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// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

import {SafeCastLibrary} from "../libraries/SafeCastLibrary.sol";
import {Checkpoints} from "../libraries/Checkpoints.sol";
import {Time} from "../libraries/Time.sol";

/**
 * @title CheckPointSystem
 * @dev This contract is used to manage checkpoints in the system.
 */
library EscrowDelegateCheckpoints {
    using Checkpoints for Checkpoints.Trace;
    using Checkpoints for Checkpoints.TraceAddress;
    using SafeCastLibrary for int128;
    using SafeCastLibrary for uint256;

    /// @notice Maximum time for a checkpoint
    int128 public constant MAX_TIME = 2 * 365 * 86400;
    /// @notice Unit of time for the clock
    uint48 public constant CLOCK_UNIT = 7 days;

    struct EscrowDelegateStore {
        /// @notice Global checkpoints
        Checkpoints.Trace _globalCheckpoints;
        /// @notice Mapping of global slope changes
        /// @dev Intended to be exposed with a getter
        mapping(uint256 => int128) globalSlopeChanges;
        /// @notice escrow lock checkpoints
        mapping(uint256 => Checkpoints.Trace) _escrowCheckpoints;
        /// @notice Delegate checkpoints
        mapping(address => Checkpoints.Trace) _delegateCheckpoints;
        /// @notice escrow lock to delegatee mapping
        mapping(uint256 => Checkpoints.TraceAddress) _escrowDelegateeAddress;
        /// @notice Delegatee slope changes
        /// @dev Intended to be exposed with a getter
        mapping(address => mapping(uint256 => int128)) delegateeSlopeChanges;
    }

    event CheckpointGlobal(uint48 timestamp, int128 slope, int128 bias, int128 permanent);
    event CheckpointDelegate(address delegatee, uint48 timestamp, int128 slope, int128 bias, int128 permanent);
    event CheckpointEscrow(uint256 escrowId, uint48 timestamp, int128 slope, int128 bias, int128 permanent);

    /**
     * @notice Clock used for flagging checkpoints.
     * @return Current timestamp
     */
    function clock() public view returns (uint48) {
        return Time.timestamp();
    }

    /**
     * @notice Clock used for flagging global checkpoints.
     * @return Current timestamp rounded to the nearest clock unit
     */
    function globalClock() public view returns (uint48) {
        return toGlobalClock(Time.timestamp());
    }

    /**
     * @notice Converts a timestamp to a global clock value.
     * @param timestamp The timestamp to convert
     * @return The converted global clock value
     */
    function toGlobalClock(uint256 timestamp) internal pure returns (uint48) {
        return uint48((timestamp / CLOCK_UNIT) * CLOCK_UNIT);
    }

    /**
     * @dev Record global and per-escrow data to checkpoints. Used by VotingEscrow system.
     * @param store_ The EscrowDelegateStore struct containing all the storage mappings.
     * @param escrowId NFT escrow lock ID. No escrow checkpoint if 0
     * @param uOldAmount Locked amount from last checkpoint
     * @param uNewAmount Locked amount from current checkpoint
     * @param uOldEndTime Last checkpoint time
     * @param uNewEndTime Current checkpoint time
     */
    function checkpoint(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        int128 uOldAmount,
        int128 uNewAmount,
        uint256 uOldEndTime,
        uint256 uNewEndTime
    ) external {
        int128 oldDslope = 0;
        int128 newDslope = 0;
        Checkpoints.Point memory uOldPoint = Checkpoints.blankPoint();
        Checkpoints.Point memory uNewPoint = Checkpoints.blankPoint();
        /// @notice if this is not rounded to CLOCK_UNIT
        /// the system will not be able to go too long without checkpoints
        uNewEndTime = toGlobalClock(uNewEndTime);
        if (escrowId != 0) {
            // Calculate slopes and biases
            // Kept at zero when they have to
            uNewPoint.permanent = uNewEndTime == 0 ? uNewAmount : int128(0);
            uOldPoint.permanent = uOldEndTime == 0 ? uOldAmount : int128(0);
            if (uOldEndTime > block.timestamp && uOldAmount > 0) {
                /// @dev  Calculate the slope based on the older checkpoint amount
                uOldPoint.slope = (uOldAmount) / MAX_TIME;
                uOldPoint.bias = (uOldPoint.slope * (uOldEndTime - block.timestamp).toInt128());
            }
            if (uNewEndTime > block.timestamp && uNewAmount > 0) {
                uNewPoint.slope = (uNewAmount) / MAX_TIME;
                uNewPoint.bias = (uNewPoint.slope * (uNewEndTime - block.timestamp).toInt128());
            }
            oldDslope = store_.globalSlopeChanges[uOldEndTime];
            if (uNewEndTime != 0) {
                if (uNewEndTime == uOldEndTime) {
                    newDslope = oldDslope;
                } else {
                    newDslope = store_.globalSlopeChanges[uNewEndTime];
                }
            }

            // Schedule the slope changes (slope is going down)
            // We subtract new escrow slope from [_newLocked.endTime]
            // and add old_escrow_slope to [_oldLocked.end]
            if (uOldEndTime > block.timestamp) {
                // oldDslope was <something> - uOld.slope, so we cancel that
                oldDslope += uOldPoint.slope;
                if (uOldEndTime == uNewEndTime) {
                    oldDslope -= uNewPoint.slope; // It was a new deposit, not extension
                }
                store_.globalSlopeChanges[uOldEndTime] = oldDslope;
            }

            if (uNewEndTime > block.timestamp) {
                // update slope if new lock is greater than old lock and is not permanent or if old lock is permanent
                if ((uNewEndTime > uOldEndTime)) {
                    newDslope -= uNewPoint.slope; // old slope disappeared at this point
                    store_.globalSlopeChanges[uNewEndTime] = newDslope;
                }
                // else: we recorded it already in oldDslope
            }
            /// @dev Add the new point to the escrowId Checkpoints.Trace
            _pushPointAtClock(store_._escrowCheckpoints[escrowId], uNewPoint);
            emit CheckpointEscrow(escrowId, clock(), uNewPoint.slope, uNewPoint.bias, uNewPoint.permanent);

            (, uint48 delegateTs, address delegateeAddress) = store_
                ._escrowDelegateeAddress[escrowId]
                .latestCheckpoint();

            if (delegateTs != 0) {
                /// @notice this can likely be handled more efficiently
                _checkpointDelegatee(store_, delegateeAddress, uOldPoint, uOldEndTime, false);
                _checkpointDelegatee(store_, delegateeAddress, uNewPoint, uNewEndTime, true);
            }
        }
        /// @dev If escrowId is 0,  this  will still create a global checkpoint
        globalCheckpoint(store_, escrowId, uOldPoint, uNewPoint);
    }

    /**
     * @dev Function to update global checkpoint
     */
    function globalCheckpoint(EscrowDelegateStore storage store_) external {
        globalCheckpoint(store_, 0, Checkpoints.blankPoint(), Checkpoints.blankPoint());
    }

    /**
     * @dev Function to update global checkpoint with new points
     * @param escrowId The ID of the escrow lock
     * - If
     * @param uOldPoint The old point to be updated
     * @param uNewPoint The new point to be updated
     */
    function globalCheckpoint(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        Checkpoints.Point memory uOldPoint,
        Checkpoints.Point memory uNewPoint
    ) public {
        (, uint48 lastPoint, Checkpoints.Point memory lastGlobal) = store_._globalCheckpoints.latestCheckpoint();
        uint48 lastCheckpoint = lastPoint != 0 ? lastPoint : uint48(block.timestamp);

        {
            // Go over weeks to fill history and calculate what the current point is
            uint48 testTime = toGlobalClock(lastCheckpoint); /// @dev  lastCheckpoint > tesTime
            uint256 maxTime = testTime + MAX_TIME.toUint256();

            while (testTime < block.timestamp) {
                testTime += CLOCK_UNIT;
                int128 dSlope = 0;
                if (testTime > block.timestamp) {
                    testTime = block.timestamp.toUint48();
                } else {
                    dSlope = store_.globalSlopeChanges[testTime];
                }
                if (dSlope != 0) {
                    lastGlobal.bias -= lastGlobal.slope * uint256(testTime - lastCheckpoint).toInt128();
                    lastGlobal.slope += dSlope;
                    if (lastGlobal.bias < 0) {
                        lastGlobal.bias = 0;
                    }
                    if (lastGlobal.slope < 0) {
                        lastGlobal.slope = 0;
                    }

                    lastCheckpoint = testTime;
                    store_._globalCheckpoints.push(lastCheckpoint, lastGlobal);
                }
                if (testTime > maxTime) break;
            }
        }

        if (escrowId != 0) {
            lastGlobal.bias = lastGlobal.bias - ((lastGlobal.slope * (block.timestamp - lastCheckpoint).toInt128()));

            lastGlobal.slope += uNewPoint.slope - uOldPoint.slope;
            lastGlobal.bias += uNewPoint.bias - uOldPoint.bias;
            lastGlobal.permanent += uNewPoint.permanent - uOldPoint.permanent;
        } else {
            // Initial value of testTime is always larger than the ts of the last point
            uint256 testTime = block.timestamp;
            lastGlobal.bias -= (lastGlobal.slope * (testTime - lastCheckpoint).toInt128());
        }

        _pushPointAtClock(store_._globalCheckpoints, lastGlobal);
        emit CheckpointGlobal(clock(), lastGlobal.slope, lastGlobal.bias, lastGlobal.permanent);
    }

    /**
     * @dev Function to calculate total voting power at some point in the past
     * @param _delegateeAddress The address of the delegatee
     * @param timestamp Time to calculate the total voting power at
     * @return Total voting power at that time
     */
    function getAdjustedVotes(
        EscrowDelegateStore storage store_,
        address _delegateeAddress,
        uint48 timestamp
    ) external view returns (uint256) {
        Checkpoints.Point memory lastPoint = _getAdjustedVotesCheckpoint(store_, _delegateeAddress, timestamp);
        return (lastPoint.bias + lastPoint.permanent).toUint256();
    }

    /**
     * @dev Function to get delegated votes checkpoint at some point in the past
     * @param _delegateeAddress The address of the delegatee
     * @param timestamp Time to calculate the total voting power at
     * @return Total voting power at that time
     */
    function _getAdjustedVotesCheckpoint(
        EscrowDelegateStore storage store_,
        address _delegateeAddress,
        uint48 timestamp
    ) internal view returns (Checkpoints.Point memory) {
        (bool exists, uint48 lastCheckpointTs, Checkpoints.Point memory lastPoint) = store_
            ._delegateCheckpoints[_delegateeAddress]
            .upperLookupRecent(timestamp);
        if (!exists) return lastPoint;
        uint48 testTime = toGlobalClock(lastCheckpointTs); /// @dev  lastCheckpointTs > tesTime
        uint256 maxTime = testTime + MAX_TIME.toUint256();
        while (testTime < timestamp) {
            testTime += CLOCK_UNIT;
            int128 dSlope = 0;
            if (testTime > timestamp) {
                testTime = timestamp;
            } else {
                dSlope = store_.delegateeSlopeChanges[_delegateeAddress][testTime];
            }
            if (dSlope != 0) {
                lastPoint.bias -= lastPoint.slope * uint256(testTime - lastCheckpointTs).toInt128();
                lastPoint.slope += dSlope;
                if (lastPoint.bias < 0) {
                    lastPoint.bias = 0;
                }
                if (lastPoint.slope < 0) {
                    lastPoint.slope = 0;
                }
                lastCheckpointTs = uint48(testTime);
            }
            if (testTime > maxTime) break;
        }
        int128 change = lastPoint.slope * uint256(timestamp - lastCheckpointTs).toInt128();
        lastPoint.bias = lastPoint.bias < change ? int128(0) : lastPoint.bias - change;

        return lastPoint;
    }

    /**
     * @notice Public function to get the delegatee of an escrow lock
     * @param escrowId The ID of the escrow
     * @return The address of the delegate
     */
    function getEscrowDelegatee(EscrowDelegateStore storage store_, uint256 escrowId) external view returns (address) {
        return getEscrowDelegateeAtTime(store_, escrowId, block.timestamp.toUint48());
    }

    /**
     * @notice Public function to get the delegatee of an escrow lock
     * @param escrowId The ID of the escrow lock
     * @param timestamp The timestamp to get the delegate at
     * @return The address of the delegate
     */
    function getEscrowDelegateeAtTime(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        uint48 timestamp
    ) public view returns (address) {
        return store_._escrowDelegateeAddress[escrowId].upperLookupRecent(timestamp);
    }

    /**
     * @dev Function to record escrow delegation checkpoints. Used by voting system.
     * @param escrowId The ID of the escrow lock
     * @param delegatee The address of the delegatee
     * @param endTime The end time of the delegation
     */
    function delegate(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        address delegatee,
        uint256 endTime
    ) external returns (address oldDelegatee, address newDelegatee) {
        oldDelegatee = store_._escrowDelegateeAddress[escrowId].latest();
        if (oldDelegatee == delegatee) return (oldDelegatee, delegatee);

        (, uint48 ts, Checkpoints.Point memory lastPoint) = store_._escrowCheckpoints[escrowId].latestCheckpoint();
        lastPoint.bias -= ((lastPoint.slope * (block.timestamp - ts).toInt128()));
        if (lastPoint.bias < 0) {
            lastPoint.bias = 0;
        }

        if (oldDelegatee != delegatee && oldDelegatee != address(0)) {
            _checkpointDelegatee(store_, oldDelegatee, lastPoint, endTime, false);
        }
        // Delegate to new delegator
        _checkpointDelegatee(store_, delegatee, lastPoint, endTime, true);
        _pushAddressAtClock(store_._escrowDelegateeAddress[escrowId], delegatee);
        return (oldDelegatee, delegatee);
    }

    /**
     * @dev Function to update delegatee's `delegatedBalance` by `balance`.
     *      Only updates if delegating to a new delegatee.
     * @param delegateeAddress The address of the delegatee
     * @param escrowPoint The point of the escrow
     * @param endTime The end time of the delegation
     * @param increase Whether to increase or decrease the balance
     */
    function _checkpointDelegatee(
        EscrowDelegateStore storage store_,
        address delegateeAddress,
        Checkpoints.Point memory escrowPoint,
        uint256 endTime,
        bool increase
    ) internal {
        (Checkpoints.Point memory lastPoint, uint48 lastCheckpoint) = baseCheckpointDelegatee(store_, delegateeAddress);

        int128 baseBias = lastPoint.bias - (lastPoint.slope * (block.timestamp - lastCheckpoint).toInt128());

        if (!increase) {
            if (endTime > block.timestamp) {
                store_.delegateeSlopeChanges[delegateeAddress][endTime] += escrowPoint.slope;
                lastPoint.slope = escrowPoint.slope < lastPoint.slope ? lastPoint.slope - escrowPoint.slope : int128(0);
            }
            lastPoint.bias = escrowPoint.bias < baseBias ? baseBias - escrowPoint.bias : int128(0);
            lastPoint.permanent = escrowPoint.permanent < lastPoint.permanent
                ? lastPoint.permanent - escrowPoint.permanent
                : int128(0);
        } else {
            if (endTime > block.timestamp) {
                store_.delegateeSlopeChanges[delegateeAddress][endTime] -= escrowPoint.slope;
                lastPoint.slope = lastPoint.slope + escrowPoint.slope;
            }
            lastPoint.bias = baseBias + escrowPoint.bias;
            lastPoint.permanent = lastPoint.permanent + escrowPoint.permanent;
        }
        /// @dev bias can be rounded up by lack of precision. If slope is 0 we are out
        if (lastPoint.slope == 0) {
            lastPoint.bias = 0;
        }
        _pushPointAtClock(store_._delegateCheckpoints[delegateeAddress], lastPoint);
        emit CheckpointDelegate(delegateeAddress, clock(), lastPoint.slope, lastPoint.bias, lastPoint.permanent);
    }

    /**
     * @dev Function to update delegatee's checkpoint
     * @param delegateeAddress The address of the delegatee
     * @return lastPoint The last point of the delegatee
     * @return lastCheckpoint The last checkpoint time of the delegatee
     */
    function baseCheckpointDelegatee(
        EscrowDelegateStore storage store_,
        address delegateeAddress
    ) public returns (Checkpoints.Point memory lastPoint, uint48 lastCheckpoint) {
        (bool exists, uint48 ts, Checkpoints.Point memory point) = store_
            ._delegateCheckpoints[delegateeAddress]
            .latestCheckpoint();
        lastPoint = point;
        lastCheckpoint = ts;
        if (exists) {
            // Go over days to fill history and calculate what the current point is
            uint48 testTime = toGlobalClock(lastCheckpoint); /// @dev  lastCheckpoint > tesTime

            uint256 maxTime = testTime + MAX_TIME.toUint256();

            // Iterate over time until current block timestamp or maxtime
            while (testTime < block.timestamp) {
                testTime += CLOCK_UNIT;
                int128 dSlope = 0;
                if (testTime > block.timestamp) {
                    testTime = uint48(block.timestamp);
                } else {
                    dSlope = store_.delegateeSlopeChanges[delegateeAddress][testTime];
                }
                if (dSlope != 0) {
                    lastPoint.bias -= lastPoint.slope * uint256(testTime - lastCheckpoint).toInt128();
                    lastPoint.slope += dSlope;
                    if (lastPoint.bias < 0) {
                        lastPoint.bias = 0;
                    }
                    if (lastPoint.slope < 0) {
                        lastPoint.slope = 0;
                    }
                    lastCheckpoint = uint48(testTime);
                    store_._delegateCheckpoints[delegateeAddress].push(lastCheckpoint, lastPoint);
                }
                if (testTime > maxTime) break;
            }
        }
        emit CheckpointDelegate(delegateeAddress, clock(), lastPoint.slope, lastPoint.bias, lastPoint.permanent);
    }

    /**
     * @dev Function to calculate total voting power at some point in the past
     * @param timestamp Time to calculate the total voting power at
     * @return Total voting power at that time
     */
    function getAdjustedGlobalVotes(
        EscrowDelegateStore storage store_,
        uint48 timestamp
    ) external view returns (uint256) {
        Checkpoints.Point memory lastPoint = _getAdjustedCheckpoint(store_, timestamp);
        return (lastPoint.bias + lastPoint.permanent).toUint256();
    }

    /**
     * @dev Function to get latest checkpoint of some point in the past
     * @param timestamp Time to calculate the total voting power at
     * @return Total voting power at that time
     */
    function _getAdjustedCheckpoint(
        EscrowDelegateStore storage store_,
        uint48 timestamp
    ) internal view returns (Checkpoints.Point memory) {
        uint48 clockTime = timestamp;
        (bool exists, uint48 lastCheckpointTs, Checkpoints.Point memory lastGlobal) = store_
            ._globalCheckpoints
            .upperLookupRecent(clockTime);
        if (!exists) return lastGlobal;
        uint48 testTime = toGlobalClock(lastCheckpointTs); /// @dev  lastCheckpointTs > tesTime
        uint256 maxTime = testTime + MAX_TIME.toUint256();

        // Iterate over time until the specified timestamp or maxtime is reached
        while (testTime < timestamp) {
            testTime += CLOCK_UNIT;
            int128 dSlope = 0;
            if (testTime > timestamp) {
                testTime = timestamp;
            } else {
                dSlope = store_.globalSlopeChanges[testTime];
            }
            if (dSlope != 0) {
                lastGlobal.bias -= lastGlobal.slope * uint256(testTime - lastCheckpointTs).toInt128();
                lastGlobal.slope += dSlope;
                if (lastGlobal.bias < 0) {
                    lastGlobal.bias = 0;
                }
                if (lastGlobal.slope < 0) {
                    lastGlobal.slope = 0;
                }
                lastCheckpointTs = uint48(testTime);
            }
            if (testTime > maxTime) break;
        }

        int128 change = lastGlobal.slope * uint256(clockTime - lastCheckpointTs).toInt128();
        lastGlobal.bias = lastGlobal.bias < change ? int128(0) : lastGlobal.bias - change;

        return lastGlobal;
    }

    /**
     * @notice Get the current bias for `escrowId` at `timestamp`
     * @dev Adheres to the ERC20 `balanceOf` interface for Aragon compatibility
     * @dev Fetches last escrow point prior to a certain timestamp, then walks forward to timestamp.
     * @param escrowId NFT for lock
     * @param timestamp Epoch time to return bias power at
     * @return NFT bias
     */
    function getAdjustedEscrowBias(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        uint256 timestamp
    ) external view returns (uint256) {
        uint48 clockTime = timestamp.toUint48();
        (Checkpoints.Point memory lastPoint,) = getAdjustedEscrow(store_, escrowId, clockTime);
        if (lastPoint.permanent != 0) return lastPoint.permanent.toUint256();
        return lastPoint.bias.toUint256();
    }

    /**
     * @notice Get the current bias for `escrowId` at `timestamp`
     * @dev Adheres to the ERC20 `balanceOf` interface for Aragon compatibility
     * @dev Fetches last escrow point prior to a certain timestamp, then walks forward to timestamp.
     * @param escrowId NFT for lock
     * @param timestamp Epoch time to return bias power at
     * @return NFT bias
     */
    function getAdjustedEscrow(
        EscrowDelegateStore storage store_,
        uint256 escrowId,
        uint256 timestamp
    ) public view returns (Checkpoints.Point memory, uint48) {
        uint48 clockTime = timestamp.toUint48();
        (bool exists, uint48 ts, Checkpoints.Point memory lastPoint) = store_
            ._escrowCheckpoints[escrowId]
            .upperLookupRecent(clockTime);
        if (!exists) return (lastPoint, ts);
        int128 change = ((lastPoint.slope * uint256(clockTime - ts).toInt128()));
        lastPoint.bias = lastPoint.bias < change ? int128(0) : lastPoint.bias - change;
        return (lastPoint, ts);
    }

    function getFirstEscrowPoint(
        EscrowDelegateStore storage store_,
        uint256 escrowId
    ) internal view returns (Checkpoints.Point memory, uint48) {
        (, uint48 ts, Checkpoints.Point memory point) =  store_._escrowCheckpoints[escrowId].firstCheckpoint();
        return (point, ts);
    }

    /// -----------------------------------------------------------------------
    /// Private functions
    /// -----------------------------------------------------------------------

    /**
     * @dev Function to push an address to the checkpoint
     * @param store The storage to push the address to
     * @param value The address to be pushed
     * @return The old and new address
     */
    function _pushAddressAtClock(
        Checkpoints.TraceAddress storage store,
        address value
    ) private returns (address, address) {
        return store.push(clock(), value);
    }

    /**
     * @dev Function to push a struct to the checkpoint
     * @param store The storage to push the struct to
     * @param value The struct to be pushed
     * @return The old and new struct
     */
    function _pushPointAtClock(
        Checkpoints.Trace storage store,
        Checkpoints.Point memory value
    ) private returns (Checkpoints.Point memory, Checkpoints.Point memory) {
        return store.push(clock(), value);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @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 up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev 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 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // 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 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv 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.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

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

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

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

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

    /**
     * @notice Calculates 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) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

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

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// SPDX-License-Identifier: MIT
// This file was derived from OpenZeppelin Contracts (last updated v5.0.0) (utils/structs/Checkpoints.sol)

pragma solidity 0.8.13;

import {Math} from "@openzeppelin/contracts/utils/math/Math.sol";

/**
 * @dev This library defines the `Trace*` struct, for checkpointing values as they change at different points in
 * time, and later looking up past values by block number. See {Votes} as an example.
 *
 * To create a history of checkpoints define a variable type `Checkpoints.Trace*` in your contract, and store a new
 * checkpoint for the current transaction block using the {push} function.
 */
library Checkpoints {
    struct Trace {
        Checkpoint[] _checkpoints;
    }

    /**
     * @dev Struct to keep track of the voting power over time.
     */
    struct Point {
        /// @dev The voting power at a specific time
        /// - MUST never be negative.
        int128 bias;
        /// @dev The rate at which the voting power decreases over time.
        int128 slope;
        /// @dev The value of tokens which do not decrease over time, representing permanent voting power
        /// - MUST never be negative.
        int128 permanent;
    }

    struct Checkpoint {
        uint48 _key;
        Point _value;
    }

    /**
     * @dev A value was attempted to be inserted on a past checkpoint.
     */
    error CheckpointUnorderedInsertions();

    /**
     * @dev Pushes a (`key`, `value`) pair into a Trace so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     *
     * IMPORTANT: Never accept `key` as a user input, since an arbitrary `type(uint48).max` key set will disable the
     * library.
     */
    function push(Trace storage self, uint48 key, Point memory value) internal returns (Point memory, Point memory) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the first (oldest) checkpoint with key greater or equal than the search key, or zero if
     * there is none.
     */
    function lowerLookup(Trace storage self, uint48 key) internal view returns (Point memory) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? blankPoint() : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     */
    function upperLookup(
        Trace storage self,
        uint48 key
    ) internal view returns (bool exists, uint48 _key, Point memory _value) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);

        exists = pos != 0;
        _value = exists ? _unsafeAccess(self._checkpoints, pos - 1)._value : blankPoint();
        _key = exists ? _unsafeAccess(self._checkpoints, pos - 1)._key : 0;
    }

    /**
     * @dev Returns the value in the last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     *
     * NOTE: This is a variant of {upperLookup} that is optimised to find "recent" checkpoint (checkpoints with high
     * keys).
     */
    function upperLookupRecent(
        Trace storage self,
        uint48 key
    ) internal view returns (bool exists, uint48 _key, Point memory _value) {
        uint256 len = self._checkpoints.length;

        uint256 low = 0;
        uint256 high = len;

        if (len > 5) {
            uint256 mid = len - Math.sqrt(len);
            if (key < _unsafeAccess(self._checkpoints, mid)._key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        uint256 pos = _upperBinaryLookup(self._checkpoints, key, low, high);

        exists = pos != 0;
        _value = exists ? _unsafeAccess(self._checkpoints, pos - 1)._value : blankPoint();
        _key = exists ? _unsafeAccess(self._checkpoints, pos - 1)._key : 0;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(Trace storage self) internal view returns (Point memory) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? blankPoint() : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(
        Trace storage self
    ) internal view returns (bool exists, uint48 _key, Point memory _value) {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, blankPoint());
        } else {
            Checkpoint memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function firstCheckpoint(
        Trace storage self
    ) internal view returns (bool exists, uint48 _key, Point memory _value) {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, blankPoint());
        } else {
            Checkpoint memory ckpt = _unsafeAccess(self._checkpoints, 0);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(Trace storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Returns checkpoint at given position.
     */
    function at(Trace storage self, uint48 pos) internal view returns (Checkpoint memory) {
        return self._checkpoints[pos];
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(
        Checkpoint[] storage self,
        uint48 key,
        Point memory value
    ) private returns (Point memory, Point memory) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            Checkpoint memory last = _unsafeAccess(self, pos - 1);

            // Checkpoint keys must be non-decreasing.
            if (last._key > key) {
                revert CheckpointUnorderedInsertions();
            }

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(Checkpoint({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(Checkpoint({_key: key, _value: value}));
            return (blankPoint(), value);
        }
    }

    /**
     * @dev Return the index of the last (most recent) checkpoint with key lower or equal than the search key, or `high`
     * if there is none. `low` and `high` define a section where to do the search, with inclusive `low` and exclusive
     * `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        Checkpoint[] storage self,
        uint48 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the first (oldest) checkpoint with key is greater or equal than the search key, or
     * `high` if there is none. `low` and `high` define a section where to do the search, with inclusive `low` and
     * exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        Checkpoint[] storage self,
        uint48 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(Checkpoint[] storage self, uint256 pos) private view returns (Checkpoint storage result) {
        return self[pos];
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _realUnsafeAccess(
        Checkpoint[] storage self,
        uint256 pos
    ) private pure returns (Checkpoint storage result) {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }

    function blankPoint() internal pure returns (Point memory) {
        return Point({bias: 0, slope: 0, permanent: 0});
    }

    struct TraceAddress {
        CheckpointAddress[] _checkpoints;
    }

    struct CheckpointAddress {
        uint48 _key;
        address _value;
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into a TraceAddress so that it is stored as the checkpoint.
     *
     * Returns previous value and new value.
     *
     * IMPORTANT: Never accept `key` as a user input, since an arbitrary `type(uint48).max` key set will disable the
     * library.
     */
    function push(TraceAddress storage self, uint48 key, address value) internal returns (address, address) {
        return _insert(self._checkpoints, key, value);
    }

    /**
     * @dev Returns the value in the first (oldest) checkpoint with key greater or equal than the search key, or zero if
     * there is none.
     */
    function lowerLookup(TraceAddress storage self, uint48 key) internal view returns (address) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _lowerBinaryLookup(self._checkpoints, key, 0, len);
        return pos == len ? address(0) : _unsafeAccess(self._checkpoints, pos)._value;
    }

    /**
     * @dev Returns the value in the last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     */
    function upperLookup(TraceAddress storage self, uint48 key) internal view returns (address) {
        uint256 len = self._checkpoints.length;
        uint256 pos = _upperBinaryLookup(self._checkpoints, key, 0, len);
        return pos == 0 ? address(0) : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the last (most recent) checkpoint with key lower or equal than the search key, or zero
     * if there is none.
     *
     * NOTE: This is a variant of {upperLookup} that is optimised to find "recent" checkpoint (checkpoints with high
     * keys).
     */
    function upperLookupRecent(TraceAddress storage self, uint48 key) internal view returns (address) {
        uint256 len = self._checkpoints.length;

        uint256 low = 0;
        uint256 high = len;

        if (len > 5) {
            uint256 mid = len - Math.sqrt(len);
            if (key < _unsafeAccess(self._checkpoints, mid)._key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        uint256 pos = _upperBinaryLookup(self._checkpoints, key, low, high);

        return pos == 0 ? address(0) : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns the value in the most recent checkpoint, or zero if there are no checkpoints.
     */
    function latest(TraceAddress storage self) internal view returns (address) {
        uint256 pos = self._checkpoints.length;
        return pos == 0 ? address(0) : _unsafeAccess(self._checkpoints, pos - 1)._value;
    }

    /**
     * @dev Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
     * in the most recent checkpoint.
     */
    function latestCheckpoint(
        TraceAddress storage self
    ) internal view returns (bool exists, uint48 _key, address _value) {
        uint256 pos = self._checkpoints.length;
        if (pos == 0) {
            return (false, 0, address(0));
        } else {
            CheckpointAddress memory ckpt = _unsafeAccess(self._checkpoints, pos - 1);
            return (true, ckpt._key, ckpt._value);
        }
    }

    /**
     * @dev Returns the number of checkpoint.
     */
    function length(TraceAddress storage self) internal view returns (uint256) {
        return self._checkpoints.length;
    }

    /**
     * @dev Returns checkpoint at given position.
     */
    function at(TraceAddress storage self, uint48 pos) internal view returns (CheckpointAddress memory) {
        return self._checkpoints[pos];
    }

    /**
     * @dev Pushes a (`key`, `value`) pair into an ordered list of checkpoints, either by inserting a new checkpoint,
     * or by updating the last one.
     */
    function _insert(CheckpointAddress[] storage self, uint48 key, address value) private returns (address, address) {
        uint256 pos = self.length;

        if (pos > 0) {
            // Copying to memory is important here.
            CheckpointAddress memory last = _unsafeAccess(self, pos - 1);

            // Checkpoint keys must be non-decreasing.
            if (last._key > key) {
                revert CheckpointUnorderedInsertions();
            }

            // Update or push new checkpoint
            if (last._key == key) {
                _unsafeAccess(self, pos - 1)._value = value;
            } else {
                self.push(CheckpointAddress({_key: key, _value: value}));
            }
            return (last._value, value);
        } else {
            self.push(CheckpointAddress({_key: key, _value: value}));
            return (address(0), value);
        }
    }

    /**
     * @dev Return the index of the last (most recent) checkpoint with key lower or equal than the search key, or `high`
     * if there is none. `low` and `high` define a section where to do the search, with inclusive `low` and exclusive
     * `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _upperBinaryLookup(
        CheckpointAddress[] storage self,
        uint48 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key > key) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    /**
     * @dev Return the index of the first (oldest) checkpoint with key is greater or equal than the search key, or
     * `high` if there is none. `low` and `high` define a section where to do the search, with inclusive `low` and
     * exclusive `high`.
     *
     * WARNING: `high` should not be greater than the array's length.
     */
    function _lowerBinaryLookup(
        CheckpointAddress[] storage self,
        uint48 key,
        uint256 low,
        uint256 high
    ) private view returns (uint256) {
        while (low < high) {
            uint256 mid = Math.average(low, high);
            if (_unsafeAccess(self, mid)._key < key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return high;
    }

    /**
     * @dev Access an element of the array without performing bounds check. The position is assumed to be within bounds.
     */
    function _unsafeAccess(
        CheckpointAddress[] storage self,
        uint256 pos
    ) private pure returns (CheckpointAddress storage result) {
        assembly {
            mstore(0, self.slot)
            result.slot := add(keccak256(0, 0x20), pos)
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

/// @title SafeCast Library
/// @author velodrome.finance
/// @notice Safely convert unsigned and signed integers without overflow / underflow
library SafeCastLibrary {
    error SafeCastOverflow();
    error SafeCastUnderflow();

    /// @dev Safely convert uint256 to int128
    function toInt128(uint256 value) internal pure returns (int128) {
        if (value > uint128(type(int128).max)) revert SafeCastOverflow();
        return int128(uint128(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 SafeCastOverflow();
        return uint48(value);
    }

    /// @dev Safely convert int128 to uint256
    function toUint256(int128 value) internal pure returns (uint256) {
        if (value < 0) revert SafeCastUnderflow();
        return uint256(int256(value));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

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

/**
 * @notice Adapted from OpenZeppelin's Time library: v5.0.0 for solc 0.8.13
 * @dev This library provides helpers for manipulating time-related objects.
 *
 * It uses the following types:
 * - `uint48` for timepoints
 * - `uint32` for durations
 *
 * While the library doesn't provide specific types for timepoints and duration, it does provide:
 * - a `Delay` type to represent duration that can be programmed to change value automatically at a given point
 * - additional helper functions
 */
library Time {
    using Time for *;

    /**
     * @dev Get the block timestamp as a Timepoint.
     */
    function timestamp() internal view returns (uint48) {
        return SafeCastLibrary.toUint48(block.timestamp);
    }

    /**
     * @dev Get the block number as a Timepoint.
     */
    function blockNumber() internal view returns (uint48) {
        return SafeCastLibrary.toUint48(block.number);
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 1000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {}
}

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[{"inputs":[],"name":"CheckpointUnorderedInsertions","type":"error"},{"inputs":[],"name":"SafeCastOverflow","type":"error"},{"inputs":[],"name":"SafeCastUnderflow","type":"error"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"address","name":"delegatee","type":"address"},{"indexed":false,"internalType":"uint48","name":"timestamp","type":"uint48"},{"indexed":false,"internalType":"int128","name":"slope","type":"int128"},{"indexed":false,"internalType":"int128","name":"bias","type":"int128"},{"indexed":false,"internalType":"int128","name":"permanent","type":"int128"}],"name":"CheckpointDelegate","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint256","name":"escrowId","type":"uint256"},{"indexed":false,"internalType":"uint48","name":"timestamp","type":"uint48"},{"indexed":false,"internalType":"int128","name":"slope","type":"int128"},{"indexed":false,"internalType":"int128","name":"bias","type":"int128"},{"indexed":false,"internalType":"int128","name":"permanent","type":"int128"}],"name":"CheckpointEscrow","type":"event"},{"anonymous":false,"inputs":[{"indexed":false,"internalType":"uint48","name":"timestamp","type":"uint48"},{"indexed":false,"internalType":"int128","name":"slope","type":"int128"},{"indexed":false,"internalType":"int128","name":"bias","type":"int128"},{"indexed":false,"internalType":"int128","name":"permanent","type":"int128"}],"name":"CheckpointGlobal","type":"event"},{"inputs":[],"name":"CLOCK_UNIT","outputs":[{"internalType":"uint48","name":"","type":"uint48"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"MAX_TIME","outputs":[{"internalType":"int128","name":"","type":"int128"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"clock","outputs":[{"internalType":"uint48","name":"","type":"uint48"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"globalClock","outputs":[{"internalType":"uint48","name":"","type":"uint48"}],"stateMutability":"view","type":"function"}]

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