DynamicKinkModel

{{
  "language": "Solidity",
  "sources": {
    "silo-core/contracts/interestRateModel/kink/DynamicKinkModel.sol": {
      "content": "// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.28;

import {SafeCast} from "openzeppelin5/utils/math/SafeCast.sol";
import {Math} from "openzeppelin5/utils/math/Math.sol";
import {SignedMath} from "openzeppelin5/utils/math/SignedMath.sol";
import {Initializable} from "openzeppelin5/proxy/utils/Initializable.sol";

import {Ownable1and2Steps} from "common/access/Ownable1and2Steps.sol";

import {PRBMathSD59x18} from "../../lib/PRBMathSD59x18.sol";
import {ISilo} from "../../interfaces/ISilo.sol";
import {IDynamicKinkModel} from "../../interfaces/IDynamicKinkModel.sol";
import {IDynamicKinkModelConfig} from "../../interfaces/IDynamicKinkModelConfig.sol";

import {DynamicKinkModelConfig} from "./DynamicKinkModelConfig.sol";
import {KinkMath} from "../../lib/KinkMath.sol";
import {SiloMathLib} from "../../lib/SiloMathLib.sol";

/// @title DynamicKinkModel
/// @notice Refer to Silo DynamicKinkModel paper for more details:
/// silo-core/docs/Kink_Interest_Rate_Model_V2_2025_09_23.pdf
/// @dev it follows `IInterestRateModel` interface except `initialize` method
/// @custom:security-contact security@silo.finance
contract DynamicKinkModel is IDynamicKinkModel, Ownable1and2Steps, Initializable {
    using KinkMath for int256;
    using KinkMath for int96;
    using KinkMath for uint256;

    /// @dev DP in 18 decimal points used for integer calculations
    int256 internal constant _DP = int256(1e18);

    /// @dev universal limit for several DynamicKinkModel config parameters. Follow the model whitepaper for more
    ///     information. Units of measure vary per variable type. Any config within these limits is considered
    ///     valid.
    int256 public constant UNIVERSAL_LIMIT = 1e9 * _DP;

    /// @dev maximum value of current interest rate the model will return. This is 1,000% APR in 18-decimals.
    int256 public constant RCUR_CAP = 10 * _DP;

    /// @dev seconds per year used in interest calculations.
    int256 public constant ONE_YEAR = 365 days;

    /// @dev maximum value of compound interest per second the model will return. This is per-second rate.
    int256 public constant RCOMP_CAP_PER_SECOND = RCUR_CAP / ONE_YEAR;

    /// @dev maximum exp() input to prevent an overflow.
    int256 public constant X_MAX = 11 * _DP;

    uint32 public constant MAX_TIMELOCK = 7 days;

    /// @dev this is used for storing the current or pending model state
    ModelState internal _modelState;

    /// @inheritdoc IDynamicKinkModel
    uint256 public activateConfigAt;

    /// @dev Map of all configs for the model, used for restoring to last state
    mapping(IDynamicKinkModelConfig current => History prev) public configsHistory;

    IDynamicKinkModelConfig internal _irmConfig;

    constructor() Ownable1and2Steps(address(0xdead)) {
        // lock the implementation
        _transferOwnership(address(0));
        _disableInitializers();
    }

    function initialize(
        IDynamicKinkModel.Config calldata _config,
        IDynamicKinkModel.ImmutableArgs calldata _immutableArgs,
        address _initialOwner,
        address _silo
    )
        external
        virtual
        initializer
    {
        require(_silo != address(0), EmptySilo());
        require(_immutableArgs.timelock <= MAX_TIMELOCK, InvalidTimelock());
        require(_immutableArgs.rcompCap > 0, InvalidRcompCap());
        require(_immutableArgs.rcompCap <= RCUR_CAP, InvalidRcompCap());

        IDynamicKinkModel.ImmutableConfig memory immutableConfig = IDynamicKinkModel.ImmutableConfig({
            timelock: _immutableArgs.timelock,
            rcompCapPerSecond: int96(_immutableArgs.rcompCap / ONE_YEAR) // forge-lint: disable-line(unsafe-typecast)
        });

        _modelState.silo = _silo;

        _updateConfiguration({_config: _config, _immutableConfig: immutableConfig, _init: true});

        _transferOwnership(_initialOwner);

        emit Initialized(_initialOwner, _silo);
    }

    /// @inheritdoc IDynamicKinkModel
    function updateConfig(IDynamicKinkModel.Config calldata _config) external virtual onlyOwner {
        _updateConfiguration(_config);
    }

    /// @inheritdoc IDynamicKinkModel
    function cancelPendingUpdateConfig() external virtual onlyOwner {
        require(pendingConfigExists(), NoPendingUpdateToCancel());

        IDynamicKinkModelConfig pendingConfig = _irmConfig;
        History memory currentState = configsHistory[pendingConfig];

        _irmConfig = currentState.irmConfig;
        _modelState.k = currentState.k;

        configsHistory[pendingConfig] = History(0, IDynamicKinkModelConfig(address(0)));

        activateConfigAt = 0;

        emit PendingUpdateConfigCanceled(pendingConfig);
    }

    /// @inheritdoc IDynamicKinkModel
    function getCompoundInterestRateAndUpdate(
        uint256 _collateralAssets,
        uint256 _debtAssets,
        uint256 _interestRateTimestamp
    )
        external
        virtual
        returns (uint256 rcomp) 
    {
        int96 newK;
        uint256 result; 

        (result, newK) = _getCompoundInterestRate(CompoundInterestRateArgs({
            silo: msg.sender,
            collateralAssets: _collateralAssets,
            debtAssets: _debtAssets,
            interestRateTimestamp: _interestRateTimestamp,
            blockTimestamp: block.timestamp,
            usePending: false
        }));

        rcomp = result;

        if (pendingConfigExists()) {
            configsHistory[_irmConfig].k = newK;
        } else {
            _modelState.k = newK;
        }
    }

    /// @inheritdoc IDynamicKinkModel
    function getCompoundInterestRate(address _silo, uint256 _blockTimestamp)
        external
        view
        virtual
        returns (uint256 rcomp)
    {
        (rcomp,) = _getCompoundInterestRate({_silo: _silo, _blockTimestamp: _blockTimestamp, _usePending: false});
    }

    function getPendingCompoundInterestRate(address _silo, uint256 _blockTimestamp)
        external
        view
        virtual
        returns (uint256 rcomp)
    {
        (rcomp,) = _getCompoundInterestRate({_silo: _silo, _blockTimestamp: _blockTimestamp, _usePending: true});
    }

    /// @notice it reverts for invalid silo
    function getCurrentInterestRate(address _silo, uint256 _blockTimestamp)
        external
        view
        virtual
        returns (uint256 rcur)
    {
        rcur = _getCurrentInterestRate({_silo: _silo, _blockTimestamp: _blockTimestamp, _usePending: false});
    }

    function getPendingCurrentInterestRate(address _silo, uint256 _blockTimestamp)
        external
        view
        virtual
        returns (uint256 rcur)
    {
        rcur = _getCurrentInterestRate({_silo: _silo, _blockTimestamp: _blockTimestamp, _usePending: true});
    }

    /// @inheritdoc IDynamicKinkModel
    function irmConfig() public view returns (IDynamicKinkModelConfig config) {
        config = pendingConfigExists() ? configsHistory[_irmConfig].irmConfig : _irmConfig;
    }

    /// @inheritdoc IDynamicKinkModel
    function modelState() public view returns (ModelState memory state) {
        if (!pendingConfigExists()) return _modelState;

        // in case of pending config, we need to read k from history
        state.silo = _modelState.silo;
        state.k = configsHistory[_irmConfig].k;
    }

    /// @inheritdoc IDynamicKinkModel
    function pendingIrmConfig() public view returns (address config) {
        config = pendingConfigExists() ? address(_irmConfig) : address(0);
    }

    /// @inheritdoc IDynamicKinkModel
    function getModelStateAndConfig(bool _usePending)
        public
        view
        virtual
        returns (ModelState memory state, Config memory config, ImmutableConfig memory immutableConfig)
    {
        IDynamicKinkModelConfig irmConfigToUse;

        if (_usePending) {
            irmConfigToUse = IDynamicKinkModelConfig(pendingIrmConfig());
            require(address(irmConfigToUse) != address(0), NoPendingConfig());

            state = _modelState;
        } else {
            irmConfigToUse = irmConfig();
            state = modelState();
        }

        (config, immutableConfig) = irmConfigToUse.getConfig();
    }

    /// @inheritdoc IDynamicKinkModel
    function verifyConfig(IDynamicKinkModel.Config memory _config) public view virtual {
        require(_config.ulow.inClosedInterval(0, _DP), InvalidUlow());
        require(_config.u1.inClosedInterval(0, _DP), InvalidU1());
        require(_config.u2.inClosedInterval(_config.u1, _DP), InvalidU2());

        require(_config.ucrit.inClosedInterval(_config.ulow, _DP), InvalidUcrit());

        require(_config.rmin.inClosedInterval(0, _DP), InvalidRmin());

        require(_config.kmin.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidKmin());
        require(_config.kmax.inClosedInterval(_config.kmin, UNIVERSAL_LIMIT), InvalidKmax());

        // we store k as int96, so we double check if it is in the range of int96
        require(_config.kmin.inClosedInterval(0, type(int96).max), InvalidKmin());
        require(_config.kmax.inClosedInterval(_config.kmin, type(int96).max), InvalidKmax());

        require(_config.alpha.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidAlpha());

        require(_config.cminus.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidCminus());
        require(_config.cplus.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidCplus());

        require(_config.c1.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidC1());
        require(_config.c2.inClosedInterval(0, UNIVERSAL_LIMIT), InvalidC2());

        require(_config.dmax.inClosedInterval(_config.c2, UNIVERSAL_LIMIT), InvalidDmax());
    }

    function pendingConfigExists() public view returns (bool) {
        return activateConfigAt > block.timestamp;
    }

    /// @inheritdoc IDynamicKinkModel
    function currentInterestRate( // solhint-disable-line function-max-lines, code-complexity
        Config memory _cfg,
        ModelState memory _state, 
        int256 _t0, 
        int256 _t1,
        int256 _u,
        int256 _tba
    )
        public
        pure
        virtual
        returns (int256 rcur)
    {
        if (_tba == 0) return 0; // no debt, no interest

        int256 T = _t1 - _t0;

        // k is stored capped, so we can use it as is
        int256 k = _state.k;

        if (_u < _cfg.u1) {
            k = SignedMath.max(k - (_cfg.c1 + _cfg.cminus * (_cfg.u1 - _u) / _DP) * T, _cfg.kmin);
        } else if (_u > _cfg.u2) {
            k = SignedMath.min(
                k + SignedMath.min(_cfg.c2 + _cfg.cplus * (_u - _cfg.u2) / _DP, _cfg.dmax) * T, _cfg.kmax
            );
        }

        int256 excessU; // additional interest rate
        if (_u >= _cfg.ulow) {
            excessU = _u - _cfg.ulow;

            if (_u >= _cfg.ucrit) {
                excessU = excessU + _cfg.alpha * (_u - _cfg.ucrit) / _DP;
            }

            rcur = excessU * k * ONE_YEAR / _DP + _cfg.rmin * ONE_YEAR;
        } else {
            rcur = _cfg.rmin * ONE_YEAR;
        }

        require(rcur >= 0, NegativeRcur());
        rcur = SignedMath.min(rcur, RCUR_CAP);
    }

    /// @inheritdoc IDynamicKinkModel
    function compoundInterestRate( // solhint-disable-line code-complexity, function-max-lines
        Config memory _cfg,
        ModelState memory _state,
        int256 _rcompCapPerSecond,
        int256 _t0,
        int256 _t1,
        int256 _u,
        int256 _tba
    )
        public
        pure
        virtual
        returns (int256 rcomp, int256 k)
    {
        LocalVarsRCOMP memory _l;

        require(_t0 <= _t1, InvalidTimestamp());

        _l.T = _t1 - _t0;
        // if there is no time change, then k should not change
        if (_l.T == 0) return (0, _state.k);

        // rate of change of k
        if (_u < _cfg.u1) {
            _l.roc = -_cfg.c1 - _cfg.cminus * (_cfg.u1 - _u) / _DP;
        } else if (_u > _cfg.u2) {
            _l.roc = SignedMath.min(_cfg.c2 + _cfg.cplus * (_u - _cfg.u2) / _DP, _cfg.dmax);
        }

        k = _state.k;

        // slope of the kink at t1 ignoring lower and upper bounds
        _l.k1 = k + _l.roc * _l.T;

        // calculate the resulting slope state
        if (_l.k1 > _cfg.kmax) {
            _l.x = _cfg.kmax * _l.T - (_cfg.kmax - k) ** 2 / (2 * _l.roc);
            k = _cfg.kmax;
        } else if (_l.k1 < _cfg.kmin) {
            _l.x = _cfg.kmin * _l.T - (k - _cfg.kmin) ** 2 / (2 * _l.roc);
            k = _cfg.kmin;
        } else {
            _l.x = (k + _l.k1) * _l.T / 2;
            k = _l.k1;
        }

        if (_u >= _cfg.ulow) {
            _l.f = _u - _cfg.ulow;

            if (_u >= _cfg.ucrit) {
                _l.f = _l.f + _cfg.alpha * (_u - _cfg.ucrit) / _DP;
            }
        }

        _l.x = _cfg.rmin * _l.T + _l.f * _l.x / _DP;

        // Overflow Checks

        // limit x, so the exp() function will not overflow, we have unchecked math there
        require(_l.x <= X_MAX, XOverflow());

        rcomp = PRBMathSD59x18.exp(_l.x) - _DP;
        require(rcomp >= 0, NegativeRcomp());

        // limit rcomp
        if (rcomp > _rcompCapPerSecond * _l.T) {
            rcomp = _rcompCapPerSecond * _l.T;
            // k should be set to min only on overflow or cap
            k = _cfg.kmin;
        }

        // no debt, no interest, overriding min APR
        if (_tba == 0) rcomp = 0;
    }

    function _updateConfiguration(IDynamicKinkModel.Config memory _config) internal virtual {
        // even if _irmConfig is pending timelock, immutable config can be pulled from it
        (, IDynamicKinkModel.ImmutableConfig memory immutableConfig) = _irmConfig.getConfig();
        _updateConfiguration({_config: _config, _immutableConfig: immutableConfig, _init: false});
    }

    function _updateConfiguration(
        IDynamicKinkModel.Config memory _config,
        IDynamicKinkModel.ImmutableConfig memory _immutableConfig,
        bool _init
    ) internal virtual {
        require(!pendingConfigExists(), PendingUpdate());

        activateConfigAt = _init ? block.timestamp : block.timestamp + _immutableConfig.timelock;

        verifyConfig(_config);

        IDynamicKinkModelConfig newCfg = IDynamicKinkModelConfig(new DynamicKinkModelConfig(_config, _immutableConfig));

        configsHistory[newCfg] = History({k: _modelState.k, irmConfig: _irmConfig});
        _modelState.k = _config.kmin;
        _irmConfig = newCfg;

        emit NewConfig(newCfg, activateConfigAt);
    }

    function _getCompoundInterestRate(
        address _silo,
        uint256 _blockTimestamp,
        bool _usePending
    )
        internal
        view
        virtual
        returns (uint256 rcomp, int96 k)
    {
        ISilo.UtilizationData memory data = ISilo(_silo).utilizationData();

        (rcomp, k) = _getCompoundInterestRate(CompoundInterestRateArgs({
            silo: _silo,
            collateralAssets: data.collateralAssets,
            debtAssets: data.debtAssets,
            interestRateTimestamp: data.interestRateTimestamp,
            blockTimestamp: _blockTimestamp,
            usePending: _usePending
        }));
    }

    function _getCompoundInterestRate(CompoundInterestRateArgs memory _args)
        internal
        view
        virtual
        returns (uint256 rcomp, int96 k)
    {
        (ModelState memory state, Config memory cfg, ImmutableConfig memory immutableCfg) =
            getModelStateAndConfig(_args.usePending);

        require(_args.silo == state.silo, InvalidSilo());

        // k should be set to min on overflow
        if (_args.interestRateTimestamp.wouldOverflowOnCastToInt256()) return (0, cfg.kmin);
        if (_args.blockTimestamp.wouldOverflowOnCastToInt256()) return (0, cfg.kmin);
        if (_args.collateralAssets.wouldOverflowOnCastToInt256()) return (0, cfg.kmin);
        if (_args.debtAssets.wouldOverflowOnCastToInt256()) return (0, cfg.kmin);

        try this.compoundInterestRate({
            _cfg: cfg,
            _state: state,
            _rcompCapPerSecond: immutableCfg.rcompCapPerSecond,
            _t0: int256(uint256(_args.interestRateTimestamp)),
            _t1: int256(_args.blockTimestamp),
            _u: _calculateUtiliation(_args.collateralAssets, _args.debtAssets),
            _tba: int256(_args.debtAssets)
        }) returns (int256 rcompInt, int256 newK) {
            rcomp = SafeCast.toUint256(rcompInt);
            k = _capK(newK, cfg.kmin, cfg.kmax);
        } catch {
            rcomp = 0;
            k = cfg.kmin; // k should be set to min on overflow
        }
    }

    function _getCurrentInterestRate(address _silo, uint256 _blockTimestamp, bool _usePending)
        internal
        view
        virtual
        returns (uint256 rcur)
    {
        (ModelState memory state, Config memory cfg,) = getModelStateAndConfig(_usePending);
        require(_silo == state.silo, InvalidSilo());

        ISilo.UtilizationData memory data = ISilo(state.silo).utilizationData();

        if (data.debtAssets.wouldOverflowOnCastToInt256()) return 0;
        if (_blockTimestamp.wouldOverflowOnCastToInt256()) return 0;

        try this.currentInterestRate({
            _cfg: cfg,
            _state: state,
            _t0: SafeCast.toInt256(data.interestRateTimestamp),
            _t1: int256(_blockTimestamp), // forge-lint: disable-line(unsafe-typecast)
            _u: _calculateUtiliation(data.collateralAssets, data.debtAssets),
            _tba: int256(data.debtAssets) // forge-lint: disable-line(unsafe-typecast)
        }) returns (int256 rcurInt) {
            rcur = SafeCast.toUint256(rcurInt);
        } catch {
            rcur = 0;
        }
    }

    // hard rule: utilization in the model should never be above 100%.
    function _calculateUtiliation(uint256 _collateralAssets, uint256 _debtAssets)
        internal
        pure
        virtual
        returns (int256 u)
    {
        // forge-lint: disable-next-line(unsafe-typecast)
        u = int256(SiloMathLib.calculateUtilization(uint256(_DP), _collateralAssets, _debtAssets));
    }

    /// @dev we expect _kmin and _kmax to be in the range of int96
    function _capK(int256 _k, int256 _kmin, int256 _kmax) internal pure virtual returns (int96 cappedK) {
        require(_kmin <= _kmax, InvalidKRange());

        // safe to cast to int96, because we know, that _kmin and _kmax are in the range of int96
        cappedK = int96(SignedMath.max(_kmin, SignedMath.min(_kmax, _k)));
    }
}
"
    },
    "gitmodules/openzeppelin-contracts-5/contracts/utils/math/SafeCast.sol": {
      "content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.20;

/**
 * @dev Wrappers over Solidity's uintXX/intXX/bool casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeCast {
    /**
     * @dev Value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in an uint of `bits` size.
     */
    error SafeCastOverflowedIntToUint(int256 value);

    /**
     * @dev Value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedIntDowncast(uint8 bits, int256 value);

    /**
     * @dev An uint value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedUintToInt(uint256 value);

    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        if (value > type(uint248).max) {
            revert SafeCastOverflowedUintDowncast(248, value);
        }
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        if (value > type(uint240).max) {
            revert SafeCastOverflowedUintDowncast(240, value);
        }
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        if (value > type(uint232).max) {
            revert SafeCastOverflowedUintDowncast(232, value);
        }
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        if (value > type(uint224).max) {
            revert SafeCastOverflowedUintDowncast(224, value);
        }
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        if (value > type(uint216).max) {
            revert SafeCastOverflowedUintDowncast(216, value);
        }
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        if (value > type(uint208).max) {
            revert SafeCastOverflowedUintDowncast(208, value);
        }
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        if (value > type(uint200).max) {
            revert SafeCastOverflowedUintDowncast(200, value);
        }
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        if (value > type(uint192).max) {
            revert SafeCastOverflowedUintDowncast(192, value);
        }
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        if (value > type(uint184).max) {
            revert SafeCastOverflowedUintDowncast(184, value);
        }
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        if (value > type(uint176).max) {
            revert SafeCastOverflowedUintDowncast(176, value);
        }
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        if (value > type(uint168).max) {
            revert SafeCastOverflowedUintDowncast(168, value);
        }
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        if (value > type(uint160).max) {
            revert SafeCastOverflowedUintDowncast(160, value);
        }
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        if (value > type(uint152).max) {
            revert SafeCastOverflowedUintDowncast(152, value);
        }
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        if (value > type(uint144).max) {
            revert SafeCastOverflowedUintDowncast(144, value);
        }
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        if (value > type(uint136).max) {
            revert SafeCastOverflowedUintDowncast(136, value);
        }
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        if (value > type(uint128).max) {
            revert SafeCastOverflowedUintDowncast(128, value);
        }
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        if (value > type(uint120).max) {
            revert SafeCastOverflowedUintDowncast(120, value);
        }
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        if (value > type(uint112).max) {
            revert SafeCastOverflowedUintDowncast(112, value);
        }
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        if (value > type(uint104).max) {
            revert SafeCastOverflowedUintDowncast(104, value);
        }
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        if (value > type(uint96).max) {
            revert SafeCastOverflowedUintDowncast(96, value);
        }
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        if (value > type(uint88).max) {
            revert SafeCastOverflowedUintDowncast(88, value);
        }
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        if (value > type(uint80).max) {
            revert SafeCastOverflowedUintDowncast(80, value);
        }
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        if (value > type(uint72).max) {
            revert SafeCastOverflowedUintDowncast(72, value);
        }
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        if (value > type(uint64).max) {
            revert SafeCastOverflowedUintDowncast(64, value);
        }
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        if (value > type(uint56).max) {
            revert SafeCastOverflowedUintDowncast(56, value);
        }
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        if (value > type(uint48).max) {
            revert SafeCastOverflowedUintDowncast(48, value);
        }
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        if (value > type(uint40).max) {
            revert SafeCastOverflowedUintDowncast(40, value);
        }
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        if (value > type(uint32).max) {
            revert SafeCastOverflowedUintDowncast(32, value);
        }
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        if (value > type(uint24).max) {
            revert SafeCastOverflowedUintDowncast(24, value);
        }
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        if (value > type(uint16).max) {
            revert SafeCastOverflowedUintDowncast(16, value);
        }
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        if (value > type(uint8).max) {
            revert SafeCastOverflowedUintDowncast(8, value);
        }
        return uint8(value);
    }

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

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(248, value);
        }
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(240, value);
        }
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(232, value);
        }
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(224, value);
        }
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(216, value);
        }
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(208, value);
        }
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(200, value);
        }
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(192, value);
        }
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(184, value);
        }
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(176, value);
        }
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(168, value);
        }
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(160, value);
        }
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(152, value);
        }
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(144, value);
        }
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(136, value);
        }
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(128, value);
        }
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(120, value);
        }
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(112, value);
        }
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(104, value);
        }
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(96, value);
        }
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(88, value);
        }
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(80, value);
        }
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(72, value);
        }
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(64, value);
        }
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(56, value);
        }
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(48, value);
        }
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(40, value);
        }
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(32, value);
        }
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(24, value);
        }
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(16, value);
        }
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(8, value);
        }
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        if (value > uint256(type(int256).max)) {
            revert SafeCastOverflowedUintToInt(value);
        }
        return int256(value);
    }

    /**
     * @dev Cast a boolean (false or true) to a uint256 (0 or 1) with no jump.
     */
    function toUint(bool b) internal pure returns (uint256 u) {
        /// @solidity memory-safe-assembly
        assembly {
            u := iszero(iszero(b))
        }
    }
}
"
    },
    "gitmodules/openzeppelin-contracts-5/contracts/utils/math/Math.sol": {
      "content": "// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "../Panic.sol";
import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Returns the addition of two unsigned integers, with an success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a success flag (no division by zero).
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a / b);
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a success flag (no division by zero).
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }

        // The following calculation ensures accurate ceiling division without overflow.
        // Since a is non-zero, (a - 1) / b will not overflow.
        // The largest possible result occurs when (a - 1) / b is type(uint256).max,
        // but the largest value we can obtain is type(uint256).max - 1, which happens
        // when a = type(uint256).max and b = 1.
        unchecked {
            return a == 0 ? 0 : (a - 1) / b + 1;
        }
    }

    /**
     * @dev Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     *
     * Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv) with further edits by
     * Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2²⁵⁶ + prod0.
            uint256 prod0 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= prod1) {
                Panic.panic(denominator == 0 ? Panic.DIVISION_BY_ZERO : Panic.UNDER_OVERFLOW);
            }

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

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

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

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator.
            // Always >= 1. See https://cs.stackexchange.com/q/138556/92363.

            uint256 twos = denominator & (0 - denominator);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

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

                // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

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

            // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also
            // works in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @dev Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, expect 0.
     * If n is not a prime, then Z/nZ is not a field, and some elements might not be inversible.
     *
     * If the input value is not inversible, 0 is returned.
     *
     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Ferma's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`.
     */
    function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
        unchecked {
            if (n == 0) return 0;

            // The inverse modulo is calculated using the Extended Euclidean Algorithm (iterative version)
            // Used to compute integers x and y such that: ax + ny = gcd(a, n).
            // When the gcd is 1, then the inverse of a modulo n exists and it's x.
            // ax + ny = 1