255).
     * @param d The input value.
     * @return v_ The reciprocal of d.
     */
    function _reciprocal(uint256 d) internal pure returns (uint256 v_) {
        if (d & 0x8000000000000000000000000000000000000000000000000000000000000000 == 0) {
            revert HugeUintDivisionFailed();
        }
        v_ = _div256(type(uint256).max, type(uint256).max - d, d);
    }

    /**
     * @notice Computes the reciprocal `v = floor((2^768-1) / d) - 2^256`, where d is a uint512 integer.
     * @dev Credits chfast (Apache 2.0 License): <https://github.com/chfast/intx>.
     * @param d0 LSB of the input.
     * @param d1 MSB of the input.
     * @return v_ The reciprocal of d.
     */
    function _reciprocal_2(uint256 d0, uint256 d1) internal pure returns (uint256 v_) {
        v_ = _reciprocal(d1);
        uint256 p;
        assembly {
            p := mul(d1, v_)
            p := add(p, d0)
            if lt(p, d0) {
                // carry out
                v_ := sub(v_, 1)
                if iszero(lt(p, d1)) {
                    v_ := sub(v_, 1)
                    p := sub(p, d1)
                }
                p := sub(p, d1)
            }
        }
        (uint256 t0, uint256 t1) = _mul256(v_, d0);
        assembly {
            p := add(p, t1)
            if lt(p, t1) {
                // carry out
                v_ := sub(v_, 1)
                if and(iszero(lt(p, d1)), or(gt(p, d1), iszero(lt(t0, d0)))) {
                    // if (<p, t0> >= <d1, d0>)
                    v_ := sub(v_, 1)
                }
            }
        }
    }

    /**
     * @notice Counts the number of consecutive zero bits, starting from the left.
     * @dev Credits Solady (MIT license): <https://github.com/Vectorized/solady>.
     * @param x An unsigned integer.
     * @return n_ The number of zeroes starting from the most significant bit.
     */
    function _clz(uint256 x) internal pure returns (uint256 n_) {
        if (x == 0) {
            return 256;
        }
        assembly {
            n_ := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            n_ := or(n_, shl(6, lt(0xffffffffffffffff, shr(n_, x))))
            n_ := or(n_, shl(5, lt(0xffffffff, shr(n_, x))))
            n_ := or(n_, shl(4, lt(0xffff, shr(n_, x))))
            n_ := or(n_, shl(3, lt(0xff, shr(n_, x))))
            n_ :=
                add(
                    xor(
                        n_,
                        byte(
                            and(0x1f, shr(shr(n_, x), 0x8421084210842108cc6318c6db6d54be)),
                            0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff
                        )
                    ),
                    iszero(x)
                )
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

import {LibBit} from "./LibBit.sol";

/// @notice Library for storage of packed unsigned booleans.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibBitmap.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibBitmap.sol)
/// @author Modified from Solidity-Bits (https://github.com/estarriolvetch/solidity-bits/blob/main/contracts/BitMaps.sol)
library LibBitmap {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The constant returned when a bitmap scan does not find a result.
    uint256 internal constant NOT_FOUND = type(uint256).max;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                          STRUCTS                           */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev A bitmap in storage.
    struct Bitmap {
        mapping(uint256 => uint256) map;
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         OPERATIONS                         */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns the boolean value of the bit at `index` in `bitmap`.
    function get(Bitmap storage bitmap, uint256 index) internal view returns (bool isSet) {
        // It is better to set `isSet` to either 0 or 1, than zero vs non-zero.
        // Both cost the same amount of gas, but the former allows the returned value
        // to be reused without cleaning the upper bits.
        uint256 b = (bitmap.map[index >> 8] >> (index & 0xff)) & 1;
        /// @solidity memory-safe-assembly
        assembly {
            isSet := b
        }
    }

    /// @dev Updates the bit at `index` in `bitmap` to true.
    function set(Bitmap storage bitmap, uint256 index) internal {
        bitmap.map[index >> 8] |= (1 << (index & 0xff));
    }

    /// @dev Updates the bit at `index` in `bitmap` to false.
    function unset(Bitmap storage bitmap, uint256 index) internal {
        bitmap.map[index >> 8] &= ~(1 << (index & 0xff));
    }

    /// @dev Flips the bit at `index` in `bitmap`.
    /// Returns the boolean result of the flipped bit.
    function toggle(Bitmap storage bitmap, uint256 index) internal returns (bool newIsSet) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, index))
            let storageSlot := keccak256(0x00, 0x40)
            let shift := and(index, 0xff)
            let storageValue := xor(sload(storageSlot), shl(shift, 1))
            // It makes sense to return the `newIsSet`,
            // as it allow us to skip an additional warm `sload`,
            // and it costs minimal gas (about 15),
            // which may be optimized away if the returned value is unused.
            newIsSet := and(1, shr(shift, storageValue))
            sstore(storageSlot, storageValue)
        }
    }

    /// @dev Updates the bit at `index` in `bitmap` to `shouldSet`.
    function setTo(Bitmap storage bitmap, uint256 index, bool shouldSet) internal {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, index))
            let storageSlot := keccak256(0x00, 0x40)
            let storageValue := sload(storageSlot)
            let shift := and(index, 0xff)
            sstore(
                storageSlot,
                // Unsets the bit at `shift` via `and`, then sets its new value via `or`.
                or(and(storageValue, not(shl(shift, 1))), shl(shift, iszero(iszero(shouldSet))))
            )
        }
    }

    /// @dev Consecutively sets `amount` of bits starting from the bit at `start`.
    function setBatch(Bitmap storage bitmap, uint256 start, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            let max := not(0)
            let shift := and(start, 0xff)
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, start))
            if iszero(lt(add(shift, amount), 257)) {
                let storageSlot := keccak256(0x00, 0x40)
                sstore(storageSlot, or(sload(storageSlot), shl(shift, max)))
                let bucket := add(mload(0x00), 1)
                let bucketEnd := add(mload(0x00), shr(8, add(amount, shift)))
                amount := and(add(amount, shift), 0xff)
                shift := 0
                for {} iszero(eq(bucket, bucketEnd)) { bucket := add(bucket, 1) } {
                    mstore(0x00, bucket)
                    sstore(keccak256(0x00, 0x40), max)
                }
                mstore(0x00, bucket)
            }
            let storageSlot := keccak256(0x00, 0x40)
            sstore(storageSlot, or(sload(storageSlot), shl(shift, shr(sub(256, amount), max))))
        }
    }

    /// @dev Consecutively unsets `amount` of bits starting from the bit at `start`.
    function unsetBatch(Bitmap storage bitmap, uint256 start, uint256 amount) internal {
        /// @solidity memory-safe-assembly
        assembly {
            let shift := and(start, 0xff)
            mstore(0x20, bitmap.slot)
            mstore(0x00, shr(8, start))
            if iszero(lt(add(shift, amount), 257)) {
                let storageSlot := keccak256(0x00, 0x40)
                sstore(storageSlot, and(sload(storageSlot), not(shl(shift, not(0)))))
                let bucket := add(mload(0x00), 1)
                let bucketEnd := add(mload(0x00), shr(8, add(amount, shift)))
                amount := and(add(amount, shift), 0xff)
                shift := 0
                for {} iszero(eq(bucket, bucketEnd)) { bucket := add(bucket, 1) } {
                    mstore(0x00, bucket)
                    sstore(keccak256(0x00, 0x40), 0)
                }
                mstore(0x00, bucket)
            }
            let storageSlot := keccak256(0x00, 0x40)
            sstore(
                storageSlot, and(sload(storageSlot), not(shl(shift, shr(sub(256, amount), not(0)))))
            )
        }
    }

    /// @dev Returns number of set bits within a range by
    /// scanning `amount` of bits starting from the bit at `start`.
    function popCount(Bitmap storage bitmap, uint256 start, uint256 amount)
        internal
        view
        returns (uint256 count)
    {
        unchecked {
            uint256 bucket = start >> 8;
            uint256 shift = start & 0xff;
            if (!(amount + shift < 257)) {
                count = LibBit.popCount(bitmap.map[bucket] >> shift);
                uint256 bucketEnd = bucket + ((amount + shift) >> 8);
                amount = (amount + shift) & 0xff;
                shift = 0;
                for (++bucket; bucket != bucketEnd; ++bucket) {
                    count += LibBit.popCount(bitmap.map[bucket]);
                }
            }
            count += LibBit.popCount((bitmap.map[bucket] >> shift) << (256 - amount));
        }
    }

    /// @dev Returns the index of the most significant set bit in `[0..upTo]`.
    /// If no set bit is found, returns `NOT_FOUND`.
    function findLastSet(Bitmap storage bitmap, uint256 upTo)
        internal
        view
        returns (uint256 setBitIndex)
    {
        setBitIndex = NOT_FOUND;
        uint256 bucket = upTo >> 8;
        uint256 bits;
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, bucket)
            mstore(0x20, bitmap.slot)
            let offset := and(0xff, not(upTo)) // `256 - (255 & upTo) - 1`.
            bits := shr(offset, shl(offset, sload(keccak256(0x00, 0x40))))
            if iszero(or(bits, iszero(bucket))) {
                for {} 1 {} {
                    bucket := add(bucket, setBitIndex) // `sub(bucket, 1)`.
                    mstore(0x00, bucket)
                    bits := sload(keccak256(0x00, 0x40))
                    if or(bits, iszero(bucket)) { break }
                }
            }
        }
        if (bits != 0) {
            setBitIndex = (bucket << 8) | LibBit.fls(bits);
            /// @solidity memory-safe-assembly
            assembly {
                setBitIndex := or(setBitIndex, sub(0, gt(setBitIndex, upTo)))
            }
        }
    }

    /// @dev Returns the index of the least significant unset bit in `[begin..upTo]`.
    /// If no unset bit is found, returns `NOT_FOUND`.
    function findFirstUnset(Bitmap storage bitmap, uint256 begin, uint256 upTo)
        internal
        view
        returns (uint256 unsetBitIndex)
    {
        unsetBitIndex = NOT_FOUND;
        uint256 bucket = begin >> 8;
        uint256 negBits;
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, bucket)
            mstore(0x20, bitmap.slot)
            let offset := and(0xff, begin)
            negBits := shl(offset, shr(offset, not(sload(keccak256(0x00, 0x40)))))
            if iszero(negBits) {
                let lastBucket := shr(8, upTo)
                for {} 1 {} {
                    bucket := add(bucket, 1)
                    mstore(0x00, bucket)
                    negBits := not(sload(keccak256(0x00, 0x40)))
                    if or(negBits, gt(bucket, lastBucket)) { break }
                }
                if gt(bucket, lastBucket) {
                    negBits := shl(and(0xff, not(upTo)), shr(and(0xff, not(upTo)), negBits))
                }
            }
        }
        if (negBits != 0) {
            uint256 r = (bucket << 8) | LibBit.ffs(negBits);
            /// @solidity memory-safe-assembly
            assembly {
                unsetBitIndex := or(r, sub(0, or(gt(r, upTo), lt(r, begin))))
            }
        }
    }
}

// SPDX-License-Identifier: MIT
// based on the OpenZeppelin implementation
pragma solidity ^0.8.20;

import { IUsdnProtocolTypes as Types } from "../interfaces/UsdnProtocol/IUsdnProtocolTypes.sol";

/**
 * @notice A sequence of items with the ability to efficiently push and pop items (i.e. insert and remove) on both ends
 * of the sequence (called front and back).
 * @dev Storage use is optimized, and all operations are O(1) constant time.
 *
 * The struct is called `Deque` and holds {IUsdnProtocolTypes.PendingAction}'s. This data structure can only be used in
 * storage, and not in memory.
 */
library DoubleEndedQueue {
    /// @dev An operation (e.g. {front}) couldn't be completed due to the queue being empty.
    error QueueEmpty();

    /// @dev A push operation couldn't be completed due to the queue being full.
    error QueueFull();

    /// @dev An operation (e.g. {atRaw}) couldn't be completed due to an index being out of bounds.
    error QueueOutOfBounds();

    /**
     * @dev Indices are 128 bits so begin and end are packed in a single storage slot for efficient access.
     *
     * Struct members have an underscore prefix indicating that they are "private" and should not be read or written to
     * directly. Use the functions provided below instead. Modifying the struct manually may violate assumptions and
     * lead to unexpected behavior.
     *
     * The first item is at `data[begin]` and the last item is at `data[end - 1]`. This range can wrap around.
     * @param _begin The index of the first item in the queue.
     * @param _end The index of the item after the last item in the queue.
     * @param _data The items in the queue.
     */
    struct Deque {
        uint128 _begin;
        uint128 _end;
        mapping(uint128 index => Types.PendingAction) _data;
    }

    /**
     * @dev Inserts an item at the end of the queue.
     * Reverts with {QueueFull} if the queue is full.
     * @param deque The queue.
     * @param value The item to insert.
     * @return backIndex_ The raw index of the inserted item.
     */
    function pushBack(Deque storage deque, Types.PendingAction memory value) external returns (uint128 backIndex_) {
        unchecked {
            backIndex_ = deque._end;
            if (backIndex_ + 1 == deque._begin) {
                revert QueueFull();
            }
            deque._data[backIndex_] = value;
            deque._end = backIndex_ + 1;
        }
    }

    /**
     * @dev Removes the item at the end of the queue and returns it.
     * Reverts with {QueueEmpty} if the queue is empty.
     * @param deque The queue.
     * @return value_ The removed item.
     */
    function popBack(Deque storage deque) public returns (Types.PendingAction memory value_) {
        unchecked {
            uint128 backIndex = deque._end;
            if (backIndex == deque._begin) {
                revert QueueEmpty();
            }
            --backIndex;
            value_ = deque._data[backIndex];
            delete deque._data[backIndex];
            deque._end = backIndex;
        }
    }

    /**
     * @dev Inserts an item at the beginning of the queue.
     * Reverts with {QueueFull} if the queue is full.
     * @param deque The queue.
     * @param value The item to insert.
     * @return frontIndex_ The raw index of the inserted item.
     */
    function pushFront(Deque storage deque, Types.PendingAction memory value) external returns (uint128 frontIndex_) {
        unchecked {
            frontIndex_ = deque._begin - 1;
            if (frontIndex_ == deque._end) {
                revert QueueFull();
            }
            deque._data[frontIndex_] = value;
            deque._begin = frontIndex_;
        }
    }

    /**
     * @dev Removes the item at the beginning of the queue and returns it.
     * Reverts with {QueueEmpty} if the queue is empty.
     * @param deque The queue.
     * @return value_ The removed item.
     */
    function popFront(Deque storage deque) public returns (Types.PendingAction memory value_) {
        unchecked {
            uint128 frontIndex = deque._begin;
            if (frontIndex == deque._end) {
                revert QueueEmpty();
            }
            value_ = deque._data[frontIndex];
            delete deque._data[frontIndex];
            deque._begin = frontIndex + 1;
        }
    }

    /**
     * @dev Returns the item at the beginning of the queue.
     * Reverts with {QueueEmpty} if the queue is empty.
     * @param deque The queue.
     * @return value_ The item at the front of the queue.
     * @return rawIndex_ The raw index of the returned item.
     */
    function front(Deque storage deque) external view returns (Types.PendingAction memory value_, uint128 rawIndex_) {
        if (empty(deque)) {
            revert QueueEmpty();
        }
        rawIndex_ = deque._begin;
        value_ = deque._data[rawIndex_];
    }

    /**
     * @dev Returns the item at the end of the queue.
     * Reverts with {QueueEmpty} if the queue is empty.
     * @param deque The queue.
     * @return value_ The item at the back of the queue.
     * @return rawIndex_ The raw index of the returned item.
     */
    function back(Deque storage deque) external view returns (Types.PendingAction memory value_, uint128 rawIndex_) {
        if (empty(deque)) {
            revert QueueEmpty();
        }
        unchecked {
            rawIndex_ = deque._end - 1;
            value_ = deque._data[rawIndex_];
        }
    }

    /**
     * @dev Returns the item at a position in the queue given by `index`, with the first item at 0 and the last item at
     * `length(deque) - 1`.
     * Reverts with {QueueOutOfBounds} if the index is out of bounds.
     * @param deque The queue.
     * @param index The index of the item to return.
     * @return value_ The item at the given index.
     * @return rawIndex_ The raw index of the item.
     */
    function at(Deque storage deque, uint256 index)
        external
        view
        returns (Types.PendingAction memory value_, uint128 rawIndex_)
    {
        if (index >= length(deque)) {
            revert QueueOutOfBounds();
        }
        // by construction, length is a uint128, so the check above ensures that
        // the index can be safely downcast to a uint128
        unchecked {
            rawIndex_ = deque._begin + uint128(index);
            value_ = deque._data[rawIndex_];
        }
    }

    /**
     * @dev Returns the item at a position in the queue given by `rawIndex`, indexing into the underlying storage array
     * directly.
     * Reverts with {QueueOutOfBounds} if the index is out of bounds.
     * @param deque The queue.
     * @param rawIndex The index of the item to return.
     * @return value_ The item at the given index.
     */
    function atRaw(Deque storage deque, uint128 rawIndex) external view returns (Types.PendingAction memory value_) {
        if (!isValid(deque, rawIndex)) {
            revert QueueOutOfBounds();
        }
        value_ = deque._data[rawIndex];
    }

    /**
     * @dev Deletes the item at a position in the queue given by `rawIndex`, indexing into the underlying storage array
     * directly. If clearing the front or back item, then the bounds are updated. Otherwise, the values are simply set
     * to zero and the queue's begin and end indices are not updated.
     * @param deque The queue.
     * @param rawIndex The index of the item to delete.
     */
    function clearAt(Deque storage deque, uint128 rawIndex) external {
        uint128 backIndex = deque._end;
        unchecked {
            backIndex--;
        }
        if (rawIndex == deque._begin) {
            popFront(deque); // reverts if empty
        } else if (rawIndex == backIndex) {
            popBack(deque); // reverts if empty
        } else {
            // we don't care to revert if this is not a valid index, since we're just clearing it
            delete deque._data[rawIndex];
        }
    }

    /**
     * @dev Checks if the raw index is valid (in bounds).
     * @param deque The queue.
     * @param rawIndex The raw index to check.
     * @return valid_ Whether the raw index is valid.
     */
    function isValid(Deque storage deque, uint128 rawIndex) public view returns (bool valid_) {
        if (deque._begin > deque._end) {
            // here the values are split at the beginning and end of the range, so invalid indices are in the middle
            if (rawIndex < deque._begin && rawIndex >= deque._end) {
                return false;
            }
        } else if (rawIndex < deque._begin || rawIndex >= deque._end) {
            return false;
        }
        valid_ = true;
    }

    /**
     * @dev Returns the number of items in the queue.
     * @param deque The queue.
     * @return length_ The number of items in the queue.
     */
    function length(Deque storage deque) public view returns (uint256 length_) {
        unchecked {
            length_ = uint256(deque._end - deque._begin);
        }
    }

    /**
     * @dev Returns true if the queue is empty.
     * @param deque The queue.
     * @return empty_ True if the queue is empty.
     */
    function empty(Deque storage deque) internal view returns (bool empty_) {
        empty_ = deque._end == deque._begin;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IUsdnProtocolTypes as Types } from "../UsdnProtocol/IUsdnProtocolTypes.sol";
import { PriceInfo } from "./IOracleMiddlewareTypes.sol";

/**
 * @title Base Oracle Middleware interface
 * @notice This interface exposes the only functions used or required by the USDN Protocol.
 * @dev Any current or future implementation of the oracle middleware must be compatible with
 * this interface without any modification.
 */
interface IBaseOracleMiddleware {
    /**
     * @notice Parse and validate `data` and returns the corresponding price data.
     * @dev The data format is specific to the middleware and is simply forwarded from the user transaction's calldata.
     * A fee amounting to exactly {validationCost} (with the same `data` and `action`) must be sent or the transaction
     * will revert.
     * @param actionId A unique identifier for the current action. This identifier can be used to link an `Initiate`
     * call with the corresponding `Validate` call.
     * @param targetTimestamp The target timestamp for validating the price data. For validation actions, this is the
     * timestamp of the initiation.
     * @param action Type of action for which the price is requested. The middleware may use this to alter the
     * validation of the price or the returned price.
     * @param data The data to be used to communicate with oracles, the format varies from middleware to middleware and
     * can be different depending on the action.
     * @return result_ The price and timestamp as {IOracleMiddlewareTypes.PriceInfo}.
     */
    function parseAndValidatePrice(
        bytes32 actionId,
        uint128 targetTimestamp,
        Types.ProtocolAction action,
        bytes calldata data
    ) external payable returns (PriceInfo memory result_);

    /**
     * @notice Gets the required delay (in seconds) between the moment an action is initiated and the timestamp of the
     * price data used to validate that action.
     * @return delay_ The validation delay.
     */
    function getValidationDelay() external view returns (uint256 delay_);

    /**
     * @notice Gets The maximum amount of time (in seconds) after initiation during which a low-latency price oracle can
     * be used for validation.
     * @return delay_ The maximum delay for low-latency validation.
     */
    function getLowLatencyDelay() external view returns (uint16 delay_);

    /**
     * @notice Gets the number of decimals for the price.
     * @return decimals_ The number of decimals.
     */
    function getDecimals() external view returns (uint8 decimals_);

    /**
     * @notice Returns the cost of one price validation for the given action (in native token).
     * @param data Price data for which to get the fee.
     * @param action Type of the action for which the price is requested.
     * @return cost_ The cost of one price validation (in native token).
     */
    function validationCost(bytes calldata data, Types.ProtocolAction action) external view returns (uint256 cost_);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IUsdnProtocolTypes as Types } from "../UsdnProtocol/IUsdnProtocolTypes.sol";
import { IRebalancerTypes } from "./IRebalancerTypes.sol";

interface IBaseRebalancer {
    /**
     * @notice Returns the necessary data for the USDN protocol to update the position.
     * @return pendingAssets_ The amount of assets that are pending inclusion in the protocol.
     * @return maxLeverage_ The maximum leverage of the rebalancer.
     * @return currentPosId_ The ID of the current position (`tick` == `NO_POSITION_TICK` if no position).
     */
    function getCurrentStateData()
        external
        view
        returns (uint128 pendingAssets_, uint256 maxLeverage_, Types.PositionId memory currentPosId_);

    /**
     * @notice Returns the minimum amount of assets a user can deposit in the rebalancer.
     * @return minAssetDeposit_ The minimum amount of assets that can be deposited by a user.
     */
    function getMinAssetDeposit() external view returns (uint256 minAssetDeposit_);

    /**
     * @notice Returns the data regarding the assets deposited by the provided user.
     * @param user The address of the user.
     * @return data_ The data regarding the assets deposited by the provided user.
     */
    function getUserDepositData(address user) external view returns (IRebalancerTypes.UserDeposit memory data_);

    /**
     * @notice Indicates that the previous version of the position was closed and a new one was opened.
     * @dev If `previousPosValue` equals 0, it means the previous version got liquidated.
     * @param newPosId The position ID of the new position.
     * @param previousPosValue The amount of assets left in the previous position.
     */
    function updatePosition(Types.PositionId calldata newPosId, uint128 previousPosValue) external;

    /* -------------------------------------------------------------------------- */
    /*                                    Admin                                   */
    /* -------------------------------------------------------------------------- */

    /**
     * @notice Sets the minimum amount of assets to be deposited by a user.
     * @dev The new minimum amount must be greater than or equal to the minimum long position of the USDN protocol.
     * This function can only be called by the owner or the USDN protocol.
     * @param minAssetDeposit The new minimum amount of assets to be deposited.
     */
    function setMinAssetDeposit(uint256 minAssetDeposit) external;
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { IERC20Metadata } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import { IERC20Permit } from "@openzeppelin/contracts/token/ERC20/extensions/IERC20Permit.sol";

import { IRebaseCallback } from "./IRebaseCallback.sol";
import { IUsdnErrors } from "./IUsdnErrors.sol";
import { IUsdnEvents } from "./IUsdnEvents.sol";

/**
 * @title USDN token interface
 * @notice Implements the ERC-20 token standard as well as the EIP-2612 permit extension. Additional functions related
 * to the specifics of this token are included below.
 */
interface IUsdn is IERC20, IERC20Metadata, IERC20Permit, IUsdnEvents, IUsdnErrors {
    /**
     * @notice Returns the total number of shares in existence.
     * @return shares_ The number of shares.
     */
    function totalShares() external view returns (uint256 shares_);

    /**
     * @notice Returns the number of shares owned by `account`.
     * @param account The account to query.
     * @return shares_ The number of shares.
     */
    function sharesOf(address account) external view returns (uint256 shares_);

    /**
     * @notice Transfers a given amount of shares from the `msg.sender` to `to`.
     * @param to Recipient of the shares.
     * @param value Number of shares to transfer.
     * @return success_ Indicates whether the transfer was successfully executed.
     */
    function transferShares(address to, uint256 value) external returns (bool success_);

    /**
     * @notice Transfers a given amount of shares from the `from` to `to`.
     * @dev There should be sufficient allowance for the spender. Be mindful of the rebase logic. The allowance is in
     * tokens. So, after a rebase, the same amount of shares will be worth a higher amount of tokens. In that case,
     * the allowance of the initial approval will not be enough to transfer the new amount of tokens. This can
     * also happen when your transaction is in the mempool and the rebase happens before your transaction. Also note
     * that the amount of tokens deduced from the allowance is rounded up, so the `convertToTokensRoundUp` function
     * should be used when converting shares into an allowance value.
     * @param from The owner of the shares.
     * @param to Recipient of the shares.
     * @param value Number of shares to transfer.
     * @return success_ Indicates whether the transfer was successfully executed.
     */
    function transferSharesFrom(address from, address to, uint256 value) external returns (bool success_);

    /**
     * @notice Mints new shares, providing a token value.
     * @dev Caller must have the MINTER_ROLE.
     * @param to Account to receive the new shares.
     * @param amount Amount of tokens to mint, is internally converted to the proper shares amounts.
     */
    function mint(address to, uint256 amount) external;

    /**
     * @notice Mints new shares, providing a share value.
     * @dev Caller must have the MINTER_ROLE.
     * @param to Account to receive the new shares.
     * @param amount Amount of shares to mint.
     * @return mintedTokens_ Amount of tokens that were minted (informational).
     */
    function mintShares(address to, uint256 amount) external returns (uint256 mintedTokens_);

    /**
     * @notice Destroys a `value` amount of tokens from the caller, reducing the total supply.
     * @param value Amount of tokens to burn, is internally converted to the proper shares amounts.
     */
    function burn(uint256 value) external;

    /**
     * @notice Destroys a `value` amount of tokens from `account`, deducting from the caller's allowance.
     * @param account Account to burn tokens from.
     * @param value Amount of tokens to burn, is internally converted to the proper shares amounts.
     */
    function burnFrom(address account, uint256 value) external;

    /**
     * @notice Destroys a `value` amount of shares from the caller, reducing the total supply.
     * @param value Amount of shares to burn.
     */
    function burnShares(uint256 value) external;

    /**
     * @notice Destroys a `value` amount of shares from `account`, deducting from the caller's allowance.
     * @dev There should be sufficient allowance for the spender. Be mindful of the rebase logic. The allowance is in
     * tokens. So, after a rebase, the same amount of shares will be worth a higher amount of tokens. In that case,
     * the allowance of the initial approval will not be enough to transfer the new amount of tokens. This can
     * also happen when your transaction is in the mempool and the rebase happens before your transaction. Also note
     * that the amount of tokens deduced from the allowance is rounded up, so the `convertToTokensRoundUp` function
     * should be used when converting shares into an allowance value.
     * @param account Account to burn shares from.
     * @param value Amount of shares to burn.
     */
    function burnSharesFrom(address account, uint256 value) external;

    /**
     * @notice Converts a number of tokens to the corresponding amount of shares.
     * @dev The conversion reverts with `UsdnMaxTokensExceeded` if the corresponding amount of shares overflows.
     * @param amountTokens The amount of tokens to convert to shares.
     * @return shares_ The corresponding amount of shares.
     */
    function convertToShares(uint256 amountTokens) external view returns (uint256 shares_);

    /**
     * @notice Converts a number of shares to the corresponding amount of tokens.
     * @dev The conversion never overflows as we are performing a division. The conversion rounds to the nearest amount
     * of tokens that minimizes the error when converting back to shares.
     * @param amountShares The amount of shares to convert to tokens.
     * @return tokens_ The corresponding amount of tokens.
     */
    function convertToTokens(uint256 amountShares) external view returns (uint256 tokens_);

    /**
     * @notice Converts a number of shares to the corresponding amount of tokens, rounding up.
     * @dev Use this function to determine the amount of a token approval, as we always round up when deducting from
     * a token transfer allowance.
     * @param amountShares The amount of shares to convert to tokens.
     * @return tokens_ The corresponding amount of tokens, rounded up.
     */
    function convertToTokensRoundUp(uint256 amountShares) external view returns (uint256 tokens_);

    /**
     * @notice Returns the current maximum tokens supply, given the current divisor.
     * @dev This function is used to check if a conversion operation would overflow.
     * @return maxTokens_ The maximum number of tokens that can exist.
     */
    function maxTokens() external view returns (uint256 maxTokens_);

    /**
     * @notice Decreases the global divisor, which effectively grows all balances and the total supply.
     * @dev If the provided divisor is larger than or equal to the current divisor value, no rebase will happen
     * If the new divisor is smaller than `MIN_DIVISOR`, the value will be clamped to `MIN_DIVISOR`.
     * Caller must have the `REBASER_ROLE`.
     * @param newDivisor The new divisor, should be strictly smaller than the current one and greater or equal to
     * `MIN_DIVISOR`.
     * @return rebased_ Whether a rebase happened.
     * @return oldDivisor_ The previous value of the divisor.
     * @return callbackResult_ The result of the callback, if a rebase happened and a callback handler is defined.
     */
    function rebase(uint256 newDivisor)
        external
        returns (bool rebased_, uint256 oldDivisor_, bytes memory callbackResult_);

    /**
     * @notice Sets the rebase handler address.
     * @dev Emits a `RebaseHandlerUpdated` event.
     * If set to the zero address, no handler will be called after a rebase.
     * Caller must have the `DEFAULT_ADMIN_ROLE`.
     * @param newHandler The new handler address.
     */
    function setRebaseHandler(IRebaseCallback newHandler) external;

    /* -------------------------------------------------------------------------- */
    /*                             Dev view functions                             */
    /* -------------------------------------------------------------------------- */

    /**
     * @notice Gets the current value of the divisor that converts between tokens and shares.
     * @return divisor_ The current divisor.
     */
    function divisor() external view returns (uint256 divisor_);

    /**
     * @notice Gets the rebase handler address, which is called whenever a rebase happens.
     * @return rebaseHandler_ The rebase handler address.
     */
    function rebaseHandler() external view returns (IRebaseCallback rebaseHandler_);

    /**
     * @notice Gets the minter role signature.
     * @return minter_role_ The role signature.
     */
    function MINTER_ROLE() external pure returns (bytes32 minter_role_);

    /**
     * @notice Gets the rebaser role signature.
     * @return rebaser_role_ The role signature.
     */
    function REBASER_ROLE() external pure returns (bytes32 rebaser_role_);

    /**
     * @notice Gets the maximum value of the divisor, which is also the initial value.
     * @return maxDivisor_ The maximum divisor.
     */
    function MAX_DIVISOR() external pure returns (uint256 maxDivisor_);

    /**
     * @notice Gets the minimum acceptable value of the divisor.
     * @dev The minimum divisor that can be set. This corresponds to a growth of 1B times. Technically, 1e5 would still
     * work without precision errors.
     * @return minDivisor_ The minimum divisor.
     */
    function MIN_DIVISOR() external pure returns (uint256 minDivisor_);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC-20 standard as defined in the ERC.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the value of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the value of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

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

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Library for bit twiddling and boolean operations.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibBit.sol)
/// @author Inspired by (https://graphics.stanford.edu/~seander/bithacks.html)
library LibBit {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  BIT TWIDDLING OPERATIONS                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Find last set.
    /// Returns the index of the most significant bit of `x`,
    /// counting from the least significant bit position.
    /// If `x` is zero, returns 256.
    function fls(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := or(shl(8, iszero(x)), shl(7, lt(0xffffffffffffffffffffffffffffffff, x)))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0x0706060506020504060203020504030106050205030304010505030400000000))
        }
    }

    /// @dev Count leading zeros.
    /// Returns the number of zeros preceding the most significant one bit.
    /// If `x` is zero, returns 256.
    function clz(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            r := add(xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff)), iszero(x))
        }
    }

    /// @dev Find first set.
    /// Returns the index of the least significant bit of `x`,
    /// counting from the least significant bit position.
    /// If `x` is zero, returns 256.
    /// Equivalent to `ctz` (count trailing zeros), which gives
    /// the number of zeros following the least significant one bit.
    function ffs(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // Isolate the least significant bit.
            x := and(x, add(not(x), 1))
            // For the upper 3 bits of the result, use a De Bruijn-like lookup.
            // Credit to adhusson: https://blog.adhusson.com/cheap-find-first-set-evm/
            // forgefmt: disable-next-item
            r := shl(5, shr(252, shl(shl(2, shr(250, mul(x,
                0xb6db6db6ddddddddd34d34d349249249210842108c6318c639ce739cffffffff))),
                0x8040405543005266443200005020610674053026020000107506200176117077)))
            // For the lower 5 bits of the result, use a De Bruijn lookup.
            // forgefmt: disable-next-item
            r := or(r, byte(and(div(0xd76453e0, shr(r, x)), 0x1f),
                0x001f0d1e100c1d070f090b19131c1706010e11080a1a141802121b1503160405))
        }
    }

    /// @dev Returns the number of set bits in `x`.
    function popCount(uint256 x) internal pure returns (uint256 c) {
        /// @solidity memory-safe-assembly
        assembly {
            let max := not(0)
            let isMax := eq(x, max)
            x := sub(x, and(shr(1, x), div(max, 3)))
            x := add(and(x, div(max, 5)), and(shr(2, x), div(max, 5)))
            x := and(add(x, shr(4, x)), div(max, 17))
            c := or(shl(8, isMax), shr(248, mul(x, div(max, 255))))
        }
    }

    /// @dev Returns whether `x` is a power of 2.
    function isPo2(uint256 x) internal pure returns (bool result) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `x && !(x & (x - 1))`.
            result := iszero(add(and(x, sub(x, 1)), iszero(x)))
        }
    }

    /// @dev Returns `x` reversed at the bit level.
    function reverseBits(uint256 x) internal pure returns (uint256 r) {
        uint256 m0 = 0x0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f;
        uint256 m1 = m0 ^ (m0 << 2);
        uint256 m2 = m1 ^ (m1 << 1);
        r = reverseBytes(x);
        r = (m2 & (r >> 1)) | ((m2 & r) << 1);
        r = (m1 & (r >> 2)) | ((m1 & r) << 2);
        r = (m0 & (r >> 4)) | ((m0 & r) << 4);
    }

    /// @dev Returns `x` reversed at the byte level.
    function reverseBytes(uint256 x) internal pure returns (uint256 r) {
        unchecked {
            // Computing masks on-the-fly reduces bytecode size by about 200 bytes.
            uint256 m0 = 0x100000000000000000000000000000001 * (~toUint(x == uint256(0)) >> 192);
            uint256 m1 = m0 ^ (m0 << 32);
            uint256 m2 = m1 ^ (m1 << 16);
            uint256 m3 = m2 ^ (m2 << 8);
            r = (m3 & (x >> 8)) | ((m3 & x) << 8);
            r = (m2 & (r >> 16)) | ((m2 & r) << 16);
            r = (m1 & (r >> 32)) | ((m1 & r) << 32);
            r = (m0 & (r >> 64)) | ((m0 & r) << 64);
            r = (r >> 128) | (r << 128);
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                     BOOLEAN OPERATIONS                     */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    // A Solidity bool on the stack or memory is represented as a 256-bit word.
    // Non-zero values are true, zero is false.
    // A clean bool is either 0 (false) or 1 (true) under the hood.
    // Usually, if not always, the bool result of a regular Solidity expression,
    // or the argument of a public/external function will be a clean bool.
    // You can usually use the raw variants for more performance.
    // If uncertain, test (best with exact compiler settings).
    // Or use the non-raw variants (compiler can sometimes optimize out the double `iszero`s).

    /// @dev Returns `x & y`. Inputs must be clean.
    function rawAnd(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := and(x, y)
        }
    }

    /// @dev Returns `x & y`.
    function and(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := and(iszero(iszero(x)), iszero(iszero(y)))
        }
    }

    /// @dev Returns `x | y`. Inputs must be clean.
    function rawOr(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(x, y)
        }
    }

    /// @dev Returns `x | y`.
    function or(bool x, bool y) internal pure returns (bool z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := or(iszero(iszero(x)), iszero(iszero(y)))
        }
    }

    /// @dev Returns 1 if `b` is true, else 0. Input must be clean.
    function rawToUint(bool b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := b
        }
    }

    /// @dev Returns 1 if `b` is true, else 0.
    function toUint(bool b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := iszero(iszero(b))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/**
 * @notice The price and timestamp returned by the oracle middleware.
 * @param price The validated asset price, potentially adjusted by the middleware.
 * @param neutralPrice The neutral/average price of the asset.
 * @param timestamp The timestamp of the price data.
 */
struct PriceInfo {
    uint256 price;
    uint256 neutralPrice;
    uint256 timestamp;
}

/**
 * @notice The price and timestamp returned by the Chainlink oracle.
 * @param price The asset price formatted by the middleware.
 * @param timestamp When the price was published on chain.
 */
struct ChainlinkPriceInfo {
    int256 price;
    uint256 timestamp;
}

/**
 * @notice Representation of a Pyth price with a uint256 price.
 * @param price The price of the asset.
 * @param conf The confidence interval around the price (in dollars, absolute value).
 * @param publishTime Unix timestamp describing when the price was published.
 */
struct FormattedPythPrice {
    uint256 price;
    uint256 conf;
    uint256 publishTime;
}

/**
 * @notice The price and timestamp returned by the Redstone oracle.
 * @param price The asset price formatted by the middleware.
 * @param timestamp The timestamp of the price data.
 */
struct RedstonePriceInfo {
    uint256 price;
    uint256 timestamp;
}

/**
 * @notice The different confidence interval of a Pyth price.
 * @dev Applied to the neutral price and available as `price`.
 * @param Up Adjusted price at the upper bound of the confidence interval.
 * @param Down Adjusted price at the lower bound of the confidence interval.
 * @param None Neutral price without adjustment.
 */
enum ConfidenceInterval {
    Up,
    Down,
    None
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/**
 * @title Rebalancer Types
 * @notice Defines all custom types used by the Rebalancer contract.
 */
interface IRebalancerTypes {
    /**
     * @notice Represents the deposit data of a user.
     * @dev A value of zero for `initiateTimestamp` indicates that the deposit or withdrawal has been validated.
     * @param initiateTimestamp The timestamp when the deposit or withdrawal was initiated.
     * @param amount The amount of assets deposited by the user.
     * @param entryPositionVersion The version of the position the user entered.
     */
    struct UserDeposit {
        uint40 initiateTimestamp;
        uint88 amount; // maximum 309'485'009 tokens with 18 decimals
        uint128 entryPositionVersion;
    }

    /**
     * @notice Represents data for a specific version of a position.
     * @dev The difference between `amount` here and the amount saved in the USDN protocol is the liquidation bonus.
     * @param amount The amount of assets used as collateral to open the position.
     * @param tick The tick of the position.
     * @param tickVersion The version of the tick.
     * @param index The index of the position in the tick list.
     * @param entryAccMultiplier The accumulated PnL multiplier of all positions up to this one.
     */
    struct PositionData {
        uint128 amount;
        int24 tick;
        uint256 tickVersion;
        uint256 index;
        uint256 entryAccMultiplier;
    }

    /**
     * @notice Defines parameters related to the validation process for rebalancer deposits and withdrawals.
     * @dev If `validationDeadline` has passed, the user must wait until the cooldown duration has elapsed. Then, for
     * deposit actions, the user must retrieve its funds using {IRebalancer.resetDepositAssets}. For withdrawal actions,
     * the user can simply initiate a new withdrawal.
     * @param validationDelay The minimum duration in seconds between an initiate action and the corresponding validate
     * action.
     * @param validationDeadline The maximum duration in seconds between an initiate action and the corresponding
     * validate action.
     * @param actionCooldown The duration in seconds from the initiate action during which the user can't interact with
     * the rebalancer if the `validationDeadline` is exceeded.
     * @param closeDelay The Duration in seconds from the last rebalancer long position opening during which the user
     * can't perform an {IRebalancer.initiateClosePosition}.
     */
    struct TimeLimits {
        uint64 validationDelay;
        uint64 validationDeadline;
        uint64 actionCooldown;
        uint64 closeDelay;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

interface IRebaseCallback {
    /**
     * @notice Called by the USDN token after a rebase has happened.
     * @param oldDivisor The value of the divisor before the rebase.
     * @param newDivisor The value of the divisor after the rebase (necessarily smaller than `oldDivisor`).
     * @return result_ Arbitrary data that will be forwarded to the caller of `rebase`.
     */
    function rebaseCallback(uint256 oldDivisor, uint256 newDivisor) external returns (bytes memory result_);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/**
 * @title Errors for the USDN token contract
 * @notice Defines all custom errors emitted by the USDN token contract.
 */
interface IUsdnErrors {
    /**
     * @dev The amount of tokens exceeds the maximum allowed limit.
     * @param value The invalid token value.
     */
    error UsdnMaxTokensExceeded(uint256 value);

    /**
     * @dev The sender's share balance is insufficient.
     * @param sender The sender's address.
     * @param balance The current share balance of the sender.
     * @param needed The required amount of shares for the transfer.
     */
    error UsdnInsufficientSharesBalance(address sender, uint256 balance, uint256 needed);

    /// @dev The divisor value in storage is invalid (< 1).
    error UsdnInvalidDivisor();
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

import { IRebaseCallback } from "./IRebaseCallback.sol";

/**
 * @title Events for the USDN token contract
 * @notice Defines all custom events emitted by the USDN token contract.
 */
interface IUsdnEvents {
    /**
     * @notice The divisor was updated, emitted during a rebase.
     * @param oldDivisor The divisor value before the rebase.
     * @param newDivisor The new divisor value.
     */
    event Rebase(uint256 oldDivisor, uint256 newDivisor);

    /**
     * @notice The rebase handler address was updated.
     * @dev The rebase handler is a contract that is called when a rebase occurs.
     * @param newHandler The address of the new rebase handler contract.
     */
    event RebaseHandlerUpdated(IRebaseCallback newHandler);
}