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// SPDX-License-Identifier: BUSL-1.1
pragma solidity >=0.8.22;

import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { SafeERC20 } from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import { ERC721 } from "@openzeppelin/contracts/token/ERC721/ERC721.sol";

import { SablierLockupBase } from "./abstracts/SablierLockupBase.sol";
import { ILockupNFTDescriptor } from "./interfaces/ILockupNFTDescriptor.sol";
import { ISablierLockup } from "./interfaces/ISablierLockup.sol";
import { Errors } from "./libraries/Errors.sol";
import { Helpers } from "./libraries/Helpers.sol";
import { VestingMath } from "./libraries/VestingMath.sol";
import { Lockup, LockupDynamic, LockupLinear, LockupTranched } from "./types/DataTypes.sol";

/*

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██╔════╝██╔══██╗██╔══██╗██║     ██║██╔════╝██╔══██╗    ██║     ██╔═══██╗██╔════╝██║ ██╔╝██║   ██║██╔══██╗
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███████║██║  ██║██████╔╝███████╗██║███████╗██║  ██║    ███████╗╚██████╔╝╚██████╗██║  ██╗╚██████╔╝██║
╚══════╝╚═╝  ╚═╝╚═════╝ ╚══════╝╚═╝╚══════╝╚═╝  ╚═╝    ╚══════╝ ╚═════╝  ╚═════╝╚═╝  ╚═╝ ╚═════╝ ╚═╝

*/

/// @title SablierLockup
/// @notice See the documentation in {ISablierLockup}.
contract SablierLockup is ISablierLockup, SablierLockupBase {
    using SafeERC20 for IERC20;

    /*//////////////////////////////////////////////////////////////////////////
                                  STATE VARIABLES
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockup
    uint256 public immutable override MAX_COUNT;

    /// @dev Cliff timestamp mapped by stream IDs. This is used in Lockup Linear models.
    mapping(uint256 streamId => uint40 cliffTime) internal _cliffs;

    /// @dev Stream segments mapped by stream IDs. This is used in Lockup Dynamic models.
    mapping(uint256 streamId => LockupDynamic.Segment[] segments) internal _segments;

    /// @dev Stream tranches mapped by stream IDs. This is used in Lockup Tranched models.
    mapping(uint256 streamId => LockupTranched.Tranche[] tranches) internal _tranches;

    /// @dev Unlock amounts mapped by stream IDs. This is used in Lockup Linear models.
    mapping(uint256 streamId => LockupLinear.UnlockAmounts unlockAmounts) internal _unlockAmounts;

    /*//////////////////////////////////////////////////////////////////////////
                                     CONSTRUCTOR
    //////////////////////////////////////////////////////////////////////////*/

    /// @param initialAdmin The address of the initial contract admin.
    /// @param initialNFTDescriptor The address of the NFT descriptor contract.
    /// @param maxCount The maximum number of segments and tranched allowed in Lockup Dynamic and Lockup Tranched
    /// models, respectively.
    constructor(
        address initialAdmin,
        ILockupNFTDescriptor initialNFTDescriptor,
        uint256 maxCount
    )
        ERC721("Sablier Lockup NFT", "SAB-LOCKUP")
        SablierLockupBase(initialAdmin, initialNFTDescriptor)
    {
        MAX_COUNT = maxCount;
        nextStreamId = 1;
    }

    /*//////////////////////////////////////////////////////////////////////////
                           USER-FACING CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockup
    function getCliffTime(uint256 streamId) external view override notNull(streamId) returns (uint40 cliffTime) {
        if (_streams[streamId].lockupModel != Lockup.Model.LOCKUP_LINEAR) {
            revert Errors.SablierLockup_NotExpectedModel(_streams[streamId].lockupModel, Lockup.Model.LOCKUP_LINEAR);
        }

        cliffTime = _cliffs[streamId];
    }

    /// @inheritdoc ISablierLockup
    function getSegments(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (LockupDynamic.Segment[] memory segments)
    {
        if (_streams[streamId].lockupModel != Lockup.Model.LOCKUP_DYNAMIC) {
            revert Errors.SablierLockup_NotExpectedModel(_streams[streamId].lockupModel, Lockup.Model.LOCKUP_DYNAMIC);
        }

        segments = _segments[streamId];
    }

    /// @inheritdoc ISablierLockup
    function getTranches(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (LockupTranched.Tranche[] memory tranches)
    {
        if (_streams[streamId].lockupModel != Lockup.Model.LOCKUP_TRANCHED) {
            revert Errors.SablierLockup_NotExpectedModel(_streams[streamId].lockupModel, Lockup.Model.LOCKUP_TRANCHED);
        }

        tranches = _tranches[streamId];
    }

    /// @inheritdoc ISablierLockup
    function getUnlockAmounts(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (LockupLinear.UnlockAmounts memory unlockAmounts)
    {
        if (_streams[streamId].lockupModel != Lockup.Model.LOCKUP_LINEAR) {
            revert Errors.SablierLockup_NotExpectedModel(_streams[streamId].lockupModel, Lockup.Model.LOCKUP_LINEAR);
        }

        unlockAmounts = _unlockAmounts[streamId];
    }

    /*//////////////////////////////////////////////////////////////////////////
                         USER-FACING NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockup
    function createWithDurationsLD(
        Lockup.CreateWithDurations calldata params,
        LockupDynamic.SegmentWithDuration[] calldata segmentsWithDuration
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Use the block timestamp as the start time.
        uint40 startTime = uint40(block.timestamp);

        // Generate the canonical segments.
        LockupDynamic.Segment[] memory segments = Helpers.calculateSegmentTimestamps(segmentsWithDuration, startTime);

        // Declare the timestamps for the stream.
        Lockup.Timestamps memory timestamps =
            Lockup.Timestamps({ start: startTime, end: segments[segments.length - 1].timestamp });

        // Checks, Effects and Interactions: create the stream.
        streamId = _createLD(
            Lockup.CreateWithTimestamps({
                sender: params.sender,
                recipient: params.recipient,
                totalAmount: params.totalAmount,
                token: params.token,
                cancelable: params.cancelable,
                transferable: params.transferable,
                timestamps: timestamps,
                shape: params.shape,
                broker: params.broker
            }),
            segments
        );
    }

    /// @inheritdoc ISablierLockup
    function createWithDurationsLL(
        Lockup.CreateWithDurations calldata params,
        LockupLinear.UnlockAmounts calldata unlockAmounts,
        LockupLinear.Durations calldata durations
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Set the current block timestamp as the stream's start time.
        Lockup.Timestamps memory timestamps = Lockup.Timestamps({ start: uint40(block.timestamp), end: 0 });

        uint40 cliffTime;

        // Calculate the cliff time and the end time.
        if (durations.cliff > 0) {
            cliffTime = timestamps.start + durations.cliff;
        }
        timestamps.end = timestamps.start + durations.total;

        // Checks, Effects and Interactions: create the stream.
        streamId = _createLL(
            Lockup.CreateWithTimestamps({
                sender: params.sender,
                recipient: params.recipient,
                totalAmount: params.totalAmount,
                token: params.token,
                cancelable: params.cancelable,
                transferable: params.transferable,
                timestamps: timestamps,
                shape: params.shape,
                broker: params.broker
            }),
            unlockAmounts,
            cliffTime
        );
    }

    /// @inheritdoc ISablierLockup
    function createWithDurationsLT(
        Lockup.CreateWithDurations calldata params,
        LockupTranched.TrancheWithDuration[] calldata tranchesWithDuration
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Use the block timestamp as the start time.
        uint40 startTime = uint40(block.timestamp);

        // Generate the canonical tranches.
        LockupTranched.Tranche[] memory tranches = Helpers.calculateTrancheTimestamps(tranchesWithDuration, startTime);

        // Declare the timestamps for the stream.
        Lockup.Timestamps memory timestamps =
            Lockup.Timestamps({ start: startTime, end: tranches[tranches.length - 1].timestamp });

        // Checks, Effects and Interactions: create the stream.
        streamId = _createLT(
            Lockup.CreateWithTimestamps({
                sender: params.sender,
                recipient: params.recipient,
                totalAmount: params.totalAmount,
                token: params.token,
                cancelable: params.cancelable,
                transferable: params.transferable,
                timestamps: timestamps,
                shape: params.shape,
                broker: params.broker
            }),
            tranches
        );
    }

    /// @inheritdoc ISablierLockup
    function createWithTimestampsLD(
        Lockup.CreateWithTimestamps calldata params,
        LockupDynamic.Segment[] calldata segments
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Checks, Effects and Interactions: create the stream.
        streamId = _createLD(params, segments);
    }

    /// @inheritdoc ISablierLockup
    function createWithTimestampsLL(
        Lockup.CreateWithTimestamps calldata params,
        LockupLinear.UnlockAmounts calldata unlockAmounts,
        uint40 cliffTime
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Checks, Effects and Interactions: create the stream.
        streamId = _createLL(params, unlockAmounts, cliffTime);
    }

    /// @inheritdoc ISablierLockup
    function createWithTimestampsLT(
        Lockup.CreateWithTimestamps calldata params,
        LockupTranched.Tranche[] calldata tranches
    )
        external
        payable
        override
        noDelegateCall
        returns (uint256 streamId)
    {
        // Checks, Effects and Interactions: create the stream.
        streamId = _createLT(params, tranches);
    }

    /*//////////////////////////////////////////////////////////////////////////
                           INTERNAL CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc SablierLockupBase
    function _calculateStreamedAmount(uint256 streamId) internal view override returns (uint128) {
        // Load in memory the parameters used in {VestingMath}.
        uint40 blockTimestamp = uint40(block.timestamp);
        uint128 depositedAmount = _streams[streamId].amounts.deposited;
        Lockup.Model lockupModel = _streams[streamId].lockupModel;
        uint128 streamedAmount;
        Lockup.Timestamps memory timestamps =
            Lockup.Timestamps({ start: _streams[streamId].startTime, end: _streams[streamId].endTime });

        // Calculate the streamed amount for the Lockup Dynamic model.
        if (lockupModel == Lockup.Model.LOCKUP_DYNAMIC) {
            streamedAmount = VestingMath.calculateLockupDynamicStreamedAmount({
                depositedAmount: depositedAmount,
                segments: _segments[streamId],
                blockTimestamp: blockTimestamp,
                timestamps: timestamps,
                withdrawnAmount: _streams[streamId].amounts.withdrawn
            });
        }
        // Calculate the streamed amount for the Lockup Linear model.
        else if (lockupModel == Lockup.Model.LOCKUP_LINEAR) {
            streamedAmount = VestingMath.calculateLockupLinearStreamedAmount({
                depositedAmount: depositedAmount,
                blockTimestamp: blockTimestamp,
                timestamps: timestamps,
                cliffTime: _cliffs[streamId],
                unlockAmounts: _unlockAmounts[streamId],
                withdrawnAmount: _streams[streamId].amounts.withdrawn
            });
        }
        // Calculate the streamed amount for the Lockup Tranched model.
        else if (lockupModel == Lockup.Model.LOCKUP_TRANCHED) {
            streamedAmount = VestingMath.calculateLockupTranchedStreamedAmount({
                depositedAmount: depositedAmount,
                blockTimestamp: blockTimestamp,
                timestamps: timestamps,
                tranches: _tranches[streamId]
            });
        }

        return streamedAmount;
    }

    /*//////////////////////////////////////////////////////////////////////////
                           INTERNAL NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev Common logic for creating a stream.
    /// @return The common parameters emitted in the create event between all Lockup models.
    function _create(
        uint256 streamId,
        Lockup.CreateWithTimestamps memory params,
        Lockup.CreateAmounts memory createAmounts,
        Lockup.Model lockupModel
    )
        internal
        returns (Lockup.CreateEventCommon memory)
    {
        // Effect: create the stream.
        _streams[streamId] = Lockup.Stream({
            sender: params.sender,
            startTime: params.timestamps.start,
            endTime: params.timestamps.end,
            isCancelable: params.cancelable,
            wasCanceled: false,
            token: params.token,
            isDepleted: false,
            isStream: true,
            isTransferable: params.transferable,
            lockupModel: lockupModel,
            amounts: Lockup.Amounts({ deposited: createAmounts.deposit, withdrawn: 0, refunded: 0 })
        });

        // Effect: mint the NFT to the recipient.
        _mint({ to: params.recipient, tokenId: streamId });

        unchecked {
            // Effect: bump the next stream ID.
            nextStreamId = streamId + 1;
        }

        // Interaction: transfer the deposit amount.
        params.token.safeTransferFrom({ from: msg.sender, to: address(this), value: createAmounts.deposit });

        // Interaction: pay the broker fee, if not zero.
        if (createAmounts.brokerFee > 0) {
            params.token.safeTransferFrom({ from: msg.sender, to: params.broker.account, value: createAmounts.brokerFee });
        }

        return Lockup.CreateEventCommon({
            funder: msg.sender,
            sender: params.sender,
            recipient: params.recipient,
            amounts: createAmounts,
            token: params.token,
            cancelable: params.cancelable,
            transferable: params.transferable,
            timestamps: params.timestamps,
            shape: params.shape,
            broker: params.broker.account
        });
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _createLD(
        Lockup.CreateWithTimestamps memory params,
        LockupDynamic.Segment[] memory segments
    )
        internal
        returns (uint256 streamId)
    {
        // Check: validate the user-provided parameters and segments.
        Lockup.CreateAmounts memory createAmounts = Helpers.checkCreateLockupDynamic({
            sender: params.sender,
            timestamps: params.timestamps,
            totalAmount: params.totalAmount,
            segments: segments,
            maxCount: MAX_COUNT,
            brokerFee: params.broker.fee,
            shape: params.shape,
            maxBrokerFee: MAX_BROKER_FEE
        });

        // Load the stream ID in a variable.
        streamId = nextStreamId;

        // Effect: store the segments. Since Solidity lacks a syntax for copying arrays of structs directly from
        // memory to storage, a manual approach is necessary. See https://github.com/ethereum/solidity/issues/12783.
        uint256 segmentCount = segments.length;
        for (uint256 i = 0; i < segmentCount; ++i) {
            _segments[streamId].push(segments[i]);
        }

        // Effect: create the stream,  mint the NFT and transfer the deposit amount.
        Lockup.CreateEventCommon memory commonParams = _create({
            streamId: streamId,
            params: params,
            createAmounts: createAmounts,
            lockupModel: Lockup.Model.LOCKUP_DYNAMIC
        });

        // Log the newly created stream.
        emit ISablierLockup.CreateLockupDynamicStream({
            streamId: streamId,
            commonParams: commonParams,
            segments: segments
        });
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _createLL(
        Lockup.CreateWithTimestamps memory params,
        LockupLinear.UnlockAmounts memory unlockAmounts,
        uint40 cliffTime
    )
        internal
        returns (uint256 streamId)
    {
        // Check: validate the user-provided parameters and cliff time.
        Lockup.CreateAmounts memory createAmounts = Helpers.checkCreateLockupLinear({
            sender: params.sender,
            timestamps: params.timestamps,
            cliffTime: cliffTime,
            totalAmount: params.totalAmount,
            unlockAmounts: unlockAmounts,
            brokerFee: params.broker.fee,
            shape: params.shape,
            maxBrokerFee: MAX_BROKER_FEE
        });

        // Load the stream ID in a variable.
        streamId = nextStreamId;

        // Effect: set the start unlock amount if it is non-zero.
        if (unlockAmounts.start > 0) {
            _unlockAmounts[streamId].start = unlockAmounts.start;
        }

        // Effect: update cliff time if it is non-zero.
        if (cliffTime > 0) {
            _cliffs[streamId] = cliffTime;

            // Effect: set the cliff unlock amount if it is non-zero.
            if (unlockAmounts.cliff > 0) {
                _unlockAmounts[streamId].cliff = unlockAmounts.cliff;
            }
        }

        // Effect: create the stream,  mint the NFT and transfer the deposit amount.
        Lockup.CreateEventCommon memory commonParams = _create({
            streamId: streamId,
            params: params,
            createAmounts: createAmounts,
            lockupModel: Lockup.Model.LOCKUP_LINEAR
        });

        // Log the newly created stream.
        emit ISablierLockup.CreateLockupLinearStream({
            streamId: streamId,
            commonParams: commonParams,
            cliffTime: cliffTime,
            unlockAmounts: unlockAmounts
        });
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _createLT(
        Lockup.CreateWithTimestamps memory params,
        LockupTranched.Tranche[] memory tranches
    )
        internal
        returns (uint256 streamId)
    {
        // Check: validate the user-provided parameters and tranches.
        Lockup.CreateAmounts memory createAmounts = Helpers.checkCreateLockupTranched({
            sender: params.sender,
            timestamps: params.timestamps,
            totalAmount: params.totalAmount,
            tranches: tranches,
            maxCount: MAX_COUNT,
            brokerFee: params.broker.fee,
            shape: params.shape,
            maxBrokerFee: MAX_BROKER_FEE
        });

        // Load the stream ID in a variable.
        streamId = nextStreamId;

        // Effect: store the tranches. Since Solidity lacks a syntax for copying arrays of structs directly from
        // memory to storage, a manual approach is necessary. See https://github.com/ethereum/solidity/issues/12783.
        uint256 trancheCount = tranches.length;
        for (uint256 i = 0; i < trancheCount; ++i) {
            _tranches[streamId].push(tranches[i]);
        }

        // Effect: create the stream,  mint the NFT and transfer the deposit amount.
        Lockup.CreateEventCommon memory commonParams = _create({
            streamId: streamId,
            params: params,
            createAmounts: createAmounts,
            lockupModel: Lockup.Model.LOCKUP_TRANCHED
        });

        // Log the newly created stream.
        emit ISablierLockup.CreateLockupTranchedStream({
            streamId: streamId,
            commonParams: commonParams,
            tranches: tranches
        });
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

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

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

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

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 value) external returns (bool);

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";
import {IERC20Permit} from "../extensions/IERC20Permit.sol";
import {Address} from "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    /**
     * @dev An operation with an ERC20 token failed.
     */
    error SafeERC20FailedOperation(address token);

    /**
     * @dev Indicates a failed `decreaseAllowance` request.
     */
    error SafeERC20FailedDecreaseAllowance(address spender, uint256 currentAllowance, uint256 requestedDecrease);

    /**
     * @dev Transfer `value` amount of `token` from the calling contract to `to`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transfer, (to, value)));
    }

    /**
     * @dev Transfer `value` amount of `token` from `from` to `to`, spending the approval given by `from` to the
     * calling contract. If `token` returns no value, non-reverting calls are assumed to be successful.
     */
    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeCall(token.transferFrom, (from, to, value)));
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        forceApprove(token, spender, oldAllowance + value);
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `requestedDecrease`. If `token` returns no
     * value, non-reverting calls are assumed to be successful.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 requestedDecrease) internal {
        unchecked {
            uint256 currentAllowance = token.allowance(address(this), spender);
            if (currentAllowance < requestedDecrease) {
                revert SafeERC20FailedDecreaseAllowance(spender, currentAllowance, requestedDecrease);
            }
            forceApprove(token, spender, currentAllowance - requestedDecrease);
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Meant to be used with tokens that require the approval
     * to be set to zero before setting it to a non-zero value, such as USDT.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        bytes memory approvalCall = abi.encodeCall(token.approve, (spender, value));

        if (!_callOptionalReturnBool(token, approvalCall)) {
            _callOptionalReturn(token, abi.encodeCall(token.approve, (spender, 0)));
            _callOptionalReturn(token, approvalCall);
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data);
        if (returndata.length != 0 && !abi.decode(returndata, (bool))) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturn} that silents catches all reverts and returns a bool instead.
     */
    function _callOptionalReturnBool(IERC20 token, bytes memory data) private returns (bool) {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We cannot use {Address-functionCall} here since this should return false
        // and not revert is the subcall reverts.

        (bool success, bytes memory returndata) = address(token).call(data);
        return success && (returndata.length == 0 || abi.decode(returndata, (bool))) && address(token).code.length > 0;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/ERC721.sol)

pragma solidity ^0.8.20;

import {IERC721} from "./IERC721.sol";
import {IERC721Receiver} from "./IERC721Receiver.sol";
import {IERC721Metadata} from "./extensions/IERC721Metadata.sol";
import {Context} from "../../utils/Context.sol";
import {Strings} from "../../utils/Strings.sol";
import {IERC165, ERC165} from "../../utils/introspection/ERC165.sol";
import {IERC721Errors} from "../../interfaces/draft-IERC6093.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata extension, but not including the Enumerable extension, which is available separately as
 * {ERC721Enumerable}.
 */
abstract contract ERC721 is Context, ERC165, IERC721, IERC721Metadata, IERC721Errors {
    using Strings for uint256;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    mapping(uint256 tokenId => address) private _owners;

    mapping(address owner => uint256) private _balances;

    mapping(uint256 tokenId => address) private _tokenApprovals;

    mapping(address owner => mapping(address operator => bool)) private _operatorApprovals;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC721).interfaceId ||
            interfaceId == type(IERC721Metadata).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view virtual returns (uint256) {
        if (owner == address(0)) {
            revert ERC721InvalidOwner(address(0));
        }
        return _balances[owner];
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view virtual returns (address) {
        return _requireOwned(tokenId);
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual returns (string memory) {
        _requireOwned(tokenId);

        string memory baseURI = _baseURI();
        return bytes(baseURI).length > 0 ? string.concat(baseURI, tokenId.toString()) : "";
    }

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overridden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return "";
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual {
        _approve(to, tokenId, _msgSender());
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId) public view virtual returns (address) {
        _requireOwned(tokenId);

        return _getApproved(tokenId);
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator) public view virtual returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(address from, address to, uint256 tokenId) public virtual {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        // Setting an "auth" arguments enables the `_isAuthorized` check which verifies that the token exists
        // (from != 0). Therefore, it is not needed to verify that the return value is not 0 here.
        address previousOwner = _update(to, tokenId, _msgSender());
        if (previousOwner != from) {
            revert ERC721IncorrectOwner(from, tokenId, previousOwner);
        }
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId) public {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory data) public virtual {
        transferFrom(from, to, tokenId);
        _checkOnERC721Received(from, to, tokenId, data);
    }

    /**
     * @dev Returns the owner of the `tokenId`. Does NOT revert if token doesn't exist
     *
     * IMPORTANT: Any overrides to this function that add ownership of tokens not tracked by the
     * core ERC721 logic MUST be matched with the use of {_increaseBalance} to keep balances
     * consistent with ownership. The invariant to preserve is that for any address `a` the value returned by
     * `balanceOf(a)` must be equal to the number of tokens such that `_ownerOf(tokenId)` is `a`.
     */
    function _ownerOf(uint256 tokenId) internal view virtual returns (address) {
        return _owners[tokenId];
    }

    /**
     * @dev Returns the approved address for `tokenId`. Returns 0 if `tokenId` is not minted.
     */
    function _getApproved(uint256 tokenId) internal view virtual returns (address) {
        return _tokenApprovals[tokenId];
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `owner`'s tokens, or `tokenId` in
     * particular (ignoring whether it is owned by `owner`).
     *
     * WARNING: This function assumes that `owner` is the actual owner of `tokenId` and does not verify this
     * assumption.
     */
    function _isAuthorized(address owner, address spender, uint256 tokenId) internal view virtual returns (bool) {
        return
            spender != address(0) &&
            (owner == spender || isApprovedForAll(owner, spender) || _getApproved(tokenId) == spender);
    }

    /**
     * @dev Checks if `spender` can operate on `tokenId`, assuming the provided `owner` is the actual owner.
     * Reverts if `spender` does not have approval from the provided `owner` for the given token or for all its assets
     * the `spender` for the specific `tokenId`.
     *
     * WARNING: This function assumes that `owner` is the actual owner of `tokenId` and does not verify this
     * assumption.
     */
    function _checkAuthorized(address owner, address spender, uint256 tokenId) internal view virtual {
        if (!_isAuthorized(owner, spender, tokenId)) {
            if (owner == address(0)) {
                revert ERC721NonexistentToken(tokenId);
            } else {
                revert ERC721InsufficientApproval(spender, tokenId);
            }
        }
    }

    /**
     * @dev Unsafe write access to the balances, used by extensions that "mint" tokens using an {ownerOf} override.
     *
     * NOTE: the value is limited to type(uint128).max. This protect against _balance overflow. It is unrealistic that
     * a uint256 would ever overflow from increments when these increments are bounded to uint128 values.
     *
     * WARNING: Increasing an account's balance using this function tends to be paired with an override of the
     * {_ownerOf} function to resolve the ownership of the corresponding tokens so that balances and ownership
     * remain consistent with one another.
     */
    function _increaseBalance(address account, uint128 value) internal virtual {
        unchecked {
            _balances[account] += value;
        }
    }

    /**
     * @dev Transfers `tokenId` from its current owner to `to`, or alternatively mints (or burns) if the current owner
     * (or `to`) is the zero address. Returns the owner of the `tokenId` before the update.
     *
     * The `auth` argument is optional. If the value passed is non 0, then this function will check that
     * `auth` is either the owner of the token, or approved to operate on the token (by the owner).
     *
     * Emits a {Transfer} event.
     *
     * NOTE: If overriding this function in a way that tracks balances, see also {_increaseBalance}.
     */
    function _update(address to, uint256 tokenId, address auth) internal virtual returns (address) {
        address from = _ownerOf(tokenId);

        // Perform (optional) operator check
        if (auth != address(0)) {
            _checkAuthorized(from, auth, tokenId);
        }

        // Execute the update
        if (from != address(0)) {
            // Clear approval. No need to re-authorize or emit the Approval event
            _approve(address(0), tokenId, address(0), false);

            unchecked {
                _balances[from] -= 1;
            }
        }

        if (to != address(0)) {
            unchecked {
                _balances[to] += 1;
            }
        }

        _owners[tokenId] = to;

        emit Transfer(from, to, tokenId);

        return from;
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        address previousOwner = _update(to, tokenId, address(0));
        if (previousOwner != address(0)) {
            revert ERC721InvalidSender(address(0));
        }
    }

    /**
     * @dev Mints `tokenId`, transfers it to `to` and checks for `to` acceptance.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(address to, uint256 tokenId, bytes memory data) internal virtual {
        _mint(to, tokenId);
        _checkOnERC721Received(address(0), to, tokenId, data);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     * This is an internal function that does not check if the sender is authorized to operate on the token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal {
        address previousOwner = _update(address(0), tokenId, address(0));
        if (previousOwner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        }
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(address from, address to, uint256 tokenId) internal {
        if (to == address(0)) {
            revert ERC721InvalidReceiver(address(0));
        }
        address previousOwner = _update(to, tokenId, address(0));
        if (previousOwner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        } else if (previousOwner != from) {
            revert ERC721IncorrectOwner(from, tokenId, previousOwner);
        }
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking that contract recipients
     * are aware of the ERC721 standard to prevent tokens from being forever locked.
     *
     * `data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is like {safeTransferFrom} in the sense that it invokes
     * {IERC721Receiver-onERC721Received} on the receiver, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `tokenId` token must exist and be owned by `from`.
     * - `to` cannot be the zero address.
     * - `from` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(address from, address to, uint256 tokenId) internal {
        _safeTransfer(from, to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeTransfer-address-address-uint256-}[`_safeTransfer`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeTransfer(address from, address to, uint256 tokenId, bytes memory data) internal virtual {
        _transfer(from, to, tokenId);
        _checkOnERC721Received(from, to, tokenId, data);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * The `auth` argument is optional. If the value passed is non 0, then this function will check that `auth` is
     * either the owner of the token, or approved to operate on all tokens held by this owner.
     *
     * Emits an {Approval} event.
     *
     * Overrides to this logic should be done to the variant with an additional `bool emitEvent` argument.
     */
    function _approve(address to, uint256 tokenId, address auth) internal {
        _approve(to, tokenId, auth, true);
    }

    /**
     * @dev Variant of `_approve` with an optional flag to enable or disable the {Approval} event. The event is not
     * emitted in the context of transfers.
     */
    function _approve(address to, uint256 tokenId, address auth, bool emitEvent) internal virtual {
        // Avoid reading the owner unless necessary
        if (emitEvent || auth != address(0)) {
            address owner = _requireOwned(tokenId);

            // We do not use _isAuthorized because single-token approvals should not be able to call approve
            if (auth != address(0) && owner != auth && !isApprovedForAll(owner, auth)) {
                revert ERC721InvalidApprover(auth);
            }

            if (emitEvent) {
                emit Approval(owner, to, tokenId);
            }
        }

        _tokenApprovals[tokenId] = to;
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Requirements:
     * - operator can't be the address zero.
     *
     * Emits an {ApprovalForAll} event.
     */
    function _setApprovalForAll(address owner, address operator, bool approved) internal virtual {
        if (operator == address(0)) {
            revert ERC721InvalidOperator(operator);
        }
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Reverts if the `tokenId` doesn't have a current owner (it hasn't been minted, or it has been burned).
     * Returns the owner.
     *
     * Overrides to ownership logic should be done to {_ownerOf}.
     */
    function _requireOwned(uint256 tokenId) internal view returns (address) {
        address owner = _ownerOf(tokenId);
        if (owner == address(0)) {
            revert ERC721NonexistentToken(tokenId);
        }
        return owner;
    }

    /**
     * @dev Private function to invoke {IERC721Receiver-onERC721Received} on a target address. This will revert if the
     * recipient doesn't accept the token transfer. The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param data bytes optional data to send along with the call
     */
    function _checkOnERC721Received(address from, address to, uint256 tokenId, bytes memory data) private {
        if (to.code.length > 0) {
            try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, data) returns (bytes4 retval) {
                if (retval != IERC721Receiver.onERC721Received.selector) {
                    revert ERC721InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert ERC721InvalidReceiver(to);
                } else {
                    /// @solidity memory-safe-assembly
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity >=0.8.22;

import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { SafeERC20 } from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import { ERC721 } from "@openzeppelin/contracts/token/ERC721/ERC721.sol";
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { IERC165 } from "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";

import { ILockupNFTDescriptor } from "./../interfaces/ILockupNFTDescriptor.sol";
import { ISablierLockupBase } from "./../interfaces/ISablierLockupBase.sol";
import { ISablierLockupRecipient } from "./../interfaces/ISablierLockupRecipient.sol";
import { Errors } from "./../libraries/Errors.sol";
import { Lockup } from "./../types/DataTypes.sol";
import { Adminable } from "./Adminable.sol";
import { Batch } from "./Batch.sol";
import { NoDelegateCall } from "./NoDelegateCall.sol";

/// @title SablierLockupBase
/// @notice See the documentation in {ISablierLockupBase}.
abstract contract SablierLockupBase is
    Batch, // 1 inherited components
    NoDelegateCall, // 0 inherited components
    Adminable, // 1 inherited components
    ISablierLockupBase, // 6 inherited components
    ERC721 // 6 inherited components
{
    using SafeERC20 for IERC20;

    /*//////////////////////////////////////////////////////////////////////////
                                  STATE VARIABLES
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockupBase
    UD60x18 public constant override MAX_BROKER_FEE = UD60x18.wrap(0.1e18);

    /// @inheritdoc ISablierLockupBase
    uint256 public override nextStreamId;

    /// @inheritdoc ISablierLockupBase
    ILockupNFTDescriptor public override nftDescriptor;

    /// @dev Mapping of contracts allowed to hook to Sablier when a stream is canceled or when tokens are withdrawn.
    mapping(address recipient => bool allowed) internal _allowedToHook;

    /// @dev Lockup streams mapped by unsigned integers.
    mapping(uint256 id => Lockup.Stream stream) internal _streams;

    /*//////////////////////////////////////////////////////////////////////////
                                     CONSTRUCTOR
    //////////////////////////////////////////////////////////////////////////*/

    /// @param initialAdmin The address of the initial contract admin.
    /// @param initialNFTDescriptor The address of the initial NFT descriptor.
    constructor(address initialAdmin, ILockupNFTDescriptor initialNFTDescriptor) Adminable(initialAdmin) {
        nftDescriptor = initialNFTDescriptor;
    }

    /*//////////////////////////////////////////////////////////////////////////
                                      MODIFIERS
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev Checks that `streamId` does not reference a null stream.
    modifier notNull(uint256 streamId) {
        if (!_streams[streamId].isStream) {
            revert Errors.SablierLockupBase_Null(streamId);
        }
        _;
    }

    /*//////////////////////////////////////////////////////////////////////////
                           USER-FACING CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockupBase
    function getDepositedAmount(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 depositedAmount)
    {
        depositedAmount = _streams[streamId].amounts.deposited;
    }

    /// @inheritdoc ISablierLockupBase
    function getEndTime(uint256 streamId) external view override notNull(streamId) returns (uint40 endTime) {
        endTime = _streams[streamId].endTime;
    }

    /// @inheritdoc ISablierLockupBase
    function getLockupModel(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (Lockup.Model lockupModel)
    {
        lockupModel = _streams[streamId].lockupModel;
    }

    /// @inheritdoc ISablierLockupBase
    function getRecipient(uint256 streamId) external view override returns (address recipient) {
        // Check the stream NFT exists and return the owner, which is the stream's recipient.
        recipient = _requireOwned({ tokenId: streamId });
    }

    /// @inheritdoc ISablierLockupBase
    function getRefundedAmount(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 refundedAmount)
    {
        refundedAmount = _streams[streamId].amounts.refunded;
    }

    /// @inheritdoc ISablierLockupBase
    function getSender(uint256 streamId) external view override notNull(streamId) returns (address sender) {
        sender = _streams[streamId].sender;
    }

    /// @inheritdoc ISablierLockupBase
    function getStartTime(uint256 streamId) external view override notNull(streamId) returns (uint40 startTime) {
        startTime = _streams[streamId].startTime;
    }

    /// @inheritdoc ISablierLockupBase
    function getUnderlyingToken(uint256 streamId) external view override notNull(streamId) returns (IERC20 token) {
        token = _streams[streamId].token;
    }

    /// @inheritdoc ISablierLockupBase
    function getWithdrawnAmount(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 withdrawnAmount)
    {
        withdrawnAmount = _streams[streamId].amounts.withdrawn;
    }

    /// @inheritdoc ISablierLockupBase
    function isAllowedToHook(address recipient) external view returns (bool result) {
        result = _allowedToHook[recipient];
    }

    /// @inheritdoc ISablierLockupBase
    function isCancelable(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        if (_statusOf(streamId) != Lockup.Status.SETTLED) {
            result = _streams[streamId].isCancelable;
        }
    }

    /// @inheritdoc ISablierLockupBase
    function isCold(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        Lockup.Status status = _statusOf(streamId);
        result = status == Lockup.Status.SETTLED || status == Lockup.Status.CANCELED || status == Lockup.Status.DEPLETED;
    }

    /// @inheritdoc ISablierLockupBase
    function isDepleted(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        result = _streams[streamId].isDepleted;
    }

    /// @inheritdoc ISablierLockupBase
    function isStream(uint256 streamId) external view override returns (bool result) {
        result = _streams[streamId].isStream;
    }

    /// @inheritdoc ISablierLockupBase
    function isTransferable(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        result = _streams[streamId].isTransferable;
    }

    /// @inheritdoc ISablierLockupBase
    function isWarm(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        Lockup.Status status = _statusOf(streamId);
        result = status == Lockup.Status.PENDING || status == Lockup.Status.STREAMING;
    }

    /// @inheritdoc ISablierLockupBase
    function refundableAmountOf(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 refundableAmount)
    {
        // These checks are needed because {_calculateStreamedAmount} does not look up the stream's status. Note that
        // checking for `isCancelable` also checks if the stream `wasCanceled` thanks to the protocol invariant that
        // canceled streams are not cancelable anymore.
        if (_streams[streamId].isCancelable && !_streams[streamId].isDepleted) {
            refundableAmount = _streams[streamId].amounts.deposited - _calculateStreamedAmount(streamId);
        }
        // Otherwise, the result is implicitly zero.
    }

    /// @inheritdoc ISablierLockupBase
    function statusOf(uint256 streamId) external view override notNull(streamId) returns (Lockup.Status status) {
        status = _statusOf(streamId);
    }

    /// @inheritdoc ISablierLockupBase
    function streamedAmountOf(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 streamedAmount)
    {
        streamedAmount = _streamedAmountOf(streamId);
    }

    /// @inheritdoc ERC721
    function supportsInterface(bytes4 interfaceId) public view override(IERC165, ERC721) returns (bool) {
        // 0x49064906 is the ERC-165 interface ID required by ERC-4906
        return interfaceId == 0x49064906 || super.supportsInterface(interfaceId);
    }

    /// @inheritdoc ERC721
    function tokenURI(uint256 streamId) public view override(IERC721Metadata, ERC721) returns (string memory uri) {
        // Check: the stream NFT exists.
        _requireOwned({ tokenId: streamId });

        // Generate the URI describing the stream NFT.
        uri = nftDescriptor.tokenURI({ sablier: this, streamId: streamId });
    }

    /// @inheritdoc ISablierLockupBase
    function wasCanceled(uint256 streamId) external view override notNull(streamId) returns (bool result) {
        result = _streams[streamId].wasCanceled;
    }

    /// @inheritdoc ISablierLockupBase
    function withdrawableAmountOf(uint256 streamId)
        external
        view
        override
        notNull(streamId)
        returns (uint128 withdrawableAmount)
    {
        withdrawableAmount = _withdrawableAmountOf(streamId);
    }

    /*//////////////////////////////////////////////////////////////////////////
                         USER-FACING NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc ISablierLockupBase
    function allowToHook(address recipient) external override onlyAdmin {
        // Check: non-zero code size.
        if (recipient.code.length == 0) {
            revert Errors.SablierLockupBase_AllowToHookZeroCodeSize(recipient);
        }

        // Check: recipients implements the ERC-165 interface ID required by {ISablierLockupRecipient}.
        bytes4 interfaceId = type(ISablierLockupRecipient).interfaceId;
        if (!ISablierLockupRecipient(recipient).supportsInterface(interfaceId)) {
            revert Errors.SablierLockupBase_AllowToHookUnsupportedInterface(recipient);
        }

        // Effect: put the recipient on the allowlist.
        _allowedToHook[recipient] = true;

        // Log the allowlist addition.
        emit ISablierLockupBase.AllowToHook({ admin: msg.sender, recipient: recipient });
    }

    /// @inheritdoc ISablierLockupBase
    function burn(uint256 streamId) external payable override noDelegateCall notNull(streamId) {
        // Check: only depleted streams can be burned.
        if (!_streams[streamId].isDepleted) {
            revert Errors.SablierLockupBase_StreamNotDepleted(streamId);
        }

        // Retrieve the current owner.
        address currentRecipient = _ownerOf(streamId);

        // Check:
        // 1. NFT exists (see {IERC721.getApproved}).
        // 2. `msg.sender` is either the owner of the NFT or an approved third party.
        if (!_isCallerStreamRecipientOrApproved(streamId, currentRecipient)) {
            revert Errors.SablierLockupBase_Unauthorized(streamId, msg.sender);
        }

        // Effect: burn the NFT.
        _burn({ tokenId: streamId });
    }

    /// @inheritdoc ISablierLockupBase
    function cancel(uint256 streamId) public payable override noDelegateCall notNull(streamId) {
        // Check: the stream is neither depleted nor canceled.
        if (_streams[streamId].isDepleted) {
            revert Errors.SablierLockupBase_StreamDepleted(streamId);
        } else if (_streams[streamId].wasCanceled) {
            revert Errors.SablierLockupBase_StreamCanceled(streamId);
        }

        // Check: `msg.sender` is the stream's sender.
        if (!_isCallerStreamSender(streamId)) {
            revert Errors.SablierLockupBase_Unauthorized(streamId, msg.sender);
        }

        // Checks, Effects and Interactions: cancel the stream.
        _cancel(streamId);
    }

    /// @inheritdoc ISablierLockupBase
    function cancelMultiple(uint256[] calldata streamIds) external payable override noDelegateCall {
        // Iterate over the provided array of stream IDs and cancel each stream.
        uint256 count = streamIds.length;
        for (uint256 i = 0; i < count; ++i) {
            // Effects and Interactions: cancel the stream.
            cancel(streamIds[i]);
        }
    }

    /// @inheritdoc ISablierLockupBase
    function collectFees() external override {
        uint256 feeAmount = address(this).balance;

        // Effect: transfer the fees to the admin.
        (bool success,) = admin.call{ value: feeAmount }("");

        // Revert if the call failed.
        if (!success) {
            revert Errors.SablierLockupBase_FeeTransferFail(admin, feeAmount);
        }

        // Log the fee withdrawal.
        emit ISablierLockupBase.CollectFees({ admin: admin, feeAmount: feeAmount });
    }

    /// @inheritdoc ISablierLockupBase
    function renounce(uint256 streamId) public payable override noDelegateCall notNull(streamId) {
        // Check: the stream is not cold.
        Lockup.Status status = _statusOf(streamId);
        if (status == Lockup.Status.DEPLETED) {
            revert Errors.SablierLockupBase_StreamDepleted(streamId);
        } else if (status == Lockup.Status.CANCELED) {
            revert Errors.SablierLockupBase_StreamCanceled(streamId);
        } else if (status == Lockup.Status.SETTLED) {
            revert Errors.SablierLockupBase_StreamSettled(streamId);
        }

        // Check: `msg.sender` is the stream's sender.
        if (!_isCallerStreamSender(streamId)) {
            revert Errors.SablierLockupBase_Unauthorized(streamId, msg.sender);
        }

        // Checks and Effects: renounce the stream.
        _renounce(streamId);

        // Log the renouncement.
        emit ISablierLockupBase.RenounceLockupStream(streamId);
    }

    /// @inheritdoc ISablierLockupBase
    function renounceMultiple(uint256[] calldata streamIds) external payable override noDelegateCall {
        // Iterate over the provided array of stream IDs and renounce each stream.
        uint256 count = streamIds.length;
        for (uint256 i = 0; i < count; ++i) {
            // Call the existing renounce function for each stream ID.
            renounce(streamIds[i]);
        }
    }

    /// @inheritdoc ISablierLockupBase
    function setNFTDescriptor(ILockupNFTDescriptor newNFTDescriptor) external override onlyAdmin {
        // Effect: set the NFT descriptor.
        ILockupNFTDescriptor oldNftDescriptor = nftDescriptor;
        nftDescriptor = newNFTDescriptor;

        // Log the change of the NFT descriptor.
        emit ISablierLockupBase.SetNFTDescriptor({
            admin: msg.sender,
            oldNFTDescriptor: oldNftDescriptor,
            newNFTDescriptor: newNFTDescriptor
        });

        // Refresh the NFT metadata for all streams.
        emit BatchMetadataUpdate({ _fromTokenId: 1, _toTokenId: nextStreamId - 1 });
    }

    /// @inheritdoc ISablierLockupBase
    function withdraw(
        uint256 streamId,
        address to,
        uint128 amount
    )
        public
        payable
        override
        noDelegateCall
        notNull(streamId)
    {
        // Check: the stream is not depleted.
        if (_streams[streamId].isDepleted) {
            revert Errors.SablierLockupBase_StreamDepleted(streamId);
        }

        // Check: the withdrawal address is not zero.
        if (to == address(0)) {
            revert Errors.SablierLockupBase_WithdrawToZeroAddress(streamId);
        }

        // Retrieve the recipient from storage.
        address recipient = _ownerOf(streamId);

        // Check: `msg.sender` is neither the stream's recipient nor an approved third party, the withdrawal address
        // must be the recipient.
        if (to != recipient && !_isCallerStreamRecipientOrApproved(streamId, recipient)) {
            revert Errors.SablierLockupBase_WithdrawalAddressNotRecipient(streamId, msg.sender, to);
        }

        // Check: the withdraw amount is not zero.
        if (amount == 0) {
            revert Errors.SablierLockupBase_WithdrawAmountZero(streamId);
        }

        // Check: the withdraw amount is not greater than the withdrawable amount.
        uint128 withdrawableAmount = _withdrawableAmountOf(streamId);
        if (amount > withdrawableAmount) {
            revert Errors.SablierLockupBase_Overdraw(streamId, amount, withdrawableAmount);
        }

        // Effects and Interactions: make the withdrawal.
        _withdraw(streamId, to, amount);

        // Emit an ERC-4906 event to trigger an update of the NFT metadata.
        emit MetadataUpdate({ _tokenId: streamId });

        // Interaction: if `msg.sender` is not the recipient and the recipient is on the allowlist, run the hook.
        if (msg.sender != recipient && _allowedToHook[recipient]) {
            bytes4 selector = ISablierLockupRecipient(recipient).onSablierLockupWithdraw({
                streamId: streamId,
                caller: msg.sender,
                to: to,
                amount: amount
            });

            // Check: the recipient's hook returned the correct selector.
            if (selector != ISablierLockupRecipient.onSablierLockupWithdraw.selector) {
                revert Errors.SablierLockupBase_InvalidHookSelector(recipient);
            }
        }
    }

    /// @inheritdoc ISablierLockupBase
    function withdrawMax(uint256 streamId, address to) external payable override returns (uint128 withdrawnAmount) {
        withdrawnAmount = _withdrawableAmountOf(streamId);
        withdraw({ streamId: streamId, to: to, amount: withdrawnAmount });
    }

    /// @inheritdoc ISablierLockupBase
    function withdrawMaxAndTransfer(
        uint256 streamId,
        address newRecipient
    )
        external
        payable
        override
        noDelegateCall
        notNull(streamId)
        returns (uint128 withdrawnAmount)
    {
        // Retrieve the current owner. This also checks that the NFT was not burned.
        address currentRecipient = _ownerOf(streamId);

        // Check: `msg.sender` is neither the stream's recipient nor an approved third party.
        if (!_isCallerStreamRecipientOrApproved(streamId, currentRecipient)) {
            revert Errors.SablierLockupBase_Unauthorized(streamId, msg.sender);
        }

        // Skip the withdrawal if the withdrawable amount is zero.
        withdrawnAmount = _withdrawableAmountOf(streamId);
        if (withdrawnAmount > 0) {
            withdraw({ streamId: streamId, to: currentRecipient, amount: withdrawnAmount });
        }

        // Checks and Effects: transfer the NFT.
        _transfer({ from: currentRecipient, to: newRecipient, tokenId: streamId });
    }

    /// @inheritdoc ISablierLockupBase
    function withdrawMultiple(
        uint256[] calldata streamIds,
        uint128[] calldata amounts
    )
        external
        payable
        override
        noDelegateCall
    {
        // Check: there is an equal number of `streamIds` and `amounts`.
        uint256 streamIdsCount = streamIds.length;
        uint256 amountsCount = amounts.length;
        if (streamIdsCount != amountsCount) {
            revert Errors.SablierLockupBase_WithdrawArrayCountsNotEqual(streamIdsCount, amountsCount);
        }

        // Iterate over the provided array of stream IDs and withdraw from each stream to the recipient.
        for (uint256 i = 0; i < streamIdsCount; ++i) {
            // Checks, Effects and Interactions: withdraw using delegatecall.
            (bool success, bytes memory result) = address(this).delegatecall(
                abi.encodeCall(ISablierLockupBase.withdraw, (streamIds[i], _ownerOf(streamIds[i]), amounts[i]))
            );
            // If the withdrawal reverts, log it using an event, and continue with the next stream.
            if (!success) {
                emit InvalidWithdrawalInWithdrawMultiple(streamIds[i], result);
            }
        }
    }

    /*//////////////////////////////////////////////////////////////////////////
                             INTERNAL CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Calculates the streamed amount of the stream without looking up the stream's status.
    /// @dev This function is implemented by child contracts, so the logic varies depending on the model.
    function _calculateStreamedAmount(uint256 streamId) internal view virtual returns (uint128);

    /// @notice Checks whether `msg.sender` is the stream's recipient or an approved third party, when the
    /// `recipient` is known in advance.
    /// @param streamId The stream ID for the query.
    /// @param recipient The address of the stream's recipient.
    function _isCallerStreamRecipientOrApproved(uint256 streamId, address recipient) internal view returns (bool) {
        return msg.sender == recipient || isApprovedForAll({ owner: recipient, operator: msg.sender })
            || getApproved(streamId) == msg.sender;
    }

    /// @notice Checks whether `msg.sender` is the stream's sender.
    /// @param streamId The stream ID for the query.
    function _isCallerStreamSender(uint256 streamId) internal view returns (bool) {
        return msg.sender == _streams[streamId].sender;
    }

    /// @dev Retrieves the stream's status without performing a null check.
    function _statusOf(uint256 streamId) internal view returns (Lockup.Status) {
        if (_streams[streamId].isDepleted) {
            return Lockup.Status.DEPLETED;
        } else if (_streams[streamId].wasCanceled) {
            return Lockup.Status.CANCELED;
        }

        if (block.timestamp < _streams[streamId].startTime) {
            return Lockup.Status.PENDING;
        }

        if (_calculateStreamedAmount(streamId) < _streams[streamId].amounts.deposited) {
            return Lockup.Status.STREAMING;
        } else {
            return Lockup.Status.SETTLED;
        }
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _streamedAmountOf(uint256 streamId) internal view returns (uint128) {
        Lockup.Amounts memory amounts = _streams[streamId].amounts;

        if (_streams[streamId].isDepleted) {
            return amounts.withdrawn;
        } else if (_streams[streamId].wasCanceled) {
            return amounts.deposited - amounts.refunded;
        }

        return _calculateStreamedAmount(streamId);
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _withdrawableAmountOf(uint256 streamId) internal view returns (uint128) {
        return _streamedAmountOf(streamId) - _streams[streamId].amounts.withdrawn;
    }

    /*//////////////////////////////////////////////////////////////////////////
                           INTERNAL NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _cancel(uint256 streamId) internal {
        // Calculate the streamed amount.
        uint128 streamedAmount = _calculateStreamedAmount(streamId);

        // Retrieve the amounts from storage.
        Lockup.Amounts memory amounts = _streams[streamId].amounts;

        // Check: the stream is not settled.
        if (streamedAmount >= amounts.deposited) {
            revert Errors.SablierLockupBase_StreamSettled(streamId);
        }

        // Check: the stream is cancelable.
        if (!_streams[streamId].isCancelable) {
            revert Errors.SablierLockupBase_StreamNotCancelable(streamId);
        }

        // Calculate the sender's amount.
        uint128 senderAmount;
        unchecked {
            senderAmount = amounts.deposited - streamedAmount;
        }

        // Calculate the recipient's amount.
        uint128 recipientAmount = streamedAmount - amounts.withdrawn;

        // Effect: mark the stream as canceled.
        _streams[streamId].wasCanceled = true;

        // Effect: make the stream not cancelable anymore, because a stream can only be canceled once.
        _streams[streamId].isCancelable = false;

        // Effect: if there are no tokens left for the recipient to withdraw, mark the stream as depleted.
        if (recipientAmount == 0) {
            _streams[streamId].isDepleted = true;
        }

        // Effect: set the refunded amount.
        _streams[streamId].amounts.refunded = senderAmount;

        // Retrieve the sender and the recipient from storage.
        address sender = _streams[streamId].sender;
        address recipient = _ownerOf(streamId);

        // Retrieve the ERC-20 token from storage.
        IERC20 token = _streams[streamId].token;

        // Interaction: refund the sender.
        token.safeTransfer({ to: sender, value: senderAmount });

        // Log the cancellation.
        emit ISablierLockupBase.CancelLockupStream(streamId, sender, recipient, token, senderAmount, recipientAmount);

        // Emit an ERC-4906 event to trigger an update of the NFT metadata.
        emit MetadataUpdate({ _tokenId: streamId });

        // Interaction: if the recipient is on the allowlist, run the hook.
        if (_allowedToHook[recipient]) {
            bytes4 selector = ISablierLockupRecipient(recipient).onSablierLockupCancel({
                streamId: streamId,
                sender: sender,
                senderAmount: senderAmount,
                recipientAmount: recipientAmount
            });

            // Check: the recipient's hook returned the correct selector.
            if (selector != ISablierLockupRecipient.onSablierLockupCancel.selector) {
                revert Errors.SablierLockupBase_InvalidHookSelector(recipient);
            }
        }
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _renounce(uint256 streamId) internal {
        // Check: the stream is cancelable.
        if (!_streams[streamId].isCancelable) {
            revert Errors.SablierLockupBase_StreamNotCancelable(streamId);
        }

        // Effect: renounce the stream by making it not cancelable.
        _streams[streamId].isCancelable = false;
    }

    /// @notice Overrides the {ERC-721._update} function to check that the stream is transferable, and emits an
    /// ERC-4906 event.
    /// @dev There are two cases when the transferable flag is ignored:
    /// - If the current owner is 0, then the update is a mint and is allowed.
    /// - If `to` is 0, then the update is a burn and is also allowed.
    /// @param to The address of the new recipient of the stream.
    /// @param streamId ID of the stream to update.
    /// @param auth Optional parameter. If the value is not zero, the overridden implementation will check that
    /// `auth` is either the recipient of the stream, or an approved third party.
    /// @return The original recipient of the `streamId` before the update.
    function _update(address to, uint256 streamId, address auth) internal override returns (address) {
        address from = _ownerOf(streamId);

        if (from != address(0) && to != address(0) && !_streams[streamId].isTransferable) {
            revert Errors.SablierLockupBase_NotTransferable(streamId);
        }

        // Emit an ERC-4906 event to trigger an update of the NFT metadata.
        emit MetadataUpdate({ _tokenId: streamId });

        return super._update(to, streamId, auth);
    }

    /// @dev See the documentation for the user-facing functions that call this internal function.
    function _withdraw(uint256 streamId, address to, uint128 amount) internal {
        // Effect: update the withdrawn amount.
        _streams[streamId].amounts.withdrawn = _streams[streamId].amounts.withdrawn + amount;

        // Retrieve the amounts from storage.
        Lockup.Amounts memory amounts = _streams[streamId].amounts;

        // Using ">=" instead of "==" for additional safety reasons. In the event of an unforeseen increase in the
        // withdrawn amount, the stream will still be marked as depleted.
        if (amounts.withdrawn >= amounts.deposited - amounts.refunded) {
            // Effect: mark the stream as depleted.
            _streams[streamId].isDepleted = true;

            // Effect: make the stream not cancelable anymore, because a depleted stream cannot be canceled.
            _streams[streamId].isCancelable = false;
        }

        // Retrieve the ERC-20 token from storage.
        IERC20 token = _streams[streamId].token;

        // Interaction: perform the ERC-20 transfer.
        token.safeTransfer({ to: to, value: amount });

        // Log the withdrawal.
        emit ISablierLockupBase.WithdrawFromLockupStream(streamId, to, token, amount);
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";

/// @title ILockupNFTDescriptor
/// @notice This contract generates the URI describing the Sablier stream NFTs.
/// @dev Inspired by Uniswap V3 Positions NFTs.
interface ILockupNFTDescriptor {
    /// @notice Produces the URI describing a particular stream NFT.
    /// @dev This is a data URI with the JSON contents directly inlined.
    /// @param sablier The address of the Sablier contract the stream was created in.
    /// @param streamId The ID of the stream for which to produce a description.
    /// @return uri The URI of the ERC721-compliant metadata.
    function tokenURI(IERC721Metadata sablier, uint256 streamId) external view returns (string memory uri);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { Lockup, LockupDynamic, LockupLinear, LockupTranched } from "../types/DataTypes.sol";
import { ISablierLockupBase } from "./ISablierLockupBase.sol";

/// @title ISablierLockup
/// @notice Creates and manages Lockup streams with various distribution models.
interface ISablierLockup is ISablierLockupBase {
    /*//////////////////////////////////////////////////////////////////////////
                                       EVENTS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Emitted when a stream is created using Lockup dynamic model.
    /// @param streamId The ID of the newly created stream.
    /// @param commonParams Common parameters emitted in Create events across all Lockup models.
    /// @param segments The segments the protocol uses to compose the dynamic distribution function.
    event CreateLockupDynamicStream(
        uint256 indexed streamId, Lockup.CreateEventCommon commonParams, LockupDynamic.Segment[] segments
    );

    /// @notice Emitted when a stream is created using Lockup linear model.
    /// @param streamId The ID of the newly created stream.
    /// @param commonParams Common parameters emitted in Create events across all Lockup models.
    /// @param cliffTime The Unix timestamp for the cliff period's end. A value of zero means there is no cliff.
    /// @param unlockAmounts Struct encapsulating (i) the amount to unlock at the start time and (ii) the amount to
    /// unlock at the cliff time.
    event CreateLockupLinearStream(
        uint256 indexed streamId,
        Lockup.CreateEventCommon commonParams,
        uint40 cliffTime,
        LockupLinear.UnlockAmounts unlockAmounts
    );

    /// @notice Emitted when a stream is created using Lockup tranched model.
    /// @param streamId The ID of the newly created stream.
    /// @param commonParams Common parameters emitted in Create events across all Lockup models.
    /// @param tranches The tranches the protocol uses to compose the tranched distribution function.
    event CreateLockupTranchedStream(
        uint256 indexed streamId, Lockup.CreateEventCommon commonParams, LockupTranched.Tranche[] tranches
    );

    /*//////////////////////////////////////////////////////////////////////////
                                 CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice The maximum number of segments and tranches allowed in Dynamic and Tranched streams respectively.
    /// @dev This is initialized at construction time and cannot be changed later.
    function MAX_COUNT() external view returns (uint256);

    /// @notice Retrieves the stream's cliff time, which is a Unix timestamp.  A value of zero means there is no cliff.
    /// @dev Reverts if `streamId` references a null stream or a non Lockup Linear stream.
    /// @param streamId The stream ID for the query.
    function getCliffTime(uint256 streamId) external view returns (uint40 cliffTime);

    /// @notice Retrieves the segments used to compose the dynamic distribution function.
    /// @dev Reverts if `streamId` references a null stream or a non Lockup Dynamic stream.
    /// @param streamId The stream ID for the query.
    /// @return segments See the documentation in {DataTypes}.
    function getSegments(uint256 streamId) external view returns (LockupDynamic.Segment[] memory segments);

    /// @notice Retrieves the tranches used to compose the tranched distribution function.
    /// @dev Reverts if `streamId` references a null stream or a non Lockup Tranched stream.
    /// @param streamId The stream ID for the query.
    /// @return tranches See the documentation in {DataTypes}.
    function getTranches(uint256 streamId) external view returns (LockupTranched.Tranche[] memory tranches);

    /// @notice Retrieves the unlock amounts used to compose the linear distribution function.
    /// @dev Reverts if `streamId` references a null stream or a non Lockup Linear stream.
    /// @param streamId The stream ID for the query.
    /// @return unlockAmounts See the documentation in {DataTypes}.
    function getUnlockAmounts(uint256 streamId)
        external
        view
        returns (LockupLinear.UnlockAmounts memory unlockAmounts);

    /*//////////////////////////////////////////////////////////////////////////
                               NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Creates a stream by setting the start time to `block.timestamp`, and the end time to the sum of
    /// `block.timestamp` and all specified time durations. The segment timestamps are derived from these
    /// durations. The stream is funded by `msg.sender` and is wrapped in an ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupDynamicStream} and {MetadataUpdate} event.
    ///
    /// Requirements:
    /// - All requirements in {createWithTimestampsLD} must be met for the calculated parameters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param segmentsWithDuration Segments with durations used to compose the dynamic distribution function. Timestamps
    /// are calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.
    /// @return streamId The ID of the newly created stream.
    function createWithDurationsLD(
        Lockup.CreateWithDurations calldata params,
        LockupDynamic.SegmentWithDuration[] calldata segmentsWithDuration
    )
        external
        payable
        returns (uint256 streamId);

    /// @notice Creates a stream by setting the start time to `block.timestamp`, and the end time to
    /// the sum of `block.timestamp` and `durations.total`. The stream is funded by `msg.sender` and is wrapped in an
    /// ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupLinearStream} and {MetadataUpdate} event.
    ///
    /// Requirements:
    /// - All requirements in {createWithTimestampsLL} must be met for the calculated parameters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param durations Struct encapsulating (i) cliff period duration and (ii) total stream duration, both in seconds.
    /// @param unlockAmounts Struct encapsulating (i) the amount to unlock at the start time and (ii) the amount to
    /// unlock at the cliff time.
    /// @return streamId The ID of the newly created stream.
    function createWithDurationsLL(
        Lockup.CreateWithDurations calldata params,
        LockupLinear.UnlockAmounts calldata unlockAmounts,
        LockupLinear.Durations calldata durations
    )
        external
        payable
        returns (uint256 streamId);

    /// @notice Creates a stream by setting the start time to `block.timestamp`, and the end time to the sum of
    /// `block.timestamp` and all specified time durations. The tranche timestamps are derived from these
    /// durations. The stream is funded by `msg.sender` and is wrapped in an ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupTrancheStream} and {MetadataUpdate} event.
    ///
    /// Requirements:
    /// - All requirements in {createWithTimestampsLT} must be met for the calculated parameters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param tranchesWithDuration Tranches with durations used to compose the tranched distribution function.
    /// Timestamps are calculated by starting from `block.timestamp` and adding each duration to the previous timestamp.
    /// @return streamId The ID of the newly created stream.
    function createWithDurationsLT(
        Lockup.CreateWithDurations calldata params,
        LockupTranched.TrancheWithDuration[] calldata tranchesWithDuration
    )
        external
        payable
        returns (uint256 streamId);

    /// @notice Creates a stream with the provided segment timestamps, implying the end time from the last timestamp.
    /// The stream is funded by `msg.sender` and is wrapped in an ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupDynamicStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - As long as the segment timestamps are arranged in ascending order, it is not an error for some
    /// of them to be in the past.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `params.totalAmount` must be greater than zero.
    /// - If set, `params.broker.fee` must not be greater than `MAX_BROKER_FEE`.
    /// - `params.timestamps.start` must be greater than zero and less than the first segment's timestamp.
    /// - `segments` must have at least one segment, but not more than `MAX_COUNT`.
    /// - The segment timestamps must be arranged in ascending order.
    /// - `params.timestamps.end` must be equal to the last segment's timestamp.
    /// - The sum of the segment amounts must equal the deposit amount.
    /// - `params.recipient` must not be the zero address.
    /// - `params.sender` must not be the zero address.
    /// - `msg.sender` must have allowed this contract to spend at least `params.totalAmount` tokens.
    /// - `params.shape.length` must not be greater than 32 characters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param segments Segments used to compose the dynamic distribution function.
    /// @return streamId The ID of the newly created stream.
    function createWithTimestampsLD(
        Lockup.CreateWithTimestamps calldata params,
        LockupDynamic.Segment[] calldata segments
    )
        external
        payable
        returns (uint256 streamId);

    /// @notice Creates a stream with the provided start time and end time. The stream is funded by `msg.sender` and is
    /// wrapped in an ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupLinearStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - A cliff time of zero means there is no cliff.
    /// - As long as the times are ordered, it is not an error for the start or the cliff time to be in the past.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `params.totalAmount` must be greater than zero.
    /// - If set, `params.broker.fee` must not be greater than `MAX_BROKER_FEE`.
    /// - `params.timestamps.start` must be greater than zero and less than `params.timestamps.end`.
    /// - If set, `cliffTime` must be greater than `params.timestamps.start` and less than
    /// `params.timestamps.end`.
    /// - `params.recipient` must not be the zero address.
    /// - `params.sender` must not be the zero address.
    /// - The sum of `params.unlockAmounts.start` and `params.unlockAmounts.cliff` must be less than or equal to
    /// deposit amount.
    /// - If `params.timestamps.cliff` not set, the `params.unlockAmounts.cliff` must be zero.
    /// - `msg.sender` must have allowed this contract to spend at least `params.totalAmount` tokens.
    /// - `params.shape.length` must not be greater than 32 characters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param cliffTime The Unix timestamp for the cliff period's end. A value of zero means there is no cliff.
    /// @param unlockAmounts Struct encapsulating (i) the amount to unlock at the start time and (ii) the amount to
    /// unlock at the cliff time.
    /// @return streamId The ID of the newly created stream.
    function createWithTimestampsLL(
        Lockup.CreateWithTimestamps calldata params,
        LockupLinear.UnlockAmounts calldata unlockAmounts,
        uint40 cliffTime
    )
        external
        payable
        returns (uint256 streamId);

    /// @notice Creates a stream with the provided tranche timestamps, implying the end time from the last timestamp.
    /// The stream is funded by `msg.sender` and is wrapped in an ERC-721 NFT.
    ///
    /// @dev Emits a {Transfer}, {CreateLockupTrancheStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - As long as the tranche timestamps are arranged in ascending order, it is not an error for some
    /// of them to be in the past.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `params.totalAmount` must be greater than zero.
    /// - If set, `params.broker.fee` must not be greater than `MAX_BROKER_FEE`.
    /// - `params.timestamps.start` must be greater than zero and less than the first tranche's timestamp.
    /// - `tranches` must have at least one tranche, but not more than `MAX_COUNT`.
    /// - The tranche timestamps must be arranged in ascending order.
    /// - `params.timestamps.end` must be equal to the last tranche's timestamp.
    /// - The sum of the tranche amounts must equal the deposit amount.
    /// - `params.recipient` must not be the zero address.
    /// - `params.sender` must not be the zero address.
    /// - `msg.sender` must have allowed this contract to spend at least `params.totalAmount` tokens.
    /// - `params.shape.length` must not be greater than 32 characters.
    ///
    /// @param params Struct encapsulating the function parameters, which are documented in {DataTypes}.
    /// @param tranches Tranches used to compose the tranched distribution function.
    /// @return streamId The ID of the newly created stream.
    function createWithTimestampsLT(
        Lockup.CreateWithTimestamps calldata params,
        LockupTranched.Tranche[] calldata tranches
    )
        external
        payable
        returns (uint256 streamId);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";

import { Lockup } from "../types/DataTypes.sol";

/// @title Errors
/// @notice Library containing all custom errors the protocol may revert with.
library Errors {
    /*//////////////////////////////////////////////////////////////////////////
                                      GENERICS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Thrown when an unexpected error occurs during a batch call.
    error BatchError(bytes errorData);

    /// @notice Thrown when `msg.sender` is not the admin.
    error CallerNotAdmin(address admin, address caller);

    /// @notice Thrown when trying to delegate call to a function that disallows delegate calls.
    error DelegateCall();

    /*//////////////////////////////////////////////////////////////////////////
                                SABLIER-BATCH-LOCKUP
    //////////////////////////////////////////////////////////////////////////*/

    error SablierBatchLockup_BatchSizeZero();

    /*//////////////////////////////////////////////////////////////////////////
                               LOCKUP-NFT-DESCRIPTOR
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Thrown when trying to generate the token URI for an unknown ERC-721 NFT contract.
    error LockupNFTDescriptor_UnknownNFT(IERC721Metadata nft, string symbol);

    /*//////////////////////////////////////////////////////////////////////////
                                    HELPERS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Thrown when the broker fee exceeds the maximum allowed fee.
    error SablierHelpers_BrokerFeeTooHigh(UD60x18 brokerFee, UD60x18 maxBrokerFee);

    /// @notice Thrown when trying to create a linear stream with a cliff time not strictly less than the end time.
    error SablierHelpers_CliffTimeNotLessThanEndTime(uint40 cliffTime, uint40 endTime);

    /// @notice Thrown when trying to create a stream with a non zero cliff unlock amount when the cliff time is zero.
    error SablierHelpers_CliffTimeZeroUnlockAmountNotZero(uint128 cliffUnlockAmount);

    /// @notice Thrown when trying to create a dynamic stream with a deposit amount not equal to the sum of the segment
    /// amounts.
    error SablierHelpers_DepositAmountNotEqualToSegmentAmountsSum(uint128 depositAmount, uint128 segmentAmountsSum);

    /// @notice Thrown when trying to create a tranched stream with a deposit amount not equal to the sum of the tranche
    /// amounts.
    error SablierHelpers_DepositAmountNotEqualToTrancheAmountsSum(uint128 depositAmount, uint128 trancheAmountsSum);

    /// @notice Thrown when trying to create a stream with a zero deposit amount.
    error SablierHelpers_DepositAmountZero();

    /// @notice Thrown when trying to create a dynamic stream with end time not equal to the last segment's timestamp.
    error SablierHelpers_EndTimeNotEqualToLastSegmentTimestamp(uint40 endTime, uint40 lastSegmentTimestamp);

    /// @notice Thrown when trying to create a tranched stream with end time not equal to the last tranche's timestamp.
    error SablierHelpers_EndTimeNotEqualToLastTrancheTimestamp(uint40 endTime, uint40 lastTrancheTimestamp);

    /// @notice Thrown when trying to create a dynamic stream with more segments than the maximum allowed.
    error SablierHelpers_SegmentCountTooHigh(uint256 count);

    /// @notice Thrown when trying to create a dynamic stream with no segments.
    error SablierHelpers_SegmentCountZero();

    /// @notice Thrown when trying to create a dynamic stream with unordered segment timestamps.
    error SablierHelpers_SegmentTimestampsNotOrdered(uint256 index, uint40 previousTimestamp, uint40 currentTimestamp);

    /// @notice Thrown when trying to create a stream with the sender as the zero address.
    error SablierHelpers_SenderZeroAddress();

    /// @notice Thrown when trying to create a stream with a shape string exceeding 32 bytes.
    error SablierHelpers_ShapeExceeds32Bytes(uint256 shapeLength);

    /// @notice Thrown when trying to create a linear stream with a start time not strictly less than the cliff time,
    /// when the cliff time does not have a zero value.
    error SablierHelpers_StartTimeNotLessThanCliffTime(uint40 startTime, uint40 cliffTime);

    /// @notice Thrown when trying to create a linear stream with a start time not strictly less than the end time.
    error SablierHelpers_StartTimeNotLessThanEndTime(uint40 startTime, uint40 endTime);

    /// @notice Thrown when trying to create a dynamic stream with a start time not strictly less than the first
    /// segment timestamp.
    error SablierHelpers_StartTimeNotLessThanFirstSegmentTimestamp(uint40 startTime, uint40 firstSegmentTimestamp);

    /// @notice Thrown when trying to create a tranched stream with a start time not strictly less than the first
    /// tranche timestamp.
    error SablierHelpers_StartTimeNotLessThanFirstTrancheTimestamp(uint40 startTime, uint40 firstTrancheTimestamp);

    /// @notice Thrown when trying to create a stream with a zero start time.
    error SablierHelpers_StartTimeZero();

    /// @notice Thrown when trying to create a tranched stream with more tranches than the maximum allowed.
    error SablierHelpers_TrancheCountTooHigh(uint256 count);

    /// @notice Thrown when trying to create a tranched stream with no tranches.
    error SablierHelpers_TrancheCountZero();

    /// @notice Thrown when trying to create a tranched stream with unordered tranche timestamps.
    error SablierHelpers_TrancheTimestampsNotOrdered(uint256 index, uint40 previousTimestamp, uint40 currentTimestamp);

    /// @notice Thrown when trying to create a stream with the sum of the unlock amounts greater than the deposit
    /// amount.
    error SablierHelpers_UnlockAmountsSumTooHigh(
        uint128 depositAmount, uint128 startUnlockAmount, uint128 cliffUnlockAmount
    );

    /*//////////////////////////////////////////////////////////////////////////
                                SABLIER-LOCKUP-BASE
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Thrown when trying to allow to hook a contract that doesn't implement the interface correctly.
    error SablierLockupBase_AllowToHookUnsupportedInterface(address recipient);

    /// @notice Thrown when trying to allow to hook an address with no code.
    error SablierLockupBase_AllowToHookZeroCodeSize(address recipient);

    /// @notice Thrown when the fee transfer fails.
    error SablierLockupBase_FeeTransferFail(address admin, uint256 feeAmount);

    /// @notice Thrown when the hook does not return the correct selector.
    error SablierLockupBase_InvalidHookSelector(address recipient);

    /// @notice Thrown when trying to transfer Stream NFT when transferability is disabled.
    error SablierLockupBase_NotTransferable(uint256 tokenId);

    /// @notice Thrown when the ID references a null stream.
    error SablierLockupBase_Null(uint256 streamId);

    /// @notice Thrown when trying to withdraw an amount greater than the withdrawable amount.
    error SablierLockupBase_Overdraw(uint256 streamId, uint128 amount, uint128 withdrawableAmount);

    /// @notice Thrown when trying to cancel or renounce a canceled stream.
    error SablierLockupBase_StreamCanceled(uint256 streamId);

    /// @notice Thrown when trying to cancel, renounce, or withdraw from a depleted stream.
    error SablierLockupBase_StreamDepleted(uint256 streamId);

    /// @notice Thrown when trying to cancel or renounce a stream that is not cancelable.
    error SablierLockupBase_StreamNotCancelable(uint256 streamId);

    /// @notice Thrown when trying to burn a stream that is not depleted.
    error SablierLockupBase_StreamNotDepleted(uint256 streamId);

    /// @notice Thrown when trying to cancel or renounce a settled stream.
    error SablierLockupBase_StreamSettled(uint256 streamId);

    /// @notice Thrown when `msg.sender` lacks authorization to perform an action.
    error SablierLockupBase_Unauthorized(uint256 streamId, address caller);

    /// @notice Thrown when trying to withdraw to an address other than the recipient's.
    error SablierLockupBase_WithdrawalAddressNotRecipient(uint256 streamId, address caller, address to);

    /// @notice Thrown when trying to withdraw zero tokens from a stream.
    error SablierLockupBase_WithdrawAmountZero(uint256 streamId);

    /// @notice Thrown when trying to withdraw from multiple streams and the number of stream IDs does
    /// not match the number of withdraw amounts.
    error SablierLockupBase_WithdrawArrayCountsNotEqual(uint256 streamIdsCount, uint256 amountsCount);

    /// @notice Thrown when trying to withdraw to the zero address.
    error SablierLockupBase_WithdrawToZeroAddress(uint256 streamId);

    /*//////////////////////////////////////////////////////////////////////////
                                    SABLIER-LOCKUP
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Thrown when a function is called on a stream that does not use the expected Lockup model.
    error SablierLockup_NotExpectedModel(Lockup.Model actualLockupModel, Lockup.Model expectedLockupModel);
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity >=0.8.22;

import { UD60x18, ud } from "@prb/math/src/UD60x18.sol";
import { Lockup, LockupDynamic, LockupLinear, LockupTranched } from "./../types/DataTypes.sol";
import { Errors } from "./Errors.sol";

/// @title Helpers
/// @notice Library with functions needed to validate input parameters across lockup streams.
library Helpers {
    /*//////////////////////////////////////////////////////////////////////////
                                CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev Calculate the timestamps and return the segments.
    function calculateSegmentTimestamps(
        LockupDynamic.SegmentWithDuration[] memory segmentsWithDuration,
        uint40 startTime
    )
        public
        pure
        returns (LockupDynamic.Segment[] memory segmentsWithTimestamps)
    {
        uint256 segmentCount = segmentsWithDuration.length;
        segmentsWithTimestamps = new LockupDynamic.Segment[](segmentCount);

        // It is safe to use unchecked arithmetic because {SablierLockup._createLD} will nonetheless
        // check the correctness of the calculated segment timestamps.
        unchecked {
            // The first segment is precomputed because it is needed in the for loop below.
            segmentsWithTimestamps[0] = LockupDynamic.Segment({
                amount: segmentsWithDuration[0].amount,
                exponent: segmentsWithDuration[0].exponent,
                timestamp: startTime + segmentsWithDuration[0].duration
            });

            // Copy the segment amounts and exponents, and calculate the segment timestamps.
            for (uint256 i = 1; i < segmentCount; ++i) {
                segmentsWithTimestamps[i] = LockupDynamic.Segment({
                    amount: segmentsWithDuration[i].amount,
                    exponent: segmentsWithDuration[i].exponent,
                    timestamp: segmentsWithTimestamps[i - 1].timestamp + segmentsWithDuration[i].duration
                });
            }
        }
    }

    /// @dev Calculate the timestamps and return the tranches.
    function calculateTrancheTimestamps(
        LockupTranched.TrancheWithDuration[] memory tranchesWithDuration,
        uint40 startTime
    )
        public
        pure
        returns (LockupTranched.Tranche[] memory tranchesWithTimestamps)
    {
        uint256 trancheCount = tranchesWithDuration.length;
        tranchesWithTimestamps = new LockupTranched.Tranche[](trancheCount);

        // It is safe to use unchecked arithmetic because {SablierLockup-_createLT} will nonetheless check the
        // correctness of the calculated tranche timestamps.
        unchecked {
            // The first tranche is precomputed because it is needed in the for loop below.
            tranchesWithTimestamps[0] = LockupTranched.Tranche({
                amount: tranchesWithDuration[0].amount,
                timestamp: startTime + tranchesWithDuration[0].duration
            });

            // Copy the tranche amounts and calculate the tranche timestamps.
            for (uint256 i = 1; i < trancheCount; ++i) {
                tranchesWithTimestamps[i] = LockupTranched.Tranche({
                    amount: tranchesWithDuration[i].amount,
                    timestamp: tranchesWithTimestamps[i - 1].timestamp + tranchesWithDuration[i].duration
                });
            }
        }
    }

    /// @dev Checks the parameters of the {SablierLockup-_createLD} function.
    function checkCreateLockupDynamic(
        address sender,
        Lockup.Timestamps memory timestamps,
        uint128 totalAmount,
        LockupDynamic.Segment[] memory segments,
        uint256 maxCount,
        UD60x18 brokerFee,
        string memory shape,
        UD60x18 maxBrokerFee
    )
        public
        pure
        returns (Lockup.CreateAmounts memory createAmounts)
    {
        // Check: verify the broker fee and calculate the amounts.
        createAmounts = _checkAndCalculateBrokerFee(totalAmount, brokerFee, maxBrokerFee);

        // Check: validate the user-provided common parameters.
        _checkCreateStream(sender, createAmounts.deposit, timestamps.start, shape);

        // Check: validate the user-provided segments.
        _checkSegments(segments, createAmounts.deposit, timestamps, maxCount);
    }

    /// @dev Checks the parameters of the {SablierLockup-_createLL} function.
    function checkCreateLockupLinear(
        address sender,
        Lockup.Timestamps memory timestamps,
        uint40 cliffTime,
        uint128 totalAmount,
        LockupLinear.UnlockAmounts memory unlockAmounts,
        UD60x18 brokerFee,
        string memory shape,
        UD60x18 maxBrokerFee
    )
        public
        pure
        returns (Lockup.CreateAmounts memory createAmounts)
    {
        // Check: verify the broker fee and calculate the amounts.
        createAmounts = _checkAndCalculateBrokerFee(totalAmount, brokerFee, maxBrokerFee);

        // Check: validate the user-provided common parameters.
        _checkCreateStream(sender, createAmounts.deposit, timestamps.start, shape);

        // Check: validate the user-provided cliff and end times.
        _checkTimestampsAndUnlockAmounts(createAmounts.deposit, timestamps, cliffTime, unlockAmounts);
    }

    /// @dev Checks the parameters of the {SablierLockup-_createLT} function.
    function checkCreateLockupTranched(
        address sender,
        Lockup.Timestamps memory timestamps,
        uint128 totalAmount,
        LockupTranched.Tranche[] memory tranches,
        uint256 maxCount,
        UD60x18 brokerFee,
        string memory shape,
        UD60x18 maxBrokerFee
    )
        public
        pure
        returns (Lockup.CreateAmounts memory createAmounts)
    {
        // Check: verify the broker fee and calculate the amounts.
        createAmounts = _checkAndCalculateBrokerFee(totalAmount, brokerFee, maxBrokerFee);

        // Check: validate the user-provided common parameters.
        _checkCreateStream(sender, createAmounts.deposit, timestamps.start, shape);

        // Check: validate the user-provided segments.
        _checkTranches(tranches, createAmounts.deposit, timestamps, maxCount);
    }

    /*//////////////////////////////////////////////////////////////////////////
                            PRIVATE CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev Checks the broker fee is not greater than `maxBrokerFee`, and then calculates the broker fee amount and
    /// the deposit amount from the total amount.
    function _checkAndCalculateBrokerFee(
        uint128 totalAmount,
        UD60x18 brokerFee,
        UD60x18 maxBrokerFee
    )
        private
        pure
        returns (Lockup.CreateAmounts memory amounts)
    {
        // When the total amount is zero, the broker fee is also zero.
        if (totalAmount == 0) {
            return Lockup.CreateAmounts(0, 0);
        }

        // If the broker fee is zero, the deposit amount is the total amount.
        if (brokerFee.isZero()) {
            return Lockup.CreateAmounts(totalAmount, 0);
        }

        // Check: the broker fee is not greater than `maxBrokerFee`.
        if (brokerFee.gt(maxBrokerFee)) {
            revert Errors.SablierHelpers_BrokerFeeTooHigh(brokerFee, maxBrokerFee);
        }

        // Calculate the broker fee amount.
        amounts.brokerFee = ud(totalAmount).mul(brokerFee).intoUint128();

        // Assert that the total amount is strictly greater than the broker fee amount.
        assert(totalAmount > amounts.brokerFee);

        // Calculate the deposit amount (the amount to stream, net of the broker fee).
        amounts.deposit = totalAmount - amounts.brokerFee;
    }

    /// @dev Checks the user-provided cliff, end times and unlock amounts of a lockup linear stream.
    function _checkTimestampsAndUnlockAmounts(
        uint128 depositAmount,
        Lockup.Timestamps memory timestamps,
        uint40 cliffTime,
        LockupLinear.UnlockAmounts memory unlockAmounts
    )
        private
        pure
    {
        // Since a cliff time of zero means there is no cliff, the following checks are performed only if it's not zero.
        if (cliffTime > 0) {
            // Check: the start time is strictly less than the cliff time.
            if (timestamps.start >= cliffTime) {
                revert Errors.SablierHelpers_StartTimeNotLessThanCliffTime(timestamps.start, cliffTime);
            }

            // Check: the cliff time is strictly less than the end time.
            if (cliffTime >= timestamps.end) {
                revert Errors.SablierHelpers_CliffTimeNotLessThanEndTime(cliffTime, timestamps.end);
            }
        }
        // Check: the cliff unlock amount is zero when the cliff time is zero.
        else if (unlockAmounts.cliff > 0) {
            revert Errors.SablierHelpers_CliffTimeZeroUnlockAmountNotZero(unlockAmounts.cliff);
        }

        // Check: the start time is strictly less than the end time.
        if (timestamps.start >= timestamps.end) {
            revert Errors.SablierHelpers_StartTimeNotLessThanEndTime(timestamps.start, timestamps.end);
        }

        // Check: the sum of the start and cliff unlock amounts is not greater than the deposit amount.
        if (unlockAmounts.start + unlockAmounts.cliff > depositAmount) {
            revert Errors.SablierHelpers_UnlockAmountsSumTooHigh(
                depositAmount, unlockAmounts.start, unlockAmounts.cliff
            );
        }
    }

    /// @dev Checks the user-provided common parameters across lockup streams.
    function _checkCreateStream(
        address sender,
        uint128 depositAmount,
        uint40 startTime,
        string memory shape
    )
        private
        pure
    {
        // Check: the sender is not the zero address.
        if (sender == address(0)) {
            revert Errors.SablierHelpers_SenderZeroAddress();
        }

        // Check: the deposit amount is not zero.
        if (depositAmount == 0) {
            revert Errors.SablierHelpers_DepositAmountZero();
        }

        // Check: the start time is not zero.
        if (startTime == 0) {
            revert Errors.SablierHelpers_StartTimeZero();
        }

        // Check: the shape is not greater than 32 bytes.
        if (bytes(shape).length > 32) {
            revert Errors.SablierHelpers_ShapeExceeds32Bytes(bytes(shape).length);
        }
    }

    /// @dev Checks:
    ///
    /// 1. The first timestamp is strictly greater than the start time.
    /// 2. The timestamps are ordered chronologically.
    /// 3. There are no duplicate timestamps.
    /// 4. The deposit amount is equal to the sum of all segment amounts.
    /// 5. The end time equals the last segment's timestamp.
    function _checkSegments(
        LockupDynamic.Segment[] memory segments,
        uint128 depositAmount,
        Lockup.Timestamps memory timestamps,
        uint256 maxSegmentCount
    )
        private
        pure
    {
        // Check: the segment count is not zero.
        uint256 segmentCount = segments.length;
        if (segmentCount == 0) {
            revert Errors.SablierHelpers_SegmentCountZero();
        }

        // Check: the segment count is not greater than the maximum allowed.
        if (segmentCount > maxSegmentCount) {
            revert Errors.SablierHelpers_SegmentCountTooHigh(segmentCount);
        }

        // Check: the start time is strictly less than the first segment timestamp.
        if (timestamps.start >= segments[0].timestamp) {
            revert Errors.SablierHelpers_StartTimeNotLessThanFirstSegmentTimestamp(
                timestamps.start, segments[0].timestamp
            );
        }

        // Check: the end time equals the last segment's timestamp.
        if (timestamps.end != segments[segmentCount - 1].timestamp) {
            revert Errors.SablierHelpers_EndTimeNotEqualToLastSegmentTimestamp(
                timestamps.end, segments[segmentCount - 1].timestamp
            );
        }

        // Pre-declare the variables needed in the for loop.
        uint128 segmentAmountsSum;
        uint40 currentSegmentTimestamp;
        uint40 previousSegmentTimestamp;

        // Iterate over the segments to:
        //
        // 1. Calculate the sum of all segment amounts.
        // 2. Check that the timestamps are ordered.
        for (uint256 index = 0; index < segmentCount; ++index) {
            // Add the current segment amount to the sum.
            segmentAmountsSum += segments[index].amount;

            // Check: the current timestamp is strictly greater than the previous timestamp.
            currentSegmentTimestamp = segments[index].timestamp;
            if (currentSegmentTimestamp <= previousSegmentTimestamp) {
                revert Errors.SablierHelpers_SegmentTimestampsNotOrdered(
                    index, previousSegmentTimestamp, currentSegmentTimestamp
                );
            }

            // Make the current timestamp the previous timestamp of the next loop iteration.
            previousSegmentTimestamp = currentSegmentTimestamp;
        }

        // Check: the deposit amount is equal to the segment amounts sum.
        if (depositAmount != segmentAmountsSum) {
            revert Errors.SablierHelpers_DepositAmountNotEqualToSegmentAmountsSum(depositAmount, segmentAmountsSum);
        }
    }

    /// @dev Checks:
    ///
    /// 1. The first timestamp is strictly greater than the start time.
    /// 2. The timestamps are ordered chronologically.
    /// 3. There are no duplicate timestamps.
    /// 4. The deposit amount is equal to the sum of all tranche amounts.
    /// 5. The end time equals the last tranche's timestamp.
    function _checkTranches(
        LockupTranched.Tranche[] memory tranches,
        uint128 depositAmount,
        Lockup.Timestamps memory timestamps,
        uint256 maxTrancheCount
    )
        private
        pure
    {
        // Check: the tranche count is not zero.
        uint256 trancheCount = tranches.length;
        if (trancheCount == 0) {
            revert Errors.SablierHelpers_TrancheCountZero();
        }

        // Check: the tranche count is not greater than the maximum allowed.
        if (trancheCount > maxTrancheCount) {
            revert Errors.SablierHelpers_TrancheCountTooHigh(trancheCount);
        }

        // Check: the start time is strictly less than the first tranche timestamp.
        if (timestamps.start >= tranches[0].timestamp) {
            revert Errors.SablierHelpers_StartTimeNotLessThanFirstTrancheTimestamp(
                timestamps.start, tranches[0].timestamp
            );
        }

        // Check: the end time equals the tranche's timestamp.
        if (timestamps.end != tranches[trancheCount - 1].timestamp) {
            revert Errors.SablierHelpers_EndTimeNotEqualToLastTrancheTimestamp(
                timestamps.end, tranches[trancheCount - 1].timestamp
            );
        }

        // Pre-declare the variables needed in the for loop.
        uint128 trancheAmountsSum;
        uint40 currentTrancheTimestamp;
        uint40 previousTrancheTimestamp;

        // Iterate over the tranches to:
        //
        // 1. Calculate the sum of all tranche amounts.
        // 2. Check that the timestamps are ordered.
        for (uint256 index = 0; index < trancheCount; ++index) {
            // Add the current tranche amount to the sum.
            trancheAmountsSum += tranches[index].amount;

            // Check: the current timestamp is strictly greater than the previous timestamp.
            currentTrancheTimestamp = tranches[index].timestamp;
            if (currentTrancheTimestamp <= previousTrancheTimestamp) {
                revert Errors.SablierHelpers_TrancheTimestampsNotOrdered(
                    index, previousTrancheTimestamp, currentTrancheTimestamp
                );
            }

            // Make the current timestamp the previous timestamp of the next loop iteration.
            previousTrancheTimestamp = currentTrancheTimestamp;
        }

        // Check: the deposit amount is equal to the tranche amounts sum.
        if (depositAmount != trancheAmountsSum) {
            revert Errors.SablierHelpers_DepositAmountNotEqualToTrancheAmountsSum(depositAmount, trancheAmountsSum);
        }
    }
}

// SPDX-License-Identifier: BUSL-1.1
pragma solidity >=0.8.22;

import { PRBMathCastingUint128 as CastingUint128 } from "@prb/math/src/casting/Uint128.sol";
import { PRBMathCastingUint40 as CastingUint40 } from "@prb/math/src/casting/Uint40.sol";
import { SD59x18 } from "@prb/math/src/SD59x18.sol";
import { UD60x18, ud } from "@prb/math/src/UD60x18.sol";

import { Lockup, LockupDynamic, LockupLinear, LockupTranched } from "./../types/DataTypes.sol";

/// @title VestingMath
/// @notice Library with functions needed to calculate vested amount across lockup streams.
library VestingMath {
    using CastingUint128 for uint128;
    using CastingUint40 for uint40;

    /// @notice Calculates the streamed amount for a Lockup dynamic stream.
    /// @dev Lockup dynamic model uses the following distribution function:
    ///
    /// $$
    /// f(x) = x^{exp} * csa + \Sigma(esa)
    /// $$
    ///
    /// Where:
    ///
    /// - $x$ is the elapsed time divided by the total duration of the current segment.
    /// - $exp$ is the current segment exponent.
    /// - $csa$ is the current segment amount.
    /// - $\Sigma(esa)$ is the sum of all vested segments' amounts.
    ///
    /// Notes:
    /// 1. Normalization to 18 decimals is not needed because there is no mix of amounts with different decimals.
    /// 2. The stream's start time must be in the past so that the calculations below do not overflow.
    /// 3. The stream's end time must be in the future so that the loop below does not panic with an "index out of
    /// bounds" error.
    ///
    /// Assumptions:
    /// 1. The sum of all segment amounts does not overflow uint128 and equals the deposited amount.
    /// 2. The first segment's timestamp is greater than the start time.
    /// 3. The last segment's timestamp equals the end time.
    /// 4. The segment timestamps are arranged in ascending order.
    function calculateLockupDynamicStreamedAmount(
        uint128 depositedAmount,
        LockupDynamic.Segment[] memory segments,
        uint40 blockTimestamp,
        Lockup.Timestamps memory timestamps,
        uint128 withdrawnAmount
    )
        public
        pure
        returns (uint128)
    {
        // If the start time is in the future, return zero.
        if (timestamps.start > blockTimestamp) {
            return 0;
        }

        // If the end time is not in the future, return the deposited amount.
        if (timestamps.end <= blockTimestamp) {
            return depositedAmount;
        }

        unchecked {
            // Sum the amounts in all segments that precede the block timestamp.
            uint128 previousSegmentAmounts;
            uint40 currentSegmentTimestamp = segments[0].timestamp;
            uint256 index = 0;
            while (currentSegmentTimestamp < blockTimestamp) {
                previousSegmentAmounts += segments[index].amount;
                index += 1;
                currentSegmentTimestamp = segments[index].timestamp;
            }

            // After exiting the loop, the current segment is at `index`.
            SD59x18 currentSegmentAmount = segments[index].amount.intoSD59x18();
            SD59x18 currentSegmentExponent = segments[index].exponent.intoSD59x18();
            currentSegmentTimestamp = segments[index].timestamp;

            uint40 previousTimestamp;
            if (index == 0) {
                // When the current segment's index is equal to 0, the current segment is the first, so use the start
                // time as the previous timestamp.
                previousTimestamp = timestamps.start;
            } else {
                // Otherwise, when the current segment's index is greater than zero, it means that the segment is not
                // the first. In this case, use the previous segment's timestamp.
                previousTimestamp = segments[index - 1].timestamp;
            }

            // Calculate how much time has passed since the segment started, and the total duration of the segment.
            SD59x18 elapsedTime = (blockTimestamp - previousTimestamp).intoSD59x18();
            SD59x18 segmentDuration = (currentSegmentTimestamp - previousTimestamp).intoSD59x18();

            // Divide the elapsed time by the total duration of the segment.
            SD59x18 elapsedTimePercentage = elapsedTime.div(segmentDuration);

            // Calculate the streamed amount using the special formula.
            SD59x18 multiplier = elapsedTimePercentage.pow(currentSegmentExponent);
            SD59x18 segmentStreamedAmount = multiplier.mul(currentSegmentAmount);

            // Although the segment streamed amount should never exceed the total segment amount, this condition is
            // checked without asserting to avoid locking tokens in case of a bug. If this situation occurs, the
            // amount streamed in the segment is considered zero (except for past withdrawals), and the segment is
            // effectively voided.
            if (segmentStreamedAmount.gt(currentSegmentAmount)) {
                return previousSegmentAmounts > withdrawnAmount ? previousSegmentAmounts : withdrawnAmount;
            }

            // Calculate the total streamed amount by adding the previous segment amounts and the amount streamed in
            // the current segment. Casting to uint128 is safe due to the if statement above.
            return previousSegmentAmounts + uint128(segmentStreamedAmount.intoUint256());
        }
    }

    /// @notice Calculates the streamed amount for a Lockup linear stream.
    /// @dev Lockup linear model uses the following distribution function:
    ///
    /// $$
    ///        ( x * sa + s, block timestamp < cliff time
    /// f(x) = (
    ///        ( x * sa + s + c, block timestamp => cliff time
    /// $$
    ///
    /// Where:
    ///
    /// - $x$ is the elapsed time in the streamable range divided by the total streamable range.
    /// - $sa$ is the streamable amount, i.e. deposited amount minus unlock amounts' sum.
    /// - $s$ is the start unlock amount.
    /// - $c$ is the cliff unlock amount.
    ///
    /// Assumptions:
    /// 1. The sum of the unlock amounts (start and cliff) does not overflow uint128 and is less than or equal to
    /// the deposit amount.
    /// 2. The start time is before the end time.
    /// 3. If the cliff time is not zero, it is after the start time and before the end time.
    function calculateLockupLinearStreamedAmount(
        uint128 depositedAmount,
        uint40 blockTimestamp,
        Lockup.Timestamps memory timestamps,
        uint40 cliffTime,
        LockupLinear.UnlockAmounts memory unlockAmounts,
        uint128 withdrawnAmount
    )
        public
        pure
        returns (uint128)
    {
        // If the start time is in the future, return zero.
        if (timestamps.start > blockTimestamp) {
            return 0;
        }

        // If the end time is not in the future, return the deposited amount.
        if (timestamps.end <= blockTimestamp) {
            return depositedAmount;
        }

        // If the cliff time is in the future, return the start unlock amount.
        if (cliffTime > blockTimestamp) {
            return unlockAmounts.start;
        }

        unchecked {
            uint128 unlockAmountsSum = unlockAmounts.start + unlockAmounts.cliff;

            //  If the sum of the unlock amounts is greater than or equal to the deposited amount, return the deposited
            // amount. The ">=" operator is used as a safety measure in case of a bug, as the sum of the unlock amounts
            // should never exceed the deposited amount.
            if (unlockAmountsSum >= depositedAmount) {
                return depositedAmount;
            }

            UD60x18 elapsedTime;
            UD60x18 streamableRange;

            // Calculate the streamable range.
            if (cliffTime == 0) {
                elapsedTime = ud(blockTimestamp - timestamps.start);
                streamableRange = ud(timestamps.end - timestamps.start);
            } else {
                elapsedTime = ud(blockTimestamp - cliffTime);
                streamableRange = ud(timestamps.end - cliffTime);
            }

            UD60x18 elapsedTimePercentage = elapsedTime.div(streamableRange);
            UD60x18 streamableAmount = ud(depositedAmount - unlockAmountsSum);

            // The streamed amount is the sum of the unlock amounts plus the product of elapsed time percentage and
            // streamable amount.
            uint128 streamedAmount = unlockAmountsSum + (elapsedTimePercentage.mul(streamableAmount)).intoUint128();

            // Although the streamed amount should never exceed the deposited amount, this condition is checked
            // without asserting to avoid locking tokens in case of a bug. If this situation occurs, the withdrawn
            // amount is considered to be the streamed amount, and the stream is effectively frozen.
            if (streamedAmount > depositedAmount) {
                return withdrawnAmount;
            }

            return streamedAmount;
        }
    }

    /// @notice Calculates the streamed amount for a Lockup tranched stream.
    /// @dev Lockup tranched model uses the following distribution function:
    ///
    /// $$
    /// f(x) = \Sigma(eta)
    /// $$
    ///
    /// Where:
    ///
    /// - $\Sigma(eta)$ is the sum of all vested tranches' amounts.
    ///
    /// Assumptions:
    /// 1. The sum of all tranche amounts does not overflow uint128, and equals the deposited amount.
    /// 2. The first tranche's timestamp is greater than the start time.
    /// 3. The last tranche's timestamp equals the end time.
    /// 4. The tranche timestamps are arranged in ascending order.
    function calculateLockupTranchedStreamedAmount(
        uint128 depositedAmount,
        uint40 blockTimestamp,
        Lockup.Timestamps memory timestamps,
        LockupTranched.Tranche[] memory tranches
    )
        public
        pure
        returns (uint128)
    {
        // If the start time is in the future, return zero.
        if (timestamps.start > blockTimestamp) {
            return 0;
        }

        // If the end time is not in the future, return the deposited amount.
        if (timestamps.end <= blockTimestamp) {
            return depositedAmount;
        }

        // If the first tranche's timestamp is in the future, return zero.
        if (tranches[0].timestamp > blockTimestamp) {
            return 0;
        }

        // Sum the amounts in all tranches that have already been vested.
        // Using unchecked arithmetic is safe because the sum of the tranche amounts is equal to the total amount
        // at this point.
        uint128 streamedAmount = tranches[0].amount;
        uint256 tranchesCount = tranches.length;
        for (uint256 i = 1; i < tranchesCount; ++i) {
            // The loop breaks at the first tranche with a timestamp in the future. A tranche is considered vested if
            // its timestamp is less than or equal to the block timestamp.
            if (tranches[i].timestamp > blockTimestamp) {
                break;
            }
            unchecked {
                streamedAmount += tranches[i].amount;
            }
        }

        return streamedAmount;
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { UD2x18 } from "@prb/math/src/UD2x18.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";

// This file defines all structs used in Lockup, most of which are organized under three namespaces:
//
// - BatchLockup
// - Lockup
// - LockupDynamic
// - LockupLinear
// - LockupTranched
//
// You will notice that some structs contain "slot" annotations - they are used to indicate the
// storage layout of the struct. It is more gas efficient to group small data types together so
// that they fit in a single 32-byte slot.

/// @dev Namespace for the structs used in `BatchLockup` contract.
library BatchLockup {
    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithDurationsLD} except for the token.
    struct CreateWithDurationsLD {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        LockupDynamic.SegmentWithDuration[] segmentsWithDuration;
        string shape;
        Broker broker;
    }

    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithDurationsLL} except for the token.
    struct CreateWithDurationsLL {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        LockupLinear.Durations durations;
        LockupLinear.UnlockAmounts unlockAmounts;
        string shape;
        Broker broker;
    }

    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithDurationsLT} except for the token.
    struct CreateWithDurationsLT {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        LockupTranched.TrancheWithDuration[] tranchesWithDuration;
        string shape;
        Broker broker;
    }

    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithTimestampsLD} except for the token.
    struct CreateWithTimestampsLD {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        uint40 startTime;
        LockupDynamic.Segment[] segments;
        string shape;
        Broker broker;
    }

    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithTimestampsLL} except for the token.
    struct CreateWithTimestampsLL {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        Lockup.Timestamps timestamps;
        uint40 cliffTime;
        LockupLinear.UnlockAmounts unlockAmounts;
        string shape;
        Broker broker;
    }

    /// @notice A struct encapsulating all parameters of {SablierLockup.createWithTimestampsLT} except for the token.
    struct CreateWithTimestampsLT {
        address sender;
        address recipient;
        uint128 totalAmount;
        bool cancelable;
        bool transferable;
        uint40 startTime;
        LockupTranched.Tranche[] tranches;
        string shape;
        Broker broker;
    }
}

/// @notice Struct encapsulating the broker parameters passed to the create functions. Both can be set to zero.
/// @param account The address receiving the broker's fee.
/// @param fee The broker's percentage fee from the total amount, denoted as a fixed-point number where 1e18 is 100%.
struct Broker {
    address account;
    UD60x18 fee;
}

/// @notice Namespace for the structs used in all Lockup models.
library Lockup {
    /// @notice Struct encapsulating the deposit, withdrawn, and refunded amounts, all denoted in units of the token's
    /// decimals.
    /// @dev Because the deposited and the withdrawn amount are often read together, declaring them in the same slot
    /// saves gas.
    /// @param deposited The initial amount deposited in the stream, net of broker fee.
    /// @param withdrawn The cumulative amount withdrawn from the stream.
    /// @param refunded The amount refunded to the sender. Unless the stream was canceled, this is always zero.
    struct Amounts {
        // slot 0
        uint128 deposited;
        uint128 withdrawn;
        // slot 1
        uint128 refunded;
    }

    /// @notice Struct encapsulating (i) the deposit amount and (ii) the broker fee amount, both denoted in units of the
    /// token's decimals.
    /// @param deposit The amount to deposit in the stream.
    /// @param brokerFee The broker fee amount.
    struct CreateAmounts {
        uint128 deposit;
        uint128 brokerFee;
    }

    /// @notice Struct encapsulating the common parameters emitted in the `Create` event.
    /// @param funder The address which has funded the stream.
    /// @param sender The address distributing the tokens, which is able to cancel the stream.
    /// @param recipient The address receiving the tokens, as well as the NFT owner.
    /// @param amounts Struct encapsulating (i) the deposit amount, and (ii) the broker fee amount, both denoted
    /// in units of the token's decimals.
    /// @param token The contract address of the ERC-20 token to be distributed.
    /// @param cancelable Boolean indicating whether the stream is cancelable or not.
    /// @param transferable Boolean indicating whether the stream NFT is transferable or not.
    /// @param timestamps Struct encapsulating (i) the stream's start time and (ii) end time, all as Unix timestamps.
    /// @param shape An optional parameter to specify the shape of the distribution function. This helps differentiate
    /// streams in the UI.
    /// @param broker The address of the broker who has helped create the stream, e.g. a front-end website.
    struct CreateEventCommon {
        address funder;
        address sender;
        address recipient;
        Lockup.CreateAmounts amounts;
        IERC20 token;
        bool cancelable;
        bool transferable;
        Lockup.Timestamps timestamps;
        string shape;
        address broker;
    }

    /// @notice Struct encapsulating the parameters of the `createWithDurations` functions.
    /// @param sender The address distributing the tokens, with the ability to cancel the stream. It doesn't have to be
    /// the same as `msg.sender`.
    /// @param recipient The address receiving the tokens, as well as the NFT owner.
    /// @param totalAmount The total amount, including the deposit and any broker fee, denoted in units of the token's
    /// decimals.
    /// @param token The contract address of the ERC-20 token to be distributed.
    /// @param cancelable Indicates if the stream is cancelable.
    /// @param transferable Indicates if the stream NFT is transferable.
    /// @param shape An optional parameter to specify the shape of the distribution function. This helps differentiate
    /// streams in the UI.
    /// @param broker Struct encapsulating (i) the address of the broker assisting in creating the stream, and (ii) the
    /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
    struct CreateWithDurations {
        address sender;
        address recipient;
        uint128 totalAmount;
        IERC20 token;
        bool cancelable;
        bool transferable;
        string shape;
        Broker broker;
    }

    /// @notice Struct encapsulating the parameters of the `createWithTimestamps` functions.
    /// @param sender The address distributing the tokens, with the ability to cancel the stream. It doesn't have to be
    /// the same as `msg.sender`.
    /// @param recipient The address receiving the tokens, as well as the NFT owner.
    /// @param totalAmount The total amount, including the deposit and any broker fee, denoted in units of the token's
    /// decimals.
    /// @param token The contract address of the ERC-20 token to be distributed.
    /// @param cancelable Indicates if the stream is cancelable.
    /// @param transferable Indicates if the stream NFT is transferable.
    /// @param timestamps Struct encapsulating (i) the stream's start time and (ii) end time, both as Unix timestamps.
    /// @param shape An optional parameter to specify the shape of the distribution function. This helps differentiate
    /// streams in the UI.
    /// @param broker Struct encapsulating (i) the address of the broker assisting in creating the stream, and (ii) the
    /// percentage fee paid to the broker from `totalAmount`, denoted as a fixed-point number. Both can be set to zero.
    struct CreateWithTimestamps {
        address sender;
        address recipient;
        uint128 totalAmount;
        IERC20 token;
        bool cancelable;
        bool transferable;
        Timestamps timestamps;
        string shape;
        Broker broker;
    }

    /// @notice Enum representing the different distribution models used to create lockup streams.
    /// @dev These distribution models determine the vesting function used in the calculations of the unlocked tokens.
    enum Model {
        LOCKUP_LINEAR,
        LOCKUP_DYNAMIC,
        LOCKUP_TRANCHED
    }

    /// @notice Enum representing the different statuses of a stream.
    /// @dev The status can have a "temperature":
    /// 1. Warm: Pending, Streaming. The passage of time alone can change the status.
    /// 2. Cold: Settled, Canceled, Depleted. The passage of time alone cannot change the status.
    /// @custom:value0 PENDING Stream created but not started; tokens are in a pending state.
    /// @custom:value1 STREAMING Active stream where tokens are currently being streamed.
    /// @custom:value2 SETTLED All tokens have been streamed; recipient is due to withdraw them.
    /// @custom:value3 CANCELED Canceled stream; remaining tokens await recipient's withdrawal.
    /// @custom:value4 DEPLETED Depleted stream; all tokens have been withdrawn and/or refunded.
    enum Status {
        // Warm
        PENDING,
        STREAMING,
        // Cold
        SETTLED,
        CANCELED,
        DEPLETED
    }

    /// @notice A common data structure to be stored in all Lockup models.
    /// @dev The fields are arranged like this to save gas via tight variable packing.
    /// @param sender The address distributing the tokens, with the ability to cancel the stream.
    /// @param startTime The Unix timestamp indicating the stream's start.
    /// @param endTime The Unix timestamp indicating the stream's end.
    /// @param isCancelable Boolean indicating if the stream is cancelable.
    /// @param wasCanceled Boolean indicating if the stream was canceled.
    /// @param token The contract address of the ERC-20 token to be distributed.
    /// @param isDepleted Boolean indicating if the stream is depleted.
    /// @param isStream Boolean indicating if the struct entity exists.
    /// @param isTransferable Boolean indicating if the stream NFT is transferable.
    /// @param lockupModel The distribution model of the stream.
    /// @param amounts Struct encapsulating the deposit, withdrawn, and refunded amounts, both denoted in units of the
    /// token's decimals.
    struct Stream {
        // slot 0
        address sender;
        uint40 startTime;
        uint40 endTime;
        bool isCancelable;
        bool wasCanceled;
        // slot 1
        IERC20 token;
        bool isDepleted;
        bool isStream;
        bool isTransferable;
        Model lockupModel;
        // slot 2 and 3
        Amounts amounts;
    }

    /// @notice Struct encapsulating the Lockup timestamps.
    /// @param start The Unix timestamp for the stream's start.
    /// @param end The Unix timestamp for the stream's end.
    struct Timestamps {
        uint40 start;
        uint40 end;
    }
}

/// @notice Namespace for the structs used only in Lockup Dynamic model.
library LockupDynamic {
    /// @notice Segment struct to be stored in the Lockup Dynamic model.
    /// @param amount The amount of tokens streamed in the segment, denoted in units of the token's decimals.
    /// @param exponent The exponent of the segment, denoted as a fixed-point number.
    /// @param timestamp The Unix timestamp indicating the segment's end.
    struct Segment {
        // slot 0
        uint128 amount;
        UD2x18 exponent;
        uint40 timestamp;
    }

    /// @notice Segment struct used at runtime in {SablierLockup.createWithDurationsLD} function.
    /// @param amount The amount of tokens streamed in the segment, denoted in units of the token's decimals.
    /// @param exponent The exponent of the segment, denoted as a fixed-point number.
    /// @param duration The time difference in seconds between the segment and the previous one.
    struct SegmentWithDuration {
        uint128 amount;
        UD2x18 exponent;
        uint40 duration;
    }
}

/// @notice Namespace for the structs used only in Lockup Linear model.
library LockupLinear {
    /// @notice Struct encapsulating the cliff duration and the total duration used at runtime in
    /// {SablierLockup.createWithDurationsLL} function.
    /// @param cliff The cliff duration in seconds.
    /// @param total The total duration in seconds.
    struct Durations {
        uint40 cliff;
        uint40 total;
    }

    /// @notice Struct encapsulating the unlock amounts for the stream.
    /// @dev The sum of `start` and `cliff` must be less than or equal to deposit amount. Both amounts can be zero.
    /// @param start The amount to be unlocked at the start time.
    /// @param cliff The amount to be unlocked at the cliff time.
    struct UnlockAmounts {
        // slot 0
        uint128 start;
        uint128 cliff;
    }
}

/// @notice Namespace for the structs used only in Lockup Tranched model.
library LockupTranched {
    /// @notice Tranche struct to be stored in the Lockup Tranched model.
    /// @param amount The amount of tokens to be unlocked in the tranche, denoted in units of the token's decimals.
    /// @param timestamp The Unix timestamp indicating the tranche's end.
    struct Tranche {
        // slot 0
        uint128 amount;
        uint40 timestamp;
    }

    /// @notice Tranche struct used at runtime in {SablierLockup.createWithDurationsLT} function.
    /// @param amount The amount of tokens to be unlocked in the tranche, denoted in units of the token's decimals.
    /// @param duration The time difference in seconds between the tranche and the previous one.
    struct TrancheWithDuration {
        uint128 amount;
        uint40 duration;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * ==== Security Considerations
 *
 * There are two important considerations concerning the use of `permit`. The first is that a valid permit signature
 * expresses an allowance, and it should not be assumed to convey additional meaning. In particular, it should not be
 * considered as an intention to spend the allowance in any specific way. The second is that because permits have
 * built-in replay protection and can be submitted by anyone, they can be frontrun. A protocol that uses permits should
 * take this into consideration and allow a `permit` call to fail. Combining these two aspects, a pattern that may be
 * generally recommended is:
 *
 * ```solidity
 * function doThingWithPermit(..., uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public {
 *     try token.permit(msg.sender, address(this), value, deadline, v, r, s) {} catch {}
 *     doThing(..., value);
 * }
 *
 * function doThing(..., uint256 value) public {
 *     token.safeTransferFrom(msg.sender, address(this), value);
 *     ...
 * }
 * ```
 *
 * Observe that: 1) `msg.sender` is used as the owner, leaving no ambiguity as to the signer intent, and 2) the use of
 * `try/catch` allows the permit to fail and makes the code tolerant to frontrunning. (See also
 * {SafeERC20-safeTransferFrom}).
 *
 * Additionally, note that smart contract wallets (such as Argent or Safe) are not able to produce permit signatures, so
 * contracts should have entry points that don't rely on permit.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     *
     * CAUTION: See Security Considerations above.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

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

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

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

pragma solidity ^0.8.20;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error AddressInsufficientBalance(address account);

    /**
     * @dev There's no code at `target` (it is not a contract).
     */
    error AddressEmptyCode(address target);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedInnerCall();

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.20/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        if (address(this).balance < amount) {
            revert AddressInsufficientBalance(address(this));
        }

        (bool success, ) = recipient.call{value: amount}("");
        if (!success) {
            revert FailedInnerCall();
        }
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason or custom error, it is bubbled
     * up by this function (like regular Solidity function calls). However, if
     * the call reverted with no returned reason, this function reverts with a
     * {FailedInnerCall} error.
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        if (address(this).balance < value) {
            revert AddressInsufficientBalance(address(this));
        }
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and reverts if the target
     * was not a contract or bubbling up the revert reason (falling back to {FailedInnerCall}) in case of an
     * unsuccessful call.
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata
    ) internal view returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            // only check if target is a contract if the call was successful and the return data is empty
            // otherwise we already know that it was a contract
            if (returndata.length == 0 && target.code.length == 0) {
                revert AddressEmptyCode(target);
            }
            return returndata;
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and reverts if it wasn't, either by bubbling the
     * revert reason or with a default {FailedInnerCall} error.
     */
    function verifyCallResult(bool success, bytes memory returndata) internal pure returns (bytes memory) {
        if (!success) {
            _revert(returndata);
        } else {
            return returndata;
        }
    }

    /**
     * @dev Reverts with returndata if present. Otherwise reverts with {FailedInnerCall}.
     */
    function _revert(bytes memory returndata) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert FailedInnerCall();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.20;

import {IERC165} from "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon
     *   a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must have been allowed to move this token by either {approve} or
     *   {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon
     *   a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(address from, address to, uint256 tokenId) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Note that the caller is responsible to confirm that the recipient is capable of receiving ERC721
     * or else they may be permanently lost. Usage of {safeTransferFrom} prevents loss, though the caller must
     * understand this adds an external call which potentially creates a reentrancy vulnerability.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 tokenId) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the address zero.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool approved) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.20;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be
     * reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.20;

import {IERC721} from "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

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

pragma solidity ^0.8.20;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

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

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

pragma solidity ^0.8.20;

import {Math} from "./math/Math.sol";
import {SignedMath} from "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(value < 0 ? "-" : "", toString(SignedMath.abs(value)));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        uint256 localValue = value;
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal
     * representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return bytes(a).length == bytes(b).length && keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

import {IERC165} from "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(address sender, uint256 balance, uint256 needed);

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

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

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

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

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

/**
 * @dev Standard ERC721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in EIP-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

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

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

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

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

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

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

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

/**
 * @dev Standard ERC1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(address sender, uint256 balance, uint256 needed, uint256 tokenId);

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/introspection/IERC165.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

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

/*

██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗
██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║
██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║
██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║
██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║
╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝

██╗   ██╗██████╗  ██████╗  ██████╗ ██╗  ██╗ ██╗ █████╗
██║   ██║██╔══██╗██╔════╝ ██╔═████╗╚██╗██╔╝███║██╔══██╗
██║   ██║██║  ██║███████╗ ██║██╔██║ ╚███╔╝ ╚██║╚█████╔╝
██║   ██║██║  ██║██╔═══██╗████╔╝██║ ██╔██╗  ██║██╔══██╗
╚██████╔╝██████╔╝╚██████╔╝╚██████╔╝██╔╝ ██╗ ██║╚█████╔╝
 ╚═════╝ ╚═════╝  ╚═════╝  ╚═════╝ ╚═╝  ╚═╝ ╚═╝ ╚════╝

*/

import "./ud60x18/Casting.sol";
import "./ud60x18/Constants.sol";
import "./ud60x18/Conversions.sol";
import "./ud60x18/Errors.sol";
import "./ud60x18/Helpers.sol";
import "./ud60x18/Math.sol";
import "./ud60x18/ValueType.sol";

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IERC4906 } from "@openzeppelin/contracts/interfaces/IERC4906.sol";
import { IERC20 } from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import { IERC721Metadata } from "@openzeppelin/contracts/token/ERC721/extensions/IERC721Metadata.sol";
import { UD60x18 } from "@prb/math/src/UD60x18.sol";

import { Lockup } from "../types/DataTypes.sol";
import { IAdminable } from "./IAdminable.sol";
import { IBatch } from "./IBatch.sol";
import { ILockupNFTDescriptor } from "./ILockupNFTDescriptor.sol";

/// @title ISablierLockupBase
/// @notice Common logic between all Sablier Lockup contracts.
interface ISablierLockupBase is
    IAdminable, // 0 inherited components
    IBatch, // 0 inherited components
    IERC4906, // 2 inherited components
    IERC721Metadata // 2 inherited components
{
    /*//////////////////////////////////////////////////////////////////////////
                                       EVENTS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Emitted when the admin allows a new recipient contract to hook to Sablier.
    /// @param admin The address of the current contract admin.
    /// @param recipient The address of the recipient contract put on the allowlist.
    event AllowToHook(address indexed admin, address recipient);

    /// @notice Emitted when a stream is canceled.
    /// @param streamId The ID of the stream.
    /// @param sender The address of the stream's sender.
    /// @param recipient The address of the stream's recipient.
    /// @param token The contract address of the ERC-20 token that has been distributed.
    /// @param senderAmount The amount of tokens refunded to the stream's sender, denoted in units of the token's
    /// decimals.
    /// @param recipientAmount The amount of tokens left for the stream's recipient to withdraw, denoted in units of the
    /// token's decimals.
    event CancelLockupStream(
        uint256 streamId,
        address indexed sender,
        address indexed recipient,
        IERC20 indexed token,
        uint128 senderAmount,
        uint128 recipientAmount
    );

    /// @notice Emitted when the accrued fees are collected.
    /// @param admin The address of the current contract admin, which has received the fees.
    /// @param feeAmount The amount of collected fees.
    event CollectFees(address indexed admin, uint256 indexed feeAmount);

    /// @notice Emitted when withdrawing from multiple streams and one particular withdrawal reverts.
    /// @param streamId The stream ID that reverted during withdraw.
    /// @param revertData The error data returned by the reverted withdraw.
    event InvalidWithdrawalInWithdrawMultiple(uint256 streamId, bytes revertData);

    /// @notice Emitted when a sender gives up the right to cancel a stream.
    /// @param streamId The ID of the stream.
    event RenounceLockupStream(uint256 indexed streamId);

    /// @notice Emitted when the admin sets a new NFT descriptor contract.
    /// @param admin The address of the current contract admin.
    /// @param oldNFTDescriptor The address of the old NFT descriptor contract.
    /// @param newNFTDescriptor The address of the new NFT descriptor contract.
    event SetNFTDescriptor(
        address indexed admin, ILockupNFTDescriptor oldNFTDescriptor, ILockupNFTDescriptor newNFTDescriptor
    );

    /// @notice Emitted when tokens are withdrawn from a stream.
    /// @param streamId The ID of the stream.
    /// @param to The address that has received the withdrawn tokens.
    /// @param token The contract address of the ERC-20 token that has been withdrawn.
    /// @param amount The amount of tokens withdrawn, denoted in units of the token's decimals.
    event WithdrawFromLockupStream(uint256 indexed streamId, address indexed to, IERC20 indexed token, uint128 amount);

    /*//////////////////////////////////////////////////////////////////////////
                                 CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Retrieves the maximum broker fee that can be charged by the broker, denoted as a fixed-point
    /// number where 1e18 is 100%.
    /// @dev This value is hard coded as a constant.
    function MAX_BROKER_FEE() external view returns (UD60x18);

    /// @notice Retrieves the amount deposited in the stream, denoted in units of the token's decimals.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getDepositedAmount(uint256 streamId) external view returns (uint128 depositedAmount);

    /// @notice Retrieves the stream's end time, which is a Unix timestamp.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getEndTime(uint256 streamId) external view returns (uint40 endTime);

    /// @notice Retrieves the distribution models used to create the stream.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getLockupModel(uint256 streamId) external view returns (Lockup.Model lockupModel);

    /// @notice Retrieves the stream's recipient.
    /// @dev Reverts if the NFT has been burned.
    /// @param streamId The stream ID for the query.
    function getRecipient(uint256 streamId) external view returns (address recipient);

    /// @notice Retrieves the amount refunded to the sender after a cancellation, denoted in units of the token's
    /// decimals. This amount is always zero unless the stream was canceled.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getRefundedAmount(uint256 streamId) external view returns (uint128 refundedAmount);

    /// @notice Retrieves the stream's sender.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getSender(uint256 streamId) external view returns (address sender);

    /// @notice Retrieves the stream's start time, which is a Unix timestamp.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getStartTime(uint256 streamId) external view returns (uint40 startTime);

    /// @notice Retrieves the address of the underlying ERC-20 token being distributed.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getUnderlyingToken(uint256 streamId) external view returns (IERC20 token);

    /// @notice Retrieves the amount withdrawn from the stream, denoted in units of the token's decimals.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function getWithdrawnAmount(uint256 streamId) external view returns (uint128 withdrawnAmount);

    /// @notice Retrieves a flag indicating whether the provided address is a contract allowed to hook to Sablier
    /// when a stream is canceled or when tokens are withdrawn.
    /// @dev See {ISablierLockupRecipient} for more information.
    function isAllowedToHook(address recipient) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream can be canceled. When the stream is cold, this
    /// flag is always `false`.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isCancelable(uint256 streamId) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream is cold, i.e. settled, canceled, or depleted.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isCold(uint256 streamId) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream is depleted.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isDepleted(uint256 streamId) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream exists.
    /// @dev Does not revert if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isStream(uint256 streamId) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream NFT can be transferred.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isTransferable(uint256 streamId) external view returns (bool result);

    /// @notice Retrieves a flag indicating whether the stream is warm, i.e. either pending or streaming.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function isWarm(uint256 streamId) external view returns (bool result);

    /// @notice Counter for stream IDs, used in the create functions.
    function nextStreamId() external view returns (uint256);

    /// @notice Contract that generates the non-fungible token URI.
    function nftDescriptor() external view returns (ILockupNFTDescriptor);

    /// @notice Calculates the amount that the sender would be refunded if the stream were canceled, denoted in units
    /// of the token's decimals.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function refundableAmountOf(uint256 streamId) external view returns (uint128 refundableAmount);

    /// @notice Retrieves the stream's status.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function statusOf(uint256 streamId) external view returns (Lockup.Status status);

    /// @notice Calculates the amount streamed to the recipient, denoted in units of the token's decimals.
    /// @dev Reverts if `streamId` references a null stream.
    ///
    /// Notes:
    /// - Upon cancellation of the stream, the amount streamed is calculated as the difference between the deposited
    /// amount and the refunded amount. Ultimately, when the stream becomes depleted, the streamed amount is equivalent
    /// to the total amount withdrawn.
    ///
    /// @param streamId The stream ID for the query.
    function streamedAmountOf(uint256 streamId) external view returns (uint128 streamedAmount);

    /// @notice Retrieves a flag indicating whether the stream was canceled.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function wasCanceled(uint256 streamId) external view returns (bool result);

    /// @notice Calculates the amount that the recipient can withdraw from the stream, denoted in units of the token's
    /// decimals.
    /// @dev Reverts if `streamId` references a null stream.
    /// @param streamId The stream ID for the query.
    function withdrawableAmountOf(uint256 streamId) external view returns (uint128 withdrawableAmount);

    /*//////////////////////////////////////////////////////////////////////////
                               NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Allows a recipient contract to hook to Sablier when a stream is canceled or when tokens are withdrawn.
    /// Useful for implementing contracts that hold streams on behalf of users, such as vaults or staking contracts.
    ///
    /// @dev Emits an {AllowToHook} event.
    ///
    /// Notes:
    /// - Does not revert if the contract is already on the allowlist.
    /// - This is an irreversible operation. The contract cannot be removed from the allowlist.
    ///
    /// Requirements:
    /// - `msg.sender` must be the contract admin.
    /// - `recipient` must have a non-zero code size.
    /// - `recipient` must implement {ISablierLockupRecipient}.
    ///
    /// @param recipient The address of the contract to allow for hooks.
    function allowToHook(address recipient) external;

    /// @notice Burns the NFT associated with the stream.
    ///
    /// @dev Emits a {Transfer} and {MetadataUpdate} event.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `streamId` must reference a depleted stream.
    /// - The NFT must exist.
    /// - `msg.sender` must be either the NFT owner or an approved third party.
    ///
    /// @param streamId The ID of the stream NFT to burn.
    function burn(uint256 streamId) external payable;

    /// @notice Cancels the stream and refunds any remaining tokens to the sender.
    ///
    /// @dev Emits a {Transfer}, {CancelLockupStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - If there any tokens left for the recipient to withdraw, the stream is marked as canceled. Otherwise, the
    /// stream is marked as depleted.
    /// - If the address is on the allowlist, this function will invoke a hook on the recipient.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - The stream must be warm and cancelable.
    /// - `msg.sender` must be the stream's sender.
    ///
    /// @param streamId The ID of the stream to cancel.
    function cancel(uint256 streamId) external payable;

    /// @notice Cancels multiple streams and refunds any remaining tokens to the sender.
    ///
    /// @dev Emits multiple {Transfer}, {CancelLockupStream} and {MetadataUpdate} events.
    ///
    /// Notes:
    /// - Refer to the notes in {cancel}.
    ///
    /// Requirements:
    /// - All requirements from {cancel} must be met for each stream.
    ///
    /// @param streamIds The IDs of the streams to cancel.
    function cancelMultiple(uint256[] calldata streamIds) external payable;

    /// @notice Collects the accrued fees by transferring them to the contract admin.
    ///
    /// @dev Emits a {CollectFees} event.
    ///
    /// Notes:
    /// - If the admin is a contract, it must be able to receive native token payments, e.g., ETH for Ethereum Mainnet.
    function collectFees() external;

    /// @notice Removes the right of the stream's sender to cancel the stream.
    ///
    /// @dev Emits a {RenounceLockupStream} event.
    ///
    /// Notes:
    /// - This is an irreversible operation.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `streamId` must reference a warm stream.
    /// - `msg.sender` must be the stream's sender.
    /// - The stream must be cancelable.
    ///
    /// @param streamId The ID of the stream to renounce.
    function renounce(uint256 streamId) external payable;

    /// @notice Renounces multiple streams.
    ///
    /// @dev Emits multiple {RenounceLockupStream} events.
    ///
    /// Notes:
    /// - Refer to the notes in {renounce}.
    ///
    /// Requirements:
    /// - All requirements from {renounce} must be met for each stream.
    ///
    /// @param streamIds An array of stream IDs to renounce.
    function renounceMultiple(uint256[] calldata streamIds) external payable;

    /// @notice Sets a new NFT descriptor contract, which produces the URI describing the Sablier stream NFTs.
    ///
    /// @dev Emits a {SetNFTDescriptor} and {BatchMetadataUpdate} event.
    ///
    /// Notes:
    /// - Does not revert if the NFT descriptor is the same.
    ///
    /// Requirements:
    /// - `msg.sender` must be the contract admin.
    ///
    /// @param newNFTDescriptor The address of the new NFT descriptor contract.
    function setNFTDescriptor(ILockupNFTDescriptor newNFTDescriptor) external;

    /// @notice Withdraws the provided amount of tokens from the stream to the `to` address.
    ///
    /// @dev Emits a {Transfer}, {WithdrawFromLockupStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - If `msg.sender` is not the recipient and the address is on the allowlist, this function will invoke a hook on
    /// the recipient.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - `streamId` must not reference a null or depleted stream.
    /// - `to` must not be the zero address.
    /// - `amount` must be greater than zero and must not exceed the withdrawable amount.
    /// - `to` must be the recipient if `msg.sender` is not the stream's recipient or an approved third party.
    ///
    /// @param streamId The ID of the stream to withdraw from.
    /// @param to The address receiving the withdrawn tokens.
    /// @param amount The amount to withdraw, denoted in units of the token's decimals.
    function withdraw(uint256 streamId, address to, uint128 amount) external payable;

    /// @notice Withdraws the maximum withdrawable amount from the stream to the provided address `to`.
    ///
    /// @dev Emits a {Transfer}, {WithdrawFromLockupStream} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - Refer to the notes in {withdraw}.
    ///
    /// Requirements:
    /// - Refer to the requirements in {withdraw}.
    ///
    /// @param streamId The ID of the stream to withdraw from.
    /// @param to The address receiving the withdrawn tokens.
    /// @return withdrawnAmount The amount withdrawn, denoted in units of the token's decimals.
    function withdrawMax(uint256 streamId, address to) external payable returns (uint128 withdrawnAmount);

    /// @notice Withdraws the maximum withdrawable amount from the stream to the current recipient, and transfers the
    /// NFT to `newRecipient`.
    ///
    /// @dev Emits a {WithdrawFromLockupStream}, {Transfer} and {MetadataUpdate} event.
    ///
    /// Notes:
    /// - If the withdrawable amount is zero, the withdrawal is skipped.
    /// - Refer to the notes in {withdraw}.
    ///
    /// Requirements:
    /// - `msg.sender` must be either the NFT owner or an approved third party.
    /// - Refer to the requirements in {withdraw}.
    /// - Refer to the requirements in {IERC721.transferFrom}.
    ///
    /// @param streamId The ID of the stream NFT to transfer.
    /// @param newRecipient The address of the new owner of the stream NFT.
    /// @return withdrawnAmount The amount withdrawn, denoted in units of the token's decimals.
    function withdrawMaxAndTransfer(
        uint256 streamId,
        address newRecipient
    )
        external
        payable
        returns (uint128 withdrawnAmount);

    /// @notice Withdraws tokens from streams to the recipient of each stream.
    ///
    /// @dev Emits multiple {Transfer}, {WithdrawFromLockupStream} and {MetadataUpdate} events. For each stream that
    /// reverted the withdrawal, it emits an {InvalidWithdrawalInWithdrawMultiple} event.
    ///
    /// Notes:
    /// - This function attempts to call a hook on the recipient of each stream, unless `msg.sender` is the recipient.
    ///
    /// Requirements:
    /// - Must not be delegate called.
    /// - There must be an equal number of `streamIds` and `amounts`.
    /// - Each stream ID in the array must not reference a null or depleted stream.
    /// - Each amount in the array must be greater than zero and must not exceed the withdrawable amount.
    ///
    /// @param streamIds The IDs of the streams to withdraw from.
    /// @param amounts The amounts to withdraw, denoted in units of the token's decimals.
    function withdrawMultiple(uint256[] calldata streamIds, uint128[] calldata amounts) external payable;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IERC165 } from "@openzeppelin/contracts/utils/introspection/IERC165.sol";

/// @title ISablierLockupRecipient
/// @notice Interface for recipient contracts capable of reacting to cancellations and withdrawals. For this to be able
/// to hook into Sablier, it must fully implement this interface and it must have been allowlisted by the Lockup
/// contract's admin.
/// @dev See {IERC165-supportsInterface}.
/// The implementation MUST implement the {IERC165-supportsInterface} method, which MUST return `true` when called with
/// `0xf8ee98d3`, i.e. `type(ISablierLockupRecipient).interfaceId`.
interface ISablierLockupRecipient is IERC165 {
    /// @notice Responds to cancellations.
    ///
    /// @dev Notes:
    /// - The function MUST return the selector `ISablierLockupRecipient.onSablierLockupCancel.selector`.
    /// - If this function reverts, the execution in the Lockup contract will revert as well.
    ///
    /// @param streamId The ID of the canceled stream.
    /// @param sender The stream's sender, who canceled the stream.
    /// @param senderAmount The amount of tokens refunded to the stream's sender, denoted in units of the token's
    /// decimals.
    /// @param recipientAmount The amount of tokens left for the stream's recipient to withdraw, denoted in units of
    /// the token's decimals.
    ///
    /// @return selector The selector of this function needed to validate the hook.
    function onSablierLockupCancel(
        uint256 streamId,
        address sender,
        uint128 senderAmount,
        uint128 recipientAmount
    )
        external
        returns (bytes4 selector);

    /// @notice Responds to withdrawals triggered by any address except the contract implementing this interface.
    ///
    /// @dev Notes:
    /// - The function MUST return the selector `ISablierLockupRecipient.onSablierLockupWithdraw.selector`.
    /// - If this function reverts, the execution in the Lockup contract will revert as well.
    ///
    /// @param streamId The ID of the stream being withdrawn from.
    /// @param caller The original `msg.sender` address that triggered the withdrawal.
    /// @param to The address receiving the withdrawn tokens.
    /// @param amount The amount of tokens withdrawn, denoted in units of the token's decimals.
    ///
    /// @return selector The selector of this function needed to validate the hook.
    function onSablierLockupWithdraw(
        uint256 streamId,
        address caller,
        address to,
        uint128 amount
    )
        external
        returns (bytes4 selector);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { IAdminable } from "../interfaces/IAdminable.sol";
import { Errors } from "../libraries/Errors.sol";

/// @title Adminable
/// @notice See the documentation in {IAdminable}.
abstract contract Adminable is IAdminable {
    /*//////////////////////////////////////////////////////////////////////////
                                  STATE VARIABLES
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc IAdminable
    address public override admin;

    /*//////////////////////////////////////////////////////////////////////////
                                      MODIFIERS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Reverts if called by any account other than the admin.
    modifier onlyAdmin() {
        if (admin != msg.sender) {
            revert Errors.CallerNotAdmin({ admin: admin, caller: msg.sender });
        }
        _;
    }

    /*//////////////////////////////////////////////////////////////////////////
                                     CONSTRUCTOR
    //////////////////////////////////////////////////////////////////////////*/

    /// @dev Emits a {TransferAdmin} event.
    /// @param initialAdmin The address of the initial admin.
    constructor(address initialAdmin) {
        admin = initialAdmin;
        emit TransferAdmin({ oldAdmin: address(0), newAdmin: initialAdmin });
    }

    /*//////////////////////////////////////////////////////////////////////////
                         USER-FACING NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc IAdminable
    function transferAdmin(address newAdmin) public virtual override onlyAdmin {
        // Effect: update the admin.
        admin = newAdmin;

        // Log the transfer of the admin.
        emit IAdminable.TransferAdmin({ oldAdmin: msg.sender, newAdmin: newAdmin });
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
// solhint-disable no-inline-assembly
pragma solidity >=0.8.22;

import { IBatch } from "../interfaces/IBatch.sol";

/// @title Batch
/// @notice See the documentation in {IBatch}.
abstract contract Batch is IBatch {
    /*//////////////////////////////////////////////////////////////////////////
                         USER-FACING NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @inheritdoc IBatch
    /// @dev Since `msg.value` can be reused across calls, be VERY CAREFUL when using it. Refer to
    /// https://paradigm.xyz/2021/08/two-rights-might-make-a-wrong for more information.
    function batch(bytes[] calldata calls) external payable override returns (bytes[] memory results) {
        uint256 count = calls.length;
        results = new bytes[](count);

        for (uint256 i = 0; i < count; ++i) {
            (bool success, bytes memory result) = address(this).delegatecall(calls[i]);

            // Check: If the delegatecall failed, load and bubble up the revert data.
            if (!success) {
                assembly {
                    // Get the length of the result stored in the first 32 bytes.
                    let resultSize := mload(result)

                    // Forward the pointer by 32 bytes to skip the length argument, and revert with the result.
                    revert(add(32, result), resultSize)
                }
            }

            // Push the result into the results array.
            results[i] = result;
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

import { Errors } from "../libraries/Errors.sol";

/// @title NoDelegateCall
/// @notice This contract implements logic to prevent delegate calls.
abstract contract NoDelegateCall {
    /// @dev The address of the original contract that was deployed.
    address private immutable ORIGINAL;

    /// @dev Sets the original contract address.
    constructor() {
        ORIGINAL = address(this);
    }

    /// @notice Prevents delegate calls.
    modifier noDelegateCall() {
        _preventDelegateCall();
        _;
    }

    /// @dev This function checks whether the current call is a delegate call, and reverts if it is.
    ///
    /// - A private function is used instead of inlining this logic in a modifier because Solidity copies modifiers into
    /// every function that uses them. The `ORIGINAL` address would get copied in every place the modifier is used,
    /// which would increase the contract size. By using a function instead, we can avoid this duplication of code
    /// and reduce the overall size of the contract.
    function _preventDelegateCall() private view {
        if (address(this) != ORIGINAL) {
            revert Errors.DelegateCall();
        }
    }
}

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

import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";

/// @notice Thrown when trying to cast a uint128 that doesn't fit in SD1x18.
error PRBMath_IntoSD1x18_Overflow(uint128 x);

/// @notice Thrown when trying to cast a uint128 that doesn't fit in SD21x18.
error PRBMath_IntoSD21x18_Overflow(uint128 x);

/// @notice Thrown when trying to cast a uint128 that doesn't fit in UD2x18.
error PRBMath_IntoUD2x18_Overflow(uint128 x);

/// @title PRBMathCastingUint128
/// @notice Casting utilities for uint128.
library PRBMathCastingUint128 {
    /// @notice Casts a uint128 number to SD1x18.
    /// @dev Requirements:
    /// - x ≤ uMAX_SD1x18
    function intoSD1x18(uint128 x) internal pure returns (SD1x18 result) {
        if (x > uint256(int256(uMAX_SD1x18))) {
            revert PRBMath_IntoSD1x18_Overflow(x);
        }
        result = SD1x18.wrap(int64(uint64(x)));
    }

    /// @notice Casts a uint128 number to SD21x18.
    /// @dev Requirements:
    /// - x ≤ uMAX_SD21x18
    function intoSD21x18(uint128 x) internal pure returns (SD21x18 result) {
        if (x > uint256(int256(uMAX_SD21x18))) {
            revert PRBMath_IntoSD21x18_Overflow(x);
        }
        result = SD21x18.wrap(int128(x));
    }

    /// @notice Casts a uint128 number to SD59x18.
    /// @dev There is no overflow check because uint128 ⊆ SD59x18.
    function intoSD59x18(uint128 x) internal pure returns (SD59x18 result) {
        result = SD59x18.wrap(int256(uint256(x)));
    }

    /// @notice Casts a uint128 number to UD2x18.
    /// @dev Requirements:
    /// - x ≤ uMAX_UD2x18
    function intoUD2x18(uint128 x) internal pure returns (UD2x18 result) {
        if (x > uint64(uMAX_UD2x18)) {
            revert PRBMath_IntoUD2x18_Overflow(x);
        }
        result = UD2x18.wrap(uint64(x));
    }

    /// @notice Casts a uint128 number to UD21x18.
    function intoUD21x18(uint128 x) internal pure returns (UD21x18 result) {
        result = UD21x18.wrap(x);
    }

    /// @notice Casts a uint128 number to UD60x18.
    /// @dev There is no overflow check because uint128 ⊆ UD60x18.
    function intoUD60x18(uint128 x) internal pure returns (UD60x18 result) {
        result = UD60x18.wrap(x);
    }
}

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

import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";

/// @title PRBMathCastingUint40
/// @notice Casting utilities for uint40.
library PRBMathCastingUint40 {
    /// @notice Casts a uint40 number into SD1x18.
    /// @dev There is no overflow check because uint40 ⊆ SD1x18.
    function intoSD1x18(uint40 x) internal pure returns (SD1x18 result) {
        result = SD1x18.wrap(int64(uint64(x)));
    }

    /// @notice Casts a uint40 number into SD21x18.
    /// @dev There is no overflow check because uint40 ⊆ SD21x18.
    function intoSD21x18(uint40 x) internal pure returns (SD21x18 result) {
        result = SD21x18.wrap(int128(uint128(x)));
    }

    /// @notice Casts a uint40 number into SD59x18.
    /// @dev There is no overflow check because uint40 ⊆ SD59x18.
    function intoSD59x18(uint40 x) internal pure returns (SD59x18 result) {
        result = SD59x18.wrap(int256(uint256(x)));
    }

    /// @notice Casts a uint40 number into UD2x18.
    /// @dev There is no overflow check because uint40 ⊆ UD2x18.
    function intoUD2x18(uint40 x) internal pure returns (UD2x18 result) {
        result = UD2x18.wrap(x);
    }

    /// @notice Casts a uint40 number into UD21x18.
    /// @dev There is no overflow check because uint40 ⊆ UD21x18.
    function intoUD21x18(uint40 x) internal pure returns (UD21x18 result) {
        result = UD21x18.wrap((x));
    }

    /// @notice Casts a uint40 number into UD60x18.
    /// @dev There is no overflow check because uint40 ⊆ UD60x18.
    function intoUD60x18(uint40 x) internal pure returns (UD60x18 result) {
        result = UD60x18.wrap(x);
    }
}

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

/*

██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗
██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║
██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║
██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║
██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║
╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝

███████╗██████╗ ███████╗ █████╗ ██╗  ██╗ ██╗ █████╗
██╔════╝██╔══██╗██╔════╝██╔══██╗╚██╗██╔╝███║██╔══██╗
███████╗██║  ██║███████╗╚██████║ ╚███╔╝ ╚██║╚█████╔╝
╚════██║██║  ██║╚════██║ ╚═══██║ ██╔██╗  ██║██╔══██╗
███████║██████╔╝███████║ █████╔╝██╔╝ ██╗ ██║╚█████╔╝
╚══════╝╚═════╝ ╚══════╝ ╚════╝ ╚═╝  ╚═╝ ╚═╝ ╚════╝

*/

import "./sd59x18/Casting.sol";
import "./sd59x18/Constants.sol";
import "./sd59x18/Conversions.sol";
import "./sd59x18/Errors.sol";
import "./sd59x18/Helpers.sol";
import "./sd59x18/Math.sol";
import "./sd59x18/ValueType.sol";

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

/*

██████╗ ██████╗ ██████╗ ███╗   ███╗ █████╗ ████████╗██╗  ██╗
██╔══██╗██╔══██╗██╔══██╗████╗ ████║██╔══██╗╚══██╔══╝██║  ██║
██████╔╝██████╔╝██████╔╝██╔████╔██║███████║   ██║   ███████║
██╔═══╝ ██╔══██╗██╔══██╗██║╚██╔╝██║██╔══██║   ██║   ██╔══██║
██║     ██║  ██║██████╔╝██║ ╚═╝ ██║██║  ██║   ██║   ██║  ██║
╚═╝     ╚═╝  ╚═╝╚═════╝ ╚═╝     ╚═╝╚═╝  ╚═╝   ╚═╝   ╚═╝  ╚═╝

██╗   ██╗██████╗ ██████╗ ██╗  ██╗ ██╗ █████╗
██║   ██║██╔══██╗╚════██╗╚██╗██╔╝███║██╔══██╗
██║   ██║██║  ██║ █████╔╝ ╚███╔╝ ╚██║╚█████╔╝
██║   ██║██║  ██║██╔═══╝  ██╔██╗  ██║██╔══██╗
╚██████╔╝██████╔╝███████╗██╔╝ ██╗ ██║╚█████╔╝
 ╚═════╝ ╚═════╝ ╚══════╝╚═╝  ╚═╝ ╚═╝ ╚════╝

*/

import "./ud2x18/Casting.sol";
import "./ud2x18/Constants.sol";
import "./ud2x18/Errors.sol";
import "./ud2x18/ValueType.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Muldiv operation overflow.
     */
    error MathOverflowedMulDiv();

    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 overflow flag.
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an overflow flag.
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        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 division by zero flag.
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        unchecked {
            if (b == 0) return (false, 0);
            return (true, a / b);
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        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.
            return a / b;
        }

        // (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 = 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 2^256. Also prevents denominator == 0.
            if (denominator <= prod1) {
                revert MathOverflowedMulDiv();
            }

            ///////////////////////////////////////////////
            // 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 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 (unsignedRoundsUp(rounding) && 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
     * towards zero.
     *
     * 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 + (unsignedRoundsUp(rounding) && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * 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 + (unsignedRoundsUp(rounding) && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * 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 + (unsignedRoundsUp(rounding) && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * 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 + (unsignedRoundsUp(rounding) && 1 << (result << 3) < value ? 1 : 0);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC4906.sol)

pragma solidity ^0.8.20;

import {IERC165} from "./IERC165.sol";
import {IERC721} from "./IERC721.sol";

/// @title EIP-721 Metadata Update Extension
interface IERC4906 is IERC165, IERC721 {
    /// @dev This event emits when the metadata of a token is changed.
    /// So that the third-party platforms such as NFT market could
    /// timely update the images and related attributes of the NFT.
    event MetadataUpdate(uint256 _tokenId);

    /// @dev This event emits when the metadata of a range of tokens is changed.
    /// So that the third-party platforms such as NFT market could
    /// timely update the images and related attributes of the NFTs.
    event BatchMetadataUpdate(uint256 _fromTokenId, uint256 _toTokenId);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

/// @title IAdminable
/// @notice Contract module that provides a basic access control mechanism, with an admin that can be
/// granted exclusive access to specific functions. The inheriting contract must set the initial admin
/// in the constructor.
interface IAdminable {
    /*//////////////////////////////////////////////////////////////////////////
                                       EVENTS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Emitted when the admin is transferred.
    /// @param oldAdmin The address of the old admin.
    /// @param newAdmin The address of the new admin.
    event TransferAdmin(address indexed oldAdmin, address indexed newAdmin);

    /*//////////////////////////////////////////////////////////////////////////
                                 CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice The address of the admin account or contract.
    function admin() external view returns (address);

    /*//////////////////////////////////////////////////////////////////////////
                               NON-CONSTANT FUNCTIONS
    //////////////////////////////////////////////////////////////////////////*/

    /// @notice Transfers the contract admin to a new address.
    ///
    /// @dev Notes:
    /// - Does not revert if the admin is the same.
    /// - This function can potentially leave the contract without an admin, thereby removing any
    /// functionality that is only available to the admin.
    ///
    /// Requirements:
    /// - `msg.sender` must be the contract admin.
    ///
    /// @param newAdmin The address of the new admin.
    function transferAdmin(address newAdmin) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity >=0.8.22;

/// @notice This contract implements logic to batch call any function.
interface IBatch {
    /// @notice Allows batched calls to self, i.e., `this` contract.
    /// @dev Since `msg.value` can be reused across calls, be VERY CAREFUL when using it. Refer to
    /// https://paradigm.xyz/2021/08/two-rights-might-make-a-wrong for more information.
    /// @param calls An array of inputs for each call.
    /// @return results An array of results from each call. Empty when the calls do not return anything.
    function batch(bytes[] calldata calls) external payable returns (bytes[] memory results);
}

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

import { SD1x18 } from "./ValueType.sol";

/// @dev Euler's number as an SD1x18 number.
SD1x18 constant E = SD1x18.wrap(2_718281828459045235);

/// @dev The maximum value an SD1x18 number can have.
int64 constant uMAX_SD1x18 = 9_223372036854775807;
SD1x18 constant MAX_SD1x18 = SD1x18.wrap(uMAX_SD1x18);

/// @dev The minimum value an SD1x18 number can have.
int64 constant uMIN_SD1x18 = -9_223372036854775808;
SD1x18 constant MIN_SD1x18 = SD1x18.wrap(uMIN_SD1x18);

/// @dev PI as an SD1x18 number.
SD1x18 constant PI = SD1x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD1x18.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int64 constant uUNIT = 1e18;

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

import "./Casting.sol" as Casting;

/// @notice The signed 1.18-decimal fixed-point number representation, which can have up to 1 digit and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int64. This is useful when end users want to use int64 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD1x18 is int64;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for SD1x18 global;

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

import { SD21x18 } from "./ValueType.sol";

/// @dev Euler's number as an SD21x18 number.
SD21x18 constant E = SD21x18.wrap(2_718281828459045235);

/// @dev The maximum value an SD21x18 number can have.
int128 constant uMAX_SD21x18 = 170141183460469231731_687303715884105727;
SD21x18 constant MAX_SD21x18 = SD21x18.wrap(uMAX_SD21x18);

/// @dev The minimum value an SD21x18 number can have.
int128 constant uMIN_SD21x18 = -170141183460469231731_687303715884105728;
SD21x18 constant MIN_SD21x18 = SD21x18.wrap(uMIN_SD21x18);

/// @dev PI as an SD21x18 number.
SD21x18 constant PI = SD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD21x18.
SD21x18 constant UNIT = SD21x18.wrap(1e18);
int128 constant uUNIT = 1e18;

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

import "./Casting.sol" as Casting;

/// @notice The signed 21.18-decimal fixed-point number representation, which can have up to 21 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int128. This is useful when end users want to use int128 to save gas, e.g. with tight variable packing in contract
/// storage.
type SD21x18 is int128;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for SD21x18 global;

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

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

/// @notice The signed 59.18-decimal fixed-point number representation, which can have up to 59 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type int256.
type SD59x18 is int256;

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

using {
    Casting.intoInt256,
    Casting.intoSD1x18,
    Casting.intoSD21x18,
    Casting.intoUD2x18,
    Casting.intoUD21x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for SD59x18 global;

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

using {
    Math.abs,
    Math.avg,
    Math.ceil,
    Math.div,
    Math.exp,
    Math.exp2,
    Math.floor,
    Math.frac,
    Math.gm,
    Math.inv,
    Math.log10,
    Math.log2,
    Math.ln,
    Math.mul,
    Math.pow,
    Math.powu,
    Math.sqrt
} for SD59x18 global;

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

using {
    Helpers.add,
    Helpers.and,
    Helpers.eq,
    Helpers.gt,
    Helpers.gte,
    Helpers.isZero,
    Helpers.lshift,
    Helpers.lt,
    Helpers.lte,
    Helpers.mod,
    Helpers.neq,
    Helpers.not,
    Helpers.or,
    Helpers.rshift,
    Helpers.sub,
    Helpers.uncheckedAdd,
    Helpers.uncheckedSub,
    Helpers.uncheckedUnary,
    Helpers.xor
} for SD59x18 global;

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

// The global "using for" directive makes it possible to use these operators on the SD59x18 type.
using {
    Helpers.add as +,
    Helpers.and2 as &,
    Math.div as /,
    Helpers.eq as ==,
    Helpers.gt as >,
    Helpers.gte as >=,
    Helpers.lt as <,
    Helpers.lte as <=,
    Helpers.mod as %,
    Math.mul as *,
    Helpers.neq as !=,
    Helpers.not as ~,
    Helpers.or as |,
    Helpers.sub as -,
    Helpers.unary as -,
    Helpers.xor as ^
} for SD59x18 global;

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

import { UD2x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);

/// @dev PI as a UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD2x18.
UD2x18 constant UNIT = UD2x18.wrap(1e18);
uint64 constant uUNIT = 1e18;

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

import "./Casting.sol" as Casting;

/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD2x18 is uint64;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD2x18 global;

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

import "./Casting.sol" as Casting;

/// @notice The unsigned 21.18-decimal fixed-point number representation, which can have up to 21 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint128. This is useful when end users want to use uint128 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD21x18 is uint128;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD21x18 global;

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

import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD21x18, uMIN_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for {unwrap}.
function intoInt256(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD1x18
/// - x ≤ uMAX_SD1x18
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
    }
    if (xInt > uMAX_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xInt));
}

/// @notice Casts an SD59x18 number into SD21x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD21x18
/// - x ≤ uMAX_SD21x18
function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Underflow(x);
    }
    if (xInt > uMAX_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Overflow(x);
    }
    result = SD21x18.wrap(int128(xInt));
}

/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD2x18
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD2x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD21x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD21x18
function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD21x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Overflow(x);
    }
    result = UD21x18.wrap(uint128(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD59x18 x) pure returns (uint256 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);
    }
    result = uint256(xInt);
}

/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UINT128
function intoUint128(SD59x18 x) pure returns (uint128 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT128))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
    }
    result = uint128(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

/// @notice Alias for {wrap}.
function sd(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Alias for {wrap}.
function sd59x18(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Wraps an int256 number into SD59x18.
function wrap(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

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

import { SD59x18 } from "./ValueType.sol";

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

/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);

/// @dev The maximum input permitted in {exp}.
int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp}.
int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);

/// @dev The maximum input permitted in {exp2}.
int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp2}.
int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);

/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);

/// @dev $log_2(10)$ as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);

/// @dev $log_2(e)$ as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);

/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);

/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);

/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);

/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);

/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD59x18.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);

/// @dev The unit number squared.
int256 constant uUNIT_SQUARED = 1e36;
SD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);

/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);

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

import { uMAX_SD59x18, uMIN_SD59x18, uUNIT } from "./Constants.sol";
import { PRBMath_SD59x18_Convert_Overflow, PRBMath_SD59x18_Convert_Underflow } from "./Errors.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Converts a simple integer to SD59x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x ≥ `MIN_SD59x18 / UNIT`
/// - x ≤ `MAX_SD59x18 / UNIT`
///
/// @param x The basic integer to convert.
/// @return result The same number converted to SD59x18.
function convert(int256 x) pure returns (SD59x18 result) {
    if (x < uMIN_SD59x18 / uUNIT) {
        revert PRBMath_SD59x18_Convert_Underflow(x);
    }
    if (x > uMAX_SD59x18 / uUNIT) {
        revert PRBMath_SD59x18_Convert_Overflow(x);
    }
    unchecked {
        result = SD59x18.wrap(x * uUNIT);
    }
}

/// @notice Converts an SD59x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The SD59x18 number to convert.
/// @return result The same number as a simple integer.
function convert(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x) / uUNIT;
}

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

import { SD59x18 } from "./ValueType.sol";

/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();

/// @notice Thrown when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);

/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);

/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);

/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();

/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);

/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);

/// @notice Thrown when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);

/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);

/// @notice Thrown when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);

/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();

/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);

/// @notice Thrown when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);

/// @notice Thrown when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);

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

import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() + y.unwrap());
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & bits);
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & y.unwrap());
}

/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() == y.unwrap();
}

/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() > y.unwrap();
}

/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() >= y.unwrap();
}

/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
    result = x.unwrap() == 0;
}

/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() << bits);
}

/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() < y.unwrap();
}

/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() <= y.unwrap();
}

/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % y.unwrap());
}

/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() != y.unwrap();
}

/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(~x.unwrap());
}

/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() | y.unwrap());
}

/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() - y.unwrap());
}

/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(-x.unwrap());
}

/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() + y.unwrap());
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() - y.unwrap());
    }
}

/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(-x.unwrap());
    }
}

/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() ^ y.unwrap());
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
    uEXP_MAX_INPUT,
    uEXP2_MAX_INPUT,
    uEXP_MIN_THRESHOLD,
    uEXP2_MIN_THRESHOLD,
    uHALF_UNIT,
    uLOG2_10,
    uLOG2_E,
    uMAX_SD59x18,
    uMAX_WHOLE_SD59x18,
    uMIN_SD59x18,
    uMIN_WHOLE_SD59x18,
    UNIT,
    uUNIT,
    uUNIT_SQUARED,
    ZERO
} from "./Constants.sol";
import { wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Calculates the absolute value of x.
///
/// @dev Requirements:
/// - x > MIN_SD59x18.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @return result The absolute value of x as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function abs(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();
    }
    result = xInt < 0 ? wrap(-xInt) : x;
}

/// @notice Calculates the arithmetic average of x and y.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

    unchecked {
        // This operation is equivalent to `x / 2 +  y / 2`, and it can never overflow.
        int256 sum = (xInt >> 1) + (yInt >> 1);

        if (sum < 0) {
            // If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right
            // rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.
            assembly ("memory-safe") {
                result := add(sum, and(or(xInt, yInt), 1))
            }
        } else {
            // Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.
            result = wrap(sum + (xInt & yInt & 1));
        }
    }
}

/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≤ MAX_WHOLE_SD59x18
///
/// @param x The SD59x18 number to ceil.
/// @return result The smallest whole number greater than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt > uMAX_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt > 0) {
                resultInt += uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.
///
/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute
/// values separately.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator must not be zero.
/// - The result must fit in SD59x18.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @return result The quotient as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Div_InputTooSmall();
    }

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

    // Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}.
///
/// Requirements:
/// - Refer to the requirements in {exp2}.
/// - x < 133_084258667509499441.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();

    // Any input less than the threshold returns zero.
    // This check also prevents an overflow for very small numbers.
    if (xInt < uEXP_MIN_THRESHOLD) {
        return ZERO;
    }

    // This check prevents values greater than 192e18 from being passed to {exp2}.
    if (xInt > uEXP_MAX_INPUT) {
        revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
    }

    unchecked {
        // Inline the fixed-point multiplication to save gas.
        int256 doubleUnitProduct = xInt * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Notes:
/// - If x < -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x < 192e18.
/// - The result must fit in SD59x18.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        // The inverse of any number less than the threshold is truncated to zero.
        if (xInt < uEXP2_MIN_THRESHOLD) {
            return ZERO;
        }

        unchecked {
            // Inline the fixed-point inversion to save gas.
            result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());
        }
    } else {
        // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
        if (xInt > uEXP2_MAX_INPUT) {
            revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);
        }

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

            // It is safe to cast the result to int256 due to the checks above.
            result = wrap(int256(Common.exp2(x_192x64)));
        }
    }
}

/// @notice Yields the greatest whole number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≥ MIN_WHOLE_SD59x18
///
/// @param x The SD59x18 number to floor.
/// @return result The greatest whole number less than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < uMIN_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Floor_Underflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt < 0) {
                resultInt -= uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @return result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % uUNIT);
}

/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x * y must fit in SD59x18.
/// - x * y must not be negative, since complex numbers are not supported.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == 0 || yInt == 0) {
        return ZERO;
    }

    unchecked {
        // Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.
        int256 xyInt = xInt * yInt;
        if (xyInt / xInt != yInt) {
            revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);
        }

        // The product must not be negative, since complex numbers are not supported.
        if (xyInt < 0) {
            revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
        // during multiplication. See the comments in {Common.sqrt}.
        uint256 resultUint = Common.sqrt(uint256(xyInt));
        result = wrap(int256(resultUint));
    }
}

/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(uUNIT_SQUARED / x.unwrap());
}

/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(SD59x18 x) pure returns (SD59x18 result) {
    // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
    // {log2} can return is ~195_205294292027477728.
    result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}

/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        default { result := uMAX_SD59x18 }
    }

    if (result.unwrap() == uMAX_SD59x18) {
        unchecked {
            // Inline the fixed-point division to save gas.
            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x > 0
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt <= 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    unchecked {
        int256 sign;
        if (xInt >= uUNIT) {
            sign = 1;
        } else {
            sign = -1;
            // Inline the fixed-point inversion to save gas.
            xInt = uUNIT_SQUARED / xInt;
        }

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

        // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
        // because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.
        int256 resultInt = int256(n) * uUNIT;

        // Calculate $y = x * 2^{-n}$.
        int256 y = xInt >> n;

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

        // Calculate the fractional part via the iterative approximation.
        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
        int256 DOUBLE_UNIT = 2e18;
        for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

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

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

/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev Notes:
/// - Refer to the notes in {Common.mulDiv18}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv18}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit in SD59x18.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();
    }

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

    // Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Raises x to the power of y using the following formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}, {log2}, and {mul}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

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

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

    // Calculate the result using the formula.
    result = exp2(mul(log2(x), y));
}

/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {abs} and {Common.mulDiv18}.
/// - The result must fit in SD59x18.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
    uint256 xAbs = uint256(abs(x).unwrap());

    // Calculate the first iteration of the loop in advance.
    uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);

    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.
    uint256 yAux = y;
    for (yAux >>= 1; yAux > 0; yAux >>= 1) {
        xAbs = Common.mulDiv18(xAbs, xAbs);

        // Equivalent to `y % 2 == 1`.
        if (yAux & 1 > 0) {
            resultAbs = Common.mulDiv18(resultAbs, xAbs);
        }
    }

    // The result must fit in SD59x18.
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);
    }

    unchecked {
        // Is the base negative and the exponent odd? If yes, the result should be negative.
        int256 resultInt = int256(resultAbs);
        bool isNegative = x.unwrap() < 0 && y & 1 == 1;
        if (isNegative) {
            resultInt = -resultInt;
        }
        result = wrap(resultInt);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - Only the positive root is returned.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x ≥ 0, since complex numbers are not supported.
/// - x ≤ MAX_SD59x18 / UNIT
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);
    }
    if (xInt > uMAX_SD59x18 / uUNIT) {
        revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);
    }

    unchecked {
        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.
        // In this case, the two numbers are both the square root.
        uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));
        result = wrap(int256(resultUint));
    }
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because UD2x18 ⊆ SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}

/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because UD2x18 ⊆ UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because UD2x18 ⊆ uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
    result = uint128(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because UD2x18 ⊆ uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
    result = uint256(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD2x18 x) pure returns (uint40 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
    result = UD2x18.unwrap(x);
}

/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

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

import { UD2x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

import { UD21x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD21x18 number.
UD21x18 constant E = UD21x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD21x18 number can have.
uint128 constant uMAX_UD21x18 = 340282366920938463463_374607431768211455;
UD21x18 constant MAX_UD21x18 = UD21x18.wrap(uMAX_UD21x18);

/// @dev PI as a UD21x18 number.
UD21x18 constant PI = UD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD21x18.
uint256 constant uUNIT = 1e18;
UD21x18 constant UNIT = UD21x18.wrap(1e18);

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC165.sol)

pragma solidity ^0.8.20;

import {IERC165} from "../utils/introspection/IERC165.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (interfaces/IERC721.sol)

pragma solidity ^0.8.20;

import {IERC721} from "../token/ERC721/IERC721.sol";

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

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";

/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because SD1x18 ⊆ SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}

/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD1x18 x) pure returns (uint128 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
    }
    result = uint128(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD1x18 x) pure returns (uint256 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
    }
    result = uint256(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD1x18 x) pure returns (uint40 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
    }
    if (xInt > int64(uint64(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
    }
    result = uint40(uint64(xInt));
}

/// @notice Alias for {wrap}.
function sd1x18(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
    result = SD1x18.unwrap(x);
}

/// @notice Wraps an int64 number into SD1x18.
function wrap(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD21x18 } from "./ValueType.sol";

/// @notice Casts an SD21x18 number into SD59x18.
/// @dev There is no overflow check because SD21x18 ⊆ SD59x18.
function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD21x18.unwrap(x)));
}

/// @notice Casts an SD21x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD21x18 x) pure returns (uint128 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint128_Underflow(x);
    }
    result = uint128(xInt);
}

/// @notice Casts an SD21x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD21x18 x) pure returns (uint256 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint256_Underflow(x);
    }
    result = uint256(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD21x18 x) pure returns (uint40 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Underflow(x);
    }
    if (xInt > int128(uint128(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Overflow(x);
    }
    result = uint40(uint128(xInt));
}

/// @notice Alias for {wrap}.
function sd21x18(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

/// @notice Unwraps an SD21x18 number into int128.
function unwrap(SD21x18 x) pure returns (int128 result) {
    result = SD21x18.unwrap(x);
}

/// @notice Wraps an int128 number into SD21x18.
function wrap(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD21x18 } from "./ValueType.sol";

/// @notice Casts a UD21x18 number into SD59x18.
/// @dev There is no overflow check because UD21x18 ⊆ SD59x18.
function intoSD59x18(UD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD21x18.unwrap(x))));
}

/// @notice Casts a UD21x18 number into UD60x18.
/// @dev There is no overflow check because UD21x18 ⊆ UD60x18.
function intoUD60x18(UD21x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint128(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Casts a UD21x18 number into uint256.
/// @dev There is no overflow check because UD21x18 ⊆ uint256.
function intoUint256(UD21x18 x) pure returns (uint256 result) {
    result = uint256(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD21x18 x) pure returns (uint40 result) {
    uint128 xUint = UD21x18.unwrap(x);
    if (xUint > uint128(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD21x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud21x18(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

/// @notice Unwrap a UD21x18 number into uint128.
function unwrap(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Wraps a uint128 number into UD21x18.
function wrap(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

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

import { SD1x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);

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

import { SD21x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint128.
error PRBMath_SD21x18_ToUint128_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in UD60x18.
error PRBMath_SD21x18_ToUD60x18_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint256.
error PRBMath_SD21x18_ToUint256_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Overflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Underflow(SD21x18 x);

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

import { UD21x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD21x18 number that doesn't fit in uint40.
error PRBMath_UD21x18_IntoUint40_Overflow(UD21x18 x);

{
  "remappings": [
    "@openzeppelin/contracts/=node_modules/@openzeppelin/contracts/",
    "@prb/math/=node_modules/@prb/math/",
    "forge-std/=node_modules/forge-std/",
    "solady/=node_modules/solady/",
    "solarray/=node_modules/solarray/",
    "@ensdomains/=node_modules/@ensdomains/",
    "@ethereum-waffle/=node_modules/@ethereum-waffle/",
    "eth-gas-reporter/=node_modules/eth-gas-reporter/",
    "hardhat-deploy/=node_modules/hardhat-deploy/",
    "hardhat/=node_modules/hardhat/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 570
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "none",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "shanghai",
  "viaIR": true,
  "libraries": {
    "src/libraries/Helpers.sol": {
      "Helpers": "0xf8076E4Fb5cfE8be1C26E61222DC51828Db8C1dc"
    },
    "src/libraries/VestingMath.sol": {
      "VestingMath": "0x5522CA06Ce080800AB59BA4C091e63f6f54C5E6d"
    }
  }
}

• No Contract Security Audit Submitted- Submit Audit Here

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00000000000000000000000079fb3e81aac012c08501f41296ccc145a1e15844000000000000000000000000a9dc6878c979b5cc1d98a1803f0664ad725a1f5600000000000000000000000000000000000000000000000000000000000003fc

-----Decoded View---------------
Arg [0] : initialAdmin (address): 0x79Fb3e81aAc012c08501f41296CCC145a1E15844
Arg [1] : initialNFTDescriptor (address): 0xA9dC6878C979B5cc1d98a1803F0664ad725A1f56
Arg [2] : maxCount (uint256): 1020

-----Encoded View---------------
3 Constructor Arguments found :
Arg [0] : 00000000000000000000000079fb3e81aac012c08501f41296ccc145a1e15844
Arg [1] : 000000000000000000000000a9dc6878c979b5cc1d98a1803f0664ad725a1f56
Arg [2] : 00000000000000000000000000000000000000000000000000000000000003fc