creation_sourcecode: {{
    "language": "Solidity",
    "sources": {
      "contracts/oracle/morpho/mainnet/MorphoFeedPTezETHDec24.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0\n\npragma solidity ^0.8.12;\n\nimport \"@chainlink/contracts/src/v0.8/interfaces/AggregatorV3Interface.sol\";\n\nimport \"../../BaseFeedPTPendle.sol\";\nimport \"../../FeedPTForSY.sol\";\n\n/// @title MorphoFeedPTezETHDec24\n/// @author Angle Labs, Inc.\n/// @notice Gives the price of PT-ezETH in ETH in base 18\ncontract MorphoFeedPTezETHDec24 is BaseFeedPTPendle {\n    string public constant description = \"PT-ezETH/ETH Oracle\";\n\n    constructor(\n        IAccessControlManager accessControlManager,\n        uint256 _maxImpliedRate,\n        uint32 _twapDuration\n    ) BaseFeedPTPendle(accessControlManager, _maxImpliedRate, _twapDuration) {}\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                       OVERRIDES                                                    \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    // function _pendlePTPrice(\n    //     IPMarket _market,\n    //     uint32 _twapDuration\n    // ) internal view override(BaseOraclePTPendle, FeedPTForSY) returns (uint256, uint256) {\n    //     return BaseOraclePTPendle._pendlePTPrice(_market, _twapDuration);\n    // }\n\n    function asset() public pure override returns (address) {\n        return 0xbf5495Efe5DB9ce00f80364C8B423567e58d2110;\n    }\n\n    function sy() public pure override returns (address) {\n        return 0x22E12A50e3ca49FB183074235cB1db84Fe4C716D;\n    }\n\n    function maturity() public pure override returns (uint256) {\n        return 1735171200;\n    }\n\n    function market() public pure override returns (address) {\n        return 0xD8F12bCDE578c653014F27379a6114F67F0e445f;\n    }\n}\n"
      },
      "node_modules/@chainlink/contracts/src/v0.8/interfaces/AggregatorV3Interface.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity ^0.8.0;\n\ninterface AggregatorV3Interface {\n\n  function decimals()\n    external\n    view\n    returns (\n      uint8\n    );\n\n  function description()\n    external\n    view\n    returns (\n      string memory\n    );\n\n  function version()\n    external\n    view\n    returns (\n      uint256\n    );\n\n  // getRoundData and latestRoundData should both raise \"No data present\"\n  // if they do not have data to report, instead of returning unset values\n  // which could be misinterpreted as actual reported values.\n  function getRoundData(\n    uint80 _roundId\n  )\n    external\n    view\n    returns (\n      uint80 roundId,\n      int256 answer,\n      uint256 startedAt,\n      uint256 updatedAt,\n      uint80 answeredInRound\n    );\n\n  function latestRoundData()\n    external\n    view\n    returns (\n      uint80 roundId,\n      int256 answer,\n      uint256 startedAt,\n      uint256 updatedAt,\n      uint80 answeredInRound\n    );\n\n}\n"
      },
      "contracts/oracle/BaseFeedPTPendle.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0\n\n/*\n                  *                                                  █                              \n                *****                                               ▓▓▓                             \n                  *                                               ▓▓▓▓▓▓▓                         \n                                   *            ///.           ▓▓▓▓▓▓▓▓▓▓▓▓▓                       \n                                 *****        ////////            ▓▓▓▓▓▓▓                          \n                                   *       /////////////            ▓▓▓                             \n                     ▓▓                  //////////////////          █         ▓▓                   \n                   ▓▓  ▓▓             ///////////////////////                ▓▓   ▓▓                \n                ▓▓       ▓▓        ////////////////////////////           ▓▓        ▓▓              \n              ▓▓            ▓▓    /////////▓▓▓///////▓▓▓/////////       ▓▓             ▓▓            \n           ▓▓                 ,////////////////////////////////////// ▓▓                 ▓▓         \n        ▓▓                  //////////////////////////////////////////                     ▓▓      \n      ▓▓                  //////////////////////▓▓▓▓/////////////////////                          \n                       ,////////////////////////////////////////////////////                        \n                    .//////////////////////////////////////////////////////////                     \n                     .//////////////////////////██.,//////////////////////////█                     \n                       .//////////////////////████..,./////////////////////██                       \n                        ...////////////////███████.....,.////////////////███                        \n                          ,.,////////////████████ ........,///////////████                          \n                            .,.,//////█████████      ,.......///////████                            \n                               ,..//████████           ........./████                               \n                                 ..,██████                .....,███                                 \n                                    .██                     ,.,█                                    \n                                                                                                    \n                                                                                                    \n                                                                                                    \n               ▓▓            ▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓        ▓▓               ▓▓▓▓▓▓▓▓▓▓          \n             ▓▓▓▓▓▓          ▓▓▓    ▓▓▓       ▓▓▓               ▓▓               ▓▓   ▓▓▓▓         \n           ▓▓▓    ▓▓▓        ▓▓▓    ▓▓▓       ▓▓▓    ▓▓▓        ▓▓               ▓▓▓▓▓             \n          ▓▓▓        ▓▓      ▓▓▓    ▓▓▓       ▓▓▓▓▓▓▓▓▓▓        ▓▓▓▓▓▓▓▓▓▓       ▓▓▓▓▓▓▓▓▓▓          \n*/\n\npragma solidity ^0.8.12;\n\nimport \"@chainlink/contracts/src/v0.8/interfaces/AggregatorV3Interface.sol\";\n\nimport \"../utils/AccessControlManager.sol\";\nimport \"./BaseOraclePTPendle.sol\";\n\n/// @title BaseFeedPtPendle\n/// @author Angle Labs, Inc.\n/// @notice Base Contract to implement the AggregatorV3Interface for Pendle PT tokens\nabstract contract BaseFeedPTPendle is AccessControl, AggregatorV3Interface, BaseOraclePTPendle {\n    // =================================== Errors ===================================\n\n    /// @notice Constructor for an oracle following AggregatorV3Interface\n    /// @param accessControlManager Contract managing authorization\n    constructor(\n        IAccessControlManager accessControlManager,\n        uint256 _maxImpliedRate,\n        uint32 _twapDuration\n    ) AccessControl(accessControlManager) BaseOraclePTPendle(_maxImpliedRate, _twapDuration) {}\n\n    modifier onlyGovernorOrGuardian() override(AccessControl, BaseOraclePTPendle) {\n        if (!accessControlManager.isGovernorOrGuardian(msg.sender)) revert NotGovernorOrGuardian();\n        _;\n    }\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                 AGGREGATORV3INTERFACE                                              \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    /// @inheritdoc AggregatorV3Interface\n    function decimals() external pure returns (uint8) {\n        return 18;\n    }\n\n    /// @inheritdoc AggregatorV3Interface\n    function version() external pure returns (uint256) {\n        return 1;\n    }\n\n    /// @inheritdoc AggregatorV3Interface\n    function getRoundData(\n        uint80 _roundId\n    )\n        external\n        view\n        virtual\n        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound)\n    {\n        return (0, int256(_getQuoteAmount()), 0, 0, 0);\n    }\n\n    /// @inheritdoc AggregatorV3Interface\n    function latestRoundData()\n        external\n        view\n        virtual\n        returns (uint80 roundId, int256 answer, uint256 startedAt, uint256 updatedAt, uint80 answeredInRound)\n    {\n        return (0, int256(_getQuoteAmount()), 0, 0, 0);\n    }\n}\n"
      },
      "contracts/oracle/FeedPTForSY.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0\n\npragma solidity ^0.8.12;\n\nimport { PendlePYOracleLib, PMath } from \"pendle/oracles/PendlePYOracleLib.sol\";\nimport \"pendle/interfaces/IPMarket.sol\";\n\n/// @title FeedPTForSY\n/// @author Angle Labs, Inc.\n/// @notice Override the BaseFeedPTPendle to provide the price of PT tokens based on the ibToken and not the underlying token\nabstract contract FeedPTForSY {\n    using PMath for uint256;\n\n    /// @dev Depending on the market you should use\n    ///       - getPtToSy() should be used if the underlying token is tradable,\n    ///       - getPtToAsset() if not\n    /// @dev https://docs.pendle.finance/Developers/Contracts/StandardizedYield#asset-of-sy--assetinfo-function\n    function _pendlePTPrice(IPMarket _market, uint32 _twapDuration) internal view virtual returns (uint256, uint256) {\n        (uint256 syIndex, uint256 pyIndex) = PendlePYOracleLib.getSYandPYIndexCurrent(_market);\n        if (syIndex >= pyIndex) {\n            return (PendlePYOracleLib.getPtToAssetRateRaw(_market, _twapDuration).divDown(syIndex), syIndex);\n        } else {\n            return (PendlePYOracleLib.getPtToAssetRateRaw(_market, _twapDuration).divDown(pyIndex), syIndex);\n        }\n    }\n}\n"
      },
      "contracts/utils/AccessControlManager.sol": {
        "content": "// SPDX-License-Identifier: BUSL-1.1\n\npragma solidity ^0.8.19;\n\nimport { IAccessControlManager } from \"../interfaces/IAccessControlManager.sol\";\n\nimport \"./Errors.sol\";\n\n/// @title AccessControl\n/// @author Angle Labs, Inc.\ncontract AccessControl {\n    /// @notice `accessControlManager` used to check roles\n    IAccessControlManager public accessControlManager;\n\n    /// @notice Initializes the immutable variables of the contract `accessControlManager`\n    constructor(IAccessControlManager _accessControlManager) {\n        if (address(_accessControlManager) == address(0)) revert ZeroAddress();\n        accessControlManager = _accessControlManager;\n    }\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                       MODIFIERS                                                    \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    /// @notice Checks whether the `msg.sender` has the governor role\n    modifier onlyGovernor() {\n        if (!accessControlManager.isGovernor(msg.sender)) revert NotGovernor();\n        _;\n    }\n\n    /// @notice Checks whether the `msg.sender` has the guardian role\n    modifier onlyGovernorOrGuardian() virtual {\n        if (!accessControlManager.isGovernorOrGuardian(msg.sender)) revert NotGovernorOrGuardian();\n        _;\n    }\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                       FUNCTIONS                                                    \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    /// @notice Checks whether `admin` has the governor role\n    function isGovernor(address admin) external view returns (bool) {\n        return accessControlManager.isGovernor(admin);\n    }\n\n    /// @notice Checks whether `admin` has the guardian role\n    function isGovernorOrGuardian(address admin) external view returns (bool) {\n        return accessControlManager.isGovernorOrGuardian(admin);\n    }\n}\n"
      },
      "contracts/oracle/BaseOraclePTPendle.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0\n\npragma solidity ^0.8.12;\n\nimport { UNIT, UD60x18, ud } from \"prb/math/UD60x18.sol\";\nimport \"pendle/interfaces/IPMarket.sol\";\nimport { PendlePYOracleLib } from \"pendle/oracles/PendlePYOracleLib.sol\";\nimport \"../utils/Errors.sol\";\n\n/// @title BaseOraclePTPendle\n/// @author Angle Labs, Inc.\n/// @notice Base oracle implementation for PT tokens on Pendle\nabstract contract BaseOraclePTPendle {\n    uint256 public constant BASE_18 = 1 ether;\n    uint256 public constant YEAR = 365 days;\n    // @notice The maximum implied rate for the underlying asset, if set well it allows to have a lower bound on the PT token price\n    uint256 public maxImpliedRate;\n    // @notice The duration of the TWAP used to calculate the PT price\n    uint32 public twapDuration;\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                        EVENTS                                                      \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    event MaxImpliedRateUpdated(uint256 _maxImpliedRate);\n    event TwapPTDurationUpdated(uint256 _twapDuration);\n\n    constructor(uint256 _maxImpliedRate, uint32 _twapDuration) {\n        if (_twapDuration < 15 minutes) revert TwapDurationTooLow();\n        maxImpliedRate = _maxImpliedRate;\n        twapDuration = _twapDuration;\n    }\n\n    modifier onlyGovernorOrGuardian() virtual;\n\n    function _getQuoteAmount() internal view virtual returns (uint256) {\n        (uint256 pendlePrice, uint256 index) = _pendlePTPrice(IPMarket(market()), twapDuration);\n        uint256 economicalLowerBound = (_economicalPTLowerBoundPrice() * BASE_18) / index;\n        uint256 minPrice = economicalLowerBound > pendlePrice ? pendlePrice : economicalLowerBound;\n        uint256 quote = (_detectHackRatio() * minPrice) / BASE_18;\n        return quote;\n    }\n\n    function setMaxImpliedRate(uint256 _maxImpliedRate) external onlyGovernorOrGuardian {\n        maxImpliedRate = _maxImpliedRate;\n        emit MaxImpliedRateUpdated(_maxImpliedRate);\n    }\n\n    function setTwapDuration(uint32 _twapDuration) external onlyGovernorOrGuardian {\n        if (_twapDuration < 15 minutes) revert TwapDurationTooLow();\n        twapDuration = _twapDuration;\n        emit TwapPTDurationUpdated(_twapDuration);\n    }\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                       INTERNAL                                                     \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    function _economicalPTLowerBoundPrice() internal view returns (uint256) {\n        uint256 exp = block.timestamp > maturity() ? 0 : maturity() - block.timestamp;\n        if (exp == 0) return BASE_18;\n\n        UD60x18 denominator = UNIT.add(ud(maxImpliedRate)).pow(ud(exp).div(ud(YEAR)));\n        uint256 lowerBound = UNIT.div(denominator).unwrap();\n        return lowerBound;\n    }\n\n    /// @dev Depending on the market you should use\n    ///       - getPtToSy() should be used if the underlying token is tradable,\n    ///       - getPtToAsset() if not\n    /// @dev https://docs.pendle.finance/Developers/Contracts/StandardizedYield#asset-of-sy--assetinfo-function\n    function _pendlePTPrice(IPMarket _market, uint32 _twapDuration) internal view virtual returns (uint256, uint256) {\n        return (PendlePYOracleLib.getPtToAssetRate(_market, _twapDuration), BASE_18);\n    }\n\n    function _detectHackRatio() internal view returns (uint256) {\n        uint256 assetBalanceSY = IERC20(asset()).balanceOf(sy());\n        uint256 totalSupplySY = IERC20(sy()).totalSupply();\n        return assetBalanceSY > totalSupplySY ? BASE_18 : (assetBalanceSY * BASE_18) / totalSupplySY;\n    }\n\n    /*//////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n                                                       OVERRIDES                                                    \n    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////*/\n\n    function asset() public pure virtual returns (address);\n\n    function sy() public pure virtual returns (address);\n\n    function maturity() public pure virtual returns (uint256);\n\n    function market() public pure virtual returns (address);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/oracles/PendlePYOracleLib.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nimport \"../interfaces/IPMarket.sol\";\nimport \"../core/libraries/math/PMath.sol\";\n\n// This library can & should be integrated directly for optimal gas usage.\n// If you prefer not to integrate it directly, the PendlePtOracle contract (a pre-deployed version of this contract) can be used.\nlibrary PendlePYOracleLib {\n    using PMath for uint256;\n    using PMath for int256;\n\n    /**\n     * This function returns the twap rate PT/Asset on market, but take into account the current rate of SY\n     This is to account for special cases where underlying asset becomes insolvent and has decreasing exchangeRate\n     * @param market market to get rate from\n     * @param duration twap duration\n     */\n    function getPtToAssetRate(IPMarket market, uint32 duration) internal view returns (uint256) {\n        (uint256 syIndex, uint256 pyIndex) = getSYandPYIndexCurrent(market);\n        if (syIndex >= pyIndex) {\n            return getPtToAssetRateRaw(market, duration);\n        } else {\n            return (getPtToAssetRateRaw(market, duration) * syIndex) / pyIndex;\n        }\n    }\n\n    /**\n     * This function returns the twap rate YT/Asset on market, but take into account the current rate of SY\n     This is to account for special cases where underlying asset becomes insolvent and has decreasing exchangeRate\n     * @param market market to get rate from\n     * @param duration twap duration\n     */\n    function getYtToAssetRate(IPMarket market, uint32 duration) internal view returns (uint256) {\n        (uint256 syIndex, uint256 pyIndex) = getSYandPYIndexCurrent(market);\n        if (syIndex >= pyIndex) {\n            return getYtToAssetRateRaw(market, duration);\n        } else {\n            return (getYtToAssetRateRaw(market, duration) * syIndex) / pyIndex;\n        }\n    }\n\n    /// @notice Similar to getPtToAsset but returns the rate in SY instead\n    function getPtToSyRate(IPMarket market, uint32 duration) internal view returns (uint256) {\n        (uint256 syIndex, uint256 pyIndex) = getSYandPYIndexCurrent(market);\n        if (syIndex >= pyIndex) {\n            return getPtToAssetRateRaw(market, duration).divDown(syIndex);\n        } else {\n            return getPtToAssetRateRaw(market, duration).divDown(pyIndex);\n        }\n    }\n\n    /// @notice Similar to getPtToAsset but returns the rate in SY instead\n    function getYtToSyRate(IPMarket market, uint32 duration) internal view returns (uint256) {\n        (uint256 syIndex, uint256 pyIndex) = getSYandPYIndexCurrent(market);\n        if (syIndex >= pyIndex) {\n            return getYtToAssetRateRaw(market, duration).divDown(syIndex);\n        } else {\n            return getYtToAssetRateRaw(market, duration).divDown(pyIndex);\n        }\n    }\n\n    /// @notice returns the raw rate without taking into account whether SY is solvent\n    function getPtToAssetRateRaw(IPMarket market, uint32 duration) internal view returns (uint256) {\n        uint256 expiry = market.expiry();\n\n        if (expiry <= block.timestamp) {\n            return PMath.ONE;\n        } else {\n            uint256 lnImpliedRate = _getMarketLnImpliedRate(market, duration);\n            uint256 timeToExpiry = expiry - block.timestamp;\n            uint256 assetToPtRate = MarketMathCore._getExchangeRateFromImpliedRate(lnImpliedRate, timeToExpiry).Uint();\n            return PMath.ONE.divDown(assetToPtRate);\n        }\n    }\n\n    /// @notice returns the raw rate without taking into account whether SY is solvent\n    function getYtToAssetRateRaw(IPMarket market, uint32 duration) internal view returns (uint256) {\n        return PMath.ONE - getPtToAssetRateRaw(market, duration);\n    }\n\n    function getSYandPYIndexCurrent(IPMarket market) internal view returns (uint256 syIndex, uint256 pyIndex) {\n        (IStandardizedYield SY, , IPYieldToken YT) = market.readTokens();\n\n        syIndex = SY.exchangeRate();\n        uint256 pyIndexStored = YT.pyIndexStored();\n\n        if (YT.doCacheIndexSameBlock() && YT.pyIndexLastUpdatedBlock() == block.number) {\n            pyIndex = pyIndexStored;\n        } else {\n            pyIndex = PMath.max(syIndex, pyIndexStored);\n        }\n    }\n\n    function _getMarketLnImpliedRate(IPMarket market, uint32 duration) private view returns (uint256) {\n        uint32[] memory durations = new uint32[](2);\n        durations[0] = duration;\n\n        uint216[] memory lnImpliedRateCumulative = market.observe(durations);\n        return (lnImpliedRateCumulative[1] - lnImpliedRateCumulative[0]) / duration;\n    }\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IPMarket.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nimport \"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol\";\nimport \"./IPPrincipalToken.sol\";\nimport \"./IPYieldToken.sol\";\nimport \"./IStandardizedYield.sol\";\nimport \"./IPGauge.sol\";\nimport \"../core/Market/MarketMathCore.sol\";\n\ninterface IPMarket is IERC20Metadata, IPGauge {\n    event Mint(address indexed receiver, uint256 netLpMinted, uint256 netSyUsed, uint256 netPtUsed);\n\n    event Burn(\n        address indexed receiverSy,\n        address indexed receiverPt,\n        uint256 netLpBurned,\n        uint256 netSyOut,\n        uint256 netPtOut\n    );\n\n    event Swap(\n        address indexed caller,\n        address indexed receiver,\n        int256 netPtOut,\n        int256 netSyOut,\n        uint256 netSyFee,\n        uint256 netSyToReserve\n    );\n\n    event UpdateImpliedRate(uint256 indexed timestamp, uint256 lnLastImpliedRate);\n\n    event IncreaseObservationCardinalityNext(\n        uint16 observationCardinalityNextOld,\n        uint16 observationCardinalityNextNew\n    );\n\n    function mint(\n        address receiver,\n        uint256 netSyDesired,\n        uint256 netPtDesired\n    ) external returns (uint256 netLpOut, uint256 netSyUsed, uint256 netPtUsed);\n\n    function burn(\n        address receiverSy,\n        address receiverPt,\n        uint256 netLpToBurn\n    ) external returns (uint256 netSyOut, uint256 netPtOut);\n\n    function swapExactPtForSy(\n        address receiver,\n        uint256 exactPtIn,\n        bytes calldata data\n    ) external returns (uint256 netSyOut, uint256 netSyFee);\n\n    function swapSyForExactPt(\n        address receiver,\n        uint256 exactPtOut,\n        bytes calldata data\n    ) external returns (uint256 netSyIn, uint256 netSyFee);\n\n    function redeemRewards(address user) external returns (uint256[] memory);\n\n    function readState(address router) external view returns (MarketState memory market);\n\n    function observe(uint32[] memory secondsAgos) external view returns (uint216[] memory lnImpliedRateCumulative);\n\n    function increaseObservationsCardinalityNext(uint16 cardinalityNext) external;\n\n    function readTokens() external view returns (IStandardizedYield _SY, IPPrincipalToken _PT, IPYieldToken _YT);\n\n    function getRewardTokens() external view returns (address[] memory);\n\n    function isExpired() external view returns (bool);\n\n    function expiry() external view returns (uint256);\n\n    function observations(\n        uint256 index\n    ) external view returns (uint32 blockTimestamp, uint216 lnImpliedRateCumulative, bool initialized);\n\n    function _storage()\n        external\n        view\n        returns (\n            int128 totalPt,\n            int128 totalSy,\n            uint96 lastLnImpliedRate,\n            uint16 observationIndex,\n            uint16 observationCardinality,\n            uint16 observationCardinalityNext\n        );\n}\n"
      },
      "contracts/interfaces/IAccessControlManager.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0\n\npragma solidity >=0.5.0;\n\n/// @title IAccessControlManager\n/// @author Angle Labs, Inc.\ninterface IAccessControlManager {\n    /// @notice Checks whether an address is governor of the Angle Protocol or not\n    /// @param admin Address to check\n    /// @return Whether the address has the `GOVERNOR_ROLE` or not\n    function isGovernor(address admin) external view returns (bool);\n\n    /// @notice Checks whether an address is governor or a guardian of the Angle Protocol or not\n    /// @param admin Address to check\n    /// @return Whether the address has the `GUARDIAN_ROLE` or not\n    /// @dev Governance should make sure when adding a governor to also give this governor the guardian\n    /// role by calling the `addGovernor` function\n    function isGovernorOrGuardian(address admin) external view returns (bool);\n}\n"
      },
      "contracts/utils/Errors.sol": {
        "content": "// SPDX-License-Identifier: BUSL-1.1\n\npragma solidity ^0.8.19;\n\nerror NotGovernor();\nerror NotGovernorOrGuardian();\nerror TwapDurationTooLow();\nerror ZeroAddress();\n"
      },
      "lib/prb-math/src/UD60x18.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\n/*\n\n██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗\n██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║\n██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║\n██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║\n██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║\n╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝\n\n██╗   ██╗██████╗  ██████╗  ██████╗ ██╗  ██╗ ██╗ █████╗\n██║   ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗\n██║   ██║██║  ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝\n██║   ██║██║  ██║██╔═══██╗████╔╝██║ ██╔██╗  ██║██╔══██╗\n╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝\n ╚═════╝ ╚═════╝  ╚═════╝  ╚═════╝ ╚═╝  ╚═╝ ╚═╝ ╚════╝\n\n*/\n\nimport \"./ud60x18/Casting.sol\";\nimport \"./ud60x18/Constants.sol\";\nimport \"./ud60x18/Conversions.sol\";\nimport \"./ud60x18/Errors.sol\";\nimport \"./ud60x18/Helpers.sol\";\nimport \"./ud60x18/Math.sol\";\nimport \"./ud60x18/ValueType.sol\";\n"
      },
      "lib/pendle-core-v2-public/contracts/core/libraries/math/PMath.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\n// This program is free software: you can redistribute it and/or modify\n// it under the terms of the GNU General Public License as published by\n// the Free Software Foundation, either version 3 of the License, or\n// (at your option) any later version.\n\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n\n// You should have received a copy of the GNU General Public License\n// along with this program.  If not, see <http://www.gnu.org/licenses/>.\n\npragma solidity ^0.8.0;\n\n/* solhint-disable private-vars-leading-underscore, reason-string */\n\nlibrary PMath {\n    uint256 internal constant ONE = 1e18; // 18 decimal places\n    int256 internal constant IONE = 1e18; // 18 decimal places\n\n    function subMax0(uint256 a, uint256 b) internal pure returns (uint256) {\n        unchecked {\n            return (a >= b ? a - b : 0);\n        }\n    }\n\n    function subNoNeg(int256 a, int256 b) internal pure returns (int256) {\n        require(a >= b, \"negative\");\n        return a - b; // no unchecked since if b is very negative, a - b might overflow\n    }\n\n    function mulDown(uint256 a, uint256 b) internal pure returns (uint256) {\n        uint256 product = a * b;\n        unchecked {\n            return product / ONE;\n        }\n    }\n\n    function mulDown(int256 a, int256 b) internal pure returns (int256) {\n        int256 product = a * b;\n        unchecked {\n            return product / IONE;\n        }\n    }\n\n    function divDown(uint256 a, uint256 b) internal pure returns (uint256) {\n        uint256 aInflated = a * ONE;\n        unchecked {\n            return aInflated / b;\n        }\n    }\n\n    function divDown(int256 a, int256 b) internal pure returns (int256) {\n        int256 aInflated = a * IONE;\n        unchecked {\n            return aInflated / b;\n        }\n    }\n\n    function rawDivUp(uint256 a, uint256 b) internal pure returns (uint256) {\n        return (a + b - 1) / b;\n    }\n\n    // @author Uniswap\n    function sqrt(uint256 y) internal pure returns (uint256 z) {\n        if (y > 3) {\n            z = y;\n            uint256 x = y / 2 + 1;\n            while (x < z) {\n                z = x;\n                x = (y / x + x) / 2;\n            }\n        } else if (y != 0) {\n            z = 1;\n        }\n    }\n\n    function square(uint256 x) internal pure returns (uint256) {\n        return x * x;\n    }\n\n    function squareDown(uint256 x) internal pure returns (uint256) {\n        return mulDown(x, x);\n    }\n\n    function abs(int256 x) internal pure returns (uint256) {\n        return uint256(x > 0 ? x : -x);\n    }\n\n    function neg(int256 x) internal pure returns (int256) {\n        return x * (-1);\n    }\n\n    function neg(uint256 x) internal pure returns (int256) {\n        return Int(x) * (-1);\n    }\n\n    function max(uint256 x, uint256 y) internal pure returns (uint256) {\n        return (x > y ? x : y);\n    }\n\n    function max(int256 x, int256 y) internal pure returns (int256) {\n        return (x > y ? x : y);\n    }\n\n    function min(uint256 x, uint256 y) internal pure returns (uint256) {\n        return (x < y ? x : y);\n    }\n\n    function min(int256 x, int256 y) internal pure returns (int256) {\n        return (x < y ? x : y);\n    }\n\n    /*///////////////////////////////////////////////////////////////\n                               SIGNED CASTS\n    //////////////////////////////////////////////////////////////*/\n\n    function Int(uint256 x) internal pure returns (int256) {\n        require(x <= uint256(type(int256).max));\n        return int256(x);\n    }\n\n    function Int128(int256 x) internal pure returns (int128) {\n        require(type(int128).min <= x && x <= type(int128).max);\n        return int128(x);\n    }\n\n    function Int128(uint256 x) internal pure returns (int128) {\n        return Int128(Int(x));\n    }\n\n    /*///////////////////////////////////////////////////////////////\n                               UNSIGNED CASTS\n    //////////////////////////////////////////////////////////////*/\n\n    function Uint(int256 x) internal pure returns (uint256) {\n        require(x >= 0);\n        return uint256(x);\n    }\n\n    function Uint32(uint256 x) internal pure returns (uint32) {\n        require(x <= type(uint32).max);\n        return uint32(x);\n    }\n\n    function Uint64(uint256 x) internal pure returns (uint64) {\n        require(x <= type(uint64).max);\n        return uint64(x);\n    }\n\n    function Uint112(uint256 x) internal pure returns (uint112) {\n        require(x <= type(uint112).max);\n        return uint112(x);\n    }\n\n    function Uint96(uint256 x) internal pure returns (uint96) {\n        require(x <= type(uint96).max);\n        return uint96(x);\n    }\n\n    function Uint128(uint256 x) internal pure returns (uint128) {\n        require(x <= type(uint128).max);\n        return uint128(x);\n    }\n\n    function Uint192(uint256 x) internal pure returns (uint192) {\n        require(x <= type(uint192).max);\n        return uint192(x);\n    }\n\n    function isAApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {\n        return mulDown(b, ONE - eps) <= a && a <= mulDown(b, ONE + eps);\n    }\n\n    function isAGreaterApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {\n        return a >= b && a <= mulDown(b, ONE + eps);\n    }\n\n    function isASmallerApproxB(uint256 a, uint256 b, uint256 eps) internal pure returns (bool) {\n        return a <= b && a >= mulDown(b, ONE - eps);\n    }\n}\n"
      },
      "node_modules/@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)\n\npragma solidity ^0.8.0;\n\nimport \"../IERC20.sol\";\n\n/**\n * @dev Interface for the optional metadata functions from the ERC20 standard.\n *\n * _Available since v4.1._\n */\ninterface IERC20Metadata is IERC20 {\n    /**\n     * @dev Returns the name of the token.\n     */\n    function name() external view returns (string memory);\n\n    /**\n     * @dev Returns the symbol of the token.\n     */\n    function symbol() external view returns (string memory);\n\n    /**\n     * @dev Returns the decimals places of the token.\n     */\n    function decimals() external view returns (uint8);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IPPrincipalToken.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\nimport \"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol\";\n\ninterface IPPrincipalToken is IERC20Metadata {\n    function burnByYT(address user, uint256 amount) external;\n\n    function mintByYT(address user, uint256 amount) external;\n\n    function initialize(address _YT) external;\n\n    function SY() external view returns (address);\n\n    function YT() external view returns (address);\n\n    function factory() external view returns (address);\n\n    function expiry() external view returns (uint256);\n\n    function isExpired() external view returns (bool);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IPYieldToken.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\nimport \"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol\";\nimport \"./IRewardManager.sol\";\nimport \"./IPInterestManagerYT.sol\";\n\ninterface IPYieldToken is IERC20Metadata, IRewardManager, IPInterestManagerYT {\n    event NewInterestIndex(uint256 indexed newIndex);\n\n    event Mint(\n        address indexed caller,\n        address indexed receiverPT,\n        address indexed receiverYT,\n        uint256 amountSyToMint,\n        uint256 amountPYOut\n    );\n\n    event Burn(address indexed caller, address indexed receiver, uint256 amountPYToRedeem, uint256 amountSyOut);\n\n    event RedeemRewards(address indexed user, uint256[] amountRewardsOut);\n\n    event RedeemInterest(address indexed user, uint256 interestOut);\n\n    event CollectRewardFee(address indexed rewardToken, uint256 amountRewardFee);\n\n    function mintPY(address receiverPT, address receiverYT) external returns (uint256 amountPYOut);\n\n    function redeemPY(address receiver) external returns (uint256 amountSyOut);\n\n    function redeemPYMulti(\n        address[] calldata receivers,\n        uint256[] calldata amountPYToRedeems\n    ) external returns (uint256[] memory amountSyOuts);\n\n    function redeemDueInterestAndRewards(\n        address user,\n        bool redeemInterest,\n        bool redeemRewards\n    ) external returns (uint256 interestOut, uint256[] memory rewardsOut);\n\n    function rewardIndexesCurrent() external returns (uint256[] memory);\n\n    function pyIndexCurrent() external returns (uint256);\n\n    function pyIndexStored() external view returns (uint256);\n\n    function getRewardTokens() external view returns (address[] memory);\n\n    function SY() external view returns (address);\n\n    function PT() external view returns (address);\n\n    function factory() external view returns (address);\n\n    function expiry() external view returns (uint256);\n\n    function isExpired() external view returns (bool);\n\n    function doCacheIndexSameBlock() external view returns (bool);\n\n    function pyIndexLastUpdatedBlock() external view returns (uint128);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IStandardizedYield.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\n/*\n * MIT License\n * ===========\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to deal\n * in the Software without restriction, including without limitation the rights\n * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n * copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in all\n * copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\n */\n\npragma solidity ^0.8.0;\nimport \"@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol\";\n\ninterface IStandardizedYield is IERC20Metadata {\n    /// @dev Emitted when any base tokens is deposited to mint shares\n    event Deposit(\n        address indexed caller,\n        address indexed receiver,\n        address indexed tokenIn,\n        uint256 amountDeposited,\n        uint256 amountSyOut\n    );\n\n    /// @dev Emitted when any shares are redeemed for base tokens\n    event Redeem(\n        address indexed caller,\n        address indexed receiver,\n        address indexed tokenOut,\n        uint256 amountSyToRedeem,\n        uint256 amountTokenOut\n    );\n\n    /// @dev check `assetInfo()` for more information\n    enum AssetType {\n        TOKEN,\n        LIQUIDITY\n    }\n\n    /// @dev Emitted when (`user`) claims their rewards\n    event ClaimRewards(address indexed user, address[] rewardTokens, uint256[] rewardAmounts);\n\n    /**\n     * @notice mints an amount of shares by depositing a base token.\n     * @param receiver shares recipient address\n     * @param tokenIn address of the base tokens to mint shares\n     * @param amountTokenToDeposit amount of base tokens to be transferred from (`msg.sender`)\n     * @param minSharesOut reverts if amount of shares minted is lower than this\n     * @return amountSharesOut amount of shares minted\n     * @dev Emits a {Deposit} event\n     *\n     * Requirements:\n     * - (`tokenIn`) must be a valid base token.\n     */\n    function deposit(\n        address receiver,\n        address tokenIn,\n        uint256 amountTokenToDeposit,\n        uint256 minSharesOut\n    ) external payable returns (uint256 amountSharesOut);\n\n    /**\n     * @notice redeems an amount of base tokens by burning some shares\n     * @param receiver recipient address\n     * @param amountSharesToRedeem amount of shares to be burned\n     * @param tokenOut address of the base token to be redeemed\n     * @param minTokenOut reverts if amount of base token redeemed is lower than this\n     * @param burnFromInternalBalance if true, burns from balance of `address(this)`, otherwise burns from `msg.sender`\n     * @return amountTokenOut amount of base tokens redeemed\n     * @dev Emits a {Redeem} event\n     *\n     * Requirements:\n     * - (`tokenOut`) must be a valid base token.\n     */\n    function redeem(\n        address receiver,\n        uint256 amountSharesToRedeem,\n        address tokenOut,\n        uint256 minTokenOut,\n        bool burnFromInternalBalance\n    ) external returns (uint256 amountTokenOut);\n\n    /**\n     * @notice exchangeRate * syBalance / 1e18 must return the asset balance of the account\n     * @notice vice-versa, if a user uses some amount of tokens equivalent to X asset, the amount of sy\n     he can mint must be X * exchangeRate / 1e18\n     * @dev SYUtils's assetToSy & syToAsset should be used instead of raw multiplication\n     & division\n     */\n    function exchangeRate() external view returns (uint256 res);\n\n    /**\n     * @notice claims reward for (`user`)\n     * @param user the user receiving their rewards\n     * @return rewardAmounts an array of reward amounts in the same order as `getRewardTokens`\n     * @dev\n     * Emits a `ClaimRewards` event\n     * See {getRewardTokens} for list of reward tokens\n     */\n    function claimRewards(address user) external returns (uint256[] memory rewardAmounts);\n\n    /**\n     * @notice get the amount of unclaimed rewards for (`user`)\n     * @param user the user to check for\n     * @return rewardAmounts an array of reward amounts in the same order as `getRewardTokens`\n     */\n    function accruedRewards(address user) external view returns (uint256[] memory rewardAmounts);\n\n    function rewardIndexesCurrent() external returns (uint256[] memory indexes);\n\n    function rewardIndexesStored() external view returns (uint256[] memory indexes);\n\n    /**\n     * @notice returns the list of reward token addresses\n     */\n    function getRewardTokens() external view returns (address[] memory);\n\n    /**\n     * @notice returns the address of the underlying yield token\n     */\n    function yieldToken() external view returns (address);\n\n    /**\n     * @notice returns all tokens that can mint this SY\n     */\n    function getTokensIn() external view returns (address[] memory res);\n\n    /**\n     * @notice returns all tokens that can be redeemed by this SY\n     */\n    function getTokensOut() external view returns (address[] memory res);\n\n    function isValidTokenIn(address token) external view returns (bool);\n\n    function isValidTokenOut(address token) external view returns (bool);\n\n    function previewDeposit(\n        address tokenIn,\n        uint256 amountTokenToDeposit\n    ) external view returns (uint256 amountSharesOut);\n\n    function previewRedeem(\n        address tokenOut,\n        uint256 amountSharesToRedeem\n    ) external view returns (uint256 amountTokenOut);\n\n    /**\n     * @notice This function contains information to interpret what the asset is\n     * @return assetType the type of the asset (0 for ERC20 tokens, 1 for AMM liquidity tokens,\n        2 for bridged yield bearing tokens like wstETH, rETH on Arbi whose the underlying asset doesn't exist on the chain)\n     * @return assetAddress the address of the asset\n     * @return assetDecimals the decimals of the asset\n     */\n    function assetInfo() external view returns (AssetType assetType, address assetAddress, uint8 assetDecimals);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IPGauge.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\ninterface IPGauge {\n    function totalActiveSupply() external view returns (uint256);\n\n    function activeBalance(address user) external view returns (uint256);\n\n    // only available for newer factories. please check the verified contracts\n    event RedeemRewards(address indexed user, uint256[] rewardsOut);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/core/Market/MarketMathCore.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nimport \"../libraries/math/PMath.sol\";\nimport \"../libraries/math/LogExpMath.sol\";\n\nimport \"../StandardizedYield/PYIndex.sol\";\nimport \"../libraries/MiniHelpers.sol\";\nimport \"../libraries/Errors.sol\";\n\nstruct MarketState {\n    int256 totalPt;\n    int256 totalSy;\n    int256 totalLp;\n    address treasury;\n    /// immutable variables ///\n    int256 scalarRoot;\n    uint256 expiry;\n    /// fee data ///\n    uint256 lnFeeRateRoot;\n    uint256 reserveFeePercent; // base 100\n    /// last trade data ///\n    uint256 lastLnImpliedRate;\n}\n\n// params that are expensive to compute, therefore we pre-compute them\nstruct MarketPreCompute {\n    int256 rateScalar;\n    int256 totalAsset;\n    int256 rateAnchor;\n    int256 feeRate;\n}\n\n// solhint-disable ordering\nlibrary MarketMathCore {\n    using PMath for uint256;\n    using PMath for int256;\n    using LogExpMath for int256;\n    using PYIndexLib for PYIndex;\n\n    int256 internal constant MINIMUM_LIQUIDITY = 10 ** 3;\n    int256 internal constant PERCENTAGE_DECIMALS = 100;\n    uint256 internal constant DAY = 86400;\n    uint256 internal constant IMPLIED_RATE_TIME = 365 * DAY;\n\n    int256 internal constant MAX_MARKET_PROPORTION = (1e18 * 96) / 100;\n\n    using PMath for uint256;\n    using PMath for int256;\n\n    /*///////////////////////////////////////////////////////////////\n                UINT FUNCTIONS TO PROXY TO CORE FUNCTIONS\n    //////////////////////////////////////////////////////////////*/\n\n    function addLiquidity(\n        MarketState memory market,\n        uint256 syDesired,\n        uint256 ptDesired,\n        uint256 blockTime\n    ) internal pure returns (uint256 lpToReserve, uint256 lpToAccount, uint256 syUsed, uint256 ptUsed) {\n        (int256 _lpToReserve, int256 _lpToAccount, int256 _syUsed, int256 _ptUsed) = addLiquidityCore(\n            market,\n            syDesired.Int(),\n            ptDesired.Int(),\n            blockTime\n        );\n\n        lpToReserve = _lpToReserve.Uint();\n        lpToAccount = _lpToAccount.Uint();\n        syUsed = _syUsed.Uint();\n        ptUsed = _ptUsed.Uint();\n    }\n\n    function removeLiquidity(\n        MarketState memory market,\n        uint256 lpToRemove\n    ) internal pure returns (uint256 netSyToAccount, uint256 netPtToAccount) {\n        (int256 _syToAccount, int256 _ptToAccount) = removeLiquidityCore(market, lpToRemove.Int());\n\n        netSyToAccount = _syToAccount.Uint();\n        netPtToAccount = _ptToAccount.Uint();\n    }\n\n    function swapExactPtForSy(\n        MarketState memory market,\n        PYIndex index,\n        uint256 exactPtToMarket,\n        uint256 blockTime\n    ) internal pure returns (uint256 netSyToAccount, uint256 netSyFee, uint256 netSyToReserve) {\n        (int256 _netSyToAccount, int256 _netSyFee, int256 _netSyToReserve) = executeTradeCore(\n            market,\n            index,\n            exactPtToMarket.neg(),\n            blockTime\n        );\n\n        netSyToAccount = _netSyToAccount.Uint();\n        netSyFee = _netSyFee.Uint();\n        netSyToReserve = _netSyToReserve.Uint();\n    }\n\n    function swapSyForExactPt(\n        MarketState memory market,\n        PYIndex index,\n        uint256 exactPtToAccount,\n        uint256 blockTime\n    ) internal pure returns (uint256 netSyToMarket, uint256 netSyFee, uint256 netSyToReserve) {\n        (int256 _netSyToAccount, int256 _netSyFee, int256 _netSyToReserve) = executeTradeCore(\n            market,\n            index,\n            exactPtToAccount.Int(),\n            blockTime\n        );\n\n        netSyToMarket = _netSyToAccount.neg().Uint();\n        netSyFee = _netSyFee.Uint();\n        netSyToReserve = _netSyToReserve.Uint();\n    }\n\n    /*///////////////////////////////////////////////////////////////\n                    CORE FUNCTIONS\n    //////////////////////////////////////////////////////////////*/\n\n    function addLiquidityCore(\n        MarketState memory market,\n        int256 syDesired,\n        int256 ptDesired,\n        uint256 blockTime\n    ) internal pure returns (int256 lpToReserve, int256 lpToAccount, int256 syUsed, int256 ptUsed) {\n        /// ------------------------------------------------------------\n        /// CHECKS\n        /// ------------------------------------------------------------\n        if (syDesired == 0 || ptDesired == 0) revert Errors.MarketZeroAmountsInput();\n        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();\n\n        /// ------------------------------------------------------------\n        /// MATH\n        /// ------------------------------------------------------------\n        if (market.totalLp == 0) {\n            lpToAccount = PMath.sqrt((syDesired * ptDesired).Uint()).Int() - MINIMUM_LIQUIDITY;\n            lpToReserve = MINIMUM_LIQUIDITY;\n            syUsed = syDesired;\n            ptUsed = ptDesired;\n        } else {\n            int256 netLpByPt = (ptDesired * market.totalLp) / market.totalPt;\n            int256 netLpBySy = (syDesired * market.totalLp) / market.totalSy;\n            if (netLpByPt < netLpBySy) {\n                lpToAccount = netLpByPt;\n                ptUsed = ptDesired;\n                syUsed = (market.totalSy * lpToAccount) / market.totalLp;\n            } else {\n                lpToAccount = netLpBySy;\n                syUsed = syDesired;\n                ptUsed = (market.totalPt * lpToAccount) / market.totalLp;\n            }\n        }\n\n        if (lpToAccount <= 0) revert Errors.MarketZeroAmountsOutput();\n\n        /// ------------------------------------------------------------\n        /// WRITE\n        /// ------------------------------------------------------------\n        market.totalSy += syUsed;\n        market.totalPt += ptUsed;\n        market.totalLp += lpToAccount + lpToReserve;\n    }\n\n    function removeLiquidityCore(\n        MarketState memory market,\n        int256 lpToRemove\n    ) internal pure returns (int256 netSyToAccount, int256 netPtToAccount) {\n        /// ------------------------------------------------------------\n        /// CHECKS\n        /// ------------------------------------------------------------\n        if (lpToRemove == 0) revert Errors.MarketZeroAmountsInput();\n\n        /// ------------------------------------------------------------\n        /// MATH\n        /// ------------------------------------------------------------\n        netSyToAccount = (lpToRemove * market.totalSy) / market.totalLp;\n        netPtToAccount = (lpToRemove * market.totalPt) / market.totalLp;\n\n        if (netSyToAccount == 0 && netPtToAccount == 0) revert Errors.MarketZeroAmountsOutput();\n\n        /// ------------------------------------------------------------\n        /// WRITE\n        /// ------------------------------------------------------------\n        market.totalLp = market.totalLp.subNoNeg(lpToRemove);\n        market.totalPt = market.totalPt.subNoNeg(netPtToAccount);\n        market.totalSy = market.totalSy.subNoNeg(netSyToAccount);\n    }\n\n    function executeTradeCore(\n        MarketState memory market,\n        PYIndex index,\n        int256 netPtToAccount,\n        uint256 blockTime\n    ) internal pure returns (int256 netSyToAccount, int256 netSyFee, int256 netSyToReserve) {\n        /// ------------------------------------------------------------\n        /// CHECKS\n        /// ------------------------------------------------------------\n        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();\n        if (market.totalPt <= netPtToAccount)\n            revert Errors.MarketInsufficientPtForTrade(market.totalPt, netPtToAccount);\n\n        /// ------------------------------------------------------------\n        /// MATH\n        /// ------------------------------------------------------------\n        MarketPreCompute memory comp = getMarketPreCompute(market, index, blockTime);\n\n        (netSyToAccount, netSyFee, netSyToReserve) = calcTrade(market, comp, index, netPtToAccount);\n\n        /// ------------------------------------------------------------\n        /// WRITE\n        /// ------------------------------------------------------------\n        _setNewMarketStateTrade(market, comp, index, netPtToAccount, netSyToAccount, netSyToReserve, blockTime);\n    }\n\n    function getMarketPreCompute(\n        MarketState memory market,\n        PYIndex index,\n        uint256 blockTime\n    ) internal pure returns (MarketPreCompute memory res) {\n        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();\n\n        uint256 timeToExpiry = market.expiry - blockTime;\n\n        res.rateScalar = _getRateScalar(market, timeToExpiry);\n        res.totalAsset = index.syToAsset(market.totalSy);\n\n        if (market.totalPt == 0 || res.totalAsset == 0)\n            revert Errors.MarketZeroTotalPtOrTotalAsset(market.totalPt, res.totalAsset);\n\n        res.rateAnchor = _getRateAnchor(\n            market.totalPt,\n            market.lastLnImpliedRate,\n            res.totalAsset,\n            res.rateScalar,\n            timeToExpiry\n        );\n        res.feeRate = _getExchangeRateFromImpliedRate(market.lnFeeRateRoot, timeToExpiry);\n    }\n\n    function calcTrade(\n        MarketState memory market,\n        MarketPreCompute memory comp,\n        PYIndex index,\n        int256 netPtToAccount\n    ) internal pure returns (int256 netSyToAccount, int256 netSyFee, int256 netSyToReserve) {\n        int256 preFeeExchangeRate = _getExchangeRate(\n            market.totalPt,\n            comp.totalAsset,\n            comp.rateScalar,\n            comp.rateAnchor,\n            netPtToAccount\n        );\n\n        int256 preFeeAssetToAccount = netPtToAccount.divDown(preFeeExchangeRate).neg();\n        int256 fee = comp.feeRate;\n\n        if (netPtToAccount > 0) {\n            int256 postFeeExchangeRate = preFeeExchangeRate.divDown(fee);\n            if (postFeeExchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(postFeeExchangeRate);\n\n            fee = preFeeAssetToAccount.mulDown(PMath.IONE - fee);\n        } else {\n            fee = ((preFeeAssetToAccount * (PMath.IONE - fee)) / fee).neg();\n        }\n\n        int256 netAssetToReserve = (fee * market.reserveFeePercent.Int()) / PERCENTAGE_DECIMALS;\n        int256 netAssetToAccount = preFeeAssetToAccount - fee;\n\n        netSyToAccount = netAssetToAccount < 0\n            ? index.assetToSyUp(netAssetToAccount)\n            : index.assetToSy(netAssetToAccount);\n        netSyFee = index.assetToSy(fee);\n        netSyToReserve = index.assetToSy(netAssetToReserve);\n    }\n\n    function _setNewMarketStateTrade(\n        MarketState memory market,\n        MarketPreCompute memory comp,\n        PYIndex index,\n        int256 netPtToAccount,\n        int256 netSyToAccount,\n        int256 netSyToReserve,\n        uint256 blockTime\n    ) internal pure {\n        uint256 timeToExpiry = market.expiry - blockTime;\n\n        market.totalPt = market.totalPt.subNoNeg(netPtToAccount);\n        market.totalSy = market.totalSy.subNoNeg(netSyToAccount + netSyToReserve);\n\n        market.lastLnImpliedRate = _getLnImpliedRate(\n            market.totalPt,\n            index.syToAsset(market.totalSy),\n            comp.rateScalar,\n            comp.rateAnchor,\n            timeToExpiry\n        );\n\n        if (market.lastLnImpliedRate == 0) revert Errors.MarketZeroLnImpliedRate();\n    }\n\n    function _getRateAnchor(\n        int256 totalPt,\n        uint256 lastLnImpliedRate,\n        int256 totalAsset,\n        int256 rateScalar,\n        uint256 timeToExpiry\n    ) internal pure returns (int256 rateAnchor) {\n        int256 newExchangeRate = _getExchangeRateFromImpliedRate(lastLnImpliedRate, timeToExpiry);\n\n        if (newExchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(newExchangeRate);\n\n        {\n            int256 proportion = totalPt.divDown(totalPt + totalAsset);\n\n            int256 lnProportion = _logProportion(proportion);\n\n            rateAnchor = newExchangeRate - lnProportion.divDown(rateScalar);\n        }\n    }\n\n    /// @notice Calculates the current market implied rate.\n    /// @return lnImpliedRate the implied rate\n    function _getLnImpliedRate(\n        int256 totalPt,\n        int256 totalAsset,\n        int256 rateScalar,\n        int256 rateAnchor,\n        uint256 timeToExpiry\n    ) internal pure returns (uint256 lnImpliedRate) {\n        // This will check for exchange rates < PMath.IONE\n        int256 exchangeRate = _getExchangeRate(totalPt, totalAsset, rateScalar, rateAnchor, 0);\n\n        // exchangeRate >= 1 so its ln >= 0\n        uint256 lnRate = exchangeRate.ln().Uint();\n\n        lnImpliedRate = (lnRate * IMPLIED_RATE_TIME) / timeToExpiry;\n    }\n\n    /// @notice Converts an implied rate to an exchange rate given a time to expiry. The\n    /// formula is E = e^rt\n    function _getExchangeRateFromImpliedRate(\n        uint256 lnImpliedRate,\n        uint256 timeToExpiry\n    ) internal pure returns (int256 exchangeRate) {\n        uint256 rt = (lnImpliedRate * timeToExpiry) / IMPLIED_RATE_TIME;\n\n        exchangeRate = LogExpMath.exp(rt.Int());\n    }\n\n    function _getExchangeRate(\n        int256 totalPt,\n        int256 totalAsset,\n        int256 rateScalar,\n        int256 rateAnchor,\n        int256 netPtToAccount\n    ) internal pure returns (int256 exchangeRate) {\n        int256 numerator = totalPt.subNoNeg(netPtToAccount);\n\n        int256 proportion = (numerator.divDown(totalPt + totalAsset));\n\n        if (proportion > MAX_MARKET_PROPORTION)\n            revert Errors.MarketProportionTooHigh(proportion, MAX_MARKET_PROPORTION);\n\n        int256 lnProportion = _logProportion(proportion);\n\n        exchangeRate = lnProportion.divDown(rateScalar) + rateAnchor;\n\n        if (exchangeRate < PMath.IONE) revert Errors.MarketExchangeRateBelowOne(exchangeRate);\n    }\n\n    function _logProportion(int256 proportion) internal pure returns (int256 res) {\n        if (proportion == PMath.IONE) revert Errors.MarketProportionMustNotEqualOne();\n\n        int256 logitP = proportion.divDown(PMath.IONE - proportion);\n\n        res = logitP.ln();\n    }\n\n    function _getRateScalar(MarketState memory market, uint256 timeToExpiry) internal pure returns (int256 rateScalar) {\n        rateScalar = (market.scalarRoot * IMPLIED_RATE_TIME.Int()) / timeToExpiry.Int();\n        if (rateScalar <= 0) revert Errors.MarketRateScalarBelowZero(rateScalar);\n    }\n\n    function setInitialLnImpliedRate(\n        MarketState memory market,\n        PYIndex index,\n        int256 initialAnchor,\n        uint256 blockTime\n    ) internal pure {\n        /// ------------------------------------------------------------\n        /// CHECKS\n        /// ------------------------------------------------------------\n        if (MiniHelpers.isExpired(market.expiry, blockTime)) revert Errors.MarketExpired();\n\n        /// ------------------------------------------------------------\n        /// MATH\n        /// ------------------------------------------------------------\n        int256 totalAsset = index.syToAsset(market.totalSy);\n        uint256 timeToExpiry = market.expiry - blockTime;\n        int256 rateScalar = _getRateScalar(market, timeToExpiry);\n\n        /// ------------------------------------------------------------\n        /// WRITE\n        /// ------------------------------------------------------------\n        market.lastLnImpliedRate = _getLnImpliedRate(\n            market.totalPt,\n            totalAsset,\n            rateScalar,\n            initialAnchor,\n            timeToExpiry\n        );\n    }\n}\n"
      },
      "lib/prb-math/src/ud60x18/Casting.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Errors.sol\" as CastingErrors;\nimport { MAX_UINT128, MAX_UINT40 } from \"../Common.sol\";\nimport { uMAX_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { uMAX_SD59x18 } from \"../sd59x18/Constants.sol\";\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { uMAX_UD2x18 } from \"../ud2x18/Constants.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Casts a UD60x18 number into SD1x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(UD60x18 x) pure returns (SD1x18 result) {\n    uint256 xUint = UD60x18.unwrap(x);\n    if (xUint > uint256(int256(uMAX_SD1x18))) {\n        revert CastingErrors.PRBMath_UD60x18_IntoSD1x18_Overflow(x);\n    }\n    result = SD1x18.wrap(int64(uint64(xUint)));\n}\n\n/// @notice Casts a UD60x18 number into UD2x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_UD2x18`.\nfunction intoUD2x18(UD60x18 x) pure returns (UD2x18 result) {\n    uint256 xUint = UD60x18.unwrap(x);\n    if (xUint > uMAX_UD2x18) {\n        revert CastingErrors.PRBMath_UD60x18_IntoUD2x18_Overflow(x);\n    }\n    result = UD2x18.wrap(uint64(xUint));\n}\n\n/// @notice Casts a UD60x18 number into SD59x18.\n/// @dev Requirements:\n/// - x must be less than or equal to `uMAX_SD59x18`.\nfunction intoSD59x18(UD60x18 x) pure returns (SD59x18 result) {\n    uint256 xUint = UD60x18.unwrap(x);\n    if (xUint > uint256(uMAX_SD59x18)) {\n        revert CastingErrors.PRBMath_UD60x18_IntoSD59x18_Overflow(x);\n    }\n    result = SD59x18.wrap(int256(xUint));\n}\n\n/// @notice Casts a UD60x18 number into uint128.\n/// @dev This is basically an alias for {unwrap}.\nfunction intoUint256(UD60x18 x) pure returns (uint256 result) {\n    result = UD60x18.unwrap(x);\n}\n\n/// @notice Casts a UD60x18 number into uint128.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT128`.\nfunction intoUint128(UD60x18 x) pure returns (uint128 result) {\n    uint256 xUint = UD60x18.unwrap(x);\n    if (xUint > MAX_UINT128) {\n        revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);\n    }\n    result = uint128(xUint);\n}\n\n/// @notice Casts a UD60x18 number into uint40.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(UD60x18 x) pure returns (uint40 result) {\n    uint256 xUint = UD60x18.unwrap(x);\n    if (xUint > MAX_UINT40) {\n        revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);\n    }\n    result = uint40(xUint);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud(uint256 x) pure returns (UD60x18 result) {\n    result = UD60x18.wrap(x);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud60x18(uint256 x) pure returns (UD60x18 result) {\n    result = UD60x18.wrap(x);\n}\n\n/// @notice Unwraps a UD60x18 number into uint256.\nfunction unwrap(UD60x18 x) pure returns (uint256 result) {\n    result = UD60x18.unwrap(x);\n}\n\n/// @notice Wraps a uint256 number into the UD60x18 value type.\nfunction wrap(uint256 x) pure returns (UD60x18 result) {\n    result = UD60x18.wrap(x);\n}\n"
      },
      "lib/prb-math/src/ud60x18/Constants.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD60x18 } from \"./ValueType.sol\";\n\n// NOTICE: the \"u\" prefix stands for \"unwrapped\".\n\n/// @dev Euler's number as a UD60x18 number.\nUD60x18 constant E = UD60x18.wrap(2_718281828459045235);\n\n/// @dev The maximum input permitted in {exp}.\nuint256 constant uEXP_MAX_INPUT = 133_084258667509499440;\nUD60x18 constant EXP_MAX_INPUT = UD60x18.wrap(uEXP_MAX_INPUT);\n\n/// @dev The maximum input permitted in {exp2}.\nuint256 constant uEXP2_MAX_INPUT = 192e18 - 1;\nUD60x18 constant EXP2_MAX_INPUT = UD60x18.wrap(uEXP2_MAX_INPUT);\n\n/// @dev Half the UNIT number.\nuint256 constant uHALF_UNIT = 0.5e18;\nUD60x18 constant HALF_UNIT = UD60x18.wrap(uHALF_UNIT);\n\n/// @dev $log_2(10)$ as a UD60x18 number.\nuint256 constant uLOG2_10 = 3_321928094887362347;\nUD60x18 constant LOG2_10 = UD60x18.wrap(uLOG2_10);\n\n/// @dev $log_2(e)$ as a UD60x18 number.\nuint256 constant uLOG2_E = 1_442695040888963407;\nUD60x18 constant LOG2_E = UD60x18.wrap(uLOG2_E);\n\n/// @dev The maximum value a UD60x18 number can have.\nuint256 constant uMAX_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_584007913129639935;\nUD60x18 constant MAX_UD60x18 = UD60x18.wrap(uMAX_UD60x18);\n\n/// @dev The maximum whole value a UD60x18 number can have.\nuint256 constant uMAX_WHOLE_UD60x18 = 115792089237316195423570985008687907853269984665640564039457_000000000000000000;\nUD60x18 constant MAX_WHOLE_UD60x18 = UD60x18.wrap(uMAX_WHOLE_UD60x18);\n\n/// @dev PI as a UD60x18 number.\nUD60x18 constant PI = UD60x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of UD60x18.\nuint256 constant uUNIT = 1e18;\nUD60x18 constant UNIT = UD60x18.wrap(uUNIT);\n\n/// @dev The unit number squared.\nuint256 constant uUNIT_SQUARED = 1e36;\nUD60x18 constant UNIT_SQUARED = UD60x18.wrap(uUNIT_SQUARED);\n\n/// @dev Zero as a UD60x18 number.\nUD60x18 constant ZERO = UD60x18.wrap(0);\n"
      },
      "lib/prb-math/src/ud60x18/Conversions.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { uMAX_UD60x18, uUNIT } from \"./Constants.sol\";\nimport { PRBMath_UD60x18_Convert_Overflow } from \"./Errors.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Converts a UD60x18 number to a simple integer by dividing it by `UNIT`.\n/// @dev The result is rounded toward zero.\n/// @param x The UD60x18 number to convert.\n/// @return result The same number in basic integer form.\nfunction convert(UD60x18 x) pure returns (uint256 result) {\n    result = UD60x18.unwrap(x) / uUNIT;\n}\n\n/// @notice Converts a simple integer to UD60x18 by multiplying it by `UNIT`.\n///\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UD60x18 / UNIT`.\n///\n/// @param x The basic integer to convert.\n/// @param result The same number converted to UD60x18.\nfunction convert(uint256 x) pure returns (UD60x18 result) {\n    if (x > uMAX_UD60x18 / uUNIT) {\n        revert PRBMath_UD60x18_Convert_Overflow(x);\n    }\n    unchecked {\n        result = UD60x18.wrap(x * uUNIT);\n    }\n}\n"
      },
      "lib/prb-math/src/ud60x18/Errors.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when ceiling a number overflows UD60x18.\nerror PRBMath_UD60x18_Ceil_Overflow(UD60x18 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format overflows UD60x18.\nerror PRBMath_UD60x18_Convert_Overflow(uint256 x);\n\n/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.\nerror PRBMath_UD60x18_Exp_InputTooBig(UD60x18 x);\n\n/// @notice Thrown when taking the binary exponent of a base greater than 192e18.\nerror PRBMath_UD60x18_Exp2_InputTooBig(UD60x18 x);\n\n/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows UD60x18.\nerror PRBMath_UD60x18_Gm_Overflow(UD60x18 x, UD60x18 y);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_UD60x18_IntoSD1x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD59x18.\nerror PRBMath_UD60x18_IntoSD59x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_UD60x18_IntoUD2x18_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_UD60x18_IntoUint128_Overflow(UD60x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_UD60x18_IntoUint40_Overflow(UD60x18 x);\n\n/// @notice Thrown when taking the logarithm of a number less than 1.\nerror PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);\n\n/// @notice Thrown when calculating the square root overflows UD60x18.\nerror PRBMath_UD60x18_Sqrt_Overflow(UD60x18 x);\n"
      },
      "lib/prb-math/src/ud60x18/Helpers.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { wrap } from \"./Casting.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/// @notice Implements the checked addition operation (+) in the UD60x18 type.\nfunction add(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() + y.unwrap());\n}\n\n/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.\nfunction and(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() & bits);\n}\n\n/// @notice Implements the AND (&) bitwise operation in the UD60x18 type.\nfunction and2(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() & y.unwrap());\n}\n\n/// @notice Implements the equal operation (==) in the UD60x18 type.\nfunction eq(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() == y.unwrap();\n}\n\n/// @notice Implements the greater than operation (>) in the UD60x18 type.\nfunction gt(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() > y.unwrap();\n}\n\n/// @notice Implements the greater than or equal to operation (>=) in the UD60x18 type.\nfunction gte(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() >= y.unwrap();\n}\n\n/// @notice Implements a zero comparison check function in the UD60x18 type.\nfunction isZero(UD60x18 x) pure returns (bool result) {\n    // This wouldn't work if x could be negative.\n    result = x.unwrap() == 0;\n}\n\n/// @notice Implements the left shift operation (<<) in the UD60x18 type.\nfunction lshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() << bits);\n}\n\n/// @notice Implements the lower than operation (<) in the UD60x18 type.\nfunction lt(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() < y.unwrap();\n}\n\n/// @notice Implements the lower than or equal to operation (<=) in the UD60x18 type.\nfunction lte(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() <= y.unwrap();\n}\n\n/// @notice Implements the checked modulo operation (%) in the UD60x18 type.\nfunction mod(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() % y.unwrap());\n}\n\n/// @notice Implements the not equal operation (!=) in the UD60x18 type.\nfunction neq(UD60x18 x, UD60x18 y) pure returns (bool result) {\n    result = x.unwrap() != y.unwrap();\n}\n\n/// @notice Implements the NOT (~) bitwise operation in the UD60x18 type.\nfunction not(UD60x18 x) pure returns (UD60x18 result) {\n    result = wrap(~x.unwrap());\n}\n\n/// @notice Implements the OR (|) bitwise operation in the UD60x18 type.\nfunction or(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() | y.unwrap());\n}\n\n/// @notice Implements the right shift operation (>>) in the UD60x18 type.\nfunction rshift(UD60x18 x, uint256 bits) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() >> bits);\n}\n\n/// @notice Implements the checked subtraction operation (-) in the UD60x18 type.\nfunction sub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() - y.unwrap());\n}\n\n/// @notice Implements the unchecked addition operation (+) in the UD60x18 type.\nfunction uncheckedAdd(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    unchecked {\n        result = wrap(x.unwrap() + y.unwrap());\n    }\n}\n\n/// @notice Implements the unchecked subtraction operation (-) in the UD60x18 type.\nfunction uncheckedSub(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    unchecked {\n        result = wrap(x.unwrap() - y.unwrap());\n    }\n}\n\n/// @notice Implements the XOR (^) bitwise operation in the UD60x18 type.\nfunction xor(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(x.unwrap() ^ y.unwrap());\n}\n"
      },
      "lib/prb-math/src/ud60x18/Math.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport { wrap } from \"./Casting.sol\";\nimport {\n    uEXP_MAX_INPUT,\n    uEXP2_MAX_INPUT,\n    uHALF_UNIT,\n    uLOG2_10,\n    uLOG2_E,\n    uMAX_UD60x18,\n    uMAX_WHOLE_UD60x18,\n    UNIT,\n    uUNIT,\n    uUNIT_SQUARED,\n    ZERO\n} from \"./Constants.sol\";\nimport { UD60x18 } from \"./ValueType.sol\";\n\n/*//////////////////////////////////////////////////////////////////////////\n                            MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Calculates the arithmetic average of x and y using the following formula:\n///\n/// $$\n/// avg(x, y) = (x & y) + ((xUint ^ yUint) / 2)\n/// $$\n///\n/// In English, this is what this formula does:\n///\n/// 1. AND x and y.\n/// 2. Calculate half of XOR x and y.\n/// 3. Add the two results together.\n///\n/// This technique is known as SWAR, which stands for \"SIMD within a register\". You can read more about it here:\n/// https://devblogs.microsoft.com/oldnewthing/20220207-00/?p=106223\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// @param x The first operand as a UD60x18 number.\n/// @param y The second operand as a UD60x18 number.\n/// @return result The arithmetic average as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction avg(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n    uint256 yUint = y.unwrap();\n    unchecked {\n        result = wrap((xUint & yUint) + ((xUint ^ yUint) >> 1));\n    }\n}\n\n/// @notice Yields the smallest whole number greater than or equal to x.\n///\n/// @dev This is optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional\n/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be less than or equal to `MAX_WHOLE_UD60x18`.\n///\n/// @param x The UD60x18 number to ceil.\n/// @param result The smallest whole number greater than or equal to x, as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ceil(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n    if (xUint > uMAX_WHOLE_UD60x18) {\n        revert Errors.PRBMath_UD60x18_Ceil_Overflow(x);\n    }\n\n    assembly (\"memory-safe\") {\n        // Equivalent to `x % UNIT`.\n        let remainder := mod(x, uUNIT)\n\n        // Equivalent to `UNIT - remainder`.\n        let delta := sub(uUNIT, remainder)\n\n        // Equivalent to `x + remainder > 0 ? delta : 0`.\n        result := add(x, mul(delta, gt(remainder, 0)))\n    }\n}\n\n/// @notice Divides two UD60x18 numbers, returning a new UD60x18 number.\n///\n/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n///\n/// @param x The numerator as a UD60x18 number.\n/// @param y The denominator as a UD60x18 number.\n/// @param result The quotient as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction div(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(Common.mulDiv(x.unwrap(), uUNIT, y.unwrap()));\n}\n\n/// @notice Calculates the natural exponent of x using the following formula:\n///\n/// $$\n/// e^x = 2^{x * log_2{e}}\n/// $$\n///\n/// @dev Requirements:\n/// - x must be less than 133_084258667509499441.\n///\n/// @param x The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n\n    // This check prevents values greater than 192e18 from being passed to {exp2}.\n    if (xUint > uEXP_MAX_INPUT) {\n        revert Errors.PRBMath_UD60x18_Exp_InputTooBig(x);\n    }\n\n    unchecked {\n        // Inline the fixed-point multiplication to save gas.\n        uint256 doubleUnitProduct = xUint * uLOG2_E;\n        result = exp2(wrap(doubleUnitProduct / uUNIT));\n    }\n}\n\n/// @notice Calculates the binary exponent of x using the binary fraction method.\n///\n/// @dev See https://ethereum.stackexchange.com/q/79903/24693\n///\n/// Requirements:\n/// - x must be less than 192e18.\n/// - The result must fit in UD60x18.\n///\n/// @param x The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n\n    // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.\n    if (xUint > uEXP2_MAX_INPUT) {\n        revert Errors.PRBMath_UD60x18_Exp2_InputTooBig(x);\n    }\n\n    // Convert x to the 192.64-bit fixed-point format.\n    uint256 x_192x64 = (xUint << 64) / uUNIT;\n\n    // Pass x to the {Common.exp2} function, which uses the 192.64-bit fixed-point number representation.\n    result = wrap(Common.exp2(x_192x64));\n}\n\n/// @notice Yields the greatest whole number less than or equal to x.\n/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.\n/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n/// @param x The UD60x18 number to floor.\n/// @param result The greatest whole number less than or equal to x, as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction floor(UD60x18 x) pure returns (UD60x18 result) {\n    assembly (\"memory-safe\") {\n        // Equivalent to `x % UNIT`.\n        let remainder := mod(x, uUNIT)\n\n        // Equivalent to `x - remainder > 0 ? remainder : 0)`.\n        result := sub(x, mul(remainder, gt(remainder, 0)))\n    }\n}\n\n/// @notice Yields the excess beyond the floor of x using the odd function definition.\n/// @dev See https://en.wikipedia.org/wiki/Fractional_part.\n/// @param x The UD60x18 number to get the fractional part of.\n/// @param result The fractional part of x as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction frac(UD60x18 x) pure returns (UD60x18 result) {\n    assembly (\"memory-safe\") {\n        result := mod(x, uUNIT)\n    }\n}\n\n/// @notice Calculates the geometric mean of x and y, i.e. $\\sqrt{x * y}$, rounding down.\n///\n/// @dev Requirements:\n/// - x * y must fit in UD60x18.\n///\n/// @param x The first operand as a UD60x18 number.\n/// @param y The second operand as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction gm(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n    uint256 yUint = y.unwrap();\n    if (xUint == 0 || yUint == 0) {\n        return ZERO;\n    }\n\n    unchecked {\n        // Checking for overflow this way is faster than letting Solidity do it.\n        uint256 xyUint = xUint * yUint;\n        if (xyUint / xUint != yUint) {\n            revert Errors.PRBMath_UD60x18_Gm_Overflow(x, y);\n        }\n\n        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`\n        // during multiplication. See the comments in {Common.sqrt}.\n        result = wrap(Common.sqrt(xyUint));\n    }\n}\n\n/// @notice Calculates the inverse of x.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must not be zero.\n///\n/// @param x The UD60x18 number for which to calculate the inverse.\n/// @return result The inverse as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction inv(UD60x18 x) pure returns (UD60x18 result) {\n    unchecked {\n        result = wrap(uUNIT_SQUARED / x.unwrap());\n    }\n}\n\n/// @notice Calculates the natural logarithm of x using the following formula:\n///\n/// $$\n/// ln{x} = log_2{x} / log_2{e}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The UD60x18 number for which to calculate the natural logarithm.\n/// @return result The natural logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ln(UD60x18 x) pure returns (UD60x18 result) {\n    unchecked {\n        // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that\n        // {log2} can return is ~196_205294292027477728.\n        result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);\n    }\n}\n\n/// @notice Calculates the common logarithm of x using the following formula:\n///\n/// $$\n/// log_{10}{x} = log_2{x} / log_2{10}\n/// $$\n///\n/// However, if x is an exact power of ten, a hard coded value is returned.\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The UD60x18 number for which to calculate the common logarithm.\n/// @return result The common logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log10(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n    if (xUint < uUNIT) {\n        revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);\n    }\n\n    // Note that the `mul` in this assembly block is the standard multiplication operation, not {UD60x18.mul}.\n    // prettier-ignore\n    assembly (\"memory-safe\") {\n        switch x\n        case 1 { result := mul(uUNIT, sub(0, 18)) }\n        case 10 { result := mul(uUNIT, sub(1, 18)) }\n        case 100 { result := mul(uUNIT, sub(2, 18)) }\n        case 1000 { result := mul(uUNIT, sub(3, 18)) }\n        case 10000 { result := mul(uUNIT, sub(4, 18)) }\n        case 100000 { result := mul(uUNIT, sub(5, 18)) }\n        case 1000000 { result := mul(uUNIT, sub(6, 18)) }\n        case 10000000 { result := mul(uUNIT, sub(7, 18)) }\n        case 100000000 { result := mul(uUNIT, sub(8, 18)) }\n        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }\n        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }\n        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }\n        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }\n        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }\n        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }\n        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }\n        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }\n        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }\n        case 1000000000000000000 { result := 0 }\n        case 10000000000000000000 { result := uUNIT }\n        case 100000000000000000000 { result := mul(uUNIT, 2) }\n        case 1000000000000000000000 { result := mul(uUNIT, 3) }\n        case 10000000000000000000000 { result := mul(uUNIT, 4) }\n        case 100000000000000000000000 { result := mul(uUNIT, 5) }\n        case 1000000000000000000000000 { result := mul(uUNIT, 6) }\n        case 10000000000000000000000000 { result := mul(uUNIT, 7) }\n        case 100000000000000000000000000 { result := mul(uUNIT, 8) }\n        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }\n        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }\n        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }\n        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }\n        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }\n        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }\n        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }\n        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }\n        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }\n        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }\n        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }\n        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }\n        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }\n        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }\n        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }\n        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }\n        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }\n        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }\n        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }\n        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }\n        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }\n        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }\n        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }\n        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }\n        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }\n        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }\n        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }\n        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }\n        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }\n        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }\n        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }\n        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }\n        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }\n        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }\n        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }\n        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }\n        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }\n        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }\n        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 59) }\n        default { result := uMAX_UD60x18 }\n    }\n\n    if (result.unwrap() == uMAX_UD60x18) {\n        unchecked {\n            // Inline the fixed-point division to save gas.\n            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);\n        }\n    }\n}\n\n/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:\n///\n/// $$\n/// log_2{x} = n + log_2{y}, \\text{ where } y = x*2^{-n}, \\ y \\in [1, 2)\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, the input is inverted:\n///\n/// $$\n/// log_2{x} = -log_2{\\frac{1}{x}}\n/// $$\n///\n/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation\n///\n/// Notes:\n/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.\n///\n/// Requirements:\n/// - x must be greater than zero.\n///\n/// @param x The UD60x18 number for which to calculate the binary logarithm.\n/// @return result The binary logarithm as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log2(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n\n    if (xUint < uUNIT) {\n        revert Errors.PRBMath_UD60x18_Log_InputTooSmall(x);\n    }\n\n    unchecked {\n        // Calculate the integer part of the logarithm.\n        uint256 n = Common.msb(xUint / uUNIT);\n\n        // This is the integer part of the logarithm as a UD60x18 number. The operation can't overflow because n\n        // n is at most 255 and UNIT is 1e18.\n        uint256 resultUint = n * uUNIT;\n\n        // Calculate $y = x * 2^{-n}$.\n        uint256 y = xUint >> n;\n\n        // If y is the unit number, the fractional part is zero.\n        if (y == uUNIT) {\n            return wrap(resultUint);\n        }\n\n        // Calculate the fractional part via the iterative approximation.\n        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.\n        uint256 DOUBLE_UNIT = 2e18;\n        for (uint256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {\n            y = (y * y) / uUNIT;\n\n            // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?\n            if (y >= DOUBLE_UNIT) {\n                // Add the 2^{-m} factor to the logarithm.\n                resultUint += delta;\n\n                // Halve y, which corresponds to z/2 in the Wikipedia article.\n                y >>= 1;\n            }\n        }\n        result = wrap(resultUint);\n    }\n}\n\n/// @notice Multiplies two UD60x18 numbers together, returning a new UD60x18 number.\n///\n/// @dev Uses {Common.mulDiv} to enable overflow-safe multiplication and division.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n///\n/// @dev See the documentation in {Common.mulDiv18}.\n/// @param x The multiplicand as a UD60x18 number.\n/// @param y The multiplier as a UD60x18 number.\n/// @return result The product as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mul(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    result = wrap(Common.mulDiv18(x.unwrap(), y.unwrap()));\n}\n\n/// @notice Raises x to the power of y.\n///\n/// For $1 \\leq x \\leq \\infty$, the following standard formula is used:\n///\n/// $$\n/// x^y = 2^{log_2{x} * y}\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, since the unsigned {log2} is undefined, an equivalent formula is used:\n///\n/// $$\n/// i = \\frac{1}{x}\n/// w = 2^{log_2{i} * y}\n/// x^y = \\frac{1}{w}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2} and {mul}.\n/// - Returns `UNIT` for 0^0.\n/// - It may not perform well with very small values of x. Consider using SD59x18 as an alternative.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}, {log2}, and {mul}.\n///\n/// @param x The base as a UD60x18 number.\n/// @param y The exponent as a UD60x18 number.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction pow(UD60x18 x, UD60x18 y) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n    uint256 yUint = y.unwrap();\n\n    // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.\n    if (xUint == 0) {\n        return yUint == 0 ? UNIT : ZERO;\n    }\n    // If x is `UNIT`, the result is always `UNIT`.\n    else if (xUint == uUNIT) {\n        return UNIT;\n    }\n\n    // If y is zero, the result is always `UNIT`.\n    if (yUint == 0) {\n        return UNIT;\n    }\n    // If y is `UNIT`, the result is always x.\n    else if (yUint == uUNIT) {\n        return x;\n    }\n\n    // If x is greater than `UNIT`, use the standard formula.\n    if (xUint > uUNIT) {\n        result = exp2(mul(log2(x), y));\n    }\n    // Conversely, if x is less than `UNIT`, use the equivalent formula.\n    else {\n        UD60x18 i = wrap(uUNIT_SQUARED / xUint);\n        UD60x18 w = exp2(mul(log2(i), y));\n        result = wrap(uUNIT_SQUARED / w.unwrap());\n    }\n}\n\n/// @notice Raises x (a UD60x18 number) to the power y (an unsigned basic integer) using the well-known\n/// algorithm \"exponentiation by squaring\".\n///\n/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - The result must fit in UD60x18.\n///\n/// @param x The base as a UD60x18 number.\n/// @param y The exponent as a uint256.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction powu(UD60x18 x, uint256 y) pure returns (UD60x18 result) {\n    // Calculate the first iteration of the loop in advance.\n    uint256 xUint = x.unwrap();\n    uint256 resultUint = y & 1 > 0 ? xUint : uUNIT;\n\n    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.\n    for (y >>= 1; y > 0; y >>= 1) {\n        xUint = Common.mulDiv18(xUint, xUint);\n\n        // Equivalent to `y % 2 == 1`.\n        if (y & 1 > 0) {\n            resultUint = Common.mulDiv18(resultUint, xUint);\n        }\n    }\n    result = wrap(resultUint);\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must be less than `MAX_UD60x18 / UNIT`.\n///\n/// @param x The UD60x18 number for which to calculate the square root.\n/// @return result The result as a UD60x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(UD60x18 x) pure returns (UD60x18 result) {\n    uint256 xUint = x.unwrap();\n\n    unchecked {\n        if (xUint > uMAX_UD60x18 / uUNIT) {\n            revert Errors.PRBMath_UD60x18_Sqrt_Overflow(x);\n        }\n        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two UD60x18 numbers.\n        // In this case, the two numbers are both the square root.\n        result = wrap(Common.sqrt(xUint * uUNIT));\n    }\n}\n"
      },
      "lib/prb-math/src/ud60x18/ValueType.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\nimport \"./Helpers.sol\" as Helpers;\nimport \"./Math.sol\" as Math;\n\n/// @notice The unsigned 60.18-decimal fixed-point number representation, which can have up to 60 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the Solidity type uint256.\n/// @dev The value type is defined here so it can be imported in all other files.\ntype UD60x18 is uint256;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Casting.intoSD1x18,\n    Casting.intoUD2x18,\n    Casting.intoSD59x18,\n    Casting.intoUint128,\n    Casting.intoUint256,\n    Casting.intoUint40,\n    Casting.unwrap\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                            MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes the functions in this library callable on the UD60x18 type.\nusing {\n    Math.avg,\n    Math.ceil,\n    Math.div,\n    Math.exp,\n    Math.exp2,\n    Math.floor,\n    Math.frac,\n    Math.gm,\n    Math.inv,\n    Math.ln,\n    Math.log10,\n    Math.log2,\n    Math.mul,\n    Math.pow,\n    Math.powu,\n    Math.sqrt\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                HELPER FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes the functions in this library callable on the UD60x18 type.\nusing {\n    Helpers.add,\n    Helpers.and,\n    Helpers.eq,\n    Helpers.gt,\n    Helpers.gte,\n    Helpers.isZero,\n    Helpers.lshift,\n    Helpers.lt,\n    Helpers.lte,\n    Helpers.mod,\n    Helpers.neq,\n    Helpers.not,\n    Helpers.or,\n    Helpers.rshift,\n    Helpers.sub,\n    Helpers.uncheckedAdd,\n    Helpers.uncheckedSub,\n    Helpers.xor\n} for UD60x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    OPERATORS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes it possible to use these operators on the UD60x18 type.\nusing {\n    Helpers.add as +,\n    Helpers.and2 as &,\n    Math.div as /,\n    Helpers.eq as ==,\n    Helpers.gt as >,\n    Helpers.gte as >=,\n    Helpers.lt as <,\n    Helpers.lte as <=,\n    Helpers.or as |,\n    Helpers.mod as %,\n    Math.mul as *,\n    Helpers.neq as !=,\n    Helpers.not as ~,\n    Helpers.sub as -,\n    Helpers.xor as ^\n} for UD60x18 global;\n"
      },
      "node_modules/@openzeppelin/contracts/token/ERC20/IERC20.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Interface of the ERC20 standard as defined in the EIP.\n */\ninterface IERC20 {\n    /**\n     * @dev Emitted when `value` tokens are moved from one account (`from`) to\n     * another (`to`).\n     *\n     * Note that `value` may be zero.\n     */\n    event Transfer(address indexed from, address indexed to, uint256 value);\n\n    /**\n     * @dev Emitted when the allowance of a `spender` for an `owner` is set by\n     * a call to {approve}. `value` is the new allowance.\n     */\n    event Approval(address indexed owner, address indexed spender, uint256 value);\n\n    /**\n     * @dev Returns the amount of tokens in existence.\n     */\n    function totalSupply() external view returns (uint256);\n\n    /**\n     * @dev Returns the amount of tokens owned by `account`.\n     */\n    function balanceOf(address account) external view returns (uint256);\n\n    /**\n     * @dev Moves `amount` tokens from the caller's account to `to`.\n     *\n     * Returns a boolean value indicating whether the operation succeeded.\n     *\n     * Emits a {Transfer} event.\n     */\n    function transfer(address to, uint256 amount) external returns (bool);\n\n    /**\n     * @dev Returns the remaining number of tokens that `spender` will be\n     * allowed to spend on behalf of `owner` through {transferFrom}. This is\n     * zero by default.\n     *\n     * This value changes when {approve} or {transferFrom} are called.\n     */\n    function allowance(address owner, address spender) external view returns (uint256);\n\n    /**\n     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.\n     *\n     * Returns a boolean value indicating whether the operation succeeded.\n     *\n     * IMPORTANT: Beware that changing an allowance with this method brings the risk\n     * that someone may use both the old and the new allowance by unfortunate\n     * transaction ordering. One possible solution to mitigate this race\n     * condition is to first reduce the spender's allowance to 0 and set the\n     * desired value afterwards:\n     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729\n     *\n     * Emits an {Approval} event.\n     */\n    function approve(address spender, uint256 amount) external returns (bool);\n\n    /**\n     * @dev Moves `amount` tokens from `from` to `to` using the\n     * allowance mechanism. `amount` is then deducted from the caller's\n     * allowance.\n     *\n     * Returns a boolean value indicating whether the operation succeeded.\n     *\n     * Emits a {Transfer} event.\n     */\n    function transferFrom(\n        address from,\n        address to,\n        uint256 amount\n    ) external returns (bool);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IRewardManager.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\ninterface IRewardManager {\n    function userReward(address token, address user) external view returns (uint128 index, uint128 accrued);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/interfaces/IPInterestManagerYT.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\ninterface IPInterestManagerYT {\n    event CollectInterestFee(uint256 amountInterestFee);\n\n    function userInterest(address user) external view returns (uint128 lastPYIndex, uint128 accruedInterest);\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/core/libraries/math/LogExpMath.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\n// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated\n// documentation files (the “Software”), to deal in the Software without restriction, including without limitation the\n// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to\n// permit persons to whom the Software is furnished to do so, subject to the following conditions:\n\n// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the\n// Software.\n\n// THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE\n// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR\n// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR\n// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n\npragma solidity ^0.8.0;\n\n/* solhint-disable */\n\n/**\n * @dev Exponentiation and logarithm functions for 18 decimal fixed point numbers (both base and exponent/argument).\n *\n * Exponentiation and logarithm with arbitrary bases (x^y and log_x(y)) are implemented by conversion to natural\n * exponentiation and logarithm (where the base is Euler's number).\n *\n * @author Fernando Martinelli - @fernandomartinelli\n * @author Sergio Yuhjtman - @sergioyuhjtman\n * @author Daniel Fernandez - @dmf7z\n */\nlibrary LogExpMath {\n    // All fixed point multiplications and divisions are inlined. This means we need to divide by ONE when multiplying\n    // two numbers, and multiply by ONE when dividing them.\n\n    // All arguments and return values are 18 decimal fixed point numbers.\n    int256 constant ONE_18 = 1e18;\n\n    // Internally, intermediate values are computed with higher precision as 20 decimal fixed point numbers, and in the\n    // case of ln36, 36 decimals.\n    int256 constant ONE_20 = 1e20;\n    int256 constant ONE_36 = 1e36;\n\n    // The domain of natural exponentiation is bound by the word size and number of decimals used.\n    //\n    // Because internally the result will be stored using 20 decimals, the largest possible result is\n    // (2^255 - 1) / 10^20, which makes the largest exponent ln((2^255 - 1) / 10^20) = 130.700829182905140221.\n    // The smallest possible result is 10^(-18), which makes largest negative argument\n    // ln(10^(-18)) = -41.446531673892822312.\n    // We use 130.0 and -41.0 to have some safety margin.\n    int256 constant MAX_NATURAL_EXPONENT = 130e18;\n    int256 constant MIN_NATURAL_EXPONENT = -41e18;\n\n    // Bounds for ln_36's argument. Both ln(0.9) and ln(1.1) can be represented with 36 decimal places in a fixed point\n    // 256 bit integer.\n    int256 constant LN_36_LOWER_BOUND = ONE_18 - 1e17;\n    int256 constant LN_36_UPPER_BOUND = ONE_18 + 1e17;\n\n    uint256 constant MILD_EXPONENT_BOUND = 2 ** 254 / uint256(ONE_20);\n\n    // 18 decimal constants\n    int256 constant x0 = 128000000000000000000; // 2ˆ7\n    int256 constant a0 = 38877084059945950922200000000000000000000000000000000000; // eˆ(x0) (no decimals)\n    int256 constant x1 = 64000000000000000000; // 2ˆ6\n    int256 constant a1 = 6235149080811616882910000000; // eˆ(x1) (no decimals)\n\n    // 20 decimal constants\n    int256 constant x2 = 3200000000000000000000; // 2ˆ5\n    int256 constant a2 = 7896296018268069516100000000000000; // eˆ(x2)\n    int256 constant x3 = 1600000000000000000000; // 2ˆ4\n    int256 constant a3 = 888611052050787263676000000; // eˆ(x3)\n    int256 constant x4 = 800000000000000000000; // 2ˆ3\n    int256 constant a4 = 298095798704172827474000; // eˆ(x4)\n    int256 constant x5 = 400000000000000000000; // 2ˆ2\n    int256 constant a5 = 5459815003314423907810; // eˆ(x5)\n    int256 constant x6 = 200000000000000000000; // 2ˆ1\n    int256 constant a6 = 738905609893065022723; // eˆ(x6)\n    int256 constant x7 = 100000000000000000000; // 2ˆ0\n    int256 constant a7 = 271828182845904523536; // eˆ(x7)\n    int256 constant x8 = 50000000000000000000; // 2ˆ-1\n    int256 constant a8 = 164872127070012814685; // eˆ(x8)\n    int256 constant x9 = 25000000000000000000; // 2ˆ-2\n    int256 constant a9 = 128402541668774148407; // eˆ(x9)\n    int256 constant x10 = 12500000000000000000; // 2ˆ-3\n    int256 constant a10 = 113314845306682631683; // eˆ(x10)\n    int256 constant x11 = 6250000000000000000; // 2ˆ-4\n    int256 constant a11 = 106449445891785942956; // eˆ(x11)\n\n    /**\n     * @dev Natural exponentiation (e^x) with signed 18 decimal fixed point exponent.\n     *\n     * Reverts if `x` is smaller than MIN_NATURAL_EXPONENT, or larger than `MAX_NATURAL_EXPONENT`.\n     */\n    function exp(int256 x) internal pure returns (int256) {\n        unchecked {\n            require(x >= MIN_NATURAL_EXPONENT && x <= MAX_NATURAL_EXPONENT, \"Invalid exponent\");\n\n            if (x < 0) {\n                // We only handle positive exponents: e^(-x) is computed as 1 / e^x. We can safely make x positive since it\n                // fits in the signed 256 bit range (as it is larger than MIN_NATURAL_EXPONENT).\n                // Fixed point division requires multiplying by ONE_18.\n                return ((ONE_18 * ONE_18) / exp(-x));\n            }\n\n            // First, we use the fact that e^(x+y) = e^x * e^y to decompose x into a sum of powers of two, which we call x_n,\n            // where x_n == 2^(7 - n), and e^x_n = a_n has been precomputed. We choose the first x_n, x0, to equal 2^7\n            // because all larger powers are larger than MAX_NATURAL_EXPONENT, and therefore not present in the\n            // decomposition.\n            // At the end of this process we will have the product of all e^x_n = a_n that apply, and the remainder of this\n            // decomposition, which will be lower than the smallest x_n.\n            // exp(x) = k_0 * a_0 * k_1 * a_1 * ... + k_n * a_n * exp(remainder), where each k_n equals either 0 or 1.\n            // We mutate x by subtracting x_n, making it the remainder of the decomposition.\n\n            // The first two a_n (e^(2^7) and e^(2^6)) are too large if stored as 18 decimal numbers, and could cause\n            // intermediate overflows. Instead we store them as plain integers, with 0 decimals.\n            // Additionally, x0 + x1 is larger than MAX_NATURAL_EXPONENT, which means they will not both be present in the\n            // decomposition.\n\n            // For each x_n, we test if that term is present in the decomposition (if x is larger than it), and if so deduct\n            // it and compute the accumulated product.\n\n            int256 firstAN;\n            if (x >= x0) {\n                x -= x0;\n                firstAN = a0;\n            } else if (x >= x1) {\n                x -= x1;\n                firstAN = a1;\n            } else {\n                firstAN = 1; // One with no decimal places\n            }\n\n            // We now transform x into a 20 decimal fixed point number, to have enhanced precision when computing the\n            // smaller terms.\n            x *= 100;\n\n            // `product` is the accumulated product of all a_n (except a0 and a1), which starts at 20 decimal fixed point\n            // one. Recall that fixed point multiplication requires dividing by ONE_20.\n            int256 product = ONE_20;\n\n            if (x >= x2) {\n                x -= x2;\n                product = (product * a2) / ONE_20;\n            }\n            if (x >= x3) {\n                x -= x3;\n                product = (product * a3) / ONE_20;\n            }\n            if (x >= x4) {\n                x -= x4;\n                product = (product * a4) / ONE_20;\n            }\n            if (x >= x5) {\n                x -= x5;\n                product = (product * a5) / ONE_20;\n            }\n            if (x >= x6) {\n                x -= x6;\n                product = (product * a6) / ONE_20;\n            }\n            if (x >= x7) {\n                x -= x7;\n                product = (product * a7) / ONE_20;\n            }\n            if (x >= x8) {\n                x -= x8;\n                product = (product * a8) / ONE_20;\n            }\n            if (x >= x9) {\n                x -= x9;\n                product = (product * a9) / ONE_20;\n            }\n\n            // x10 and x11 are unnecessary here since we have high enough precision already.\n\n            // Now we need to compute e^x, where x is small (in particular, it is smaller than x9). We use the Taylor series\n            // expansion for e^x: 1 + x + (x^2 / 2!) + (x^3 / 3!) + ... + (x^n / n!).\n\n            int256 seriesSum = ONE_20; // The initial one in the sum, with 20 decimal places.\n            int256 term; // Each term in the sum, where the nth term is (x^n / n!).\n\n            // The first term is simply x.\n            term = x;\n            seriesSum += term;\n\n            // Each term (x^n / n!) equals the previous one times x, divided by n. Since x is a fixed point number,\n            // multiplying by it requires dividing by ONE_20, but dividing by the non-fixed point n values does not.\n\n            term = ((term * x) / ONE_20) / 2;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 3;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 4;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 5;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 6;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 7;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 8;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 9;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 10;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 11;\n            seriesSum += term;\n\n            term = ((term * x) / ONE_20) / 12;\n            seriesSum += term;\n\n            // 12 Taylor terms are sufficient for 18 decimal precision.\n\n            // We now have the first a_n (with no decimals), and the product of all other a_n present, and the Taylor\n            // approximation of the exponentiation of the remainder (both with 20 decimals). All that remains is to multiply\n            // all three (one 20 decimal fixed point multiplication, dividing by ONE_20, and one integer multiplication),\n            // and then drop two digits to return an 18 decimal value.\n\n            return (((product * seriesSum) / ONE_20) * firstAN) / 100;\n        }\n    }\n\n    /**\n     * @dev Natural logarithm (ln(a)) with signed 18 decimal fixed point argument.\n     */\n    function ln(int256 a) internal pure returns (int256) {\n        unchecked {\n            // The real natural logarithm is not defined for negative numbers or zero.\n            require(a > 0, \"out of bounds\");\n            if (LN_36_LOWER_BOUND < a && a < LN_36_UPPER_BOUND) {\n                return _ln_36(a) / ONE_18;\n            } else {\n                return _ln(a);\n            }\n        }\n    }\n\n    /**\n     * @dev Exponentiation (x^y) with unsigned 18 decimal fixed point base and exponent.\n     *\n     * Reverts if ln(x) * y is smaller than `MIN_NATURAL_EXPONENT`, or larger than `MAX_NATURAL_EXPONENT`.\n     */\n    function pow(uint256 x, uint256 y) internal pure returns (uint256) {\n        unchecked {\n            if (y == 0) {\n                // We solve the 0^0 indetermination by making it equal one.\n                return uint256(ONE_18);\n            }\n\n            if (x == 0) {\n                return 0;\n            }\n\n            // Instead of computing x^y directly, we instead rely on the properties of logarithms and exponentiation to\n            // arrive at that r`esult. In particular, exp(ln(x)) = x, and ln(x^y) = y * ln(x). This means\n            // x^y = exp(y * ln(x)).\n\n            // The ln function takes a signed value, so we need to make sure x fits in the signed 256 bit range.\n            require(x < 2 ** 255, \"x out of bounds\");\n            int256 x_int256 = int256(x);\n\n            // We will compute y * ln(x) in a single step. Depending on the value of x, we can either use ln or ln_36. In\n            // both cases, we leave the division by ONE_18 (due to fixed point multiplication) to the end.\n\n            // This prevents y * ln(x) from overflowing, and at the same time guarantees y fits in the signed 256 bit range.\n            require(y < MILD_EXPONENT_BOUND, \"y out of bounds\");\n            int256 y_int256 = int256(y);\n\n            int256 logx_times_y;\n            if (LN_36_LOWER_BOUND < x_int256 && x_int256 < LN_36_UPPER_BOUND) {\n                int256 ln_36_x = _ln_36(x_int256);\n\n                // ln_36_x has 36 decimal places, so multiplying by y_int256 isn't as straightforward, since we can't just\n                // bring y_int256 to 36 decimal places, as it might overflow. Instead, we perform two 18 decimal\n                // multiplications and add the results: one with the first 18 decimals of ln_36_x, and one with the\n                // (downscaled) last 18 decimals.\n                logx_times_y = ((ln_36_x / ONE_18) * y_int256 + ((ln_36_x % ONE_18) * y_int256) / ONE_18);\n            } else {\n                logx_times_y = _ln(x_int256) * y_int256;\n            }\n            logx_times_y /= ONE_18;\n\n            // Finally, we compute exp(y * ln(x)) to arrive at x^y\n            require(\n                MIN_NATURAL_EXPONENT <= logx_times_y && logx_times_y <= MAX_NATURAL_EXPONENT,\n                \"product out of bounds\"\n            );\n\n            return uint256(exp(logx_times_y));\n        }\n    }\n\n    /**\n     * @dev Internal natural logarithm (ln(a)) with signed 18 decimal fixed point argument.\n     */\n    function _ln(int256 a) private pure returns (int256) {\n        unchecked {\n            if (a < ONE_18) {\n                // Since ln(a^k) = k * ln(a), we can compute ln(a) as ln(a) = ln((1/a)^(-1)) = - ln((1/a)). If a is less\n                // than one, 1/a will be greater than one, and this if statement will not be entered in the recursive call.\n                // Fixed point division requires multiplying by ONE_18.\n                return (-_ln((ONE_18 * ONE_18) / a));\n            }\n\n            // First, we use the fact that ln^(a * b) = ln(a) + ln(b) to decompose ln(a) into a sum of powers of two, which\n            // we call x_n, where x_n == 2^(7 - n), which are the natural logarithm of precomputed quantities a_n (that is,\n            // ln(a_n) = x_n). We choose the first x_n, x0, to equal 2^7 because the exponential of all larger powers cannot\n            // be represented as 18 fixed point decimal numbers in 256 bits, and are therefore larger than a.\n            // At the end of this process we will have the sum of all x_n = ln(a_n) that apply, and the remainder of this\n            // decomposition, which will be lower than the smallest a_n.\n            // ln(a) = k_0 * x_0 + k_1 * x_1 + ... + k_n * x_n + ln(remainder), where each k_n equals either 0 or 1.\n            // We mutate a by subtracting a_n, making it the remainder of the decomposition.\n\n            // For reasons related to how `exp` works, the first two a_n (e^(2^7) and e^(2^6)) are not stored as fixed point\n            // numbers with 18 decimals, but instead as plain integers with 0 decimals, so we need to multiply them by\n            // ONE_18 to convert them to fixed point.\n            // For each a_n, we test if that term is present in the decomposition (if a is larger than it), and if so divide\n            // by it and compute the accumulated sum.\n\n            int256 sum = 0;\n            if (a >= a0 * ONE_18) {\n                a /= a0; // Integer, not fixed point division\n                sum += x0;\n            }\n\n            if (a >= a1 * ONE_18) {\n                a /= a1; // Integer, not fixed point division\n                sum += x1;\n            }\n\n            // All other a_n and x_n are stored as 20 digit fixed point numbers, so we convert the sum and a to this format.\n            sum *= 100;\n            a *= 100;\n\n            // Because further a_n are  20 digit fixed point numbers, we multiply by ONE_20 when dividing by them.\n\n            if (a >= a2) {\n                a = (a * ONE_20) / a2;\n                sum += x2;\n            }\n\n            if (a >= a3) {\n                a = (a * ONE_20) / a3;\n                sum += x3;\n            }\n\n            if (a >= a4) {\n                a = (a * ONE_20) / a4;\n                sum += x4;\n            }\n\n            if (a >= a5) {\n                a = (a * ONE_20) / a5;\n                sum += x5;\n            }\n\n            if (a >= a6) {\n                a = (a * ONE_20) / a6;\n                sum += x6;\n            }\n\n            if (a >= a7) {\n                a = (a * ONE_20) / a7;\n                sum += x7;\n            }\n\n            if (a >= a8) {\n                a = (a * ONE_20) / a8;\n                sum += x8;\n            }\n\n            if (a >= a9) {\n                a = (a * ONE_20) / a9;\n                sum += x9;\n            }\n\n            if (a >= a10) {\n                a = (a * ONE_20) / a10;\n                sum += x10;\n            }\n\n            if (a >= a11) {\n                a = (a * ONE_20) / a11;\n                sum += x11;\n            }\n\n            // a is now a small number (smaller than a_11, which roughly equals 1.06). This means we can use a Taylor series\n            // that converges rapidly for values of `a` close to one - the same one used in ln_36.\n            // Let z = (a - 1) / (a + 1).\n            // ln(a) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))\n\n            // Recall that 20 digit fixed point division requires multiplying by ONE_20, and multiplication requires\n            // division by ONE_20.\n            int256 z = ((a - ONE_20) * ONE_20) / (a + ONE_20);\n            int256 z_squared = (z * z) / ONE_20;\n\n            // num is the numerator of the series: the z^(2 * n + 1) term\n            int256 num = z;\n\n            // seriesSum holds the accumulated sum of each term in the series, starting with the initial z\n            int256 seriesSum = num;\n\n            // In each step, the numerator is multiplied by z^2\n            num = (num * z_squared) / ONE_20;\n            seriesSum += num / 3;\n\n            num = (num * z_squared) / ONE_20;\n            seriesSum += num / 5;\n\n            num = (num * z_squared) / ONE_20;\n            seriesSum += num / 7;\n\n            num = (num * z_squared) / ONE_20;\n            seriesSum += num / 9;\n\n            num = (num * z_squared) / ONE_20;\n            seriesSum += num / 11;\n\n            // 6 Taylor terms are sufficient for 36 decimal precision.\n\n            // Finally, we multiply by 2 (non fixed point) to compute ln(remainder)\n            seriesSum *= 2;\n\n            // We now have the sum of all x_n present, and the Taylor approximation of the logarithm of the remainder (both\n            // with 20 decimals). All that remains is to sum these two, and then drop two digits to return a 18 decimal\n            // value.\n\n            return (sum + seriesSum) / 100;\n        }\n    }\n\n    /**\n     * @dev Intrnal high precision (36 decimal places) natural logarithm (ln(x)) with signed 18 decimal fixed point argument,\n     * for x close to one.\n     *\n     * Should only be used if x is between LN_36_LOWER_BOUND and LN_36_UPPER_BOUND.\n     */\n    function _ln_36(int256 x) private pure returns (int256) {\n        unchecked {\n            // Since ln(1) = 0, a value of x close to one will yield a very small result, which makes using 36 digits\n            // worthwhile.\n\n            // First, we transform x to a 36 digit fixed point value.\n            x *= ONE_18;\n\n            // We will use the following Taylor expansion, which converges very rapidly. Let z = (x - 1) / (x + 1).\n            // ln(x) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))\n\n            // Recall that 36 digit fixed point division requires multiplying by ONE_36, and multiplication requires\n            // division by ONE_36.\n            int256 z = ((x - ONE_36) * ONE_36) / (x + ONE_36);\n            int256 z_squared = (z * z) / ONE_36;\n\n            // num is the numerator of the series: the z^(2 * n + 1) term\n            int256 num = z;\n\n            // seriesSum holds the accumulated sum of each term in the series, starting with the initial z\n            int256 seriesSum = num;\n\n            // In each step, the numerator is multiplied by z^2\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 3;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 5;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 7;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 9;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 11;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 13;\n\n            num = (num * z_squared) / ONE_36;\n            seriesSum += num / 15;\n\n            // 8 Taylor terms are sufficient for 36 decimal precision.\n\n            // All that remains is multiplying by 2 (non fixed point).\n            return seriesSum * 2;\n        }\n    }\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/core/StandardizedYield/PYIndex.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\nimport \"../../interfaces/IPYieldToken.sol\";\nimport \"../../interfaces/IPPrincipalToken.sol\";\n\nimport \"./SYUtils.sol\";\nimport \"../libraries/math/PMath.sol\";\n\ntype PYIndex is uint256;\n\nlibrary PYIndexLib {\n    using PMath for uint256;\n    using PMath for int256;\n\n    function newIndex(IPYieldToken YT) internal returns (PYIndex) {\n        return PYIndex.wrap(YT.pyIndexCurrent());\n    }\n\n    function syToAsset(PYIndex index, uint256 syAmount) internal pure returns (uint256) {\n        return SYUtils.syToAsset(PYIndex.unwrap(index), syAmount);\n    }\n\n    function assetToSy(PYIndex index, uint256 assetAmount) internal pure returns (uint256) {\n        return SYUtils.assetToSy(PYIndex.unwrap(index), assetAmount);\n    }\n\n    function assetToSyUp(PYIndex index, uint256 assetAmount) internal pure returns (uint256) {\n        return SYUtils.assetToSyUp(PYIndex.unwrap(index), assetAmount);\n    }\n\n    function syToAssetUp(PYIndex index, uint256 syAmount) internal pure returns (uint256) {\n        uint256 _index = PYIndex.unwrap(index);\n        return SYUtils.syToAssetUp(_index, syAmount);\n    }\n\n    function syToAsset(PYIndex index, int256 syAmount) internal pure returns (int256) {\n        int256 sign = syAmount < 0 ? int256(-1) : int256(1);\n        return sign * (SYUtils.syToAsset(PYIndex.unwrap(index), syAmount.abs())).Int();\n    }\n\n    function assetToSy(PYIndex index, int256 assetAmount) internal pure returns (int256) {\n        int256 sign = assetAmount < 0 ? int256(-1) : int256(1);\n        return sign * (SYUtils.assetToSy(PYIndex.unwrap(index), assetAmount.abs())).Int();\n    }\n\n    function assetToSyUp(PYIndex index, int256 assetAmount) internal pure returns (int256) {\n        int256 sign = assetAmount < 0 ? int256(-1) : int256(1);\n        return sign * (SYUtils.assetToSyUp(PYIndex.unwrap(index), assetAmount.abs())).Int();\n    }\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/core/libraries/MiniHelpers.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nlibrary MiniHelpers {\n    function isCurrentlyExpired(uint256 expiry) internal view returns (bool) {\n        return (expiry <= block.timestamp);\n    }\n\n    function isExpired(uint256 expiry, uint256 blockTime) internal pure returns (bool) {\n        return (expiry <= blockTime);\n    }\n\n    function isTimeInThePast(uint256 timestamp) internal view returns (bool) {\n        return (timestamp <= block.timestamp); // same definition as isCurrentlyExpired\n    }\n}\n"
      },
      "lib/pendle-core-v2-public/contracts/core/libraries/Errors.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nlibrary Errors {\n    // BulkSeller\n    error BulkInsufficientSyForTrade(uint256 currentAmount, uint256 requiredAmount);\n    error BulkInsufficientTokenForTrade(uint256 currentAmount, uint256 requiredAmount);\n    error BulkInSufficientSyOut(uint256 actualSyOut, uint256 requiredSyOut);\n    error BulkInSufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);\n    error BulkInsufficientSyReceived(uint256 actualBalance, uint256 requiredBalance);\n    error BulkNotMaintainer();\n    error BulkNotAdmin();\n    error BulkSellerAlreadyExisted(address token, address SY, address bulk);\n    error BulkSellerInvalidToken(address token, address SY);\n    error BulkBadRateTokenToSy(uint256 actualRate, uint256 currentRate, uint256 eps);\n    error BulkBadRateSyToToken(uint256 actualRate, uint256 currentRate, uint256 eps);\n\n    // APPROX\n    error ApproxFail();\n    error ApproxParamsInvalid(uint256 guessMin, uint256 guessMax, uint256 eps);\n    error ApproxBinarySearchInputInvalid(\n        uint256 approxGuessMin,\n        uint256 approxGuessMax,\n        uint256 minGuessMin,\n        uint256 maxGuessMax\n    );\n\n    // MARKET + MARKET MATH CORE\n    error MarketExpired();\n    error MarketZeroAmountsInput();\n    error MarketZeroAmountsOutput();\n    error MarketZeroLnImpliedRate();\n    error MarketInsufficientPtForTrade(int256 currentAmount, int256 requiredAmount);\n    error MarketInsufficientPtReceived(uint256 actualBalance, uint256 requiredBalance);\n    error MarketInsufficientSyReceived(uint256 actualBalance, uint256 requiredBalance);\n    error MarketZeroTotalPtOrTotalAsset(int256 totalPt, int256 totalAsset);\n    error MarketExchangeRateBelowOne(int256 exchangeRate);\n    error MarketProportionMustNotEqualOne();\n    error MarketRateScalarBelowZero(int256 rateScalar);\n    error MarketScalarRootBelowZero(int256 scalarRoot);\n    error MarketProportionTooHigh(int256 proportion, int256 maxProportion);\n\n    error OracleUninitialized();\n    error OracleTargetTooOld(uint32 target, uint32 oldest);\n    error OracleZeroCardinality();\n\n    error MarketFactoryExpiredPt();\n    error MarketFactoryInvalidPt();\n    error MarketFactoryMarketExists();\n\n    error MarketFactoryLnFeeRateRootTooHigh(uint80 lnFeeRateRoot, uint256 maxLnFeeRateRoot);\n    error MarketFactoryOverriddenFeeTooHigh(uint80 overriddenFee, uint256 marketLnFeeRateRoot);\n    error MarketFactoryReserveFeePercentTooHigh(uint8 reserveFeePercent, uint8 maxReserveFeePercent);\n    error MarketFactoryZeroTreasury();\n    error MarketFactoryInitialAnchorTooLow(int256 initialAnchor, int256 minInitialAnchor);\n    error MFNotPendleMarket(address addr);\n\n    // ROUTER\n    error RouterInsufficientLpOut(uint256 actualLpOut, uint256 requiredLpOut);\n    error RouterInsufficientSyOut(uint256 actualSyOut, uint256 requiredSyOut);\n    error RouterInsufficientPtOut(uint256 actualPtOut, uint256 requiredPtOut);\n    error RouterInsufficientYtOut(uint256 actualYtOut, uint256 requiredYtOut);\n    error RouterInsufficientPYOut(uint256 actualPYOut, uint256 requiredPYOut);\n    error RouterInsufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);\n    error RouterInsufficientSyRepay(uint256 actualSyRepay, uint256 requiredSyRepay);\n    error RouterInsufficientPtRepay(uint256 actualPtRepay, uint256 requiredPtRepay);\n    error RouterNotAllSyUsed(uint256 netSyDesired, uint256 netSyUsed);\n\n    error RouterTimeRangeZero();\n    error RouterCallbackNotPendleMarket(address caller);\n    error RouterInvalidAction(bytes4 selector);\n    error RouterInvalidFacet(address facet);\n\n    error RouterKyberSwapDataZero();\n\n    error SimulationResults(bool success, bytes res);\n\n    // YIELD CONTRACT\n    error YCExpired();\n    error YCNotExpired();\n    error YieldContractInsufficientSy(uint256 actualSy, uint256 requiredSy);\n    error YCNothingToRedeem();\n    error YCPostExpiryDataNotSet();\n    error YCNoFloatingSy();\n\n    // YieldFactory\n    error YCFactoryInvalidExpiry();\n    error YCFactoryYieldContractExisted();\n    error YCFactoryZeroExpiryDivisor();\n    error YCFactoryZeroTreasury();\n    error YCFactoryInterestFeeRateTooHigh(uint256 interestFeeRate, uint256 maxInterestFeeRate);\n    error YCFactoryRewardFeeRateTooHigh(uint256 newRewardFeeRate, uint256 maxRewardFeeRate);\n\n    // SY\n    error SYInvalidTokenIn(address token);\n    error SYInvalidTokenOut(address token);\n    error SYZeroDeposit();\n    error SYZeroRedeem();\n    error SYInsufficientSharesOut(uint256 actualSharesOut, uint256 requiredSharesOut);\n    error SYInsufficientTokenOut(uint256 actualTokenOut, uint256 requiredTokenOut);\n\n    // SY-specific\n    error SYQiTokenMintFailed(uint256 errCode);\n    error SYQiTokenRedeemFailed(uint256 errCode);\n    error SYQiTokenRedeemRewardsFailed(uint256 rewardAccruedType0, uint256 rewardAccruedType1);\n    error SYQiTokenBorrowRateTooHigh(uint256 borrowRate, uint256 borrowRateMax);\n\n    error SYCurveInvalidPid();\n    error SYCurve3crvPoolNotFound();\n\n    error SYApeDepositAmountTooSmall(uint256 amountDeposited);\n    error SYBalancerInvalidPid();\n    error SYInvalidRewardToken(address token);\n\n    error SYStargateRedeemCapExceeded(uint256 amountLpDesired, uint256 amountLpRedeemable);\n\n    error SYBalancerReentrancy();\n\n    error NotFromTrustedRemote(uint16 srcChainId, bytes path);\n\n    error ApxETHNotEnoughBuffer();\n\n    // Liquidity Mining\n    error VCInactivePool(address pool);\n    error VCPoolAlreadyActive(address pool);\n    error VCZeroVePendle(address user);\n    error VCExceededMaxWeight(uint256 totalWeight, uint256 maxWeight);\n    error VCEpochNotFinalized(uint256 wTime);\n    error VCPoolAlreadyAddAndRemoved(address pool);\n\n    error VEInvalidNewExpiry(uint256 newExpiry);\n    error VEExceededMaxLockTime();\n    error VEInsufficientLockTime();\n    error VENotAllowedReduceExpiry();\n    error VEZeroAmountLocked();\n    error VEPositionNotExpired();\n    error VEZeroPosition();\n    error VEZeroSlope(uint128 bias, uint128 slope);\n    error VEReceiveOldSupply(uint256 msgTime);\n\n    error GCNotPendleMarket(address caller);\n    error GCNotVotingController(address caller);\n\n    error InvalidWTime(uint256 wTime);\n    error ExpiryInThePast(uint256 expiry);\n    error ChainNotSupported(uint256 chainId);\n\n    error FDTotalAmountFundedNotMatch(uint256 actualTotalAmount, uint256 expectedTotalAmount);\n    error FDEpochLengthMismatch();\n    error FDInvalidPool(address pool);\n    error FDPoolAlreadyExists(address pool);\n    error FDInvalidNewFinishedEpoch(uint256 oldFinishedEpoch, uint256 newFinishedEpoch);\n    error FDInvalidStartEpoch(uint256 startEpoch);\n    error FDInvalidWTimeFund(uint256 lastFunded, uint256 wTime);\n    error FDFutureFunding(uint256 lastFunded, uint256 currentWTime);\n\n    error BDInvalidEpoch(uint256 epoch, uint256 startTime);\n\n    // Cross-Chain\n    error MsgNotFromSendEndpoint(uint16 srcChainId, bytes path);\n    error MsgNotFromReceiveEndpoint(address sender);\n    error InsufficientFeeToSendMsg(uint256 currentFee, uint256 requiredFee);\n    error ApproxDstExecutionGasNotSet();\n    error InvalidRetryData();\n\n    // GENERIC MSG\n    error ArrayLengthMismatch();\n    error ArrayEmpty();\n    error ArrayOutOfBounds();\n    error ZeroAddress();\n    error FailedToSendEther();\n    error InvalidMerkleProof();\n\n    error OnlyLayerZeroEndpoint();\n    error OnlyYT();\n    error OnlyYCFactory();\n    error OnlyWhitelisted();\n\n    // Swap Aggregator\n    error SAInsufficientTokenIn(address tokenIn, uint256 amountExpected, uint256 amountActual);\n    error UnsupportedSelector(uint256 aggregatorType, bytes4 selector);\n}\n"
      },
      "lib/prb-math/src/Common.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\n// Common.sol\n//\n// Common mathematical functions used in both SD59x18 and UD60x18. Note that these global functions do not\n// always operate with SD59x18 and UD60x18 numbers.\n\n/*//////////////////////////////////////////////////////////////////////////\n                                CUSTOM ERRORS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.\nerror PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);\n\n/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.\nerror PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);\n\n/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.\nerror PRBMath_MulDivSigned_InputTooSmall();\n\n/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.\nerror PRBMath_MulDivSigned_Overflow(int256 x, int256 y);\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    CONSTANTS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @dev The maximum value a uint128 number can have.\nuint128 constant MAX_UINT128 = type(uint128).max;\n\n/// @dev The maximum value a uint40 number can have.\nuint40 constant MAX_UINT40 = type(uint40).max;\n\n/// @dev The unit number, which the decimal precision of the fixed-point types.\nuint256 constant UNIT = 1e18;\n\n/// @dev The unit number inverted mod 2^256.\nuint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;\n\n/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant\n/// bit in the binary representation of `UNIT`.\nuint256 constant UNIT_LPOTD = 262144;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\n/// @notice Calculates the binary exponent of x using the binary fraction method.\n/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.\n/// @param x The exponent as an unsigned 192.64-bit fixed-point number.\n/// @return result The result as an unsigned 60.18-decimal fixed-point number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(uint256 x) pure returns (uint256 result) {\n    unchecked {\n        // Start from 0.5 in the 192.64-bit fixed-point format.\n        result = 0x800000000000000000000000000000000000000000000000;\n\n        // The following logic multiplies the result by $\\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:\n        //\n        // 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.\n        // 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing\n        // a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,\n        // we know that `x & 0xFF` is also 1.\n        if (x & 0xFF00000000000000 > 0) {\n            if (x & 0x8000000000000000 > 0) {\n                result = (result * 0x16A09E667F3BCC909) >> 64;\n            }\n            if (x & 0x4000000000000000 > 0) {\n                result = (result * 0x1306FE0A31B7152DF) >> 64;\n            }\n            if (x & 0x2000000000000000 > 0) {\n                result = (result * 0x1172B83C7D517ADCE) >> 64;\n            }\n            if (x & 0x1000000000000000 > 0) {\n                result = (result * 0x10B5586CF9890F62A) >> 64;\n            }\n            if (x & 0x800000000000000 > 0) {\n                result = (result * 0x1059B0D31585743AE) >> 64;\n            }\n            if (x & 0x400000000000000 > 0) {\n                result = (result * 0x102C9A3E778060EE7) >> 64;\n            }\n            if (x & 0x200000000000000 > 0) {\n                result = (result * 0x10163DA9FB33356D8) >> 64;\n            }\n            if (x & 0x100000000000000 > 0) {\n                result = (result * 0x100B1AFA5ABCBED61) >> 64;\n            }\n        }\n\n        if (x & 0xFF000000000000 > 0) {\n            if (x & 0x80000000000000 > 0) {\n                result = (result * 0x10058C86DA1C09EA2) >> 64;\n            }\n            if (x & 0x40000000000000 > 0) {\n                result = (result * 0x1002C605E2E8CEC50) >> 64;\n            }\n            if (x & 0x20000000000000 > 0) {\n                result = (result * 0x100162F3904051FA1) >> 64;\n            }\n            if (x & 0x10000000000000 > 0) {\n                result = (result * 0x1000B175EFFDC76BA) >> 64;\n            }\n            if (x & 0x8000000000000 > 0) {\n                result = (result * 0x100058BA01FB9F96D) >> 64;\n            }\n            if (x & 0x4000000000000 > 0) {\n                result = (result * 0x10002C5CC37DA9492) >> 64;\n            }\n            if (x & 0x2000000000000 > 0) {\n                result = (result * 0x1000162E525EE0547) >> 64;\n            }\n            if (x & 0x1000000000000 > 0) {\n                result = (result * 0x10000B17255775C04) >> 64;\n            }\n        }\n\n        if (x & 0xFF0000000000 > 0) {\n            if (x & 0x800000000000 > 0) {\n                result = (result * 0x1000058B91B5BC9AE) >> 64;\n            }\n            if (x & 0x400000000000 > 0) {\n                result = (result * 0x100002C5C89D5EC6D) >> 64;\n            }\n            if (x & 0x200000000000 > 0) {\n                result = (result * 0x10000162E43F4F831) >> 64;\n            }\n            if (x & 0x100000000000 > 0) {\n                result = (result * 0x100000B1721BCFC9A) >> 64;\n            }\n            if (x & 0x80000000000 > 0) {\n                result = (result * 0x10000058B90CF1E6E) >> 64;\n            }\n            if (x & 0x40000000000 > 0) {\n                result = (result * 0x1000002C5C863B73F) >> 64;\n            }\n            if (x & 0x20000000000 > 0) {\n                result = (result * 0x100000162E430E5A2) >> 64;\n            }\n            if (x & 0x10000000000 > 0) {\n                result = (result * 0x1000000B172183551) >> 64;\n            }\n        }\n\n        if (x & 0xFF00000000 > 0) {\n            if (x & 0x8000000000 > 0) {\n                result = (result * 0x100000058B90C0B49) >> 64;\n            }\n            if (x & 0x4000000000 > 0) {\n                result = (result * 0x10000002C5C8601CC) >> 64;\n            }\n            if (x & 0x2000000000 > 0) {\n                result = (result * 0x1000000162E42FFF0) >> 64;\n            }\n            if (x & 0x1000000000 > 0) {\n                result = (result * 0x10000000B17217FBB) >> 64;\n            }\n            if (x & 0x800000000 > 0) {\n                result = (result * 0x1000000058B90BFCE) >> 64;\n            }\n            if (x & 0x400000000 > 0) {\n                result = (result * 0x100000002C5C85FE3) >> 64;\n            }\n            if (x & 0x200000000 > 0) {\n                result = (result * 0x10000000162E42FF1) >> 64;\n            }\n            if (x & 0x100000000 > 0) {\n                result = (result * 0x100000000B17217F8) >> 64;\n            }\n        }\n\n        if (x & 0xFF000000 > 0) {\n            if (x & 0x80000000 > 0) {\n                result = (result * 0x10000000058B90BFC) >> 64;\n            }\n            if (x & 0x40000000 > 0) {\n                result = (result * 0x1000000002C5C85FE) >> 64;\n            }\n            if (x & 0x20000000 > 0) {\n                result = (result * 0x100000000162E42FF) >> 64;\n            }\n            if (x & 0x10000000 > 0) {\n                result = (result * 0x1000000000B17217F) >> 64;\n            }\n            if (x & 0x8000000 > 0) {\n                result = (result * 0x100000000058B90C0) >> 64;\n            }\n            if (x & 0x4000000 > 0) {\n                result = (result * 0x10000000002C5C860) >> 64;\n            }\n            if (x & 0x2000000 > 0) {\n                result = (result * 0x1000000000162E430) >> 64;\n            }\n            if (x & 0x1000000 > 0) {\n                result = (result * 0x10000000000B17218) >> 64;\n            }\n        }\n\n        if (x & 0xFF0000 > 0) {\n            if (x & 0x800000 > 0) {\n                result = (result * 0x1000000000058B90C) >> 64;\n            }\n            if (x & 0x400000 > 0) {\n                result = (result * 0x100000000002C5C86) >> 64;\n            }\n            if (x & 0x200000 > 0) {\n                result = (result * 0x10000000000162E43) >> 64;\n            }\n            if (x & 0x100000 > 0) {\n                result = (result * 0x100000000000B1721) >> 64;\n            }\n            if (x & 0x80000 > 0) {\n                result = (result * 0x10000000000058B91) >> 64;\n            }\n            if (x & 0x40000 > 0) {\n                result = (result * 0x1000000000002C5C8) >> 64;\n            }\n            if (x & 0x20000 > 0) {\n                result = (result * 0x100000000000162E4) >> 64;\n            }\n            if (x & 0x10000 > 0) {\n                result = (result * 0x1000000000000B172) >> 64;\n            }\n        }\n\n        if (x & 0xFF00 > 0) {\n            if (x & 0x8000 > 0) {\n                result = (result * 0x100000000000058B9) >> 64;\n            }\n            if (x & 0x4000 > 0) {\n                result = (result * 0x10000000000002C5D) >> 64;\n            }\n            if (x & 0x2000 > 0) {\n                result = (result * 0x1000000000000162E) >> 64;\n            }\n            if (x & 0x1000 > 0) {\n                result = (result * 0x10000000000000B17) >> 64;\n            }\n            if (x & 0x800 > 0) {\n                result = (result * 0x1000000000000058C) >> 64;\n            }\n            if (x & 0x400 > 0) {\n                result = (result * 0x100000000000002C6) >> 64;\n            }\n            if (x & 0x200 > 0) {\n                result = (result * 0x10000000000000163) >> 64;\n            }\n            if (x & 0x100 > 0) {\n                result = (result * 0x100000000000000B1) >> 64;\n            }\n        }\n\n        if (x & 0xFF > 0) {\n            if (x & 0x80 > 0) {\n                result = (result * 0x10000000000000059) >> 64;\n            }\n            if (x & 0x40 > 0) {\n                result = (result * 0x1000000000000002C) >> 64;\n            }\n            if (x & 0x20 > 0) {\n                result = (result * 0x10000000000000016) >> 64;\n            }\n            if (x & 0x10 > 0) {\n                result = (result * 0x1000000000000000B) >> 64;\n            }\n            if (x & 0x8 > 0) {\n                result = (result * 0x10000000000000006) >> 64;\n            }\n            if (x & 0x4 > 0) {\n                result = (result * 0x10000000000000003) >> 64;\n            }\n            if (x & 0x2 > 0) {\n                result = (result * 0x10000000000000001) >> 64;\n            }\n            if (x & 0x1 > 0) {\n                result = (result * 0x10000000000000001) >> 64;\n            }\n        }\n\n        // In the code snippet below, two operations are executed simultaneously:\n        //\n        // 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1\n        // accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.\n        // 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.\n        //\n        // The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,\n        // integer part, $2^n$.\n        result *= UNIT;\n        result >>= (191 - (x >> 64));\n    }\n}\n\n/// @notice Finds the zero-based index of the first 1 in the binary representation of x.\n///\n/// @dev See the note on \"msb\" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set\n///\n/// Each step in this implementation is equivalent to this high-level code:\n///\n/// ```solidity\n/// if (x >= 2 ** 128) {\n///     x >>= 128;\n///     result += 128;\n/// }\n/// ```\n///\n/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:\n/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948\n///\n/// The Yul instructions used below are:\n///\n/// - \"gt\" is \"greater than\"\n/// - \"or\" is the OR bitwise operator\n/// - \"shl\" is \"shift left\"\n/// - \"shr\" is \"shift right\"\n///\n/// @param x The uint256 number for which to find the index of the most significant bit.\n/// @return result The index of the most significant bit as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction msb(uint256 x) pure returns (uint256 result) {\n    // 2^128\n    assembly (\"memory-safe\") {\n        let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^64\n    assembly (\"memory-safe\") {\n        let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^32\n    assembly (\"memory-safe\") {\n        let factor := shl(5, gt(x, 0xFFFFFFFF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^16\n    assembly (\"memory-safe\") {\n        let factor := shl(4, gt(x, 0xFFFF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^8\n    assembly (\"memory-safe\") {\n        let factor := shl(3, gt(x, 0xFF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^4\n    assembly (\"memory-safe\") {\n        let factor := shl(2, gt(x, 0xF))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^2\n    assembly (\"memory-safe\") {\n        let factor := shl(1, gt(x, 0x3))\n        x := shr(factor, x)\n        result := or(result, factor)\n    }\n    // 2^1\n    // No need to shift x any more.\n    assembly (\"memory-safe\") {\n        let factor := gt(x, 0x1)\n        result := or(result, factor)\n    }\n}\n\n/// @notice Calculates x*y÷denominator with 512-bit precision.\n///\n/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - The denominator must not be zero.\n/// - The result must fit in uint256.\n///\n/// @param x The multiplicand as a uint256.\n/// @param y The multiplier as a uint256.\n/// @param denominator The divisor as a uint256.\n/// @return result The result as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {\n    // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n    // use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256\n    // variables such that product = prod1 * 2^256 + prod0.\n    uint256 prod0; // Least significant 256 bits of the product\n    uint256 prod1; // Most significant 256 bits of the product\n    assembly (\"memory-safe\") {\n        let mm := mulmod(x, y, not(0))\n        prod0 := mul(x, y)\n        prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n    }\n\n    // Handle non-overflow cases, 256 by 256 division.\n    if (prod1 == 0) {\n        unchecked {\n            return prod0 / denominator;\n        }\n    }\n\n    // Make sure the result is less than 2^256. Also prevents denominator == 0.\n    if (prod1 >= denominator) {\n        revert PRBMath_MulDiv_Overflow(x, y, denominator);\n    }\n\n    ////////////////////////////////////////////////////////////////////////////\n    // 512 by 256 division\n    ////////////////////////////////////////////////////////////////////////////\n\n    // Make division exact by subtracting the remainder from [prod1 prod0].\n    uint256 remainder;\n    assembly (\"memory-safe\") {\n        // Compute remainder using the mulmod Yul instruction.\n        remainder := mulmod(x, y, denominator)\n\n        // Subtract 256 bit number from 512-bit number.\n        prod1 := sub(prod1, gt(remainder, prod0))\n        prod0 := sub(prod0, remainder)\n    }\n\n    unchecked {\n        // Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow\n        // because the denominator cannot be zero at this point in the function execution. The result is always >= 1.\n        // For more detail, see https://cs.stackexchange.com/q/138556/92363.\n        uint256 lpotdod = denominator & (~denominator + 1);\n        uint256 flippedLpotdod;\n\n        assembly (\"memory-safe\") {\n            // Factor powers of two out of denominator.\n            denominator := div(denominator, lpotdod)\n\n            // Divide [prod1 prod0] by lpotdod.\n            prod0 := div(prod0, lpotdod)\n\n            // Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.\n            // `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.\n            // However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693\n            flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)\n        }\n\n        // Shift in bits from prod1 into prod0.\n        prod0 |= prod1 * flippedLpotdod;\n\n        // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n        // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n        // four bits. That is, denominator * inv = 1 mod 2^4.\n        uint256 inverse = (3 * denominator) ^ 2;\n\n        // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n        // in modular arithmetic, doubling the correct bits in each step.\n        inverse *= 2 - denominator * inverse; // inverse mod 2^8\n        inverse *= 2 - denominator * inverse; // inverse mod 2^16\n        inverse *= 2 - denominator * inverse; // inverse mod 2^32\n        inverse *= 2 - denominator * inverse; // inverse mod 2^64\n        inverse *= 2 - denominator * inverse; // inverse mod 2^128\n        inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n        // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n        // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n        // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n        // is no longer required.\n        result = prod0 * inverse;\n    }\n}\n\n/// @notice Calculates x*y÷1e18 with 512-bit precision.\n///\n/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.\n///\n/// Notes:\n/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.\n/// - The result is rounded toward zero.\n/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:\n///\n/// $$\n/// \\begin{cases}\n///     x * y = MAX\\_UINT256 * UNIT \\\\\n///     (x * y) \\% UNIT \\geq \\frac{UNIT}{2}\n/// \\end{cases}\n/// $$\n///\n/// Requirements:\n/// - Refer to the requirements in {mulDiv}.\n/// - The result must fit in uint256.\n///\n/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.\n/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.\n/// @return result The result as an unsigned 60.18-decimal fixed-point number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {\n    uint256 prod0;\n    uint256 prod1;\n    assembly (\"memory-safe\") {\n        let mm := mulmod(x, y, not(0))\n        prod0 := mul(x, y)\n        prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n    }\n\n    if (prod1 == 0) {\n        unchecked {\n            return prod0 / UNIT;\n        }\n    }\n\n    if (prod1 >= UNIT) {\n        revert PRBMath_MulDiv18_Overflow(x, y);\n    }\n\n    uint256 remainder;\n    assembly (\"memory-safe\") {\n        remainder := mulmod(x, y, UNIT)\n        result :=\n            mul(\n                or(\n                    div(sub(prod0, remainder), UNIT_LPOTD),\n                    mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))\n                ),\n                UNIT_INVERSE\n            )\n    }\n}\n\n/// @notice Calculates x*y÷denominator with 512-bit precision.\n///\n/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.\n///\n/// Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - Refer to the requirements in {mulDiv}.\n/// - None of the inputs can be `type(int256).min`.\n/// - The result must fit in int256.\n///\n/// @param x The multiplicand as an int256.\n/// @param y The multiplier as an int256.\n/// @param denominator The divisor as an int256.\n/// @return result The result as an int256.\n/// @custom:smtchecker abstract-function-nondet\nfunction mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {\n    if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {\n        revert PRBMath_MulDivSigned_InputTooSmall();\n    }\n\n    // Get hold of the absolute values of x, y and the denominator.\n    uint256 xAbs;\n    uint256 yAbs;\n    uint256 dAbs;\n    unchecked {\n        xAbs = x < 0 ? uint256(-x) : uint256(x);\n        yAbs = y < 0 ? uint256(-y) : uint256(y);\n        dAbs = denominator < 0 ? uint256(-denominator) : uint256(denominator);\n    }\n\n    // Compute the absolute value of x*y÷denominator. The result must fit in int256.\n    uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);\n    if (resultAbs > uint256(type(int256).max)) {\n        revert PRBMath_MulDivSigned_Overflow(x, y);\n    }\n\n    // Get the signs of x, y and the denominator.\n    uint256 sx;\n    uint256 sy;\n    uint256 sd;\n    assembly (\"memory-safe\") {\n        // \"sgt\" is the \"signed greater than\" assembly instruction and \"sub(0,1)\" is -1 in two's complement.\n        sx := sgt(x, sub(0, 1))\n        sy := sgt(y, sub(0, 1))\n        sd := sgt(denominator, sub(0, 1))\n    }\n\n    // XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.\n    // If there are, the result should be negative. Otherwise, it should be positive.\n    unchecked {\n        result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);\n    }\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - If x is not a perfect square, the result is rounded down.\n/// - Credits to OpenZeppelin for the explanations in comments below.\n///\n/// @param x The uint256 number for which to calculate the square root.\n/// @return result The result as a uint256.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(uint256 x) pure returns (uint256 result) {\n    if (x == 0) {\n        return 0;\n    }\n\n    // For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.\n    //\n    // We know that the \"msb\" (most significant bit) of x is a power of 2 such that we have:\n    //\n    // $$\n    // msb(x) <= x <= 2*msb(x)$\n    // $$\n    //\n    // We write $msb(x)$ as $2^k$, and we get:\n    //\n    // $$\n    // k = log_2(x)\n    // $$\n    //\n    // Thus, we can write the initial inequality as:\n    //\n    // $$\n    // 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\\\\n    // sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\\\\n    // 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}\n    // $$\n    //\n    // Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.\n    uint256 xAux = uint256(x);\n    result = 1;\n    if (xAux >= 2 ** 128) {\n        xAux >>= 128;\n        result <<= 64;\n    }\n    if (xAux >= 2 ** 64) {\n        xAux >>= 64;\n        result <<= 32;\n    }\n    if (xAux >= 2 ** 32) {\n        xAux >>= 32;\n        result <<= 16;\n    }\n    if (xAux >= 2 ** 16) {\n        xAux >>= 16;\n        result <<= 8;\n    }\n    if (xAux >= 2 ** 8) {\n        xAux >>= 8;\n        result <<= 4;\n    }\n    if (xAux >= 2 ** 4) {\n        xAux >>= 4;\n        result <<= 2;\n    }\n    if (xAux >= 2 ** 2) {\n        result <<= 1;\n    }\n\n    // At this point, `result` is an estimation with at least one bit of precision. We know the true value has at\n    // most 128 bits, since it is the square root of a uint256. Newton's method converges quadratically (precision\n    // doubles at every iteration). We thus need at most 7 iteration to turn our partial result with one bit of\n    // precision into the expected uint128 result.\n    unchecked {\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n        result = (result + x / result) >> 1;\n\n        // If x is not a perfect square, round the result toward zero.\n        uint256 roundedResult = x / result;\n        if (result >= roundedResult) {\n            result = roundedResult;\n        }\n    }\n}\n"
      },
      "lib/prb-math/src/sd1x18/Constants.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @dev Euler's number as an SD1x18 number.\nSD1x18 constant E = SD1x18.wrap(2_718281828459045235);\n\n/// @dev The maximum value an SD1x18 number can have.\nint64 constant uMAX_SD1x18 = 9_223372036854775807;\nSD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);\n\n/// @dev The maximum value an SD1x18 number can have.\nint64 constant uMIN_SD1x18 = -9_223372036854775808;\nSD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);\n\n/// @dev PI as an SD1x18 number.\nSD1x18 constant PI = SD1x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of SD1x18.\nSD1x18 constant UNIT = SD1x18.wrap(1e18);\nint256 constant uUNIT = 1e18;\n"
      },
      "lib/prb-math/src/sd1x18/ValueType.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\n\n/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract\n/// storage.\ntype SD1x18 is int64;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Casting.intoSD59x18,\n    Casting.intoUD2x18,\n    Casting.intoUD60x18,\n    Casting.intoUint256,\n    Casting.intoUint128,\n    Casting.intoUint40,\n    Casting.unwrap\n} for SD1x18 global;\n"
      },
      "lib/prb-math/src/sd59x18/Constants.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD59x18 } from \"./ValueType.sol\";\n\n// NOTICE: the \"u\" prefix stands for \"unwrapped\".\n\n/// @dev Euler's number as an SD59x18 number.\nSD59x18 constant E = SD59x18.wrap(2_718281828459045235);\n\n/// @dev The maximum input permitted in {exp}.\nint256 constant uEXP_MAX_INPUT = 133_084258667509499440;\nSD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);\n\n/// @dev The maximum input permitted in {exp2}.\nint256 constant uEXP2_MAX_INPUT = 192e18 - 1;\nSD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);\n\n/// @dev Half the UNIT number.\nint256 constant uHALF_UNIT = 0.5e18;\nSD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);\n\n/// @dev $log_2(10)$ as an SD59x18 number.\nint256 constant uLOG2_10 = 3_321928094887362347;\nSD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);\n\n/// @dev $log_2(e)$ as an SD59x18 number.\nint256 constant uLOG2_E = 1_442695040888963407;\nSD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);\n\n/// @dev The maximum value an SD59x18 number can have.\nint256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;\nSD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);\n\n/// @dev The maximum whole value an SD59x18 number can have.\nint256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;\nSD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);\n\n/// @dev The minimum value an SD59x18 number can have.\nint256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;\nSD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);\n\n/// @dev The minimum whole value an SD59x18 number can have.\nint256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;\nSD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);\n\n/// @dev PI as an SD59x18 number.\nSD59x18 constant PI = SD59x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of SD59x18.\nint256 constant uUNIT = 1e18;\nSD59x18 constant UNIT = SD59x18.wrap(1e18);\n\n/// @dev The unit number squared.\nint256 constant uUNIT_SQUARED = 1e36;\nSD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);\n\n/// @dev Zero as an SD59x18 number.\nSD59x18 constant ZERO = SD59x18.wrap(0);\n"
      },
      "lib/prb-math/src/sd59x18/ValueType.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\nimport \"./Helpers.sol\" as Helpers;\nimport \"./Math.sol\" as Math;\n\n/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type int256.\ntype SD59x18 is int256;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Casting.intoInt256,\n    Casting.intoSD1x18,\n    Casting.intoUD2x18,\n    Casting.intoUD60x18,\n    Casting.intoUint256,\n    Casting.intoUint128,\n    Casting.intoUint40,\n    Casting.unwrap\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                            MATHEMATICAL FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Math.abs,\n    Math.avg,\n    Math.ceil,\n    Math.div,\n    Math.exp,\n    Math.exp2,\n    Math.floor,\n    Math.frac,\n    Math.gm,\n    Math.inv,\n    Math.log10,\n    Math.log2,\n    Math.ln,\n    Math.mul,\n    Math.pow,\n    Math.powu,\n    Math.sqrt\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                HELPER FUNCTIONS\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Helpers.add,\n    Helpers.and,\n    Helpers.eq,\n    Helpers.gt,\n    Helpers.gte,\n    Helpers.isZero,\n    Helpers.lshift,\n    Helpers.lt,\n    Helpers.lte,\n    Helpers.mod,\n    Helpers.neq,\n    Helpers.not,\n    Helpers.or,\n    Helpers.rshift,\n    Helpers.sub,\n    Helpers.uncheckedAdd,\n    Helpers.uncheckedSub,\n    Helpers.uncheckedUnary,\n    Helpers.xor\n} for SD59x18 global;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    OPERATORS\n//////////////////////////////////////////////////////////////////////////*/\n\n// The global \"using for\" directive makes it possible to use these operators on the SD59x18 type.\nusing {\n    Helpers.add as +,\n    Helpers.and2 as &,\n    Math.div as /,\n    Helpers.eq as ==,\n    Helpers.gt as >,\n    Helpers.gte as >=,\n    Helpers.lt as <,\n    Helpers.lte as <=,\n    Helpers.mod as %,\n    Math.mul as *,\n    Helpers.neq as !=,\n    Helpers.not as ~,\n    Helpers.or as |,\n    Helpers.sub as -,\n    Helpers.unary as -,\n    Helpers.xor as ^\n} for SD59x18 global;\n"
      },
      "lib/prb-math/src/ud2x18/Constants.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @dev Euler's number as a UD2x18 number.\nUD2x18 constant E = UD2x18.wrap(2_718281828459045235);\n\n/// @dev The maximum value a UD2x18 number can have.\nuint64 constant uMAX_UD2x18 = 18_446744073709551615;\nUD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);\n\n/// @dev PI as a UD2x18 number.\nUD2x18 constant PI = UD2x18.wrap(3_141592653589793238);\n\n/// @dev The unit number, which gives the decimal precision of UD2x18.\nuint256 constant uUNIT = 1e18;\nUD2x18 constant UNIT = UD2x18.wrap(1e18);\n"
      },
      "lib/prb-math/src/ud2x18/ValueType.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Casting.sol\" as Casting;\n\n/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18\n/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity\n/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract\n/// storage.\ntype UD2x18 is uint64;\n\n/*//////////////////////////////////////////////////////////////////////////\n                                    CASTING\n//////////////////////////////////////////////////////////////////////////*/\n\nusing {\n    Casting.intoSD1x18,\n    Casting.intoSD59x18,\n    Casting.intoUD60x18,\n    Casting.intoUint256,\n    Casting.intoUint128,\n    Casting.intoUint40,\n    Casting.unwrap\n} for UD2x18 global;\n"
      },
      "lib/pendle-core-v2-public/contracts/core/StandardizedYield/SYUtils.sol": {
        "content": "// SPDX-License-Identifier: GPL-3.0-or-later\npragma solidity ^0.8.0;\n\nlibrary SYUtils {\n    uint256 internal constant ONE = 1e18;\n\n    function syToAsset(uint256 exchangeRate, uint256 syAmount) internal pure returns (uint256) {\n        return (syAmount * exchangeRate) / ONE;\n    }\n\n    function syToAssetUp(uint256 exchangeRate, uint256 syAmount) internal pure returns (uint256) {\n        return (syAmount * exchangeRate + ONE - 1) / ONE;\n    }\n\n    function assetToSy(uint256 exchangeRate, uint256 assetAmount) internal pure returns (uint256) {\n        return (assetAmount * ONE) / exchangeRate;\n    }\n\n    function assetToSyUp(uint256 exchangeRate, uint256 assetAmount) internal pure returns (uint256) {\n        return (assetAmount * ONE + exchangeRate - 1) / exchangeRate;\n    }\n}\n"
      },
      "lib/prb-math/src/sd1x18/Casting.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as CastingErrors;\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @notice Casts an SD1x18 number into SD59x18.\n/// @dev There is no overflow check because the domain of SD1x18 is a subset of SD59x18.\nfunction intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {\n    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));\n}\n\n/// @notice Casts an SD1x18 number into UD2x18.\n/// - x must be positive.\nfunction intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {\n    int64 xInt = SD1x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD1x18_ToUD2x18_Underflow(x);\n    }\n    result = UD2x18.wrap(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into UD60x18.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {\n    int64 xInt = SD1x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);\n    }\n    result = UD60x18.wrap(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint256.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint256(SD1x18 x) pure returns (uint256 result) {\n    int64 xInt = SD1x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);\n    }\n    result = uint256(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint128.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint128(SD1x18 x) pure returns (uint128 result) {\n    int64 xInt = SD1x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);\n    }\n    result = uint128(uint64(xInt));\n}\n\n/// @notice Casts an SD1x18 number into uint40.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(SD1x18 x) pure returns (uint40 result) {\n    int64 xInt = SD1x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);\n    }\n    if (xInt > int64(uint64(Common.MAX_UINT40))) {\n        revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);\n    }\n    result = uint40(uint64(xInt));\n}\n\n/// @notice Alias for {wrap}.\nfunction sd1x18(int64 x) pure returns (SD1x18 result) {\n    result = SD1x18.wrap(x);\n}\n\n/// @notice Unwraps an SD1x18 number into int64.\nfunction unwrap(SD1x18 x) pure returns (int64 result) {\n    result = SD1x18.unwrap(x);\n}\n\n/// @notice Wraps an int64 number into SD1x18.\nfunction wrap(int64 x) pure returns (SD1x18 result) {\n    result = SD1x18.wrap(x);\n}\n"
      },
      "lib/prb-math/src/sd59x18/Casting.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"./Errors.sol\" as CastingErrors;\nimport { MAX_UINT128, MAX_UINT40 } from \"../Common.sol\";\nimport { uMAX_SD1x18, uMIN_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { uMAX_UD2x18 } from \"../ud2x18/Constants.sol\";\nimport { UD2x18 } from \"../ud2x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Casts an SD59x18 number into int256.\n/// @dev This is basically a functional alias for {unwrap}.\nfunction intoInt256(SD59x18 x) pure returns (int256 result) {\n    result = SD59x18.unwrap(x);\n}\n\n/// @notice Casts an SD59x18 number into SD1x18.\n/// @dev Requirements:\n/// - x must be greater than or equal to `uMIN_SD1x18`.\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < uMIN_SD1x18) {\n        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);\n    }\n    if (xInt > uMAX_SD1x18) {\n        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);\n    }\n    result = SD1x18.wrap(int64(xInt));\n}\n\n/// @notice Casts an SD59x18 number into UD2x18.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `uMAX_UD2x18`.\nfunction intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);\n    }\n    if (xInt > int256(uint256(uMAX_UD2x18))) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);\n    }\n    result = UD2x18.wrap(uint64(uint256(xInt)));\n}\n\n/// @notice Casts an SD59x18 number into UD60x18.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);\n    }\n    result = UD60x18.wrap(uint256(xInt));\n}\n\n/// @notice Casts an SD59x18 number into uint256.\n/// @dev Requirements:\n/// - x must be positive.\nfunction intoUint256(SD59x18 x) pure returns (uint256 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);\n    }\n    result = uint256(xInt);\n}\n\n/// @notice Casts an SD59x18 number into uint128.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `uMAX_UINT128`.\nfunction intoUint128(SD59x18 x) pure returns (uint128 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);\n    }\n    if (xInt > int256(uint256(MAX_UINT128))) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);\n    }\n    result = uint128(uint256(xInt));\n}\n\n/// @notice Casts an SD59x18 number into uint40.\n/// @dev Requirements:\n/// - x must be positive.\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(SD59x18 x) pure returns (uint40 result) {\n    int256 xInt = SD59x18.unwrap(x);\n    if (xInt < 0) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);\n    }\n    if (xInt > int256(uint256(MAX_UINT40))) {\n        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);\n    }\n    result = uint40(uint256(xInt));\n}\n\n/// @notice Alias for {wrap}.\nfunction sd(int256 x) pure returns (SD59x18 result) {\n    result = SD59x18.wrap(x);\n}\n\n/// @notice Alias for {wrap}.\nfunction sd59x18(int256 x) pure returns (SD59x18 result) {\n    result = SD59x18.wrap(x);\n}\n\n/// @notice Unwraps an SD59x18 number into int256.\nfunction unwrap(SD59x18 x) pure returns (int256 result) {\n    result = SD59x18.unwrap(x);\n}\n\n/// @notice Wraps an int256 number into SD59x18.\nfunction wrap(int256 x) pure returns (SD59x18 result) {\n    result = SD59x18.wrap(x);\n}\n"
      },
      "lib/prb-math/src/sd59x18/Helpers.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { wrap } from \"./Casting.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Implements the checked addition operation (+) in the SD59x18 type.\nfunction add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    return wrap(x.unwrap() + y.unwrap());\n}\n\n/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.\nfunction and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {\n    return wrap(x.unwrap() & bits);\n}\n\n/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.\nfunction and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    return wrap(x.unwrap() & y.unwrap());\n}\n\n/// @notice Implements the equal (=) operation in the SD59x18 type.\nfunction eq(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() == y.unwrap();\n}\n\n/// @notice Implements the greater than operation (>) in the SD59x18 type.\nfunction gt(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() > y.unwrap();\n}\n\n/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.\nfunction gte(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() >= y.unwrap();\n}\n\n/// @notice Implements a zero comparison check function in the SD59x18 type.\nfunction isZero(SD59x18 x) pure returns (bool result) {\n    result = x.unwrap() == 0;\n}\n\n/// @notice Implements the left shift operation (<<) in the SD59x18 type.\nfunction lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() << bits);\n}\n\n/// @notice Implements the lower than operation (<) in the SD59x18 type.\nfunction lt(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() < y.unwrap();\n}\n\n/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.\nfunction lte(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() <= y.unwrap();\n}\n\n/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.\nfunction mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() % y.unwrap());\n}\n\n/// @notice Implements the not equal operation (!=) in the SD59x18 type.\nfunction neq(SD59x18 x, SD59x18 y) pure returns (bool result) {\n    result = x.unwrap() != y.unwrap();\n}\n\n/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.\nfunction not(SD59x18 x) pure returns (SD59x18 result) {\n    result = wrap(~x.unwrap());\n}\n\n/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.\nfunction or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() | y.unwrap());\n}\n\n/// @notice Implements the right shift operation (>>) in the SD59x18 type.\nfunction rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() >> bits);\n}\n\n/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.\nfunction sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() - y.unwrap());\n}\n\n/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.\nfunction unary(SD59x18 x) pure returns (SD59x18 result) {\n    result = wrap(-x.unwrap());\n}\n\n/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.\nfunction uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    unchecked {\n        result = wrap(x.unwrap() + y.unwrap());\n    }\n}\n\n/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.\nfunction uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    unchecked {\n        result = wrap(x.unwrap() - y.unwrap());\n    }\n}\n\n/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.\nfunction uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {\n    unchecked {\n        result = wrap(-x.unwrap());\n    }\n}\n\n/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.\nfunction xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() ^ y.unwrap());\n}\n"
      },
      "lib/prb-math/src/sd59x18/Math.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport {\n    uEXP_MAX_INPUT,\n    uEXP2_MAX_INPUT,\n    uHALF_UNIT,\n    uLOG2_10,\n    uLOG2_E,\n    uMAX_SD59x18,\n    uMAX_WHOLE_SD59x18,\n    uMIN_SD59x18,\n    uMIN_WHOLE_SD59x18,\n    UNIT,\n    uUNIT,\n    uUNIT_SQUARED,\n    ZERO\n} from \"./Constants.sol\";\nimport { wrap } from \"./Helpers.sol\";\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Calculates the absolute value of x.\n///\n/// @dev Requirements:\n/// - x must be greater than `MIN_SD59x18`.\n///\n/// @param x The SD59x18 number for which to calculate the absolute value.\n/// @param result The absolute value of x as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction abs(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt == uMIN_SD59x18) {\n        revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();\n    }\n    result = xInt < 0 ? wrap(-xInt) : x;\n}\n\n/// @notice Calculates the arithmetic average of x and y.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// @param x The first operand as an SD59x18 number.\n/// @param y The second operand as an SD59x18 number.\n/// @return result The arithmetic average as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    int256 yInt = y.unwrap();\n\n    unchecked {\n        // This operation is equivalent to `x / 2 +  y / 2`, and it can never overflow.\n        int256 sum = (xInt >> 1) + (yInt >> 1);\n\n        if (sum < 0) {\n            // If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right\n            // rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.\n            assembly (\"memory-safe\") {\n                result := add(sum, and(or(xInt, yInt), 1))\n            }\n        } else {\n            // Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.\n            result = wrap(sum + (xInt & yInt & 1));\n        }\n    }\n}\n\n/// @notice Yields the smallest whole number greater than or equal to x.\n///\n/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.\n/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be less than or equal to `MAX_WHOLE_SD59x18`.\n///\n/// @param x The SD59x18 number to ceil.\n/// @param result The smallest whole number greater than or equal to x, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ceil(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt > uMAX_WHOLE_SD59x18) {\n        revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);\n    }\n\n    int256 remainder = xInt % uUNIT;\n    if (remainder == 0) {\n        result = x;\n    } else {\n        unchecked {\n            // Solidity uses C fmod style, which returns a modulus with the same sign as x.\n            int256 resultInt = xInt - remainder;\n            if (xInt > 0) {\n                resultInt += uUNIT;\n            }\n            result = wrap(resultInt);\n        }\n    }\n}\n\n/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.\n///\n/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute\n/// values separately.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv}.\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv}.\n/// - None of the inputs can be `MIN_SD59x18`.\n/// - The denominator must not be zero.\n/// - The result must fit in SD59x18.\n///\n/// @param x The numerator as an SD59x18 number.\n/// @param y The denominator as an SD59x18 number.\n/// @param result The quotient as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    int256 yInt = y.unwrap();\n    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {\n        revert Errors.PRBMath_SD59x18_Div_InputTooSmall();\n    }\n\n    // Get hold of the absolute values of x and y.\n    uint256 xAbs;\n    uint256 yAbs;\n    unchecked {\n        xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);\n        yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);\n    }\n\n    // Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.\n    uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);\n    if (resultAbs > uint256(uMAX_SD59x18)) {\n        revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);\n    }\n\n    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for\n    // negative, 0 for positive or zero).\n    bool sameSign = (xInt ^ yInt) > -1;\n\n    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.\n    unchecked {\n        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));\n    }\n}\n\n/// @notice Calculates the natural exponent of x using the following formula:\n///\n/// $$\n/// e^x = 2^{x * log_2{e}}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {exp2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}.\n/// - x must be less than 133_084258667509499441.\n///\n/// @param x The exponent as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n\n    // This check prevents values greater than 192e18 from being passed to {exp2}.\n    if (xInt > uEXP_MAX_INPUT) {\n        revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);\n    }\n\n    unchecked {\n        // Inline the fixed-point multiplication to save gas.\n        int256 doubleUnitProduct = xInt * uLOG2_E;\n        result = exp2(wrap(doubleUnitProduct / uUNIT));\n    }\n}\n\n/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:\n///\n/// $$\n/// 2^{-x} = \\frac{1}{2^x}\n/// $$\n///\n/// @dev See https://ethereum.stackexchange.com/q/79903/24693.\n///\n/// Notes:\n/// - If x is less than -59_794705707972522261, the result is zero.\n///\n/// Requirements:\n/// - x must be less than 192e18.\n/// - The result must fit in SD59x18.\n///\n/// @param x The exponent as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction exp2(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt < 0) {\n        // The inverse of any number less than this is truncated to zero.\n        if (xInt < -59_794705707972522261) {\n            return ZERO;\n        }\n\n        unchecked {\n            // Inline the fixed-point inversion to save gas.\n            result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());\n        }\n    } else {\n        // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.\n        if (xInt > uEXP2_MAX_INPUT) {\n            revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);\n        }\n\n        unchecked {\n            // Convert x to the 192.64-bit fixed-point format.\n            uint256 x_192x64 = uint256((xInt << 64) / uUNIT);\n\n            // It is safe to cast the result to int256 due to the checks above.\n            result = wrap(int256(Common.exp2(x_192x64)));\n        }\n    }\n}\n\n/// @notice Yields the greatest whole number less than or equal to x.\n///\n/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional\n/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.\n///\n/// Requirements:\n/// - x must be greater than or equal to `MIN_WHOLE_SD59x18`.\n///\n/// @param x The SD59x18 number to floor.\n/// @param result The greatest whole number less than or equal to x, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction floor(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt < uMIN_WHOLE_SD59x18) {\n        revert Errors.PRBMath_SD59x18_Floor_Underflow(x);\n    }\n\n    int256 remainder = xInt % uUNIT;\n    if (remainder == 0) {\n        result = x;\n    } else {\n        unchecked {\n            // Solidity uses C fmod style, which returns a modulus with the same sign as x.\n            int256 resultInt = xInt - remainder;\n            if (xInt < 0) {\n                resultInt -= uUNIT;\n            }\n            result = wrap(resultInt);\n        }\n    }\n}\n\n/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.\n/// of the radix point for negative numbers.\n/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part\n/// @param x The SD59x18 number to get the fractional part of.\n/// @param result The fractional part of x as an SD59x18 number.\nfunction frac(SD59x18 x) pure returns (SD59x18 result) {\n    result = wrap(x.unwrap() % uUNIT);\n}\n\n/// @notice Calculates the geometric mean of x and y, i.e. $\\sqrt{x * y}$.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x * y must fit in SD59x18.\n/// - x * y must not be negative, since complex numbers are not supported.\n///\n/// @param x The first operand as an SD59x18 number.\n/// @param y The second operand as an SD59x18 number.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    int256 yInt = y.unwrap();\n    if (xInt == 0 || yInt == 0) {\n        return ZERO;\n    }\n\n    unchecked {\n        // Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.\n        int256 xyInt = xInt * yInt;\n        if (xyInt / xInt != yInt) {\n            revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);\n        }\n\n        // The product must not be negative, since complex numbers are not supported.\n        if (xyInt < 0) {\n            revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);\n        }\n\n        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`\n        // during multiplication. See the comments in {Common.sqrt}.\n        uint256 resultUint = Common.sqrt(uint256(xyInt));\n        result = wrap(int256(resultUint));\n    }\n}\n\n/// @notice Calculates the inverse of x.\n///\n/// @dev Notes:\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x must not be zero.\n///\n/// @param x The SD59x18 number for which to calculate the inverse.\n/// @return result The inverse as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction inv(SD59x18 x) pure returns (SD59x18 result) {\n    result = wrap(uUNIT_SQUARED / x.unwrap());\n}\n\n/// @notice Calculates the natural logarithm of x using the following formula:\n///\n/// $$\n/// ln{x} = log_2{x} / log_2{e}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The SD59x18 number for which to calculate the natural logarithm.\n/// @return result The natural logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction ln(SD59x18 x) pure returns (SD59x18 result) {\n    // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that\n    // {log2} can return is ~195_205294292027477728.\n    result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);\n}\n\n/// @notice Calculates the common logarithm of x using the following formula:\n///\n/// $$\n/// log_{10}{x} = log_2{x} / log_2{10}\n/// $$\n///\n/// However, if x is an exact power of ten, a hard coded value is returned.\n///\n/// @dev Notes:\n/// - Refer to the notes in {log2}.\n///\n/// Requirements:\n/// - Refer to the requirements in {log2}.\n///\n/// @param x The SD59x18 number for which to calculate the common logarithm.\n/// @return result The common logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log10(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt < 0) {\n        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);\n    }\n\n    // Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.\n    // prettier-ignore\n    assembly (\"memory-safe\") {\n        switch x\n        case 1 { result := mul(uUNIT, sub(0, 18)) }\n        case 10 { result := mul(uUNIT, sub(1, 18)) }\n        case 100 { result := mul(uUNIT, sub(2, 18)) }\n        case 1000 { result := mul(uUNIT, sub(3, 18)) }\n        case 10000 { result := mul(uUNIT, sub(4, 18)) }\n        case 100000 { result := mul(uUNIT, sub(5, 18)) }\n        case 1000000 { result := mul(uUNIT, sub(6, 18)) }\n        case 10000000 { result := mul(uUNIT, sub(7, 18)) }\n        case 100000000 { result := mul(uUNIT, sub(8, 18)) }\n        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }\n        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }\n        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }\n        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }\n        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }\n        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }\n        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }\n        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }\n        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }\n        case 1000000000000000000 { result := 0 }\n        case 10000000000000000000 { result := uUNIT }\n        case 100000000000000000000 { result := mul(uUNIT, 2) }\n        case 1000000000000000000000 { result := mul(uUNIT, 3) }\n        case 10000000000000000000000 { result := mul(uUNIT, 4) }\n        case 100000000000000000000000 { result := mul(uUNIT, 5) }\n        case 1000000000000000000000000 { result := mul(uUNIT, 6) }\n        case 10000000000000000000000000 { result := mul(uUNIT, 7) }\n        case 100000000000000000000000000 { result := mul(uUNIT, 8) }\n        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }\n        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }\n        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }\n        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }\n        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }\n        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }\n        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }\n        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }\n        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }\n        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }\n        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }\n        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }\n        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }\n        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }\n        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }\n        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }\n        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }\n        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }\n        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }\n        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }\n        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }\n        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }\n        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }\n        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }\n        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }\n        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }\n        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }\n        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }\n        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }\n        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }\n        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }\n        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }\n        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }\n        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }\n        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }\n        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }\n        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }\n        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }\n        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }\n        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }\n        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }\n        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }\n        default { result := uMAX_SD59x18 }\n    }\n\n    if (result.unwrap() == uMAX_SD59x18) {\n        unchecked {\n            // Inline the fixed-point division to save gas.\n            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);\n        }\n    }\n}\n\n/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:\n///\n/// $$\n/// log_2{x} = n + log_2{y}, \\text{ where } y = x*2^{-n}, \\ y \\in [1, 2)\n/// $$\n///\n/// For $0 \\leq x \\lt 1$, the input is inverted:\n///\n/// $$\n/// log_2{x} = -log_2{\\frac{1}{x}}\n/// $$\n///\n/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.\n///\n/// Notes:\n/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.\n///\n/// Requirements:\n/// - x must be greater than zero.\n///\n/// @param x The SD59x18 number for which to calculate the binary logarithm.\n/// @return result The binary logarithm as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction log2(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt <= 0) {\n        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);\n    }\n\n    unchecked {\n        int256 sign;\n        if (xInt >= uUNIT) {\n            sign = 1;\n        } else {\n            sign = -1;\n            // Inline the fixed-point inversion to save gas.\n            xInt = uUNIT_SQUARED / xInt;\n        }\n\n        // Calculate the integer part of the logarithm.\n        uint256 n = Common.msb(uint256(xInt / uUNIT));\n\n        // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow\n        // because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.\n        int256 resultInt = int256(n) * uUNIT;\n\n        // Calculate $y = x * 2^{-n}$.\n        int256 y = xInt >> n;\n\n        // If y is the unit number, the fractional part is zero.\n        if (y == uUNIT) {\n            return wrap(resultInt * sign);\n        }\n\n        // Calculate the fractional part via the iterative approximation.\n        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.\n        int256 DOUBLE_UNIT = 2e18;\n        for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {\n            y = (y * y) / uUNIT;\n\n            // Is y^2 >= 2e18 and so in the range [2e18, 4e18)?\n            if (y >= DOUBLE_UNIT) {\n                // Add the 2^{-m} factor to the logarithm.\n                resultInt = resultInt + delta;\n\n                // Halve y, which corresponds to z/2 in the Wikipedia article.\n                y >>= 1;\n            }\n        }\n        resultInt *= sign;\n        result = wrap(resultInt);\n    }\n}\n\n/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.\n///\n/// @dev Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n///\n/// Requirements:\n/// - Refer to the requirements in {Common.mulDiv18}.\n/// - None of the inputs can be `MIN_SD59x18`.\n/// - The result must fit in SD59x18.\n///\n/// @param x The multiplicand as an SD59x18 number.\n/// @param y The multiplier as an SD59x18 number.\n/// @return result The product as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    int256 yInt = y.unwrap();\n    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {\n        revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();\n    }\n\n    // Get hold of the absolute values of x and y.\n    uint256 xAbs;\n    uint256 yAbs;\n    unchecked {\n        xAbs = xInt < 0 ? uint256(-xInt) : uint256(xInt);\n        yAbs = yInt < 0 ? uint256(-yInt) : uint256(yInt);\n    }\n\n    // Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.\n    uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);\n    if (resultAbs > uint256(uMAX_SD59x18)) {\n        revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);\n    }\n\n    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for\n    // negative, 0 for positive or zero).\n    bool sameSign = (xInt ^ yInt) > -1;\n\n    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.\n    unchecked {\n        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));\n    }\n}\n\n/// @notice Raises x to the power of y using the following formula:\n///\n/// $$\n/// x^y = 2^{log_2{x} * y}\n/// $$\n///\n/// @dev Notes:\n/// - Refer to the notes in {exp2}, {log2}, and {mul}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - Refer to the requirements in {exp2}, {log2}, and {mul}.\n///\n/// @param x The base as an SD59x18 number.\n/// @param y Exponent to raise x to, as an SD59x18 number\n/// @return result x raised to power y, as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    int256 yInt = y.unwrap();\n\n    // If both x and y are zero, the result is `UNIT`. If just x is zero, the result is always zero.\n    if (xInt == 0) {\n        return yInt == 0 ? UNIT : ZERO;\n    }\n    // If x is `UNIT`, the result is always `UNIT`.\n    else if (xInt == uUNIT) {\n        return UNIT;\n    }\n\n    // If y is zero, the result is always `UNIT`.\n    if (yInt == 0) {\n        return UNIT;\n    }\n    // If y is `UNIT`, the result is always x.\n    else if (yInt == uUNIT) {\n        return x;\n    }\n\n    // Calculate the result using the formula.\n    result = exp2(mul(log2(x), y));\n}\n\n/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known\n/// algorithm \"exponentiation by squaring\".\n///\n/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.\n///\n/// Notes:\n/// - Refer to the notes in {Common.mulDiv18}.\n/// - Returns `UNIT` for 0^0.\n///\n/// Requirements:\n/// - Refer to the requirements in {abs} and {Common.mulDiv18}.\n/// - The result must fit in SD59x18.\n///\n/// @param x The base as an SD59x18 number.\n/// @param y The exponent as a uint256.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {\n    uint256 xAbs = uint256(abs(x).unwrap());\n\n    // Calculate the first iteration of the loop in advance.\n    uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);\n\n    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.\n    uint256 yAux = y;\n    for (yAux >>= 1; yAux > 0; yAux >>= 1) {\n        xAbs = Common.mulDiv18(xAbs, xAbs);\n\n        // Equivalent to `y % 2 == 1`.\n        if (yAux & 1 > 0) {\n            resultAbs = Common.mulDiv18(resultAbs, xAbs);\n        }\n    }\n\n    // The result must fit in SD59x18.\n    if (resultAbs > uint256(uMAX_SD59x18)) {\n        revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);\n    }\n\n    unchecked {\n        // Is the base negative and the exponent odd? If yes, the result should be negative.\n        int256 resultInt = int256(resultAbs);\n        bool isNegative = x.unwrap() < 0 && y & 1 == 1;\n        if (isNegative) {\n            resultInt = -resultInt;\n        }\n        result = wrap(resultInt);\n    }\n}\n\n/// @notice Calculates the square root of x using the Babylonian method.\n///\n/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.\n///\n/// Notes:\n/// - Only the positive root is returned.\n/// - The result is rounded toward zero.\n///\n/// Requirements:\n/// - x cannot be negative, since complex numbers are not supported.\n/// - x must be less than `MAX_SD59x18 / UNIT`.\n///\n/// @param x The SD59x18 number for which to calculate the square root.\n/// @return result The result as an SD59x18 number.\n/// @custom:smtchecker abstract-function-nondet\nfunction sqrt(SD59x18 x) pure returns (SD59x18 result) {\n    int256 xInt = x.unwrap();\n    if (xInt < 0) {\n        revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);\n    }\n    if (xInt > uMAX_SD59x18 / uUNIT) {\n        revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);\n    }\n\n    unchecked {\n        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.\n        // In this case, the two numbers are both the square root.\n        uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));\n        result = wrap(int256(resultUint));\n    }\n}\n"
      },
      "lib/prb-math/src/ud2x18/Casting.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport \"../Common.sol\" as Common;\nimport \"./Errors.sol\" as Errors;\nimport { uMAX_SD1x18 } from \"../sd1x18/Constants.sol\";\nimport { SD1x18 } from \"../sd1x18/ValueType.sol\";\nimport { SD59x18 } from \"../sd59x18/ValueType.sol\";\nimport { UD60x18 } from \"../ud60x18/ValueType.sol\";\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @notice Casts a UD2x18 number into SD1x18.\n/// - x must be less than or equal to `uMAX_SD1x18`.\nfunction intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {\n    uint64 xUint = UD2x18.unwrap(x);\n    if (xUint > uint64(uMAX_SD1x18)) {\n        revert Errors.PRBMath_UD2x18_IntoSD1x18_Overflow(x);\n    }\n    result = SD1x18.wrap(int64(xUint));\n}\n\n/// @notice Casts a UD2x18 number into SD59x18.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of SD59x18.\nfunction intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {\n    result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));\n}\n\n/// @notice Casts a UD2x18 number into UD60x18.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of UD60x18.\nfunction intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {\n    result = UD60x18.wrap(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint128.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint128.\nfunction intoUint128(UD2x18 x) pure returns (uint128 result) {\n    result = uint128(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint256.\n/// @dev There is no overflow check because the domain of UD2x18 is a subset of uint256.\nfunction intoUint256(UD2x18 x) pure returns (uint256 result) {\n    result = uint256(UD2x18.unwrap(x));\n}\n\n/// @notice Casts a UD2x18 number into uint40.\n/// @dev Requirements:\n/// - x must be less than or equal to `MAX_UINT40`.\nfunction intoUint40(UD2x18 x) pure returns (uint40 result) {\n    uint64 xUint = UD2x18.unwrap(x);\n    if (xUint > uint64(Common.MAX_UINT40)) {\n        revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);\n    }\n    result = uint40(xUint);\n}\n\n/// @notice Alias for {wrap}.\nfunction ud2x18(uint64 x) pure returns (UD2x18 result) {\n    result = UD2x18.wrap(x);\n}\n\n/// @notice Unwrap a UD2x18 number into uint64.\nfunction unwrap(UD2x18 x) pure returns (uint64 result) {\n    result = UD2x18.unwrap(x);\n}\n\n/// @notice Wraps a uint64 number into UD2x18.\nfunction wrap(uint64 x) pure returns (UD2x18 result) {\n    result = UD2x18.wrap(x);\n}\n"
      },
      "lib/prb-math/src/sd1x18/Errors.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD1x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD60x18.\nerror PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint128.\nerror PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint256.\nerror PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.\nerror PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);\n\n/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in uint40.\nerror PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);\n"
      },
      "lib/prb-math/src/sd59x18/Errors.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { SD59x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.\nerror PRBMath_SD59x18_Abs_MinSD59x18();\n\n/// @notice Thrown when ceiling a number overflows SD59x18.\nerror PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.\nerror PRBMath_SD59x18_Convert_Overflow(int256 x);\n\n/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.\nerror PRBMath_SD59x18_Convert_Underflow(int256 x);\n\n/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.\nerror PRBMath_SD59x18_Div_InputTooSmall();\n\n/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.\nerror PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.\nerror PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);\n\n/// @notice Thrown when taking the binary exponent of a base greater than 192e18.\nerror PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);\n\n/// @notice Thrown when flooring a number underflows SD59x18.\nerror PRBMath_SD59x18_Floor_Underflow(SD59x18 x);\n\n/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.\nerror PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.\nerror PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.\nerror PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.\nerror PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD60x18.\nerror PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.\nerror PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint256.\nerror PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);\n\n/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.\nerror PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);\n\n/// @notice Thrown when taking the logarithm of a number less than or equal to zero.\nerror PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);\n\n/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.\nerror PRBMath_SD59x18_Mul_InputTooSmall();\n\n/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.\nerror PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);\n\n/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.\nerror PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);\n\n/// @notice Thrown when taking the square root of a negative number.\nerror PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);\n\n/// @notice Thrown when the calculating the square root overflows SD59x18.\nerror PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);\n"
      },
      "lib/prb-math/src/ud2x18/Errors.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity >=0.8.19;\n\nimport { UD2x18 } from \"./ValueType.sol\";\n\n/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in SD1x18.\nerror PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);\n\n/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.\nerror PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);\n"
      }
    },
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        "@prb/test/=lib/prb-math/node_modules/@prb/test/",
        "base64-sol/=node_modules/base64-sol/",
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        "oz/=lib/utils/lib/openzeppelin-contracts/contracts/",
        "pendle-core-v2-public/=lib/pendle-core-v2-public/contracts/",
        "prb-math/=lib/prb-math/src/",
        "solidity-examples/=lib/utils/lib/solidity-examples/contracts/",
        "solidity-stringutils/=lib/solidity-stringutils/"
      ],
      "optimizer": {
        "enabled": true,
        "runs": 1
      },
      "metadata": {
        "useLiteralContent": false,
        "bytecodeHash": "ipfs",
        "appendCBOR": true
      },
      "outputSelection": {
        "*": {
          "*": [
            "evm.bytecode",
            "evm.deployedBytecode",
            "devdoc",
            "userdoc",
            "metadata",
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          ]
        }
      },
      "evmVersion": "shanghai",
      "viaIR": false,
      "libraries": {}
    }
  }}