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

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// =================== sfrxUsd2OracleImplementation ===================
// ====================================================================
// Frax Finance: https://github.com/FraxFinance

import { StakedFrxUSD2, IERC20 } from "src/contracts/StakedFrxUSD2.sol";
import { ln, mul, div, pow, exp, wrap } from "@prb/math/src/ud60x18/Math.sol";
import { convert } from "@prb/math/src/ud60x18/Conversions.sol";
import { UD60x18 } from "@prb/math/src/ud60x18/ValueType.sol";
import { OracleAllowlist } from "src/contracts/misc/OracleAllowlist.sol";
import { Ownable2Step, Ownable } from "@openzeppelin/contracts/access/Ownable2Step.sol";
import { GapFirst11 } from "src/contracts/misc/StorageGap.sol";

contract SfrxUsd2OracleImplementation is GapFirst11, OracleAllowlist, Ownable2Step {
    /// @notice Slot bumping handled in `GapFirst11` contract

    struct RewardsCycleData {
        uint40 cycleEnd; // Timestamp of the end of the current rewards cycle
        uint40 lastSync; // Timestamp of the last time the rewards cycle was synced
        uint216 rewardCycleAmount; // Amount of rewards to be distributed in the current cycle
    }

    /// @notice Variables needed for price evolution
    uint256 public pricePerShareStored;
    uint256 public pricePerShareIncPerSecond;
    uint256 public lastSync;
    uint256 public constant UNDERLYING_PRECISION = 1e18;
    bool public wasInitialized;

    constructor(address initialOwner) Ownable(initialOwner) {
        wasInitialized = true;
    }

    /// @notice The ```initialize``` function set the ownable2step owner w/n a proxy context
    /// @param owner The owner of the contract
    /// @dev Only callable when not initialized
    function initialize(
        address owner,
        uint256 _newPricePerShareStored,
        uint256 _newPricePerShareIncPerSecond,
        uint256 _newLastSync
    ) external {
        if (wasInitialized) revert AlreadyInit();
        _transferOwnership(owner);
        _setAllowed(owner, true);
        _setAllowed(msg.sender, true);
        wasInitialized = true;
        setAllPricingParams(_newPricePerShareStored, _newPricePerShareIncPerSecond, _newLastSync);
        _setAllowed(msg.sender, false);
    }

    /* ========== Core ========== */

    /// @dev Adheres to chainlink's AggregatorV3Interface
    /// @return _roundId The l1Block corresponding to the last time the oracle was proofed
    /// @return _answer The price of SfrxUSD in frxUSD
    /// @return _startedAt The current timestamp
    /// @return _updatedAt The current timestamp
    /// @return _answeredInRound The l1Block corresponding to the last time the oracle was proofed
    function latestRoundData()
        external
        view
        returns (uint80 _roundId, int256 _answer, uint256 _startedAt, uint256 _updatedAt, uint80 _answeredInRound)
    {
        _answeredInRound = _roundId = uint80(block.number);
        /// @notice if rewards cycle data is stale treat, return a stale oracle response
        _startedAt = _updatedAt = block.timestamp;
        _answer = int256(previewPricePerShare());
        if (_answer < 0) revert CastError();
        if (_roundId < 0) revert CastError();
    }

    /// @dev Adheres to chainlink's AggregatorV3Interface
    /// @return The decimals intended to be used via this oracle
    function decimals() external pure returns (uint8) {
        return 18;
    }

    /// @notice Calculate current pricePerShare as of now, accounting for any elapsed time since the last sync. Same as pricePerShare().
    /// @return _newPricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    function previewPricePerShare() public view returns (uint256 _newPricePerShare) {
        // Do the calculation
        return _previewPricePerShare(block.timestamp);
    }

    /// @notice Calculate pricePerShare at a future time
    /// @param _futureTime The future time at which to calculate
    /// @return _newPricePerShare Expected pricePerShare at _asOfTime, in UNDERLYING_PRECISION
    function previewPricePerShareFuture(uint256 _futureTime) public view returns (uint256 _newPricePerShare) {
        // Do the calculation
        return _previewPricePerShare(_futureTime);
    }

    /// @notice The current price per share token, in asset tokens. Same as previewPricePerShare().
    /// @return _pricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    function pricePerShare() external view returns (uint256 _pricePerShare) {
        return previewPricePerShare();
    }

    /// @notice Calculate current pricePerShare as of the given time, accounting for any elapsed time since the last sync.
    /// @param _asOfTime The time at which to calculate. Must be now or in the future
    /// @return _newPricePerShare Expected pricePerShare at _asOfTime, in UNDERLYING_PRECISION
    function _previewPricePerShare(uint256 _asOfTime) internal view returns (uint256 _newPricePerShare) {
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!

        // Calculate the elapsed time
        uint256 _elapsedTime = _asOfTime - lastSync;

        // Continuously compounding interest. Done here instead of in _previewTotalAssets
        // p(t) = p₀ * e^((dr)*t)
        // Also might be able to use e^(xy) = (e^x)^y (to avoid overflows)
        // ---------------------------------------
        // Calculate e^x and convert back to uint256

        // Get the UD60x18 exponent first and scale down by UNDERLYING_PRECISION
        // UD60x18 _exponentUD608 = div(convert(pricePerShareIncPerSecond * _elapsedTime), convert(UNDERLYING_PRECISION));
        UD60x18 _exponentUD608 = wrap(pricePerShareIncPerSecond * _elapsedTime);
        // console2.log("=============");
        // console2.log("pricePerShareIncPerSecond: ", pricePerShareIncPerSecond);
        // console2.log("_elapsedTime: ", _elapsedTime);
        // console2.log("convert(_exponentUD608): ", convert(_exponentUD608));
        // console2.log(
        //     "convert(_exponentUD608 * UNDERLYING_PRECISION): ",
        //     convert(mul(_exponentUD608, convert(UNDERLYING_PRECISION)))
        // );

        // Get the raw e^exponent in UD60x18
        UD60x18 _ePowUD608 = exp(_exponentUD608);

        // Old
        // {
        //     // Scale the UD60x18 up by UNDERLYING_PRECISION and convert to uint256
        //     uint256 _ePowU256 = convert(mul(_ePowUD608, convert(UNDERLYING_PRECISION)));

        //     // console2.log(
        //     //     "convert(_ePowUD608 * UNDERLYING_PRECISION): ",
        //     //     convert(mul(_ePowUD608, convert(UNDERLYING_PRECISION)))
        //     // );
        //     // console2.log("_ePowU256: ", _ePowU256);

        //     // Calculate _newPricePerShare
        //     _newPricePerShare = (pricePerShareStored * _ePowU256) / UNDERLYING_PRECISION;
        //     // console2.log("_newPricePerShare: ", _newPricePerShare);
        // }

        // New
        {
            _newPricePerShare = mul(wrap(pricePerShareStored), _ePowUD608).unwrap();
        }
    }

    /* ========== Admin Gated Setters ========== */

    /// @notice The ```setAllowed``` function allows for the timelock to set the status of addresses
    ///         if allowed, an address is able to submit a proof
    /// @param _sender The msg.sender to allow
    /// @param _status The status of the msg.sender | false -> not allowed, true -> allowed
    /// @dev Requires the caller to be the timelock address
    function setAllowed(address _sender, bool _status) public override onlyOwner {
        _setAllowed(_sender, _status);
    }

    /// @notice Set pricePerShareStored, pricePerShareIncPerSecond, and lastSync in one call
    /// @param _newPricePerShareStored New stored price per share, in E18 asset tokens
    /// @param _newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    /// @param _newLastSync New lastSync, must not be gt `block.timestamp`
    /// @dev p(t) = p0*e^(r(t-t0))
    function setAllPricingParams(
        uint256 _newPricePerShareStored,
        uint256 _newPricePerShareIncPerSecond,
        uint256 _newLastSync
    ) public onlyAllowed {
        if (_newLastSync > block.timestamp) revert LastSyncMustNotBeInTheFuture();
        pricePerShareStored = _newPricePerShareStored;
        pricePerShareIncPerSecond = _newPricePerShareIncPerSecond;
        lastSync = _newLastSync;

        emit SetPricePerShareStored(_newPricePerShareStored);
        emit SetPricePerShareIncPerSecond(_newPricePerShareIncPerSecond);
        emit SetLastSync(_newLastSync);
    }

    /// @notice Set pricePerShare increase rate, per second (pricePerShareIncPerSecond). Also sets lastSync to now and pricePerShareStored to the current pricePerShare
    /// @param _newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    function setPricePerShareIncPerSecond(uint256 _newPricePerShareIncPerSecond) external onlyAllowed {
        pricePerShareStored = _previewPricePerShare(block.timestamp);
        lastSync = block.timestamp;
        pricePerShareIncPerSecond = _newPricePerShareIncPerSecond;
        emit SetPricePerShareIncPerSecond(_newPricePerShareIncPerSecond);
    }

    /// @notice Set pricePerShareStored
    /// @param _newPricePerShareStored New stored price per share, in E18 asset tokens
    function setPricePerShareStored(uint256 _newPricePerShareStored) public onlyAllowed {
        lastSync = block.timestamp;
        pricePerShareStored = _newPricePerShareStored;
        emit SetPricePerShareStored(_newPricePerShareStored);
    }

    function rewardsCycleData() external view returns (RewardsCycleData memory) {
        // Return the rewards cycle data as the max possible rate, rate is curbed by maxDistributionPerSecondPerAsset
        return
            RewardsCycleData({
                cycleEnd: uint40(604_800 + block.timestamp),
                lastSync: uint40(block.timestamp),
                rewardCycleAmount: uint216(type(uint216).max / 1e18) // max value
            });
    }

    function maxDistributionPerSecondPerAsset() external view returns (uint256) {
        return pricePerShareIncPerSecond;
    }

    function storedTotalAssets() external view returns (uint256) {
        return previewPricePerShare();
    }

    function totalAssets() external view returns (uint256) {
        return previewPricePerShare();
    }

    function totalSupply() external pure returns (uint256) {
        return 1e18;
    }

    function lastRewardsDistribution() external view returns (uint256) {
        return block.timestamp;
    }

    function description() external pure returns(string memory) {
        return "sfrxUSD/frxUSD: Rate Transport";
    }

    /* ========== Events ========== */

    /// @notice When setPricePerShareStored is called
    /// @param newPricePerShareStored New stored price per share, in E18 asset tokens
    event SetPricePerShareStored(uint256 newPricePerShareStored);

    /// @notice When setPricePerShareIncPerSecond is called
    /// @param newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    event SetPricePerShareIncPerSecond(uint256 newPricePerShareIncPerSecond);

    /// @notice When setLastSync is called
    /// @param newLastSync New lastSync
    event SetLastSync(uint256 newLastSync);

    /* ========== Errors ========== */

    /// @notice If the contract was already initialized
    error AlreadyInit();

    /// @notice If latestRoundData casting is problematic
    error CastError();

    /// @notice If the supplied lastSync time is in the future
    error LastSyncMustNotBeInTheFuture();
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity ^0.8.21;

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// ========================== StakedFrxUSD2 ===========================
// ====================================================================
// Frax Finance: https://github.com/FraxFinance
// Tested for 18-decimal underlying assets only

import { Timelock2Step } from "frax-std/access-control/v2/Timelock2Step.sol";
import { IERC20 } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { IfrxUSD } from "src/contracts/interfaces/IfrxUSD.sol";
import { SafeCastLib } from "solmate/utils/SafeCastLib.sol";
import { LinearRewardsQuasiErc4626, ERC20 } from "./LinearRewardsQuasiErc4626.sol";

/// @title Staked frxUSD
/// @notice A ERC4626-like Vault implementation with linear rewards, rewards can be capped
contract StakedFrxUSD2 is LinearRewardsQuasiErc4626, Timelock2Step {
    using SafeCastLib for *;

    /// @notice Used for initialization
    bool private _initialized;

    /// @notice Array of minters
    address[] public minters_array;

    /// @notice Mapping of the minters
    /// @dev Mapping is used for faster verification
    mapping(address => bool) public minters;

    /// @param _underlying The erc20 asset deposited
    /// @param _name The name of the vault
    /// @param _symbol The symbol of the vault
    /// @param _timelockAddress The address of the timelock/owner contract
    constructor(
        IERC20 _underlying,
        string memory _name,
        string memory _symbol,
        address _timelockAddress
    ) LinearRewardsQuasiErc4626(ERC20(address(_underlying)), _name, _symbol) Timelock2Step(_timelockAddress) {
        _initialized = true;
    }

    error AlreadyInitialized();

    /// @param _name The name of the vault
    /// @param _symbol The symbol of the vault
    /// @param _timelockAddress The address of the timelock/owner contract
    /// @param _ppsInfo [0] Initial PricePerShare [1] PricePerShare increase per sec
    function initialize(
        string memory _name,
        string memory _symbol,
        address _timelockAddress,
        uint256[2] memory _ppsInfo
    ) external {
        if (_initialized) revert AlreadyInitialized();
        _initialized = true;
        name = _name;
        symbol = _symbol;
        timelockAddress = _timelockAddress;

        // Burn all the frxUSD currently in this contract
        IfrxUSD(address(asset)).burn(asset.balanceOf(address(this)));

        // Set PricePerShare info initially
        pricePerShareStored = _ppsInfo[0];
        pricePerShareIncPerSecond = _ppsInfo[1];

        // Set lastSync to now
        lastSync = block.timestamp;
    }

    /* ========== MODIFIERS ========== */

    /// @notice A modifier that only allows a minters to call
    modifier onlyMinters() {
        if (!minters[msg.sender]) revert OnlyMinters();
        _;
    }

    /* ========== UNRESTRICTED FUNCTIONS========== */

    /// @notice Burn tokens. You do NOT receive any underlying assets when doing so
    /// @param _amount Amount of tokens to burn
    function burn(uint256 _amount) public {
        // Do the burn
        super._burn(msg.sender, _amount);

        emit Burn(msg.sender, _amount);
    }

    /* ========== RESTRICTED FUNCTIONS [MINTERS] ========== */

    /// @notice Used by minters to burn tokens
    /// @param b_address Address of the account to burn from
    /// @param b_amount Amount of tokens to burn
    function minter_burn_from(address b_address, uint256 b_amount) public onlyMinters {
        super._burn(b_address, b_amount);
        emit TokenMinterBurned(b_address, msg.sender, b_amount);
    }

    /// @notice Used by minters to mint new tokens
    /// @param m_address Address of the account to mint to
    /// @param m_amount Amount of tokens to mint
    function minter_mint(address m_address, uint256 m_amount) public onlyMinters {
        super._mint(m_address, m_amount);
        emit TokenMinterMinted(msg.sender, m_address, m_amount);
    }

    /* ========== RESTRICTED FUNCTIONS [OWNER] ========== */
    /// @notice Adds a minter
    /// @param minter_address Address of minter to add
    function addMinter(address minter_address) public {
        _requireSenderIsTimelock();
        require(minter_address != address(0), "Zero address detected");

        require(minters[minter_address] == false, "Address already exists");
        minters[minter_address] = true;
        minters_array.push(minter_address);

        emit MinterAdded(minter_address);
    }

    /// @notice Removes a non-bridge minter
    /// @param minter_address Address of minter to remove
    function removeMinter(address minter_address) public {
        _requireSenderIsTimelock();
        require(minter_address != address(0), "Zero address detected");
        require(minters[minter_address] == true, "Address nonexistant");

        // Delete from the mapping
        delete minters[minter_address];

        // 'Delete' from the array by setting the address to 0x0
        for (uint256 i = 0; i < minters_array.length; i++) {
            if (minters_array[i] == minter_address) {
                minters_array[i] = address(0); // This will leave a null in the array and keep the indices the same
                break;
            }
        }

        emit MinterRemoved(minter_address);
    }

    /// @notice Set pricePerShareStored, pricePerShareIncPerSecond, and lastSync in one call
    /// @param _newPricePerShareStored New stored price per share, in E18 asset tokens
    /// @param _newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    /// @param _newLastSync New lastSync
    /// @dev p(t) = p0*e^(r(t-t0))
    function setAllPricingParams(
        uint256 _newPricePerShareStored,
        uint256 _newPricePerShareIncPerSecond,
        uint256 _newLastSync
    ) external {
        _requireSenderIsTimelock();

        // Make sure lastSync is not in the future
        if (_newLastSync > block.timestamp) revert MustNotBeInTheFuture();

        // Set the 3 parameters
        pricePerShareStored = _newPricePerShareStored;
        pricePerShareIncPerSecond = _newPricePerShareIncPerSecond;
        lastSync = _newLastSync;

        emit SetPricePerShareStored(_newPricePerShareStored);
        emit SetPricePerShareIncPerSecond(_newPricePerShareIncPerSecond);
        emit SetLastSync(_newLastSync);
    }

    /// @notice Set pricePerShare increase rate, per second (pricePerShareIncPerSecond). Also sets lastSync to now and pricePerShareStored to the current pricePerShare
    /// @param _newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    function setPricePerShareIncPerSecond(uint256 _newPricePerShareIncPerSecond) external {
        _requireSenderIsTimelock();

        // Sync first
        sync();

        // Set pricePerShareIncPerSecond
        pricePerShareIncPerSecond = _newPricePerShareIncPerSecond;

        emit SetPricePerShareIncPerSecond(_newPricePerShareIncPerSecond);
    }

    /// @notice Set pricePerShareStored
    /// @param _newPricePerShareStored New stored price per share, in E18 asset tokens
    function setPricePerShareStored(uint256 _newPricePerShareStored) external {
        _requireSenderIsTimelock();

        // Set lastSync to now
        lastSync = block.timestamp;

        // Set pricePerShareStored
        pricePerShareStored = _newPricePerShareStored;

        emit SetPricePerShareStored(_newPricePerShareStored);
    }

    //==============================================================================
    // Errors
    //==============================================================================

    /// @notice When lastSync is trying to be set to a future date
    error MustNotBeInTheFuture();

    /// @notice When a non-minter tries to call a restricted function
    error OnlyMinters();

    //==============================================================================
    // Events
    //==============================================================================

    /// @notice Emitted when a burn happens
    /// @param from The address whose tokens were burned
    /// @param amount Amount of tokens burned
    event Burn(address indexed from, uint256 amount);

    /// @notice Emitted when a mint happens
    /// @param to Recipient of the newly-minted tokens
    /// @param amount Amount of tokens minted
    event Mint(address indexed to, uint256 amount);

    /// @notice Emitted when a non-bridge minter is added
    /// @param minter_address Address of the new minter
    event MinterAdded(address minter_address);

    /// @notice Emitted when a non-bridge minter is removed
    /// @param minter_address Address of the removed minter
    event MinterRemoved(address minter_address);

    /// @notice When setLastSync is called
    /// @param newLastSync New lastSync
    event SetLastSync(uint256 newLastSync);

    /// @notice When setPricePerShareIncPerSecond is called
    /// @param newPricePerShareIncPerSecond New stored price per share increase per second, in E18 asset tokens
    event SetPricePerShareIncPerSecond(uint256 newPricePerShareIncPerSecond);

    /// @notice When setPricePerShareStored is called
    /// @param newPricePerShareStored New stored price per share, in E18 asset tokens
    event SetPricePerShareStored(uint256 newPricePerShareStored);

    /// @notice Emitted when a non-bridge minter burns tokens
    /// @param from The account whose tokens are burned
    /// @param to The minter doing the burning
    /// @param amount Amount of tokens burned
    event TokenMinterBurned(address indexed from, address indexed to, uint256 amount);

    /// @notice Emitted when a non-bridge minter mints tokens
    /// @param from The minter doing the minting
    /// @param to The account that gets the newly minted tokens
    /// @param amount Amount of tokens minted
    event TokenMinterMinted(address indexed from, address indexed to, uint256 amount);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { wrap } from "./Casting.sol";
import {
    uEXP_MAX_INPUT,
    uEXP2_MAX_INPUT,
    uHALF_UNIT,
    uLOG2_10,
    uLOG2_E,
    uMAX_UD60x18,
    uMAX_WHOLE_UD60x18,
    UNIT,
    uUNIT,
    uUNIT_SQUARED,
    ZERO
} from "./Constants.sol";
import { UD60x18 } from "./ValueType.sol";

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Calculates the arithmetic average of x and y using the following formula:
///
/// $$
/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)
/// $$
///
/// In English, this is what this formula does:
///
/// 1. AND x and y.
/// 2. Calculate half of XOR x and y.
/// 3. Add the two results together.
///
/// This technique is known as SWAR, which stands for "SIMD within a register". You can read more about it here:
/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The arithmetic average as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();
    uint256 yUint = y.unwrap();
    unchecked {
        result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));
    }
}

/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev This is optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≤ MAX_WHOLE_UD60x18
///
/// @param x The UD60x18 number to ceil.
/// @return result The smallest whole number greater than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();
    if (xUint > uMAX_WHOLE_UD60x18) {
        revert Errors.PRBMath_UD60x18_Ceil_Overflow(x);
    }

    assembly ("memory-safe") {
        // Equivalent to `x % UNIT`.
        let remainder := mod(x, uUNIT)

        // Equivalent to `UNIT - remainder`.
        let delta := sub(uUNIT, remainder)

        // Equivalent to `x + remainder > 0 ? delta : 0`.
        result := add(x, mul(delta, gt(remainder, 0)))
    }
}

/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @param x The numerator as a UD60x18 number.
/// @param y The denominator as a UD60x18 number.
/// @return result The quotient as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(Common.mulDiv(x.unwrap(), uUNIT, y.unwrap()));
}

/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Requirements:
/// - x ≤ 133_084258667509499440
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

    // This check prevents values greater than 192e18 from being passed to {exp2}.
    if (xUint > uEXP_MAX_INPUT) {
        revert Errors.PRBMath_UD60x18_Exp_InputTooBig(x);
    }

    unchecked {
        // Inline the fixed-point multiplication to save gas.
        uint256 doubleUnitProduct = xUint * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method.
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693
///
/// Requirements:
/// - x < 192e18
/// - The result must fit in UD60x18.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

    // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
    if (xUint > uEXP2_MAX_INPUT) {
        revert Errors.PRBMath_UD60x18_Exp2_InputTooBig(x);
    }

    // Convert x to the 192.64-bit fixed-point format.
    uint256 x_192x64 = (xUint << 64) / uUNIT;

    // Pass x to the {Common.exp2} function, which uses the 192.64-bit fixed-point number representation.
    result = wrap(Common.exp2(x_192x64));
}

/// @notice Yields the greatest whole number less than or equal to x.
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
/// @param x The UD60x18 number to floor.
/// @return result The greatest whole number less than or equal to x, as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(UD60x18 x) pure returns (UD60x18 result) {
    assembly ("memory-safe") {
        // Equivalent to `x % UNIT`.
        let remainder := mod(x, uUNIT)

        // Equivalent to `x - remainder > 0 ? remainder : 0)`.
        result := sub(x, mul(remainder, gt(remainder, 0)))
    }
}

/// @notice Yields the excess beyond the floor of x using the odd function definition.
/// @dev See https://en.wikipedia.org/wiki/Fractional_part.
/// @param x The UD60x18 number to get the fractional part of.
/// @return result The fractional part of x as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function frac(UD60x18 x) pure returns (UD60x18 result) {
    assembly ("memory-safe") {
        result := mod(x, uUNIT)
    }
}

/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$, rounding down.
///
/// @dev Requirements:
/// - x * y must fit in UD60x18.
///
/// @param x The first operand as a UD60x18 number.
/// @param y The second operand as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();
    uint256 yUint = y.unwrap();
    if (xUint == 0 || yUint == 0) {
        return ZERO;
    }

    unchecked {
        // Checking for overflow this way is faster than letting Solidity do it.
        uint256 xyUint = xUint * yUint;
        if (xyUint / xUint != yUint) {
            revert Errors.PRBMath_UD60x18_Gm_Overflow(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
        // during multiplication. See the comments in {Common.sqrt}.
        result = wrap(Common.sqrt(xyUint));
    }
}

/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The UD60x18 number for which to calculate the inverse.
/// @return result The inverse as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(UD60x18 x) pure returns (UD60x18 result) {
    unchecked {
        result = wrap(uUNIT_SQUARED / x.unwrap());
    }
}

/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(UD60x18 x) pure returns (UD60x18 result) {
    unchecked {
        // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
        // {log2} can return is ~196_205294292027477728.
        result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
    }
}

/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The UD60x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();
    if (xUint < uUNIT) {
        revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this assembly block is the standard multiplication operation, not {UD60x18.mul}.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }
        default { result := uMAX_UD60x18 }
    }

    if (result.unwrap() == uMAX_UD60x18) {
        unchecked {
            // Inline the fixed-point division to save gas.
            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x ≥ UNIT
///
/// @param x The UD60x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

    if (xUint < uUNIT) {
        revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);
    }

    unchecked {
        // Calculate the integer part of the logarithm.
        uint256 n = Common.msb(xUint / uUNIT);

        // This is the integer part of the logarithm as a UD60x18 number. The operation can't overflow because n
        // n is at most 255 and UNIT is 1e18.
        uint256 resultUint = n * uUNIT;

        // Calculate $y = x * 2^{-n}$.
        uint256 y = xUint >> n;

        // If y is the unit number, the fractional part is zero.
        if (y == uUNIT) {
            return wrap(resultUint);
        }

        // Calculate the fractional part via the iterative approximation.
        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
        uint256 DOUBLE_UNIT = 2e18;
        for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

            // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
            if (y >= DOUBLE_UNIT) {
                // Add the 2^{-m} factor to the logarithm.
                resultUint += delta;

                // Halve y, which corresponds to z/2 in the Wikipedia article.
                y >>= 1;
            }
        }
        result = wrap(resultUint);
    }
}

/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.
///
/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
///
/// @dev See the documentation in {Common.mulDiv18}.
/// @param x The multiplicand as a UD60x18 number.
/// @param y The multiplier as a UD60x18 number.
/// @return result The product as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(Common.mulDiv18(x.unwrap(), y.unwrap()));
}

/// @notice Raises x to the power of y.
///
/// For $1 \leq x \leq \infty$, the following standard formula is used:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// For $0 \leq x \lt 1$, since the unsigned {log2} is undefined, an equivalent formula is used:
///
/// $$
/// i = \frac{1}{x}
/// w = 2^{log_2{i} * y}
/// x^y = \frac{1}{w}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2} and {mul}.
/// - Returns `UNIT` for 0^0.
/// - It may not perform well with very small values of x. Consider using SD59x18 as an alternative.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();
    uint256 yUint = y.unwrap();

    // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
    if (xUint == 0) {
        return yUint == 0 ? UNIT : ZERO;
    }
    // If x is `UNIT`, the result is always `UNIT`.
    else if (xUint == uUNIT) {
        return UNIT;
    }

    // If y is zero, the result is always `UNIT`.
    if (yUint == 0) {
        return UNIT;
    }
    // If y is `UNIT`, the result is always x.
    else if (yUint == uUNIT) {
        return x;
    }

    // If x is > UNIT, use the standard formula.
    if (xUint > uUNIT) {
        result = exp2(mul(log2(x), y));
    }
    // Conversely, if x < UNIT, use the equivalent formula.
    else {
        UD60x18 i = wrap(uUNIT_SQUARED / xUint);
        UD60x18 w = exp2(mul(log2(i), y));
        result = wrap(uUNIT_SQUARED / w.unwrap());
    }
}

/// @notice Raises x (a UD60x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - The result must fit in UD60x18.
///
/// @param x The base as a UD60x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {
    // Calculate the first iteration of the loop in advance.
    uint256 xUint = x.unwrap();
    uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;

    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.
    for (y >>= 1; y > 0; y >>= 1) {
        xUint = Common.mulDiv18(xUint, xUint);

        // Equivalent to `y % 2 == 1`.
        if (y & 1 > 0) {
            resultUint = Common.mulDiv18(resultUint, xUint);
        }
    }
    result = wrap(resultUint);
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x ≤ MAX_UD60x18 / UNIT
///
/// @param x The UD60x18 number for which to calculate the square root.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

    unchecked {
        if (xUint > uMAX_UD60x18 / uUNIT) {
            revert Errors.PRBMath_UD60x18_Sqrt_Overflow(x);
        }
        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two UD60x18 numbers.
        // In this case, the two numbers are both the square root.
        result = wrap(Common.sqrt(xUint * uUNIT));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { uMAX_UD60x18, uUNIT } from "./Constants.sol";
import { PRBMath_UD60x18_Convert_Overflow } from "./Errors.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The UD60x18 number to convert.
/// @return result The same number in basic integer form.
function convert(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x) / uUNIT;
}

/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x ≤ MAX_UD60x18 / UNIT
///
/// @param x The basic integer to convert.
/// @return result The same number converted to UD60x18.
function convert(uint256 x) pure returns (UD60x18 result) {
    if (x > uMAX_UD60x18 / uUNIT) {
        revert PRBMath_UD60x18_Convert_Overflow(x);
    }
    unchecked {
        result = UD60x18.wrap(x * uUNIT);
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;

/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.
/// @dev The value type is defined here so it can be imported in all other files.
type UD60x18 is uint256;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoSD1x18,
    Casting.intoSD21x18,
    Casting.intoSD59x18,
    Casting.intoUD2x18,
    Casting.intoUD21x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD60x18 global;

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
    Math.avg,
    Math.ceil,
    Math.div,
    Math.exp,
    Math.exp2,
    Math.floor,
    Math.frac,
    Math.gm,
    Math.inv,
    Math.ln,
    Math.log10,
    Math.log2,
    Math.mul,
    Math.pow,
    Math.powu,
    Math.sqrt
} for UD60x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

// The global "using for" directive makes the functions in this library callable on the UD60x18 type.
using {
    Helpers.add,
    Helpers.and,
    Helpers.eq,
    Helpers.gt,
    Helpers.gte,
    Helpers.isZero,
    Helpers.lshift,
    Helpers.lt,
    Helpers.lte,
    Helpers.mod,
    Helpers.neq,
    Helpers.not,
    Helpers.or,
    Helpers.rshift,
    Helpers.sub,
    Helpers.uncheckedAdd,
    Helpers.uncheckedSub,
    Helpers.xor
} for UD60x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                    OPERATORS
//////////////////////////////////////////////////////////////////////////*/

// The global "using for" directive makes it possible to use these operators on the UD60x18 type.
using {
    Helpers.add as +,
    Helpers.and2 as &,
    Math.div as /,
    Helpers.eq as ==,
    Helpers.gt as >,
    Helpers.gte as >=,
    Helpers.lt as <,
    Helpers.lte as <=,
    Helpers.or as |,
    Helpers.mod as %,
    Math.mul as *,
    Helpers.neq as !=,
    Helpers.not as ~,
    Helpers.sub as -,
    Helpers.xor as ^
} for UD60x18 global;

// SPDX-License-Identifier: ISC
pragma solidity ^0.8.19;

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// ========================= OracleAllowlist ==========================
// ====================================================================
// Frax Finance: https://github.com/FraxFinance

// ====================================================================

abstract contract OracleAllowlist {
    /// @notice mapping from address to boolean to indicate whether an address
    ///         is to be allowed to push
    mapping(address => bool) public isAllowed;

    /// @notice virtual function to be overriden in child allows for the list to
    ///         to be modified
    function setAllowed(address, bool) public virtual;

    /// @notice Internal function to set the allowlist
    /// @param sender The address of the wallet who's status will be changed
    /// @param status The boolean indicating status: true -> allowed | false -> not
    function _setAllowed(address sender, bool status) internal virtual {
        isAllowed[sender] = status;
        emit AllowListUpdatated(sender, status);
    }

    /// @notice modifer to be used on external functions in child
    modifier onlyAllowed() {
        if (!isAllowed[msg.sender]) revert NotAllowed();
        _;
    }

    /// Errors
    error NotAllowed();

    /// Events
    event AllowListUpdatated(address sender, bool isAllowed);
}

// 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: ISC
pragma solidity ^0.8.20;

contract GapFirst11 {
    bytes32 gap0;
    bytes32 gap1;
    bytes32 gap2;
    bytes32 gap3;
    bytes32 gap4;
    bytes32 gap5;
    bytes32 gap6;
    bytes32 gap7;
    bytes32 gap8;
    bytes32 gap9;
    bytes32 gap10;
    bytes32 gap11;
}

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

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// ========================== Timelock2Step ===========================
// ====================================================================
// Frax Finance: https://github.com/FraxFinance

// Primary Author
// Drake Evans: https://github.com/DrakeEvans

// Reviewers
// Dennis: https://github.com/denett

// ====================================================================

/// @title Timelock2Step
/// @author Drake Evans (Frax Finance) https://github.com/drakeevans
/// @dev Inspired by OpenZeppelin's Ownable2Step contract
/// @notice  An abstract contract which contains 2-step transfer and renounce logic for a timelock address
abstract contract Timelock2Step {
    /// @notice The pending timelock address
    address public pendingTimelockAddress;

    /// @notice The current timelock address
    address public timelockAddress;

    constructor(address _timelockAddress) {
        timelockAddress = _timelockAddress;
    }

    // ============================================================================================
    // Functions: External Functions
    // ============================================================================================

    /// @notice The ```transferTimelock``` function initiates the timelock transfer
    /// @dev Must be called by the current timelock
    /// @param _newTimelock The address of the nominated (pending) timelock
    function transferTimelock(address _newTimelock) external virtual {
        _requireSenderIsTimelock();
        _transferTimelock(_newTimelock);
    }

    /// @notice The ```acceptTransferTimelock``` function completes the timelock transfer
    /// @dev Must be called by the pending timelock
    function acceptTransferTimelock() external virtual {
        _requireSenderIsPendingTimelock();
        _acceptTransferTimelock();
    }

    /// @notice The ```renounceTimelock``` function renounces the timelock after setting pending timelock to current timelock
    /// @dev Pending timelock must be set to current timelock before renouncing, creating a 2-step renounce process
    function renounceTimelock() external virtual {
        _requireSenderIsTimelock();
        _requireSenderIsPendingTimelock();
        _transferTimelock(address(0));
        _setTimelock(address(0));
    }

    // ============================================================================================
    // Functions: Internal Actions
    // ============================================================================================

    /// @notice The ```_transferTimelock``` function initiates the timelock transfer
    /// @dev This function is to be implemented by a public function
    /// @param _newTimelock The address of the nominated (pending) timelock
    function _transferTimelock(address _newTimelock) internal {
        pendingTimelockAddress = _newTimelock;
        emit TimelockTransferStarted(timelockAddress, _newTimelock);
    }

    /// @notice The ```_acceptTransferTimelock``` function completes the timelock transfer
    /// @dev This function is to be implemented by a public function
    function _acceptTransferTimelock() internal {
        pendingTimelockAddress = address(0);
        _setTimelock(msg.sender);
    }

    /// @notice The ```_setTimelock``` function sets the timelock address
    /// @dev This function is to be implemented by a public function
    /// @param _newTimelock The address of the new timelock
    function _setTimelock(address _newTimelock) internal {
        emit TimelockTransferred(timelockAddress, _newTimelock);
        timelockAddress = _newTimelock;
    }

    // ============================================================================================
    // Functions: Internal Checks
    // ============================================================================================

    /// @notice The ```_isTimelock``` function checks if _address is current timelock address
    /// @param _address The address to check against the timelock
    /// @return Whether or not msg.sender is current timelock address
    function _isTimelock(address _address) internal view returns (bool) {
        return _address == timelockAddress;
    }

    /// @notice The ```_requireIsTimelock``` function reverts if _address is not current timelock address
    /// @param _address The address to check against the timelock
    function _requireIsTimelock(address _address) internal view {
        if (!_isTimelock(_address)) revert AddressIsNotTimelock(timelockAddress, _address);
    }

    /// @notice The ```_requireSenderIsTimelock``` function reverts if msg.sender is not current timelock address
    /// @dev This function is to be implemented by a public function
    function _requireSenderIsTimelock() internal view {
        _requireIsTimelock(msg.sender);
    }

    /// @notice The ```_isPendingTimelock``` function checks if the _address is pending timelock address
    /// @dev This function is to be implemented by a public function
    /// @param _address The address to check against the pending timelock
    /// @return Whether or not _address is pending timelock address
    function _isPendingTimelock(address _address) internal view returns (bool) {
        return _address == pendingTimelockAddress;
    }

    /// @notice The ```_requireIsPendingTimelock``` function reverts if the _address is not pending timelock address
    /// @dev This function is to be implemented by a public function
    /// @param _address The address to check against the pending timelock
    function _requireIsPendingTimelock(address _address) internal view {
        if (!_isPendingTimelock(_address)) revert AddressIsNotPendingTimelock(pendingTimelockAddress, _address);
    }

    /// @notice The ```_requirePendingTimelock``` function reverts if msg.sender is not pending timelock address
    /// @dev This function is to be implemented by a public function
    function _requireSenderIsPendingTimelock() internal view {
        _requireIsPendingTimelock(msg.sender);
    }

    // ============================================================================================
    // Functions: Events
    // ============================================================================================

    /// @notice The ```TimelockTransferStarted``` event is emitted when the timelock transfer is initiated
    /// @param previousTimelock The address of the previous timelock
    /// @param newTimelock The address of the new timelock
    event TimelockTransferStarted(address indexed previousTimelock, address indexed newTimelock);

    /// @notice The ```TimelockTransferred``` event is emitted when the timelock transfer is completed
    /// @param previousTimelock The address of the previous timelock
    /// @param newTimelock The address of the new timelock
    event TimelockTransferred(address indexed previousTimelock, address indexed newTimelock);

    // ============================================================================================
    // Functions: Errors
    // ============================================================================================

    /// @notice Emitted when timelock is transferred
    error AddressIsNotTimelock(address timelockAddress, address actualAddress);

    /// @notice Emitted when pending timelock is transferred
    error AddressIsNotPendingTimelock(address pendingTimelockAddress, address actualAddress);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.3.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "./IERC20.sol";
import {IERC20Metadata} from "./extensions/IERC20Metadata.sol";
import {Context} from "../../utils/Context.sol";
import {IERC20Errors} from "../../interfaces/draft-IERC6093.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC-20
 * applications.
 */
abstract contract ERC20 is Context, IERC20, IERC20Metadata, IERC20Errors {
    mapping(address account => uint256) private _balances;

    mapping(address account => mapping(address spender => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * Both values are immutable: they can only be set once during construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `value`.
     */
    function transfer(address to, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, value);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `value` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 value) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, value);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Skips emitting an {Approval} event indicating an allowance update. This is not
     * required by the ERC. See {xref-ERC20-_approve-address-address-uint256-bool-}[_approve].
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `value`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `value`.
     */
    function transferFrom(address from, address to, uint256 value) public virtual returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, value);
        _transfer(from, to, value);
        return true;
    }

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _transfer(address from, address to, uint256 value) internal {
        if (from == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        if (to == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(from, to, value);
    }

    /**
     * @dev Transfers a `value` amount of tokens from `from` to `to`, or alternatively mints (or burns) if `from`
     * (or `to`) is the zero address. All customizations to transfers, mints, and burns should be done by overriding
     * this function.
     *
     * Emits a {Transfer} event.
     */
    function _update(address from, address to, uint256 value) internal virtual {
        if (from == address(0)) {
            // Overflow check required: The rest of the code assumes that totalSupply never overflows
            _totalSupply += value;
        } else {
            uint256 fromBalance = _balances[from];
            if (fromBalance < value) {
                revert ERC20InsufficientBalance(from, fromBalance, value);
            }
            unchecked {
                // Overflow not possible: value <= fromBalance <= totalSupply.
                _balances[from] = fromBalance - value;
            }
        }

        if (to == address(0)) {
            unchecked {
                // Overflow not possible: value <= totalSupply or value <= fromBalance <= totalSupply.
                _totalSupply -= value;
            }
        } else {
            unchecked {
                // Overflow not possible: balance + value is at most totalSupply, which we know fits into a uint256.
                _balances[to] += value;
            }
        }

        emit Transfer(from, to, value);
    }

    /**
     * @dev Creates a `value` amount of tokens and assigns them to `account`, by transferring it from address(0).
     * Relies on the `_update` mechanism
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead.
     */
    function _mint(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidReceiver(address(0));
        }
        _update(address(0), account, value);
    }

    /**
     * @dev Destroys a `value` amount of tokens from `account`, lowering the total supply.
     * Relies on the `_update` mechanism.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * NOTE: This function is not virtual, {_update} should be overridden instead
     */
    function _burn(address account, uint256 value) internal {
        if (account == address(0)) {
            revert ERC20InvalidSender(address(0));
        }
        _update(account, address(0), value);
    }

    /**
     * @dev Sets `value` as the allowance of `spender` over the `owner`'s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address owner, address spender, uint256 value) internal {
        _approve(owner, spender, value, true);
    }

    /**
     * @dev Variant of {_approve} with an optional flag to enable or disable the {Approval} event.
     *
     * By default (when calling {_approve}) the flag is set to true. On the other hand, approval changes made by
     * `_spendAllowance` during the `transferFrom` operation set the flag to false. This saves gas by not emitting any
     * `Approval` event during `transferFrom` operations.
     *
     * Anyone who wishes to continue emitting `Approval` events on the`transferFrom` operation can force the flag to
     * true using the following override:
     *
     * ```solidity
     * function _approve(address owner, address spender, uint256 value, bool) internal virtual override {
     *     super._approve(owner, spender, value, true);
     * }
     * ```
     *
     * Requirements are the same as {_approve}.
     */
    function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual {
        if (owner == address(0)) {
            revert ERC20InvalidApprover(address(0));
        }
        if (spender == address(0)) {
            revert ERC20InvalidSpender(address(0));
        }
        _allowances[owner][spender] = value;
        if (emitEvent) {
            emit Approval(owner, spender, value);
        }
    }

    /**
     * @dev Updates `owner`'s allowance for `spender` based on spent `value`.
     *
     * Does not update the allowance value in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Does not emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 value) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance < type(uint256).max) {
            if (currentAllowance < value) {
                revert ERC20InsufficientAllowance(spender, currentAllowance, value);
            }
            unchecked {
                _approve(owner, spender, currentAllowance - value, false);
            }
        }
    }
}

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

interface IfrxUSD {
    function DOMAIN_SEPARATOR() external view returns (bytes32);

    function acceptOwnership() external;

    function addMinter(address minter_address) external;

    function allowance(address owner, address spender) external view returns (uint256);

    function approve(address spender, uint256 value) external returns (bool);

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

    function burn(uint256 value) external;

    function burnFrom(address account, uint256 value) external;

    function decimals() external view returns (uint8);

    function eip712Domain()
        external
        view
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        );

    function initialize(address _owner, string memory _name, string memory _symbol) external;

    function minter_burn_from(address b_address, uint256 b_amount) external;

    function minter_mint(address m_address, uint256 m_amount) external;

    function minters(address) external view returns (bool);

    function minters_array(uint256) external view returns (address);

    function name() external view returns (string memory);

    function nonces(address owner) external view returns (uint256);

    function owner() external view returns (address);

    function pendingOwner() external view returns (address);

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    function removeMinter(address minter_address) external;

    function renounceOwnership() external;

    function symbol() external view returns (string memory);

    function totalSupply() external view returns (uint256);

    function transfer(address to, uint256 value) external returns (bool);

    function transferFrom(address from, address to, uint256 value) external returns (bool);

    function transferOwnership(address newOwner) external;
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Safe unsigned integer casting library that reverts on overflow.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeCastLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/math/SafeCast.sol)
library SafeCastLib {
    function safeCastTo248(uint256 x) internal pure returns (uint248 y) {
        require(x < 1 << 248);

        y = uint248(x);
    }

    function safeCastTo240(uint256 x) internal pure returns (uint240 y) {
        require(x < 1 << 240);

        y = uint240(x);
    }

    function safeCastTo232(uint256 x) internal pure returns (uint232 y) {
        require(x < 1 << 232);

        y = uint232(x);
    }

    function safeCastTo224(uint256 x) internal pure returns (uint224 y) {
        require(x < 1 << 224);

        y = uint224(x);
    }

    function safeCastTo216(uint256 x) internal pure returns (uint216 y) {
        require(x < 1 << 216);

        y = uint216(x);
    }

    function safeCastTo208(uint256 x) internal pure returns (uint208 y) {
        require(x < 1 << 208);

        y = uint208(x);
    }

    function safeCastTo200(uint256 x) internal pure returns (uint200 y) {
        require(x < 1 << 200);

        y = uint200(x);
    }

    function safeCastTo192(uint256 x) internal pure returns (uint192 y) {
        require(x < 1 << 192);

        y = uint192(x);
    }

    function safeCastTo184(uint256 x) internal pure returns (uint184 y) {
        require(x < 1 << 184);

        y = uint184(x);
    }

    function safeCastTo176(uint256 x) internal pure returns (uint176 y) {
        require(x < 1 << 176);

        y = uint176(x);
    }

    function safeCastTo168(uint256 x) internal pure returns (uint168 y) {
        require(x < 1 << 168);

        y = uint168(x);
    }

    function safeCastTo160(uint256 x) internal pure returns (uint160 y) {
        require(x < 1 << 160);

        y = uint160(x);
    }

    function safeCastTo152(uint256 x) internal pure returns (uint152 y) {
        require(x < 1 << 152);

        y = uint152(x);
    }

    function safeCastTo144(uint256 x) internal pure returns (uint144 y) {
        require(x < 1 << 144);

        y = uint144(x);
    }

    function safeCastTo136(uint256 x) internal pure returns (uint136 y) {
        require(x < 1 << 136);

        y = uint136(x);
    }

    function safeCastTo128(uint256 x) internal pure returns (uint128 y) {
        require(x < 1 << 128);

        y = uint128(x);
    }

    function safeCastTo120(uint256 x) internal pure returns (uint120 y) {
        require(x < 1 << 120);

        y = uint120(x);
    }

    function safeCastTo112(uint256 x) internal pure returns (uint112 y) {
        require(x < 1 << 112);

        y = uint112(x);
    }

    function safeCastTo104(uint256 x) internal pure returns (uint104 y) {
        require(x < 1 << 104);

        y = uint104(x);
    }

    function safeCastTo96(uint256 x) internal pure returns (uint96 y) {
        require(x < 1 << 96);

        y = uint96(x);
    }

    function safeCastTo88(uint256 x) internal pure returns (uint88 y) {
        require(x < 1 << 88);

        y = uint88(x);
    }

    function safeCastTo80(uint256 x) internal pure returns (uint80 y) {
        require(x < 1 << 80);

        y = uint80(x);
    }

    function safeCastTo72(uint256 x) internal pure returns (uint72 y) {
        require(x < 1 << 72);

        y = uint72(x);
    }

    function safeCastTo64(uint256 x) internal pure returns (uint64 y) {
        require(x < 1 << 64);

        y = uint64(x);
    }

    function safeCastTo56(uint256 x) internal pure returns (uint56 y) {
        require(x < 1 << 56);

        y = uint56(x);
    }

    function safeCastTo48(uint256 x) internal pure returns (uint48 y) {
        require(x < 1 << 48);

        y = uint48(x);
    }

    function safeCastTo40(uint256 x) internal pure returns (uint40 y) {
        require(x < 1 << 40);

        y = uint40(x);
    }

    function safeCastTo32(uint256 x) internal pure returns (uint32 y) {
        require(x < 1 << 32);

        y = uint32(x);
    }

    function safeCastTo24(uint256 x) internal pure returns (uint24 y) {
        require(x < 1 << 24);

        y = uint24(x);
    }

    function safeCastTo16(uint256 x) internal pure returns (uint16 y) {
        require(x < 1 << 16);

        y = uint16(x);
    }

    function safeCastTo8(uint256 x) internal pure returns (uint8 y) {
        require(x < 1 << 8);

        y = uint8(x);
    }
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity ^0.8.21;

// ====================================================================
// |     ______                   _______                             |
// |    / _____________ __  __   / ____(_____  ____ _____  ________   |
// |   / /_  / ___/ __ `| |/_/  / /_  / / __ \/ __ `/ __ \/ ___/ _ \  |
// |  / __/ / /  / /_/ _>  <   / __/ / / / / / /_/ / / / / /__/  __/  |
// | /_/   /_/   \__,_/_/|_|  /_/   /_/_/ /_/\__,_/_/ /_/\___/\___/   |
// |                                                                  |
// ====================================================================
// ===================== LinearRewardsQuasiErc4626 ====================
// ====================================================================
// Frax Finance: https://github.com/FraxFinance

import { ERC20, ERC4626 } from "solmate/mixins/ERC4626.sol";
import { SafeCastLib } from "solmate/utils/SafeCastLib.sol";
import { ln, mul, div, pow, exp, wrap } from "@prb/math/src/ud60x18/Math.sol";
import { convert } from "@prb/math/src/ud60x18/Conversions.sol";
import { UD60x18 } from "@prb/math/src/ud60x18/ValueType.sol";
import "forge-std/console2.sol";

/// @title LinearRewardsErc4626
/// @notice An ERC4626 Vault implementation with linear rewards
abstract contract LinearRewardsQuasiErc4626 is ERC4626 {
    using SafeCastLib for *;

    /// @notice The precision of all integer calculations
    uint256 public constant PRECISION = 1e18;

    /// @notice One year, in seconds
    uint256 public constant ONE_YEAR = 31_536_000;

    /// @notice The rewards cycle length in seconds
    uint256 public immutable REWARDS_CYCLE_LENGTH = 604_800; // 7 days

    /// @notice Precomputed year
    UD60x18 public immutable ONE_YEAR_UD60X18;

    /// @notice Information about the current rewards cycle
    struct RewardsCycleData {
        uint40 cycleEnd; // Timestamp of the end of the current rewards cycle
        uint40 lastSync; // Timestamp of the last time the rewards cycle was synced
        uint216 rewardCycleAmount; // Amount of rewards to be distributed in the current cycle
    }

    /// @notice The rewards cycle data, stored in a single word to save gas
    RewardsCycleData public DEPRECATED__rewardsCycleData;

    /// @notice The timestamp of the last time rewards were distributed
    uint256 public DEPRECATED__lastRewardsDistribution;

    /// @notice The total amount of assets that have been distributed and deposited
    uint256 public DEPRECATED__storedTotalAssets;

    /// @notice The precision of the underlying asset
    uint256 public immutable UNDERLYING_PRECISION;

    // ---------------------------------------------
    // DEPRECATED STORAGE SLOTS (for storage order preservation)
    // ---------------------------------------------
    /// @notice The pending timelock address
    address public DEPRECATED__pendingTimelockAddress;

    /// @notice The current timelock address
    address public DEPRECATED__timelockAddress;

    /// @notice The maximum amount of rewards that can be distributed per second per 1e18 asset
    uint256 public DEPRECATED__maxDistributionPerSecondPerAsset;

    uint256 private DEPRECATED__initializeStage;

    // ---------------------------------------------
    // NEW STATE VARIABLES
    // ---------------------------------------------

    /// @notice Last stored pricePerShare. Current rate is stored + (rate * pricePerShareIncPerSecond)
    uint256 public pricePerShareStored;

    /// @notice Manually set increase in pricePerShare, per second
    uint256 public pricePerShareIncPerSecond;

    /// @notice The last time the contract was synced
    uint256 public lastSync;

    // ---------------------------------------------
    // CONSTRUCTOR
    // ---------------------------------------------

    /// @param _underlying The erc20 asset deposited
    /// @param _name The name of the vault
    /// @param _symbol The symbol of the vault
    constructor(ERC20 _underlying, string memory _name, string memory _symbol) ERC4626(_underlying, _name, _symbol) {
        if (_underlying.decimals() != 18) revert UnderlyingAssetMustBe18Decimals();
        UNDERLYING_PRECISION = 10 ** _underlying.decimals();
        ONE_YEAR_UD60X18 = convert(ONE_YEAR);
    }

    // ---------------------------------------------
    // VIEW FUNCTIONS
    // ---------------------------------------------

    /// @notice Calculate pricePerShare increase per second needed for a given APY.
    /// @param _apyE18 APY in 1.%%E18 (e.g. 5% APY = input 1.05e18). Must be >= 1e18
    /// @return _newPPSIPS The needed pricePerShare increase, per second, in UNDERLYING_PRECISION
    function calcPPSIPSForGivenAPY(uint256 _apyE18) public view returns (uint256 _newPPSIPS) {
        if (_apyE18 < 1e18) revert InvalidAPY();
        // Old
        // UD60x18 _numerator = mul(ln(convert(_apyE18)), convert(1e18)) - mul(ln(convert(1e18)), convert(1e18));
        // UD60x18 _denominator = convert(ONE_YEAR);
        // _newPPSIPS = convert(div(_numerator, _denominator));
        // New
        UD60x18 _numerator = ln(wrap(_apyE18));
        UD60x18 _denominator = ONE_YEAR_UD60X18;
        _newPPSIPS = (div(_numerator, _denominator)).unwrap();
    }

    /// @notice Calculate the total assets as of a given time.
    /// @param _asOfTime The time at which to calculate. Must be now or in the future.
    /// @return _newTotalAssets Expected total assets at _asOfTime, in UNDERLYING_PRECISION
    function _previewTotalAssets(uint256 _asOfTime) internal view returns (uint256 _newTotalAssets) {
        _newTotalAssets = (_previewPricePerShare(_asOfTime) * totalSupply) / 1e18;
    }

    /// @notice Calculate current totalAssets as of now, accounting for elapsed time
    /// @return _newTotalAssets Total assets as of right now, in UNDERLYING_PRECISION
    function previewTotalAssets() public view returns (uint256 _newTotalAssets) {
        // Do the calculation
        return _previewTotalAssets(block.timestamp);
    }

    /// @notice Calculate current totalAssets as of now, accounting for elapsed time
    /// @return _newTotalAssets Total assets as of right now, in UNDERLYING_PRECISION
    function storedTotalAssets() public view returns (uint256 _newTotalAssets) {
        return previewTotalAssets();
    }

    /// @notice Calculate totalAssets at a future time
    /// @param _futureTime The future time at which to calculate
    /// @return _newTotalAssets Expected total assets at _futureTime, in UNDERLYING_PRECISION
    function previewTotalAssetsFuture(uint256 _futureTime) public view returns (uint256 _newTotalAssets) {
        // Do the calculation
        return _previewTotalAssets(_futureTime);
    }

    /// @notice Calculate current pricePerShare as of the given time, accounting for any elapsed time since the last sync.
    /// @param _asOfTime The time at which to calculate. Must be now or in the future
    /// @return _newPricePerShare Expected pricePerShare at _asOfTime, in UNDERLYING_PRECISION
    function _previewPricePerShare(uint256 _asOfTime) internal view returns (uint256 _newPricePerShare) {
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!
        // CHECK THIS MATH!!!

        // Calculate the elapsed time
        uint256 _elapsedTime = _asOfTime - lastSync;

        // Continuously compounding interest. Done here instead of in _previewTotalAssets
        // p(t) = p₀ * e^((dr)*t)
        // Also might be able to use e^(xy) = (e^x)^y (to avoid overflows)
        // ---------------------------------------
        // Calculate e^x and convert back to uint256

        // Get the UD60x18 exponent first and scale down by UNDERLYING_PRECISION
        // OLD: UD60x18 _exponentUD60_18 = div(
        //     convert(pricePerShareIncPerSecond * _elapsedTime),
        //     convert(UNDERLYING_PRECISION)
        // );
        // Get the UD60x18 exponent first and scale down by UNDERLYING_PRECISION
        UD60x18 _exponentUD60_18 = wrap(pricePerShareIncPerSecond * _elapsedTime);
        // UD60x18 _exponentUD60_18 = div(
        //     convert(pricePerShareIncPerSecond * _elapsedTime),
        //     convert(UNDERLYING_PRECISION)
        // );

        // console2.log("=============");
        // console2.log("pricePerShareIncPerSecond: ", pricePerShareIncPerSecond);
        // console2.log("_elapsedTime: ", _elapsedTime);
        // console2.log("convert(_exponentUD60_18): ", convert(_exponentUD60_18));
        // console2.log(
        //     "convert(_exponentUD60_18 * UNDERLYING_PRECISION): ",
        //     convert(mul(_exponentUD60_18, convert(UNDERLYING_PRECISION)))
        // );

        // Get the raw e^exponent in UD60x18
        UD60x18 _ePowUD60_18 = exp(_exponentUD60_18);

        // Old
        // {
        //     // Scale the UD60x18 up by UNDERLYING_PRECISION and convert to uint256
        //     uint256 _ePowU256 = convert(mul(_ePowUD60_18, convert(UNDERLYING_PRECISION)));

        //     // console2.log(
        //     //     "convert(_ePowUD60_18 * UNDERLYING_PRECISION): ",
        //     //     convert(mul(_ePowUD60_18, convert(UNDERLYING_PRECISION)))
        //     // );
        //     // console2.log("_ePowU256: ", _ePowU256);

        //     // Calculate _newPricePerShare
        //     _newPricePerShare = (pricePerShareStored * _ePowU256) / UNDERLYING_PRECISION;
        //     // console2.log("_newPricePerShare: ", _newPricePerShare);
        // }

        // New
        {
            _newPricePerShare = mul(wrap(pricePerShareStored), _ePowUD60_18).unwrap();
        }
    }

    /// @notice Calculate current pricePerShare as of now, accounting for any elapsed time since the last sync. Same as pricePerShare().
    /// @return _newPricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    function previewPricePerShare() public view returns (uint256 _newPricePerShare) {
        // Do the calculation
        return _previewPricePerShare(block.timestamp);
    }

    /// @notice Calculate pricePerShare at a future time
    /// @param _futureTime The future time at which to calculate
    /// @return _newPricePerShare Expected pricePerShare at _asOfTime, in UNDERLYING_PRECISION
    function previewPricePerShareFuture(uint256 _futureTime) public view returns (uint256 _newPricePerShare) {
        // Do the calculation
        return _previewPricePerShare(_futureTime);
    }

    /// @notice Calculate pricePerShare and totalAssets at a given time
    /// @param _asOfTime The time at which to calculate. Must be now or in the future.
    /// @return _pricePerShare Expected pricePerShare at _asOfTime, in UNDERLYING_PRECISION
    /// @return _totalAssets Expected totalAssets at _asOfTime, in UNDERLYING_PRECISION
    function _previewPPSAndTotalAssets(
        uint256 _asOfTime
    ) internal view returns (uint256 _pricePerShare, uint256 _totalAssets) {
        _pricePerShare = _previewPricePerShare(_asOfTime);
        _totalAssets = _previewTotalAssets(_asOfTime);
    }

    /// @notice Calculate pricePerShare and totalAssets as of right now
    /// @return _pricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    /// @return _totalAssets Current totalAssets, in UNDERLYING_PRECISION
    function previewPPSAndTotalAssets() public view returns (uint256 _pricePerShare, uint256 _totalAssets) {
        return _previewPPSAndTotalAssets(block.timestamp);
    }

    /// @notice The current price per share token, in asset tokens. Same as previewPricePerShare().
    /// @return _pricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    function pricePerShare() external view returns (uint256 _pricePerShare) {
        return previewPricePerShare();
    }

    /// @notice The current totalAssets, accounting for any elapsed time since the last sync
    /// @dev This function simulates the rewards that will be distributed at the top of the block
    /// @return _totalAssets The total assets available in the vault
    function totalAssets() public view virtual override returns (uint256 _totalAssets) {
        _totalAssets = _previewTotalAssets(block.timestamp);
    }

    // ---------------------------------------------
    // WRITE FUNCTIONS
    // ---------------------------------------------

    /// @notice Update pricePerShareStored and storedTotalAssets
    /// @return _pricePerShare Current pricePerShare, in UNDERLYING_PRECISION
    function sync() public returns (uint256 _pricePerShare) {
        // Calculate the current values
        _pricePerShare = _previewPricePerShare(block.timestamp);

        // Update the state variables
        pricePerShareStored = _pricePerShare;
        lastSync = block.timestamp;
    }

    /// @notice DEPRECATED: The ```deposit``` function allows a user to mint shares by depositing underlying
    /// @param _assets The amount of underlying to deposit
    /// @param _receiver The address to send the shares to
    /// @return _shares The amount of shares minted
    function deposit(uint256 _assets, address _receiver) public override returns (uint256 _shares) {
        revert MintRedeemsDisabled();
    }

    /// @notice DEPRECATED: The ```mint``` function allows a user to mint a given number of shares
    /// @param _shares The amount of shares to mint
    /// @param _receiver The address to send the shares to
    /// @return _assets The amount of underlying deposited
    function mint(uint256 _shares, address _receiver) public override returns (uint256 _assets) {
        revert MintRedeemsDisabled();
    }

    /// @notice DEPRECATED: The ```withdraw``` function allows a user to withdraw a given amount of underlying
    /// @param _assets The amount of underlying to withdraw
    /// @param _receiver The address to send the underlying to
    /// @param _owner The address of the owner of the shares
    /// @return _shares The amount of shares burned
    function withdraw(uint256 _assets, address _receiver, address _owner) public override returns (uint256 _shares) {
        revert MintRedeemsDisabled();
    }

    /// @notice DEPRECATED: The ```redeem``` function allows a user to redeem their shares for underlying
    /// @param _shares The amount of shares to redeem
    /// @param _receiver The address to send the underlying to
    /// @param _owner The address of the owner of the shares
    /// @return _assets The amount of underlying redeemed
    function redeem(uint256 _shares, address _receiver, address _owner) public override returns (uint256 _assets) {
        revert MintRedeemsDisabled();
    }

    /// @notice DEPRECATED: The ```depositWithSignature``` function allows a user to use signed approvals to deposit
    /// @param _assets The amount of underlying to deposit
    /// @param _receiver The address to send the shares to
    /// @param _deadline The deadline for the signature
    /// @param _approveMax Whether or not to approve the maximum amount
    /// @param _v The v value of the signature
    /// @param _r The r value of the signature
    /// @param _s The s value of the signature
    /// @return _shares The amount of shares minted
    function depositWithSignature(
        uint256 _assets,
        address _receiver,
        uint256 _deadline,
        bool _approveMax,
        uint8 _v,
        bytes32 _r,
        bytes32 _s
    ) external returns (uint256 _shares) {
        revert MintRedeemsDisabled();
    }

    /*//////////////////////////////////////////////////////////////
    //////          ERC4626 ACCOUNTING LOGIC OVERRIDES
    //////////////////////////////////////////////////////////////*/

    /// @notice DEPRECATED: Will always return 0.
    function previewDeposit(uint256 assets) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function previewMint(uint256 shares) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function previewWithdraw(uint256 assets) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function previewRedeem(uint256 shares) public view override returns (uint256) {
        return 0;
    }

    /*//////////////////////////////////////////////////////////////
    //////    ERC4626 DEPOSIT/WITHDRAWAL LIMIT LOGIC OVERRIDES
    //////////////////////////////////////////////////////////////*/

    /// @notice DEPRECATED: Will always return 0.
    function maxDeposit(address) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function maxMint(address) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function maxWithdraw(address owner) public view override returns (uint256) {
        return 0;
    }

    /// @notice DEPRECATED: Will always return 0.
    function maxRedeem(address owner) public view override returns (uint256) {
        return 0;
    }

    /*//////////////////////////////////////////////////////////////
    //////    Backward compatible yield view functions to match old interface
    //////////////////////////////////////////////////////////////*/

    /// @notice DEPRECATED: use pricePerShareIncPerSecond instead
    function maxDistributionPerSecondPerAsset() external view returns (uint256) {
        // Return the maximum distribution per second per asset
        return pricePerShareIncPerSecond;
    }

    /// @notice DEPRECATED: use pricePerShareIncPerSecond instead
    function rewardsCycleData() external view returns (RewardsCycleData memory) {
        // Return the rewards cycle data as the max possible rate, rate is curbed by maxDistributionPerSecondPerAsset
        return RewardsCycleData({
            cycleEnd: uint40(block.timestamp + REWARDS_CYCLE_LENGTH),
            lastSync: uint40(block.timestamp),
            rewardCycleAmount: uint216(type(uint216).max/1E18) // max value
        });
    }

    function lastRewardsDistribution() external view returns (uint256) {
        return block.timestamp;
    }   

    //==============================================================================
    // Errors
    //==============================================================================

    /// @notice If the asset is not 18 decimals
    error UnderlyingAssetMustBe18Decimals();

    /// @notice When the provided APY is invalid
    error InvalidAPY();

    /// @notice When a user attempts to Mint/Redeem
    error MintRedeemsDisabled();

    //==============================================================================
    // Events
    //==============================================================================
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

// Common.sol
//
// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not
// always operate with SD59x18 and UD60x18 numbers.

/*//////////////////////////////////////////////////////////////////////////
                                CUSTOM ERRORS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);

/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);

/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();

/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);

/*//////////////////////////////////////////////////////////////////////////
                                    CONSTANTS
//////////////////////////////////////////////////////////////////////////*/

/// @dev The maximum value a uint128 number can have.
uint128 constant MAX_UINT128 = type(uint128).max;

/// @dev The maximum value a uint40 number can have.
uint40 constant MAX_UINT40 = type(uint40).max;

/// @dev The maximum value a uint64 number can have.
uint64 constant MAX_UINT64 = type(uint64).max;

/// @dev The unit number, which the decimal precision of the fixed-point types.
uint256 constant UNIT = 1e18;

/// @dev The unit number inverted mod 2^256.
uint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;

/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant
/// bit in the binary representation of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;

/*//////////////////////////////////////////////////////////////////////////
                                    FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function exp2(uint256 x) pure returns (uint256 result) {
    unchecked {
        // Start from 0.5 in the 192.64-bit fixed-point format.
        result = 0x800000000000000000000000000000000000000000000000;

        // The following logic multiplies the result by $\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:
        //
        // 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.
        // 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing
        // a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,
        // we know that `x & 0xFF` is also 1.
        if (x & 0xFF00000000000000 > 0) {
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
        }

        if (x & 0xFF000000000000 > 0) {
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
        }

        if (x & 0xFF0000000000 > 0) {
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
        }

        if (x & 0xFF00000000 > 0) {
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
        }

        if (x & 0xFF000000 > 0) {
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
        }

        if (x & 0xFF0000 > 0) {
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
        }

        if (x & 0xFF00 > 0) {
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
        }

        if (x & 0xFF > 0) {
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
        }

        // In the code snippet below, two operations are executed simultaneously:
        //
        // 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1
        // accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.
        // 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.
        //
        // The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,
        // integer part, $2^n$.
        result *= UNIT;
        result >>= (191 - (x >> 64));
    }
}

/// @notice Finds the zero-based index of the first 1 in the binary representation of x.
///
/// @dev See the note on "msb" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set
///
/// Each step in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
///     x >>= 128;
///     result += 128;
/// }
/// ```
///
/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// The Yul instructions used below are:
///
/// - "gt" is "greater than"
/// - "or" is the OR bitwise operator
/// - "shl" is "shift left"
/// - "shr" is "shift right"
///
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return result The index of the most significant bit as a uint256.
/// @custom:smtchecker abstract-function-nondet
function msb(uint256 x) pure returns (uint256 result) {
    // 2^128
    assembly ("memory-safe") {
        let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^64
    assembly ("memory-safe") {
        let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^32
    assembly ("memory-safe") {
        let factor := shl(5, gt(x, 0xFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^16
    assembly ("memory-safe") {
        let factor := shl(4, gt(x, 0xFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^8
    assembly ("memory-safe") {
        let factor := shl(3, gt(x, 0xFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^4
    assembly ("memory-safe") {
        let factor := shl(2, gt(x, 0xF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^2
    assembly ("memory-safe") {
        let factor := shl(1, gt(x, 0x3))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^1
    // No need to shift x any more.
    assembly ("memory-safe") {
        let factor := gt(x, 0x1)
        result := or(result, factor)
    }
}

/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - The denominator must not be zero.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as a uint256.
/// @param y The multiplier as a uint256.
/// @param denominator The divisor as a uint256.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {
    // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
    // use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256
    // variables such that product = prod1 * 2^256 + prod0.
    uint256 prod0; // Least significant 256 bits of the product
    uint256 prod1; // Most significant 256 bits of the product
    assembly ("memory-safe") {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    // Handle non-overflow cases, 256 by 256 division.
    if (prod1 == 0) {
        unchecked {
            return prod0 / denominator;
        }
    }

    // Make sure the result is less than 2^256. Also prevents denominator == 0.
    if (prod1 >= denominator) {
        revert PRBMath_MulDiv_Overflow(x, y, denominator);
    }

    ////////////////////////////////////////////////////////////////////////////
    // 512 by 256 division
    ////////////////////////////////////////////////////////////////////////////

    // Make division exact by subtracting the remainder from [prod1 prod0].
    uint256 remainder;
    assembly ("memory-safe") {
        // Compute remainder using the mulmod Yul instruction.
        remainder := mulmod(x, y, denominator)

        // Subtract 256 bit number from 512-bit number.
        prod1 := sub(prod1, gt(remainder, prod0))
        prod0 := sub(prod0, remainder)
    }

    unchecked {
        // Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow
        // because the denominator cannot be zero at this point in the function execution. The result is always >= 1.
        // For more detail, see https://cs.stackexchange.com/q/138556/92363.
        uint256 lpotdod = denominator & (~denominator + 1);
        uint256 flippedLpotdod;

        assembly ("memory-safe") {
            // Factor powers of two out of denominator.
            denominator := div(denominator, lpotdod)

            // Divide [prod1 prod0] by lpotdod.
            prod0 := div(prod0, lpotdod)

            // Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.
            // `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.
            // However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693
            flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
        }

        // Shift in bits from prod1 into prod0.
        prod0 |= prod1 * flippedLpotdod;

        // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
        // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
        // four bits. That is, denominator * inv = 1 mod 2^4.
        uint256 inverse = (3 * denominator) ^ 2;

        // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
        // in modular arithmetic, doubling the correct bits in each step.
        inverse *= 2 - denominator * inverse; // inverse mod 2^8
        inverse *= 2 - denominator * inverse; // inverse mod 2^16
        inverse *= 2 - denominator * inverse; // inverse mod 2^32
        inverse *= 2 - denominator * inverse; // inverse mod 2^64
        inverse *= 2 - denominator * inverse; // inverse mod 2^128
        inverse *= 2 - denominator * inverse; // inverse mod 2^256

        // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
        // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
        // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
        // is no longer required.
        result = prod0 * inverse;
    }
}

/// @notice Calculates x*y÷1e18 with 512-bit precision.
///
/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.
///
/// Notes:
/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.
/// - The result is rounded toward zero.
/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:
///
/// $$
/// \begin{cases}
///     x * y = MAX\_UINT256 * UNIT \\
///     (x * y) \% UNIT \geq \frac{UNIT}{2}
/// \end{cases}
/// $$
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {
    uint256 prod0;
    uint256 prod1;
    assembly ("memory-safe") {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    if (prod1 == 0) {
        unchecked {
            return prod0 / UNIT;
        }
    }

    if (prod1 >= UNIT) {
        revert PRBMath_MulDiv18_Overflow(x, y);
    }

    uint256 remainder;
    assembly ("memory-safe") {
        remainder := mulmod(x, y, UNIT)
        result :=
            mul(
                or(
                    div(sub(prod0, remainder), UNIT_LPOTD),
                    mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))
                ),
                UNIT_INVERSE
            )
    }
}

/// @notice Calculates x*y÷denominator with 512-bit precision.
///
/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.
///
/// Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit in int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
/// @custom:smtchecker abstract-function-nondet
function mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {
    if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
        revert PRBMath_MulDivSigned_InputTooSmall();
    }

    // Get hold of the absolute values of x, y and the denominator.
    uint256 xAbs;
    uint256 yAbs;
    uint256 dAbs;
    unchecked {
        xAbs = x < 0 ? uint256(-x) : uint256(x);
        yAbs = y < 0 ? uint256(-y) : uint256(y);
        dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);
    }

    // Compute the absolute value of x*y÷denominator. The result must fit in int256.
    uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);
    if (resultAbs > uint256(type(int256).max)) {
        revert PRBMath_MulDivSigned_Overflow(x, y);
    }

    // Get the signs of x, y and the denominator.
    uint256 sx;
    uint256 sy;
    uint256 sd;
    assembly ("memory-safe") {
        // "sgt" is the "signed greater than" assembly instruction and "sub(0,1)" is -1 in two's complement.
        sx := sgt(x, sub(0, 1))
        sy := sgt(y, sub(0, 1))
        sd := sgt(denominator, sub(0, 1))
    }

    // XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.
    // If there are, the result should be negative. Otherwise, it should be positive.
    unchecked {
        result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - If x is not a perfect square, the result is rounded down.
/// - Credits to OpenZeppelin for the explanations in comments below.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function sqrt(uint256 x) pure returns (uint256 result) {
    if (x == 0) {
        return 0;
    }

    // For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.
    //
    // We know that the "msb" (most significant bit) of x is a power of 2 such that we have:
    //
    // $$
    // msb(x) <= x <= 2*msb(x)$
    // $$
    //
    // We write $msb(x)$ as $2^k$, and we get:
    //
    // $$
    // k = log_2(x)
    // $$
    //
    // Thus, we can write the initial inequality as:
    //
    // $$
    // 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\
    // sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\
    // 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}
    // $$
    //
    // Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.
    uint256 xAux = uint256(x);
    result = 1;
    if (xAux >= 2 ** 128) {
        xAux >>= 128;
        result <<= 64;
    }
    if (xAux >= 2 ** 64) {
        xAux >>= 64;
        result <<= 32;
    }
    if (xAux >= 2 ** 32) {
        xAux >>= 32;
        result <<= 16;
    }
    if (xAux >= 2 ** 16) {
        xAux >>= 16;
        result <<= 8;
    }
    if (xAux >= 2 ** 8) {
        xAux >>= 8;
        result <<= 4;
    }
    if (xAux >= 2 ** 4) {
        xAux >>= 4;
        result <<= 2;
    }
    if (xAux >= 2 ** 2) {
        result <<= 1;
    }

    // At this point, `result` is an estimation with at least one bit of precision. We know the true value has at
    // most 128 bits, since it is the square root of a uint256. Newton's method converges quadratically (precision
    // doubles at every iteration). We thus need at most 7 iteration to turn our partial result with one bit of
    // precision into the expected uint128 result.
    unchecked {
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;

        // If x is not a perfect square, round the result toward zero.
        uint256 roundedResult = x / result;
        if (result >= roundedResult) {
            result = roundedResult;
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD60x18 } from "./ValueType.sol";

/// @notice Thrown when ceiling a number overflows UD60x18.
error PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);

/// @notice Thrown when converting a basic integer to the fixed-point format overflows UD60x18.
error PRBMath_UD60x18_Convert_Overflow(uint256 x);

/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);

/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);

/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows UD60x18.
error PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD21x18.
error PRBMath_UD60x18_IntoSD21x18_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD59x18.
error PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD21x18.
error PRBMath_UD60x18_IntoUD21x18_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);

/// @notice Thrown when taking the logarithm of a number less than UNIT.
error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);

/// @notice Thrown when calculating the square root overflows UD60x18.
error PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Casts a UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x ≤ uMAX_SD1x18
function intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uint256(int256(uMAX_SD1x18))) {
        revert CastingErrors.PRBMath_UD60x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(uint64(xUint)));
}

/// @notice Casts a UD60x18 number into SD21x18.
/// @dev Requirements:
/// - x ≤ uMAX_SD21x18
function intoSD21x18(UD60x18 x) pure returns (SD21x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uint256(int256(uMAX_SD21x18))) {
        revert CastingErrors.PRBMath_UD60x18_IntoSD21x18_Overflow(x);
    }
    result = SD21x18.wrap(int128(uint128(xUint)));
}

/// @notice Casts a UD60x18 number into UD2x18.
/// @dev Requirements:
/// - x ≤ uMAX_UD2x18
function intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uMAX_UD2x18) {
        revert CastingErrors.PRBMath_UD60x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(xUint));
}

/// @notice Casts a UD60x18 number into UD21x18.
/// @dev Requirements:
/// - x ≤ uMAX_UD21x18
function intoUD21x18(UD60x18 x) pure returns (UD21x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uMAX_UD21x18) {
        revert CastingErrors.PRBMath_UD60x18_IntoUD21x18_Overflow(x);
    }
    result = UD21x18.wrap(uint128(xUint));
}

/// @notice Casts a UD60x18 number into SD59x18.
/// @dev Requirements:
/// - x ≤ uMAX_SD59x18
function intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > uint256(uMAX_SD59x18)) {
        revert CastingErrors.PRBMath_UD60x18_IntoSD59x18_Overflow(x);
    }
    result = SD59x18.wrap(int256(xUint));
}

/// @notice Casts a UD60x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint256(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x);
}

/// @notice Casts a UD60x18 number into uint128.
/// @dev Requirements:
/// - x ≤ MAX_UINT128
function intoUint128(UD60x18 x) pure returns (uint128 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT128) {
        revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);
    }
    result = uint128(xUint);
}

/// @notice Casts a UD60x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD60x18 x) pure returns (uint40 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT40) {
        revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud(uint256 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(x);
}

/// @notice Alias for {wrap}.
function ud60x18(uint256 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(x);
}

/// @notice Unwraps a UD60x18 number into uint256.
function unwrap(UD60x18 x) pure returns (uint256 result) {
    result = UD60x18.unwrap(x);
}

/// @notice Wraps a uint256 number into the UD60x18 value type.
function wrap(uint256 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD60x18 } from "./ValueType.sol";

// NOTICE: the "u" prefix stands for "unwrapped".

/// @dev Euler's number as a UD60x18 number.
UD60x18 constant E = UD60x18.wrap(2_718281828459045235);

/// @dev The maximum input permitted in {exp}.
uint256 constant uEXP_MAX_INPUT = 133_084258667509499440;
UD60x18 constant EXP_MAX_INPUT = UD60x18.wrap(uEXP_MAX_INPUT);

/// @dev The maximum input permitted in {exp2}.
uint256 constant uEXP2_MAX_INPUT = 192e18 - 1;
UD60x18 constant EXP2_MAX_INPUT = UD60x18.wrap(uEXP2_MAX_INPUT);

/// @dev Half the UNIT number.
uint256 constant uHALF_UNIT = 0.5e18;
UD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);

/// @dev $log_2(10)$ as a UD60x18 number.
uint256 constant uLOG2_10 = 3_321928094887362347;
UD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);

/// @dev $log_2(e)$ as a UD60x18 number.
uint256 constant uLOG2_E = 1_442695040888963407;
UD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);

/// @dev The maximum value a UD60x18 number can have.
uint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;
UD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);

/// @dev The maximum whole value a UD60x18 number can have.
uint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;
UD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);

/// @dev PI as a UD60x18 number.
UD60x18 constant PI = UD60x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD60x18.
uint256 constant uUNIT = 1e18;
UD60x18 constant UNIT = UD60x18.wrap(uUNIT);

/// @dev The unit number squared.
uint256 constant uUNIT_SQUARED = 1e36;
UD60x18 constant UNIT_SQUARED = UD60x18.wrap(uUNIT_SQUARED);

/// @dev Zero as a UD60x18 number.
UD60x18 constant ZERO = UD60x18.wrap(0);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { wrap } from "./Casting.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the UD60x18 type.
function add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() + y.unwrap());
}

/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() & bits);
}

/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.
function and2(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() & y.unwrap());
}

/// @notice Implements the equal operation (==) in the UD60x18 type.
function eq(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() == y.unwrap();
}

/// @notice Implements the greater than operation (>) in the UD60x18 type.
function gt(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() > y.unwrap();
}

/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.
function gte(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() >= y.unwrap();
}

/// @notice Implements a zero comparison check function in the UD60x18 type.
function isZero(UD60x18 x) pure returns (bool result) {
    // This wouldn't work if x could be negative.
    result = x.unwrap() == 0;
}

/// @notice Implements the left shift operation (<<) in the UD60x18 type.
function lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() << bits);
}

/// @notice Implements the lower than operation (<) in the UD60x18 type.
function lt(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() < y.unwrap();
}

/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.
function lte(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() <= y.unwrap();
}

/// @notice Implements the checked modulo operation (%) in the UD60x18 type.
function mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() % y.unwrap());
}

/// @notice Implements the not equal operation (!=) in the UD60x18 type.
function neq(UD60x18 x, UD60x18 y) pure returns (bool result) {
    result = x.unwrap() != y.unwrap();
}

/// @notice Implements the NOT (~) bitwise operation in the UD60x18 type.
function not(UD60x18 x) pure returns (UD60x18 result) {
    result = wrap(~x.unwrap());
}

/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.
function or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() | y.unwrap());
}

/// @notice Implements the right shift operation (>>) in the UD60x18 type.
function rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.
function sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() - y.unwrap());
}

/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.
function uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    unchecked {
        result = wrap(x.unwrap() + y.unwrap());
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.
function uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    unchecked {
        result = wrap(x.unwrap() - y.unwrap());
    }
}

/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.
function xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {
    result = wrap(x.unwrap() ^ y.unwrap());
}

// 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) (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
// 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 v5.0.1) (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) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC20InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC20InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     * @param allowance Amount of tokens a `spender` is allowed to operate with.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientAllowance(address spender, uint256 allowance, uint256 needed);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC20InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `spender` to be approved. Used in approvals.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC20InvalidSpender(address spender);
}

/**
 * @dev Standard ERC-721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in ERC-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

    /**
     * @dev Indicates a `tokenId` whose `owner` is the zero address.
     * @param tokenId Identifier number of a token.
     */
    error ERC721NonexistentToken(uint256 tokenId);

    /**
     * @dev Indicates an error related to the ownership over a particular token. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param tokenId Identifier number of a token.
     * @param owner Address of the current owner of a token.
     */
    error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC721InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC721InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param tokenId Identifier number of a token.
     */
    error ERC721InsufficientApproval(address operator, uint256 tokenId);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC721InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC721InvalidOperator(address operator);
}

/**
 * @dev Standard ERC-1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC1155InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC1155InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param owner Address of the current owner of a token.
     */
    error ERC1155MissingApprovalForAll(address operator, address owner);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC1155InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC1155InvalidOperator(address operator);

    /**
     * @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
     * Used in batch transfers.
     * @param idsLength Length of the array of token identifiers
     * @param valuesLength Length of the array of token amounts
     */
    error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../tokens/ERC20.sol";
import {SafeTransferLib} from "../utils/SafeTransferLib.sol";
import {FixedPointMathLib} from "../utils/FixedPointMathLib.sol";

/// @notice Minimal ERC4626 tokenized Vault implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/mixins/ERC4626.sol)
abstract contract ERC4626 is ERC20 {
    using SafeTransferLib for ERC20;
    using FixedPointMathLib for uint256;

    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Deposit(address indexed caller, address indexed owner, uint256 assets, uint256 shares);

    event Withdraw(
        address indexed caller,
        address indexed receiver,
        address indexed owner,
        uint256 assets,
        uint256 shares
    );

    /*//////////////////////////////////////////////////////////////
                               IMMUTABLES
    //////////////////////////////////////////////////////////////*/

    ERC20 public immutable asset;

    constructor(
        ERC20 _asset,
        string memory _name,
        string memory _symbol
    ) ERC20(_name, _symbol, _asset.decimals()) {
        asset = _asset;
    }

    /*//////////////////////////////////////////////////////////////
                        DEPOSIT/WITHDRAWAL LOGIC
    //////////////////////////////////////////////////////////////*/

    function deposit(uint256 assets, address receiver) public virtual returns (uint256 shares) {
        // Check for rounding error since we round down in previewDeposit.
        require((shares = previewDeposit(assets)) != 0, "ZERO_SHARES");

        // Need to transfer before minting or ERC777s could reenter.
        asset.safeTransferFrom(msg.sender, address(this), assets);

        _mint(receiver, shares);

        emit Deposit(msg.sender, receiver, assets, shares);

        afterDeposit(assets, shares);
    }

    function mint(uint256 shares, address receiver) public virtual returns (uint256 assets) {
        assets = previewMint(shares); // No need to check for rounding error, previewMint rounds up.

        // Need to transfer before minting or ERC777s could reenter.
        asset.safeTransferFrom(msg.sender, address(this), assets);

        _mint(receiver, shares);

        emit Deposit(msg.sender, receiver, assets, shares);

        afterDeposit(assets, shares);
    }

    function withdraw(
        uint256 assets,
        address receiver,
        address owner
    ) public virtual returns (uint256 shares) {
        shares = previewWithdraw(assets); // No need to check for rounding error, previewWithdraw rounds up.

        if (msg.sender != owner) {
            uint256 allowed = allowance[owner][msg.sender]; // Saves gas for limited approvals.

            if (allowed != type(uint256).max) allowance[owner][msg.sender] = allowed - shares;
        }

        beforeWithdraw(assets, shares);

        _burn(owner, shares);

        emit Withdraw(msg.sender, receiver, owner, assets, shares);

        asset.safeTransfer(receiver, assets);
    }

    function redeem(
        uint256 shares,
        address receiver,
        address owner
    ) public virtual returns (uint256 assets) {
        if (msg.sender != owner) {
            uint256 allowed = allowance[owner][msg.sender]; // Saves gas for limited approvals.

            if (allowed != type(uint256).max) allowance[owner][msg.sender] = allowed - shares;
        }

        // Check for rounding error since we round down in previewRedeem.
        require((assets = previewRedeem(shares)) != 0, "ZERO_ASSETS");

        beforeWithdraw(assets, shares);

        _burn(owner, shares);

        emit Withdraw(msg.sender, receiver, owner, assets, shares);

        asset.safeTransfer(receiver, assets);
    }

    /*//////////////////////////////////////////////////////////////
                            ACCOUNTING LOGIC
    //////////////////////////////////////////////////////////////*/

    function totalAssets() public view virtual returns (uint256);

    function convertToShares(uint256 assets) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? assets : assets.mulDivDown(supply, totalAssets());
    }

    function convertToAssets(uint256 shares) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? shares : shares.mulDivDown(totalAssets(), supply);
    }

    function previewDeposit(uint256 assets) public view virtual returns (uint256) {
        return convertToShares(assets);
    }

    function previewMint(uint256 shares) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? shares : shares.mulDivUp(totalAssets(), supply);
    }

    function previewWithdraw(uint256 assets) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? assets : assets.mulDivUp(supply, totalAssets());
    }

    function previewRedeem(uint256 shares) public view virtual returns (uint256) {
        return convertToAssets(shares);
    }

    /*//////////////////////////////////////////////////////////////
                     DEPOSIT/WITHDRAWAL LIMIT LOGIC
    //////////////////////////////////////////////////////////////*/

    function maxDeposit(address) public view virtual returns (uint256) {
        return type(uint256).max;
    }

    function maxMint(address) public view virtual returns (uint256) {
        return type(uint256).max;
    }

    function maxWithdraw(address owner) public view virtual returns (uint256) {
        return convertToAssets(balanceOf[owner]);
    }

    function maxRedeem(address owner) public view virtual returns (uint256) {
        return balanceOf[owner];
    }

    /*//////////////////////////////////////////////////////////////
                          INTERNAL HOOKS LOGIC
    //////////////////////////////////////////////////////////////*/

    function beforeWithdraw(uint256 assets, uint256 shares) internal virtual {}

    function afterDeposit(uint256 assets, uint256 shares) internal virtual {}
}

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

/// @dev The original console.sol uses `int` and `uint` for computing function selectors, but it should
/// use `int256` and `uint256`. This modified version fixes that. This version is recommended
/// over `console.sol` if you don't need compatibility with Hardhat as the logs will show up in
/// forge stack traces. If you do need compatibility with Hardhat, you must use `console.sol`.
/// Reference: https://github.com/NomicFoundation/hardhat/issues/2178
library console2 {
    address constant CONSOLE_ADDRESS = address(0x000000000000000000636F6e736F6c652e6c6f67);

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

    function _sendLogPayload(bytes memory payload) internal pure {
        _castLogPayloadViewToPure(_sendLogPayloadView)(payload);
    }

    function _sendLogPayloadView(bytes memory payload) private view {
        uint256 payloadLength = payload.length;
        address consoleAddress = CONSOLE_ADDRESS;
        /// @solidity memory-safe-assembly
        assembly {
            let payloadStart := add(payload, 32)
            let r := staticcall(gas(), consoleAddress, payloadStart, payloadLength, 0, 0)
        }
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    function log(string memory p0, int256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,int256)", p0, p1));
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD1x18 } from "./ValueType.sol";

/// @dev Euler's number as an SD1x18 number.
SD1x18 constant E = SD1x18.wrap(2_718281828459045235);

/// @dev The maximum value an SD1x18 number can have.
int64 constant uMAX_SD1x18 = 9_223372036854775807;
SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);

/// @dev The minimum value an SD1x18 number can have.
int64 constant uMIN_SD1x18 = -9_223372036854775808;
SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);

/// @dev PI as an SD1x18 number.
SD1x18 constant PI = SD1x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD1x18.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int64 constant uUNIT = 1e18;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;

/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD1x18 is int64;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for SD1x18 global;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD21x18 } from "./ValueType.sol";

/// @dev Euler's number as an SD21x18 number.
SD21x18 constant E = SD21x18.wrap(2_718281828459045235);

/// @dev The maximum value an SD21x18 number can have.
int128 constant uMAX_SD21x18 = 170141183460469231731_687303715884105727;
SD21x18 constant MAX_SD21x18 = SD21x18.wrap(uMAX_SD21x18);

/// @dev The minimum value an SD21x18 number can have.
int128 constant uMIN_SD21x18 = -170141183460469231731_687303715884105728;
SD21x18 constant MIN_SD21x18 = SD21x18.wrap(uMIN_SD21x18);

/// @dev PI as an SD21x18 number.
SD21x18 constant PI = SD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD21x18.
SD21x18 constant UNIT = SD21x18.wrap(1e18);
int128 constant uUNIT = 1e18;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;

/// @notice The signed 21.18-decimal fixed-point number representation, which can have up to 21 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int128. This is useful when end users want to use int128 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD21x18 is int128;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for SD21x18 global;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD59x18 } from "./ValueType.sol";

// NOTICE: the "u" prefix stands for "unwrapped".

/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);

/// @dev The maximum input permitted in {exp}.
int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp}.
int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);

/// @dev The maximum input permitted in {exp2}.
int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp2}.
int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);

/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);

/// @dev $log_2(10)$ as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);

/// @dev $log_2(e)$ as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);

/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);

/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);

/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);

/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);

/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD59x18.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);

/// @dev The unit number squared.
int256 constant uUNIT_SQUARED = 1e36;
SD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);

/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;
import "./Helpers.sol" as Helpers;
import "./Math.sol" as Math;

/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int256.
type SD59x18 is int256;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoInt256,
    Casting.intoSD1x18,
    Casting.intoSD21x18,
    Casting.intoUD2x18,
    Casting.intoUD21x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for SD59x18 global;

/*//////////////////////////////////////////////////////////////////////////
                            MATHEMATICAL FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

using {
    Math.abs,
    Math.avg,
    Math.ceil,
    Math.div,
    Math.exp,
    Math.exp2,
    Math.floor,
    Math.frac,
    Math.gm,
    Math.inv,
    Math.log10,
    Math.log2,
    Math.ln,
    Math.mul,
    Math.pow,
    Math.powu,
    Math.sqrt
} for SD59x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                HELPER FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

using {
    Helpers.add,
    Helpers.and,
    Helpers.eq,
    Helpers.gt,
    Helpers.gte,
    Helpers.isZero,
    Helpers.lshift,
    Helpers.lt,
    Helpers.lte,
    Helpers.mod,
    Helpers.neq,
    Helpers.not,
    Helpers.or,
    Helpers.rshift,
    Helpers.sub,
    Helpers.uncheckedAdd,
    Helpers.uncheckedSub,
    Helpers.uncheckedUnary,
    Helpers.xor
} for SD59x18 global;

/*//////////////////////////////////////////////////////////////////////////
                                    OPERATORS
//////////////////////////////////////////////////////////////////////////*/

// The global "using for" directive makes it possible to use these operators on the SD59x18 type.
using {
    Helpers.add as +,
    Helpers.and2 as &,
    Math.div as /,
    Helpers.eq as ==,
    Helpers.gt as >,
    Helpers.gte as >=,
    Helpers.lt as <,
    Helpers.lte as <=,
    Helpers.mod as %,
    Math.mul as *,
    Helpers.neq as !=,
    Helpers.not as ~,
    Helpers.or as |,
    Helpers.sub as -,
    Helpers.unary as -,
    Helpers.xor as ^
} for SD59x18 global;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD2x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);

/// @dev PI as a UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD2x18.
UD2x18 constant UNIT = UD2x18.wrap(1e18);
uint64 constant uUNIT = 1e18;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD21x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD21x18 number.
UD21x18 constant E = UD21x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD21x18 number can have.
uint128 constant uMAX_UD21x18 = 340282366920938463463_374607431768211455;
UD21x18 constant MAX_UD21x18 = UD21x18.wrap(uMAX_UD21x18);

/// @dev PI as a UD21x18 number.
UD21x18 constant PI = UD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD21x18.
uint256 constant uUNIT = 1e18;
UD21x18 constant UNIT = UD21x18.wrap(1e18);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;

/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD2x18 is uint64;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD2x18 global;

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Casting.sol" as Casting;

/// @notice The unsigned 21.18-decimal fixed-point number representation, which can have up to 21 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint128. This is useful when end users want to use uint128 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD21x18 is uint128;

/*//////////////////////////////////////////////////////////////////////////
                                    CASTING
//////////////////////////////////////////////////////////////////////////*/

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD21x18 global;

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Modern and gas efficient ERC20 + EIP-2612 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC20.sol)
/// @author Modified from Uniswap (https://github.com/Uniswap/uniswap-v2-core/blob/master/contracts/UniswapV2ERC20.sol)
/// @dev Do not manually set balances without updating totalSupply, as the sum of all user balances must not exceed it.
abstract contract ERC20 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*//////////////////////////////////////////////////////////////
                            METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public name;

    string public symbol;

    uint8 public immutable decimals;

    /*//////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

    /*//////////////////////////////////////////////////////////////
                            EIP-2612 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 internal immutable INITIAL_CHAIN_ID;

    bytes32 internal immutable INITIAL_DOMAIN_SEPARATOR;

    mapping(address => uint256) public nonces;

    /*//////////////////////////////////////////////////////////////
                               CONSTRUCTOR
    //////////////////////////////////////////////////////////////*/

    constructor(
        string memory _name,
        string memory _symbol,
        uint8 _decimals
    ) {
        name = _name;
        symbol = _symbol;
        decimals = _decimals;

        INITIAL_CHAIN_ID = block.chainid;
        INITIAL_DOMAIN_SEPARATOR = computeDomainSeparator();
    }

    /*//////////////////////////////////////////////////////////////
                               ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 amount) public virtual returns (bool) {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);

        return true;
    }

    function transfer(address to, uint256 amount) public virtual returns (bool) {
        balanceOf[msg.sender] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(msg.sender, to, amount);

        return true;
    }

    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual returns (bool) {
        uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.

        if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;

        balanceOf[from] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(from, to, amount);

        return true;
    }

    /*//////////////////////////////////////////////////////////////
                             EIP-2612 LOGIC
    //////////////////////////////////////////////////////////////*/

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual {
        require(deadline >= block.timestamp, "PERMIT_DEADLINE_EXPIRED");

        // Unchecked because the only math done is incrementing
        // the owner's nonce which cannot realistically overflow.
        unchecked {
            address recoveredAddress = ecrecover(
                keccak256(
                    abi.encodePacked(
                        "\x19\x01",
                        DOMAIN_SEPARATOR(),
                        keccak256(
                            abi.encode(
                                keccak256(
                                    "Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"
                                ),
                                owner,
                                spender,
                                value,
                                nonces[owner]++,
                                deadline
                            )
                        )
                    )
                ),
                v,
                r,
                s
            );

            require(recoveredAddress != address(0) && recoveredAddress == owner, "INVALID_SIGNER");

            allowance[recoveredAddress][spender] = value;
        }

        emit Approval(owner, spender, value);
    }

    function DOMAIN_SEPARATOR() public view virtual returns (bytes32) {
        return block.chainid == INITIAL_CHAIN_ID ? INITIAL_DOMAIN_SEPARATOR : computeDomainSeparator();
    }

    function computeDomainSeparator() internal view virtual returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                    keccak256(bytes(name)),
                    keccak256("1"),
                    block.chainid,
                    address(this)
                )
            );
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(address to, uint256 amount) internal virtual {
        totalSupply += amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(address(0), to, amount);
    }

    function _burn(address from, uint256 amount) internal virtual {
        balanceOf[from] -= amount;

        // Cannot underflow because a user's balance
        // will never be larger than the total supply.
        unchecked {
            totalSupply -= amount;
        }

        emit Transfer(from, address(0), amount);
    }
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../tokens/ERC20.sol";

/// @notice Safe ETH and ERC20 transfer library that gracefully handles missing return values.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeTransferLib.sol)
/// @dev Use with caution! Some functions in this library knowingly create dirty bits at the destination of the free memory pointer.
/// @dev Note that none of the functions in this library check that a token has code at all! That responsibility is delegated to the caller.
library SafeTransferLib {
    /*//////////////////////////////////////////////////////////////
                             ETH OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function safeTransferETH(address to, uint256 amount) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Transfer the ETH and store if it succeeded or not.
            success := call(gas(), to, amount, 0, 0, 0, 0)
        }

        require(success, "ETH_TRANSFER_FAILED");
    }

    /*//////////////////////////////////////////////////////////////
                            ERC20 OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function safeTransferFrom(
        ERC20 token,
        address from,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0x23b872dd00000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(from, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "from" argument.
            mstore(add(freeMemoryPointer, 36), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 68), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 100 because the length of our calldata totals up like so: 4 + 32 * 3.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 100, 0, 32)
            )
        }

        require(success, "TRANSFER_FROM_FAILED");
    }

    function safeTransfer(
        ERC20 token,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0xa9059cbb00000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 68, 0, 32)
            )
        }

        require(success, "TRANSFER_FAILED");
    }

    function safeApprove(
        ERC20 token,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0x095ea7b300000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 68, 0, 32)
            )
        }

        require(success, "APPROVE_FAILED");
    }
}

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    uint256 internal constant MAX_UINT256 = 2**256 - 1;

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

    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }

    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }

    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }

    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }

    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                revert(0, 0)
            }

            // Divide x * y by the denominator.
            z := div(mul(x, y), denominator)
        }
    }

    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                revert(0, 0)
            }

            // If x * y modulo the denominator is strictly greater than 0,
            // 1 is added to round up the division of x * y by the denominator.
            z := add(gt(mod(mul(x, y), denominator), 0), div(mul(x, y), denominator))
        }
    }

    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }

                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)

                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }

                    // Store x squared.
                    let xx := mul(x, x)

                    // Round to the nearest number.
                    let xxRound := add(xx, half)

                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }

                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)

                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)

                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }

                        // Round to the nearest number.
                        let zxRound := add(zx, half)

                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }

                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }

    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/

    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.

            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.

            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, 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(y, 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }

    function unsafeMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Mod x by y. Note this will return
            // 0 instead of reverting if y is zero.
            z := mod(x, y)
        }
    }

    function unsafeDiv(uint256 x, uint256 y) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // Divide x by y. Note this will return
            // 0 instead of reverting if y is zero.
            r := div(x, y)
        }
    }

    function unsafeDivUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Add 1 to x * y if x % y > 0. Note this will
            // return 0 instead of reverting if y is zero.
            z := add(gt(mod(x, y), 0), div(x, y))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";

/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because SD1x18 ⊆ SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}

/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD1x18 x) pure returns (uint128 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
    }
    result = uint128(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD1x18 x) pure returns (uint256 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
    }
    result = uint256(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD1x18 x) pure returns (uint40 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
    }
    if (xInt > int64(uint64(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
    }
    result = uint40(uint64(xInt));
}

/// @notice Alias for {wrap}.
function sd1x18(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
    result = SD1x18.unwrap(x);
}

/// @notice Wraps an int64 number into SD1x18.
function wrap(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD21x18 } from "./ValueType.sol";

/// @notice Casts an SD21x18 number into SD59x18.
/// @dev There is no overflow check because SD21x18 ⊆ SD59x18.
function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD21x18.unwrap(x)));
}

/// @notice Casts an SD21x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD21x18 x) pure returns (uint128 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint128_Underflow(x);
    }
    result = uint128(xInt);
}

/// @notice Casts an SD21x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD21x18 x) pure returns (uint256 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint256_Underflow(x);
    }
    result = uint256(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD21x18 x) pure returns (uint40 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Underflow(x);
    }
    if (xInt > int128(uint128(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Overflow(x);
    }
    result = uint40(uint128(xInt));
}

/// @notice Alias for {wrap}.
function sd21x18(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

/// @notice Unwraps an SD21x18 number into int128.
function unwrap(SD21x18 x) pure returns (int128 result) {
    result = SD21x18.unwrap(x);
}

/// @notice Wraps an int128 number into SD21x18.
function wrap(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD21x18, uMIN_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for {unwrap}.
function intoInt256(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD1x18
/// - x ≤ uMAX_SD1x18
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
    }
    if (xInt > uMAX_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xInt));
}

/// @notice Casts an SD59x18 number into SD21x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD21x18
/// - x ≤ uMAX_SD21x18
function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Underflow(x);
    }
    if (xInt > uMAX_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Overflow(x);
    }
    result = SD21x18.wrap(int128(xInt));
}

/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD2x18
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD2x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD21x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD21x18
function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD21x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Overflow(x);
    }
    result = UD21x18.wrap(uint128(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD59x18 x) pure returns (uint256 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);
    }
    result = uint256(xInt);
}

/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UINT128
function intoUint128(SD59x18 x) pure returns (uint128 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT128))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
    }
    result = uint128(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

/// @notice Alias for {wrap}.
function sd(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Alias for {wrap}.
function sd59x18(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Wraps an int256 number into SD59x18.
function wrap(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() + y.unwrap());
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & bits);
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & y.unwrap());
}

/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() == y.unwrap();
}

/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() > y.unwrap();
}

/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() >= y.unwrap();
}

/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
    result = x.unwrap() == 0;
}

/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() << bits);
}

/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() < y.unwrap();
}

/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() <= y.unwrap();
}

/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % y.unwrap());
}

/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() != y.unwrap();
}

/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(~x.unwrap());
}

/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() | y.unwrap());
}

/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() - y.unwrap());
}

/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(-x.unwrap());
}

/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() + y.unwrap());
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() - y.unwrap());
    }
}

/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(-x.unwrap());
    }
}

/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() ^ y.unwrap());
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
    uEXP_MAX_INPUT,
    uEXP2_MAX_INPUT,
    uEXP_MIN_THRESHOLD,
    uEXP2_MIN_THRESHOLD,
    uHALF_UNIT,
    uLOG2_10,
    uLOG2_E,
    uMAX_SD59x18,
    uMAX_WHOLE_SD59x18,
    uMIN_SD59x18,
    uMIN_WHOLE_SD59x18,
    UNIT,
    uUNIT,
    uUNIT_SQUARED,
    ZERO
} from "./Constants.sol";
import { wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Calculates the absolute value of x.
///
/// @dev Requirements:
/// - x > MIN_SD59x18.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @return result The absolute value of x as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function abs(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();
    }
    result = xInt < 0 ? wrap(-xInt) : x;
}

/// @notice Calculates the arithmetic average of x and y.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

    unchecked {
        // This operation is equivalent to `x / 2 +  y / 2`, and it can never overflow.
        int256 sum = (xInt >> 1) + (yInt >> 1);

        if (sum < 0) {
            // If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right
            // rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.
            assembly ("memory-safe") {
                result := add(sum, and(or(xInt, yInt), 1))
            }
        } else {
            // Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.
            result = wrap(sum + (xInt & yInt & 1));
        }
    }
}

/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≤ MAX_WHOLE_SD59x18
///
/// @param x The SD59x18 number to ceil.
/// @return result The smallest whole number greater than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt > uMAX_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt > 0) {
                resultInt += uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.
///
/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute
/// values separately.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator must not be zero.
/// - The result must fit in SD59x18.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @return result The quotient as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Div_InputTooSmall();
    }

    // Get hold of the absolute values of x and y.
    uint256 xAbs;
    uint256 yAbs;
    unchecked {
        xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
        yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
    }

    // Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}.
///
/// Requirements:
/// - Refer to the requirements in {exp2}.
/// - x < 133_084258667509499441.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();

    // Any input less than the threshold returns zero.
    // This check also prevents an overflow for very small numbers.
    if (xInt < uEXP_MIN_THRESHOLD) {
        return ZERO;
    }

    // This check prevents values greater than 192e18 from being passed to {exp2}.
    if (xInt > uEXP_MAX_INPUT) {
        revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
    }

    unchecked {
        // Inline the fixed-point multiplication to save gas.
        int256 doubleUnitProduct = xInt * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Notes:
/// - If x < -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x < 192e18.
/// - The result must fit in SD59x18.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        // The inverse of any number less than the threshold is truncated to zero.
        if (xInt < uEXP2_MIN_THRESHOLD) {
            return ZERO;
        }

        unchecked {
            // Inline the fixed-point inversion to save gas.
            result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());
        }
    } else {
        // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
        if (xInt > uEXP2_MAX_INPUT) {
            revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);
        }

        unchecked {
            // Convert x to the 192.64-bit fixed-point format.
            uint256 x_192x64 = uint256((xInt << 64) / uUNIT);

            // It is safe to cast the result to int256 due to the checks above.
            result = wrap(int256(Common.exp2(x_192x64)));
        }
    }
}

/// @notice Yields the greatest whole number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≥ MIN_WHOLE_SD59x18
///
/// @param x The SD59x18 number to floor.
/// @return result The greatest whole number less than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < uMIN_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Floor_Underflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt < 0) {
                resultInt -= uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @return result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % uUNIT);
}

/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x * y must fit in SD59x18.
/// - x * y must not be negative, since complex numbers are not supported.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == 0 || yInt == 0) {
        return ZERO;
    }

    unchecked {
        // Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.
        int256 xyInt = xInt * yInt;
        if (xyInt / xInt != yInt) {
            revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);
        }

        // The product must not be negative, since complex numbers are not supported.
        if (xyInt < 0) {
            revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
        // during multiplication. See the comments in {Common.sqrt}.
        uint256 resultUint = Common.sqrt(uint256(xyInt));
        result = wrap(int256(resultUint));
    }
}

/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(uUNIT_SQUARED / x.unwrap());
}

/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(SD59x18 x) pure returns (SD59x18 result) {
    // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
    // {log2} can return is ~195_205294292027477728.
    result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}

/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        default { result := uMAX_SD59x18 }
    }

    if (result.unwrap() == uMAX_SD59x18) {
        unchecked {
            // Inline the fixed-point division to save gas.
            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x > 0
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt <= 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    unchecked {
        int256 sign;
        if (xInt >= uUNIT) {
            sign = 1;
        } else {
            sign = -1;
            // Inline the fixed-point inversion to save gas.
            xInt = uUNIT_SQUARED / xInt;
        }

        // Calculate the integer part of the logarithm.
        uint256 n = Common.msb(uint256(xInt / uUNIT));

        // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
        // because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.
        int256 resultInt = int256(n) * uUNIT;

        // Calculate $y = x * 2^{-n}$.
        int256 y = xInt >> n;

        // If y is the unit number, the fractional part is zero.
        if (y == uUNIT) {
            return wrap(resultInt * sign);
        }

        // Calculate the fractional part via the iterative approximation.
        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
        int256 DOUBLE_UNIT = 2e18;
        for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

            // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?
            if (y >= DOUBLE_UNIT) {
                // Add the 2^{-m} factor to the logarithm.
                resultInt = resultInt + delta;

                // Halve y, which corresponds to z/2 in the Wikipedia article.
                y >>= 1;
            }
        }
        resultInt *= sign;
        result = wrap(resultInt);
    }
}

/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev Notes:
/// - Refer to the notes in {Common.mulDiv18}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv18}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit in SD59x18.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();
    }

    // Get hold of the absolute values of x and y.
    uint256 xAbs;
    uint256 yAbs;
    unchecked {
        xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);
        yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);
    }

    // Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Raises x to the power of y using the following formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}, {log2}, and {mul}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

    // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.
    if (xInt == 0) {
        return yInt == 0 ? UNIT : ZERO;
    }
    // If x is `UNIT`, the result is always `UNIT`.
    else if (xInt == uUNIT) {
        return UNIT;
    }

    // If y is zero, the result is always `UNIT`.
    if (yInt == 0) {
        return UNIT;
    }
    // If y is `UNIT`, the result is always x.
    else if (yInt == uUNIT) {
        return x;
    }

    // Calculate the result using the formula.
    result = exp2(mul(log2(x), y));
}

/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {abs} and {Common.mulDiv18}.
/// - The result must fit in SD59x18.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
    uint256 xAbs = uint256(abs(x).unwrap());

    // Calculate the first iteration of the loop in advance.
    uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);

    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.
    uint256 yAux = y;
    for (yAux >>= 1; yAux > 0; yAux >>= 1) {
        xAbs = Common.mulDiv18(xAbs, xAbs);

        // Equivalent to `y % 2 == 1`.
        if (yAux & 1 > 0) {
            resultAbs = Common.mulDiv18(resultAbs, xAbs);
        }
    }

    // The result must fit in SD59x18.
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);
    }

    unchecked {
        // Is the base negative and the exponent odd? If yes, the result should be negative.
        int256 resultInt = int256(resultAbs);
        bool isNegative = x.unwrap() < 0 && y & 1 == 1;
        if (isNegative) {
            resultInt = -resultInt;
        }
        result = wrap(resultInt);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - Only the positive root is returned.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x ≥ 0, since complex numbers are not supported.
/// - x ≤ MAX_SD59x18 / UNIT
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);
    }
    if (xInt > uMAX_SD59x18 / uUNIT) {
        revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);
    }

    unchecked {
        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.
        // In this case, the two numbers are both the square root.
        uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));
        result = wrap(int256(resultUint));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because UD2x18 ⊆ SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}

/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because UD2x18 ⊆ UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because UD2x18 ⊆ uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
    result = uint128(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because UD2x18 ⊆ uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
    result = uint256(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD2x18 x) pure returns (uint40 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
    result = UD2x18.unwrap(x);
}

/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD21x18 } from "./ValueType.sol";

/// @notice Casts a UD21x18 number into SD59x18.
/// @dev There is no overflow check because UD21x18 ⊆ SD59x18.
function intoSD59x18(UD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD21x18.unwrap(x))));
}

/// @notice Casts a UD21x18 number into UD60x18.
/// @dev There is no overflow check because UD21x18 ⊆ UD60x18.
function intoUD60x18(UD21x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint128(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Casts a UD21x18 number into uint256.
/// @dev There is no overflow check because UD21x18 ⊆ uint256.
function intoUint256(UD21x18 x) pure returns (uint256 result) {
    result = uint256(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD21x18 x) pure returns (uint40 result) {
    uint128 xUint = UD21x18.unwrap(x);
    if (xUint > uint128(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD21x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud21x18(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

/// @notice Unwrap a UD21x18 number into uint128.
function unwrap(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Wraps a uint128 number into UD21x18.
function wrap(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD1x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD21x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint128.
error PRBMath_SD21x18_ToUint128_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in UD60x18.
error PRBMath_SD21x18_ToUD60x18_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint256.
error PRBMath_SD21x18_ToUint256_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Overflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Underflow(SD21x18 x);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { SD59x18 } from "./ValueType.sol";

/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();

/// @notice Thrown when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);

/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);

/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);

/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();

/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);

/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);

/// @notice Thrown when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);

/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);

/// @notice Thrown when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);

/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();

/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);

/// @notice Thrown when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);

/// @notice Thrown when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD2x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);

// SPDX-License-Identifier: MIT
pragma solidity >=0.8.19;

import { UD21x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD21x18 number that doesn't fit in uint40.
error PRBMath_UD21x18_IntoUint40_Overflow(UD21x18 x);

{
  "remappings": [
    "frax-std/=lib/frax-standard-solidity/src/",
    "ds-test/=lib/frax-standard-solidity/lib/forge-std/lib/ds-test/src/",
    "solmate/=lib/solmate/src/",
    "@prb/math/=node_modules/@prb/math/",
    "@openzeppelin/=node_modules/@openzeppelin/",
    "@openzeppelin-4/=node_modules/@openzeppelin-4/",
    "forge-std/=lib/frax-standard-solidity/lib/forge-std/src/",
    "frax-standard-solidity/=lib/frax-standard-solidity/src/",
    "solidity-bytes-utils/=lib/frax-standard-solidity/lib/solidity-bytes-utils/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 777777
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "none",
    "appendCBOR": false
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "cancun",
  "viaIR": false
}

• No Contract Security Audit Submitted- Submit Audit Here

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lity":"view","type":"function"},{"inputs":[],"name":"pricePerShareIncPerSecond","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"pricePerShareStored","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"renounceOwnership","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"rewardsCycleData","outputs":[{"components":[{"internalType":"uint40","name":"cycleEnd","type":"uint40"},{"internalType":"uint40","name":"lastSync","type":"uint40"},{"internalType":"uint216","name":"rewardCycleAmount","type":"uint216"}],"internalType":"struct SfrxUsd2OracleImplementation.RewardsCycleData","name":"","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"_newPricePerShareStored","type":"uint256"},{"internalType":"uint256","name":"_newPricePerShareIncPerSecond","type":"uint256"},{"internalType":"uint256","name":"_newLastSync","type":"uint256"}],"name":"setAllPricingParams","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"_sender","type":"address"},{"internalType":"bool","name":"_status","type":"bool"}],"name":"setAllowed","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"_newPricePerShareIncPerSecond","type":"uint256"}],"name":"setPricePerShareIncPerSecond","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"_newPricePerShareStored","type":"uint256"}],"name":"setPricePerShareStored","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"storedTotalAssets","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"totalAssets","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"totalSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"pure","type":"function"},{"inputs":[{"internalType":"address","name":"newOwner","type":"address"}],"name":"transferOwnership","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"wasInitialized","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"}]

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00000000000000000000000031562ae726afebe25417df01bedc72ef489f45b3

-----Decoded View---------------
Arg [0] : initialOwner (address): 0x31562ae726AFEBe25417df01bEdC72EF489F45b3

-----Encoded View---------------
1 Constructor Arguments found :
Arg [0] : 00000000000000000000000031562ae726afebe25417df01bedc72ef489f45b3