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// SPDX-License-Identifier: BSL-1.1
pragma solidity 0.8.26;

// External Dependencies
import {Ownable2Step} from
    "@openzeppelin/contracts/access/Ownable2Step.sol";
import {Ownable} from "@openzeppelin/contracts/access/Ownable.sol";
import {Pausable} from "@openzeppelin/contracts/utils/Pausable.sol";
import {ReentrancyGuard} from
    "@openzeppelin/contracts/utils/ReentrancyGuard.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import {SafeERC20} from
    "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import {IERC721} from "@openzeppelin/contracts/token/ERC721/IERC721.sol";

// Internal Dependencies
import {IDUTCHToken} from "./interfaces/IDUTCHToken.sol";
import {IDutchVault} from "./interfaces/IDutchVault.sol";
import {BondingCurve} from "./BondingCurve.sol";
import {IDutchAuctionMarketplace} from "./interfaces/IDutchAuctionMarketplace.sol";

/// @title DutchAuctionMarketplace
/// @notice NFT marketplace for Dutch (descending-price) auctions.
contract DutchAuctionMarketplace is Ownable2Step, Pausable, ReentrancyGuard, IDutchAuctionMarketplace {
    using SafeERC20 for IERC20;

    // -------------------------------------------------------------------------
    // Constants
    // -------------------------------------------------------------------------

    /// @notice Basis points denominator (100% = 10000 bps).
    uint256 private constant BPS_DENOMINATOR = 10000;

    /// @notice Maximum number of listings that can be settled in one batch.
    uint256 private constant MAX_BATCH_SIZE = 50;

    /// @notice Burn address for deflationary proceeds.
    address private constant BURN_ADDRESS = address(0xdead);

    // -------------------------------------------------------------------------
    // Immutable State
    // -------------------------------------------------------------------------

    /// @notice The DUTCH token used for settlement.
    IDUTCHToken private immutable _dutchToken;

    // -------------------------------------------------------------------------
    // Mutable State
    // -------------------------------------------------------------------------

    /// @notice Dutch Vault address (NFT Purchase Account).
    address private _dutchVaultAddress;

    /// @notice Operations wallet address.
    address private _opsWallet;

    /// @notice The BondingCurve for ETH purchases.
    BondingCurve private _bondingCurve;

    /// @notice Default auction duration in seconds.
    uint256 private _auctionDuration;

    /// @notice Settlement fee in basis points.
    uint256 private _sellerFeeOnSettled;

    /// @notice Listing fee in basis points.
    uint256 private _sellerListingFee;

    /// @notice Max listing fee in ETH.
    uint256 private _maxListingFee;

    /// @notice Listing fee split: Vault share in basis points.
    uint256 private _listingVaultSplitBps;

    /// @notice Listing fee split: Ops share in basis points.
    uint256 private _listingOpsSplitBps;

    /// @notice Seller fee on settled split: Vault share in basis points.
    uint256 private _sellerFeeOnSettledVaultSplitBps;

    /// @notice Seller fee on settled split: Ops share in basis points.
    uint256 private _sellerFeeOnSettledOpsSplitBps;

    /// @notice Seller fee on settled split: Burn share in basis points.
    uint256 private _sellerFeeOnSettledBurnSplitBps;

    /// @notice Whether collection whitelist is enabled.
    bool private _collectionWhitelistEnabled;

    /// @notice Mapping of collection address to whitelist status.
    mapping(address collection => bool allowed)
        private _isCollectionAllowed;

    /// @notice Array of allowed collection addresses for enumeration.
    address[] private _allowedCollections;

    /// @notice Total number of listings created.
    uint256 private _totalListings;

    /// @notice Listing ID counter.
    uint256 private _listingIdCounter;

    /// @notice Mapping of listing ID to listing details.
    mapping(uint256 listingId => Listing listing) private _listings;

    /// @notice Mapping of NFT (nftContract, tokenId) to listing ID.
    /// @dev Used to prevent duplicate active listings for the same NFT.
    ///      Gets overwritten if an NFT is relisted after settlement or cancellation.
    mapping(address nftContract => mapping(uint256 tokenId => uint256 listingId))
        private _nftToListingId;

    // -------------------------------------------------------------------------
    // Data Structures
    // -------------------------------------------------------------------------

    /// @notice Listing structure.
    /// @param seller Address of the NFT seller.
    /// @param nftContract Address of the NFT contract.
    /// @param tokenId Token ID of the NFT.
    /// @param maxPrice Maximum price in ETH (auction start price).
    /// @param minPrice Minimum price in ETH (auction floor price).
    /// @param startTime Auction start timestamp.
    /// @param duration Auction duration in seconds.
    /// @param settled Whether the listing has been settled.
    /// @param cancelled Whether the listing has been cancelled.
    /// @param proceedsRecipient Address to receive settlement proceeds.
    struct Listing {
        address seller;
        address nftContract;
        uint256 tokenId;
        uint256 maxPrice;
        uint256 minPrice;
        uint256 startTime;
        uint256 duration;
        bool settled;
        bool cancelled;
        address proceedsRecipient;
    }

    /// @notice Price structure for current listing price.
    /// @param priceETH Current price in ETH.
    /// @param priceDUTCH Current price in DUTCH tokens.
    struct CurrentPrice {
        uint256 priceETH;
        uint256 priceDUTCH;
    }

    // -------------------------------------------------------------------------
    // Events
    // -------------------------------------------------------------------------

    /// @notice Emitted when a listing is created.
    /// @param listingId_ The ID of the listing.
    /// @param seller_ The address of the seller.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price in ETH.
    /// @param minPrice_ The minimum price in ETH.
    /// @param startTime_ The auction start timestamp.
    /// @param duration_ The auction duration in seconds.
    event ListingCreated(
        uint256 indexed listingId_,
        address indexed seller_,
        address indexed nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_,
        uint256 startTime_,
        uint256 duration_
    );

    /// @notice Emitted when collection whitelist is enabled or disabled.
    /// @param enabled_ Whether the whitelist is enabled.
    event CollectionWhitelistSet(bool enabled_);

    /// @notice Emitted when a collection is whitelisted or de-whitelisted.
    /// @param collection_ The address of the NFT collection.
    /// @param allowed_ Whether the collection is allowed.
    event CollectionAllowedSet(address indexed collection_, bool allowed_);

    /// @notice Emitted when a listing is cancelled.
    /// @param listingId_ The ID of the cancelled listing.
    event ListingCanceled(uint256 indexed listingId_);

    /// @notice Emitted when a listing is settled.
    /// @param listingId_ The ID of the settled listing.
    /// @param buyer_ The address of the buyer.
    /// @param priceETH_ The final settlement price in ETH.
    /// @param priceDUTCH_ The final settlement price in DUTCH tokens.
    event ListingSettled(
        uint256 indexed listingId_, address indexed buyer_, uint256 priceETH_, uint256 priceDUTCH_
    );

    /// @notice Emitted when seller fee on settled is updated.
    /// @param newFeeBps_ The new fee in basis points.
    event SellerFeeOnSettledUpdated(uint256 newFeeBps_);

    /// @notice Emitted when seller listing fee is updated.
    /// @param newFeeBps_ The new fee in basis points.
    event SellerListingFeeUpdated(uint256 newFeeBps_);

    /// @notice Emitted when max listing fee is updated.
    /// @param newFee_ The new fee in ETH.
    event MaxListingFeeUpdated(uint256 newFee_);

    /// @notice Emitted when auction duration is updated.
    /// @param newDuration_ The new auction duration in seconds.
    event AuctionDurationUpdated(uint256 newDuration_);

    /// @notice Emitted when Dutch Vault address is updated.
    /// @param newAddress_ The new Dutch Vault address.
    event DutchVaultAddressUpdated(address newAddress_);

    /// @notice Emitted when ops wallet address is updated.
    /// @param newAddress_ The new ops wallet address.
    event OpsWalletUpdated(address newAddress_);

    /// @notice Emitted when listing fee split configuration is updated.
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops share in basis points.
    event ListingFeeSplitUpdated(uint256 vaultBps_, uint256 opsBps_);

    /// @notice Emitted when seller fee on settled split configuration is updated.
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops share in basis points.
    /// @param burnBps_ Burn share in basis points.
    event SellerFeeOnSettledSplitUpdated(
        uint256 vaultBps_, uint256 opsBps_, uint256 burnBps_
    );

    // -------------------------------------------------------------------------
    // Errors
    // -------------------------------------------------------------------------

    /// @notice Thrown when an invalid address is provided.
    error InvalidAddress();

    /// @notice Thrown when an invalid amount is provided.
    error InvalidAmount();

    /// @notice Thrown when caller does not own the NFT.
    error NotNFTOwner();

    /// @notice Thrown when marketplace is not approved for NFT.
    error NotApproved();

    /// @notice Thrown when ETH transfer fails.
    error ETHTransferFailed();

    /// @notice Thrown when collection is not whitelisted.
    error CollectionNotWhitelisted();

    /// @notice Thrown when listing is invalid or does not exist.
    error InvalidListing();

    /// @notice Thrown when caller is not authorized for the operation.
    error Unauthorized();

    /// @notice Thrown when price slippage exceeds buyer's tolerance.
    error SlippageExceeded(uint256 expected, uint256 actual);

    /// @notice Thrown when array lengths do not match.
    error ArrayLengthMismatch();

    /// @notice Thrown when batch size exceeds maximum allowed.
    error BatchSizeTooLarge();

    /// @notice Thrown when ETH is sent with protocol listing (no fee required).
    error NoFeeRequired();

    /// @notice Thrown when tax split percentages don't sum to 100%.
    error InvalidSplitConfig();

    /// @notice Thrown when bonding hook is not set.
    error BondingHookNotSet();

    /// @notice Thrown when ETH refund fails.
    error ETHRefundFailed();

    /// @notice Thrown when attempting to create a listing for an NFT that already has an active listing.
    error NFTAlreadyListed();

    /// @notice Thrown when NFT transfer fails.
    error NFTTransferFailed();

    // -------------------------------------------------------------------------
    // Constructor
    // -------------------------------------------------------------------------

    /// @notice Constructor.
    /// @param dutchToken_ The DUTCH token contract address.
    /// @param dutchVaultAddress_ The Dutch Vault address.
    /// @param opsWallet_ The operations wallet address.
    constructor(
        address dutchToken_,
        address dutchVaultAddress_,
        address opsWallet_
    ) Ownable(msg.sender) {
        if (dutchToken_ == address(0)) revert InvalidAddress();
        if (dutchVaultAddress_ == address(0)) revert InvalidAddress();
        if (opsWallet_ == address(0)) revert InvalidAddress();

        _dutchToken = IDUTCHToken(dutchToken_);
        _dutchVaultAddress = dutchVaultAddress_;
        _opsWallet = opsWallet_;

        // Initialize default configuration.
        _collectionWhitelistEnabled = false;
        _sellerFeeOnSettled = 200; // 2.0%
        _sellerListingFee = 50; // 0.5%
        _maxListingFee = 0.1 ether;
        _auctionDuration = 12 hours;
        _totalListings = 0;

        // Initialize default fee splits.
        // Listing fee: 75% Vault, 25% Ops.
        _listingVaultSplitBps = 7500;
        _listingOpsSplitBps = 2500;

        // Seller fee on settled split: 0% Vault, 0% Ops, 100% Burn.
        _sellerFeeOnSettledVaultSplitBps = 0;
        _sellerFeeOnSettledOpsSplitBps = 0;
        _sellerFeeOnSettledBurnSplitBps = 10000;
    }

    // -------------------------------------------------------------------------
    // View Functions
    // -------------------------------------------------------------------------

    /// @notice Get collection whitelist status.
    /// @return enabled_ Whether collection whitelist is enabled.
    function getCollectionWhitelistEnabled()
        external
        view
        returns (bool enabled_)
    {
        return _collectionWhitelistEnabled;
    }

    /// @notice Get seller fee on settled.
    /// @return feeBps_ The fee in basis points.
    function getSellerFeeOnSettled() external view returns (uint256 feeBps_) {
        return _sellerFeeOnSettled;
    }

    /// @notice Get seller listing fee.
    /// @return feeBps_ The fee in basis points.
    function getSellerListingFee() external view returns (uint256 feeBps_) {
        return _sellerListingFee;
    }

    /// @notice Get max listing fee.
    /// @return fee_ The fee in ETH.
    function getMaxListingFee() external view returns (uint256 fee_) {
        return _maxListingFee;
    }

    /// @notice Get listing fee split configuration.
    /// @return vaultBps_ Vault share in basis points.
    /// @return opsBps_ Ops share in basis points.
    function getListingFeeSplitConfig()
        external
        view
        returns (uint256 vaultBps_, uint256 opsBps_)
    {
        return (_listingVaultSplitBps, _listingOpsSplitBps);
    }

    /// @notice Get seller fee on settled split configuration.
    /// @return vaultBps_ Vault share in basis points.
    /// @return opsBps_ Ops share in basis points.
    /// @return burnBps_ Burn share in basis points.
    function getSellerFeeOnSettledSplitConfig()
        external
        view
        returns (uint256 vaultBps_, uint256 opsBps_, uint256 burnBps_)
    {
        return (
            _sellerFeeOnSettledVaultSplitBps,
            _sellerFeeOnSettledOpsSplitBps,
            _sellerFeeOnSettledBurnSplitBps
        );
    }

    /// @notice Get auction duration.
    /// @return duration_ The duration in seconds.
    function getAuctionDuration() external view returns (uint256 duration_) {
        return _auctionDuration;
    }

    /// @notice Get Dutch Token address.
    /// @return dutchToken_ The Dutch Token address.
    function getDutchToken() external view returns (address dutchToken_) {
        return address(_dutchToken);
    }

    /// @notice Get Dutch Vault address.
    /// @return vaultAddress_ The Dutch Vault address.
    function getDutchVaultAddress()
        external
        view
        returns (address vaultAddress_)
    {
        return _dutchVaultAddress;
    }

    /// @notice Get Bonding Curve address.
    /// @return bondingCurve_ The Bonding Curve address.
    function getBondingCurve() external view returns (address bondingCurve_) {
        return address(_bondingCurve);
    }

    /// @notice Get ops wallet address.
    /// @return wallet_ The ops wallet address.
    function getOpsWallet() external view returns (address wallet_) {
        return _opsWallet;
    }

    /// @notice Get total listings.
    /// @return total_ The total number of listings created.
    function getTotalListings() external view returns (uint256 total_) {
        return _totalListings;
    }

    /// @notice Get listing details.
    /// @param listingId_ The ID of the listing.
    /// @return listing_ The listing details.
    function getListing(uint256 listingId_)
        external
        view
        returns (Listing memory listing_)
    {
        return _listings[listingId_];
    }

    /// @notice Get listing for a specific NFT.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @return listingId_ The listing ID for the NFT.
    /// @return listing_ The listing for the NFT.
    /// @dev Returns the most recent listing for the NFT. Reverts if the NFT has never been listed.
    function getListingByNFT(address nftContract_, uint256 tokenId_)
        external
        view
        returns (uint256 listingId_, Listing memory listing_)
    {
        listingId_ = _nftToListingId[nftContract_][tokenId_];
        if (listingId_ >= _listingIdCounter) {
            revert InvalidListing();
        }
        
        Listing storage storedListing_ = _listings[listingId_];
        // Verify this is actually a listing for this NFT (not just default mapping value 0).
        if (
            storedListing_.nftContract != nftContract_
                || storedListing_.tokenId != tokenId_
        ) {
            revert InvalidListing();
        }
        
        return (listingId_, storedListing_);
    }

    /// @notice Get a paginated list of listings by ID.
    /// @dev Iterates over sequential listing IDs starting from `offset_`.
    /// @param offset_ The starting listing ID (inclusive).
    /// @param limit_ The maximum number of listings to return.
    /// @return listings_ Array of listings for the requested page.
    function getListingsPaginated(uint256 offset_, uint256 limit_)
        external
        view
        returns (Listing[] memory listings_)
    {
        uint256 total_ = _listingIdCounter;

        // If offset is beyond the last listing ID, return empty array.
        if (offset_ >= total_) {
            return new Listing[](0);
        }

        uint256 endExclusive_ = offset_ + limit_;
        if (endExclusive_ > total_) {
            endExclusive_ = total_;
        }

        uint256 length_ = endExclusive_ - offset_;
        listings_ = new Listing[](length_);

        for (uint256 i; i < length_; ++i) {
            listings_[i] = _listings[offset_ + i];
        }
    }

    /// @notice Check if a collection is whitelisted.
    /// @param collection_ The address of the NFT collection.
    /// @return allowed_ Whether the collection is allowed.
    function getIsCollectionAllowed(address collection_)
        external
        view
        returns (bool allowed_)
    {
        return _isCollectionAllowed[collection_];
    }

    /// @notice Get all allowed collection addresses.
    /// @return collections_ Array of allowed collection addresses.
    function getAllowedCollections()
        external
        view
        returns (address[] memory collections_)
    {
        return _allowedCollections;
    }

    /// @notice Get the number of allowed collections.
    /// @return count_ The number of allowed collections.
    function getAllowedCollectionsCount()
        external
        view
        returns (uint256 count_)
    {
        return _allowedCollections.length;
    }

    /// @notice Get current price for a listing (Dutch auction).
    /// @param listingId_ The ID of the listing.
    /// @return price_ The current price in both ETH and DUTCH.
    function getCurrentPrice(uint256 listingId_)
        external
        view
        returns (CurrentPrice memory price_)
    {
        return _getCurrentPrice(listingId_);
    }

    /// @notice Internal helper to get current price in both ETH and DUTCH.
    /// @param listingId_ The ID of the listing.
    /// @return price_ The current price in both ETH and DUTCH.
    function _getCurrentPrice(uint256 listingId_)
        internal
        view
        returns (CurrentPrice memory price_)
    {
        price_.priceETH = _getCurrentPriceETH(listingId_);
        price_.priceDUTCH = _convertETHToDUTCH(price_.priceETH);
    }

    /// @notice Internal helper to get current price in ETH only.
    /// @param listingId_ The ID of the listing.
    /// @return priceETH_ The current price in ETH.
    function _getCurrentPriceETH(uint256 listingId_)
        internal
        view
        returns (uint256 priceETH_)
    {
        // 1. Validate listing exists.
        if (listingId_ >= _listingIdCounter) revert InvalidListing();

        Listing storage listing_ = _listings[listingId_];

        // 2. Check listing is not cancelled.
        if (listing_.cancelled) revert InvalidListing();

        // 3. Check listing is not settled.
        if (listing_.settled) revert InvalidListing();

        // 4. Calculate current price based on elapsed time.
        uint256 elapsed_ = block.timestamp - listing_.startTime;

        // If auction hasn't started or just started, return max price.
        if (elapsed_ == 0) {
            return listing_.maxPrice;
        }

        // If auction has reached or passed its duration, return min price.
        if (elapsed_ >= listing_.duration) {
            return listing_.minPrice;
        }

        // Non-linear (quadratic) decay: faster drop early, slower near the end.
        // price = minPrice + priceRange * (1 - t)^4, where t = elapsed/duration.
        // We implement this in fixed-point with 1e18 precision to keep
        // intermediates bounded:
        //   t = elapsed / duration
        //   oneMinus = 1 - t
        //   factor = oneMinus^4
        uint256 priceRange_ = listing_.maxPrice - listing_.minPrice;

        // t in [0, 1e18]
        uint256 t_ = (elapsed_ * 1e18) / listing_.duration;
        uint256 oneMinus_ = 1e18 - t_;

        // factor = (1 - t)^4 = ((1 - t)^2)^2 in 1e18 fixed point.
        uint256 sq_ = (oneMinus_ * oneMinus_) / 1e18;       // (1 - t)^2
        uint256 factor_ = (sq_ * sq_) / 1e18;               // (1 - t)^4

        // adjustedRange = priceRange * factor
        uint256 adjustedRange_ = (priceRange_ * factor_) / 1e18;

        priceETH_ = listing_.minPrice + adjustedRange_;
    }

    // -------------------------------------------------------------------------
    // Owner Functions
    // -------------------------------------------------------------------------

    /// @notice Pause the marketplace.
    function pause() external onlyOwner {
        _pause();
    }

    /// @notice Unpause the marketplace.
    function unpause() external onlyOwner {
        _unpause();
    }

    /// @notice Enable or disable collection whitelist.
    /// @param enabled_ Whether to enable the whitelist.
    function setCollectionWhitelistEnabled(bool enabled_) external onlyOwner {
        _collectionWhitelistEnabled = enabled_;
        emit CollectionWhitelistSet(enabled_);
    }

    /// @notice Whitelist or de-whitelist a collection.
    /// @param collection_ The address of the NFT collection.
    /// @param allowed_ Whether the collection is allowed.
    function setCollectionAllowed(address collection_, bool allowed_)
        external
        onlyOwner
    {
        if (collection_ == address(0)) revert InvalidAddress();
        
        bool wasAllowed_ = _isCollectionAllowed[collection_];
        _isCollectionAllowed[collection_] = allowed_;
        
        // Maintain enumeration array
        if (allowed_ && !wasAllowed_) {
            // Adding to whitelist: append to array
            _allowedCollections.push(collection_);
        } else if (!allowed_ && wasAllowed_) {
            // Removing from whitelist: find and remove from array
            uint256 length_ = _allowedCollections.length;
            for (uint256 i; i < length_; ++i) {
                if (_allowedCollections[i] == collection_) {
                    // Move last element to current position and pop
                    _allowedCollections[i] = _allowedCollections[length_ - 1];
                    _allowedCollections.pop();
                    break;
                }
            }
        }
        
        emit CollectionAllowedSet(collection_, allowed_);
    }

    /// @notice Update seller fee on settled.
    /// @param feeBps_ The new fee in basis points (max 10000 = 100%).
    function setSellerFeeOnSettled(uint256 feeBps_) external onlyOwner {
        if (feeBps_ > BPS_DENOMINATOR) revert InvalidAmount();
        _sellerFeeOnSettled = feeBps_;
        emit SellerFeeOnSettledUpdated(feeBps_);
    }

    /// @notice Update seller listing fee.
    /// @param feeBps_ The new fee in basis points (max 10000 = 100%).
    function setSellerListingFee(uint256 feeBps_) external onlyOwner {
        if (feeBps_ > BPS_DENOMINATOR) revert InvalidAmount();
        _sellerListingFee = feeBps_;
        emit SellerListingFeeUpdated(feeBps_);
    }

    /// @notice Update max listing fee.
    /// @param fee_ The new fee in ETH.
    function setMaxListingFee(uint256 fee_) external onlyOwner {
        if (fee_ == 0) revert InvalidAmount();
        _maxListingFee = fee_;
        emit MaxListingFeeUpdated(fee_);
    }

    /// @notice Update listing fee split configuration.
    /// @dev Vault and Ops splits must sum to 100% (10000 BPS).
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops share in basis points.
    function setListingFeeSplitConfig(
        uint256 vaultBps_,
        uint256 opsBps_
    ) external onlyOwner {
        if (vaultBps_ + opsBps_ != BPS_DENOMINATOR) {
            revert InvalidSplitConfig();
        }

        _listingVaultSplitBps = vaultBps_;
        _listingOpsSplitBps = opsBps_;

        emit ListingFeeSplitUpdated(vaultBps_, opsBps_);
    }

    /// @notice Update seller fee on settled split configuration.
    /// @dev Vault, Ops, and Burn splits must sum to 100% (10000 BPS).
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops share in basis points.
    /// @param burnBps_ Burn share in basis points.
    function setSellerFeeOnSettledSplitConfig(
        uint256 vaultBps_,
        uint256 opsBps_,
        uint256 burnBps_
    ) external onlyOwner {
        if (vaultBps_ + opsBps_ + burnBps_ != BPS_DENOMINATOR) {
            revert InvalidSplitConfig();
        }

        _sellerFeeOnSettledVaultSplitBps = vaultBps_;
        _sellerFeeOnSettledOpsSplitBps = opsBps_;
        _sellerFeeOnSettledBurnSplitBps = burnBps_;

        emit SellerFeeOnSettledSplitUpdated(vaultBps_, opsBps_, burnBps_);
    }

    /// @notice Update auction duration.
    /// @param duration_ The new auction duration in seconds.
    function setAuctionDuration(uint256 duration_) external onlyOwner {
        if (duration_ == 0) revert InvalidAmount();
        _auctionDuration = duration_;
        emit AuctionDurationUpdated(duration_);
    }

    /// @notice Update Dutch Vault address.
    /// @param newAddress_ The new Dutch Vault address.
    function setDutchVaultAddress(address newAddress_) external onlyOwner {
        if (newAddress_ == address(0)) revert InvalidAddress();
        _dutchVaultAddress = newAddress_;
        emit DutchVaultAddressUpdated(newAddress_);
    }

    /// @notice Update ops wallet address.
    /// @param newAddress_ The new ops wallet address.
    function setOpsWallet(address newAddress_) external onlyOwner {
        if (newAddress_ == address(0)) revert InvalidAddress();
        _opsWallet = newAddress_;
        emit OpsWalletUpdated(newAddress_);
    }

    /// @notice Set bonding curve address.
    /// @dev Only callable by owner. Required for ETH purchases.
    /// @param bondingCurve_ The BondingCurve contract address.
    function setBondingCurve(address payable bondingCurve_) external onlyOwner {
        if (bondingCurve_ == address(0)) revert InvalidAddress();
        _bondingCurve = BondingCurve(bondingCurve_);
    }

    // -------------------------------------------------------------------------
    // Public Functions
    // -------------------------------------------------------------------------

    /// @notice Create a new listing.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price in ETH (auction start price).
    /// @param minPrice_ The minimum price in ETH (auction floor price).
    /// @return listingId_ The ID of the created listing.
    function createListing(
        address nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_
    ) external payable nonReentrant whenNotPaused returns (uint256 listingId_) {
        return _createListing(
            nftContract_, tokenId_, maxPrice_, minPrice_, msg.sender
        );
    }

    /// @notice Create a listing with proceeds burned.
    /// @dev Permissionless. Proceeds sent to burn address (0xdead).
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price in ETH (auction start price).
    /// @param minPrice_ The minimum price in ETH (auction floor price).
    /// @return listingId_ The ID of the created listing.
    function createListingWithBurn(
        address nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_
    ) external payable nonReentrant whenNotPaused returns (uint256 listingId_) {
        return _createListing(
            nftContract_, tokenId_, maxPrice_, minPrice_, BURN_ADDRESS
        );
    }

    /// @notice Cancel a listing.
    /// @dev Can be called by seller or current NFT owner.
    /// @param listingId_ The ID of the listing to cancel.
    function cancelListing(uint256 listingId_) external whenNotPaused {
        // 1. Validate listing exists.
        if (listingId_ >= _listingIdCounter) revert InvalidListing();

        Listing storage listing_ = _listings[listingId_];

        // 2. Check listing is not already settled.
        if (listing_.settled) revert InvalidListing();

        // 3. Check listing is not already cancelled.
        if (listing_.cancelled) revert InvalidListing();

        // 4. Check caller is seller or current NFT owner.
        address currentOwner_ =
            IERC721(listing_.nftContract).ownerOf(listing_.tokenId);
        if (
            msg.sender != listing_.seller && msg.sender != currentOwner_
        ) {
            revert Unauthorized();
        }

        // 5. Mark as cancelled.
        listing_.cancelled = true;

        // 6. Emit event.
        emit ListingCanceled(listingId_);
    }

    /// @notice Settle a listing by purchasing the NFT with DUTCH.
    /// @param listingId_ The ID of the listing to settle.
    /// @param maxPriceDUTCH_ Maximum price willing to pay (slippage protection).
    function settle(uint256 listingId_, uint256 maxPriceDUTCH_)
        public
        whenNotPaused
        nonReentrant
    {
        // 1. Validate bonding curve is set.
        if (address(_bondingCurve) == address(0)) revert BondingHookNotSet();

        // 2. Validate listing exists.
        if (listingId_ >= _listingIdCounter) revert InvalidListing();

        Listing storage listing_ = _listings[listingId_];

        // 3. Check listing is not already settled.
        if (listing_.settled) revert InvalidListing();

        // 4. Check listing is not cancelled.
        if (listing_.cancelled) revert InvalidListing();

        // 5. Get current NFT price, convert to DUTCH, and check slippage.
        CurrentPrice memory currentPrice_ = _getCurrentPrice(listingId_);
        if (currentPrice_.priceDUTCH > maxPriceDUTCH_) {
            revert SlippageExceeded(maxPriceDUTCH_, currentPrice_.priceDUTCH);
        }

        // 6. Mark as settled (before external calls).
        listing_.settled = true;

        // 7. Transfer DUTCH tokens from buyer to marketplace.
        IERC20(address(_dutchToken)).safeTransferFrom(
            msg.sender, address(this), currentPrice_.priceDUTCH
        );

        // 8. Execute common settlement logic.
        _settleInternal(listingId_, currentPrice_.priceETH, currentPrice_.priceDUTCH, msg.sender);
    }

    /// @notice Settle a listing by purchasing the NFT with ETH. Only callable for protocol-owned NFTs.
    /// @dev Converts ETH to DUTCH via bonding hook without buy tax applied, then settles normally.
    /// @param listingId_ The ID of the listing to settle.
    /// @param maxPriceETH_ Maximum price willing to pay (slippage protection).
    function settleWithETH(uint256 listingId_, uint256 maxPriceETH_)
        external
        payable
        whenNotPaused
        nonReentrant
    {
        // 1. Validate bonding curve is set.
        if (address(_bondingCurve) == address(0)) revert BondingHookNotSet();

        // 2. Validate listing exists.
        if (listingId_ >= _listingIdCounter) revert InvalidListing();

        Listing storage listing_ = _listings[listingId_];

        // 3. Check listing is not already settled.
        if (listing_.settled) revert InvalidListing();

        // 4. Check listing is not cancelled.
        if (listing_.cancelled) revert InvalidListing();

        // 5. Check listing was created by DutchVault. Only protocol-owned NFTs can be settled with ETH.
        if (listing_.seller != _dutchVaultAddress) revert InvalidListing();

        // 6. Get current NFT price, convert to DUTCH, and check slippage.
        CurrentPrice memory currentPrice_ = _getCurrentPrice(listingId_);
        if (currentPrice_.priceETH > maxPriceETH_) {
            revert SlippageExceeded(maxPriceETH_, currentPrice_.priceETH);
        }

        // 7. Mark as settled (before external calls).
        listing_.settled = true;

        // 8. Swap ETH for exact DUTCH amount via bonding curve.
        // Curve will refund excess ETH back to this contract.
        (, uint256 ethUsed_,) = _bondingCurve.buyDutchExactOut{value: msg.value}(
            currentPrice_.priceDUTCH,
            address(this)
        );

        // 9. Check slippage.
        if (ethUsed_ > maxPriceETH_) {
            revert SlippageExceeded(maxPriceETH_, ethUsed_);
        }

        // 10. Execute common settlement logic.
        _settleInternal(listingId_, ethUsed_, currentPrice_.priceDUTCH, msg.sender);

        // 11. Refund any remaining ETH to buyer.
        uint256 refund_ = msg.value - ethUsed_;
        if (refund_ > 0) {
            (bool success_, ) = payable(msg.sender).call{value: refund_}("");
            if (!success_) revert ETHRefundFailed();
        }
    }

    /// @notice Batch settle multiple listings in a single transaction.
    /// @param listingIds_ Array of listing IDs to settle.
    /// @param maxPrices_ Array of maximum prices for slippage protection.
    function batchSettle(
        uint256[] calldata listingIds_,
        uint256[] calldata maxPrices_
    ) external {
        // Validate array lengths match.
        if (listingIds_.length != maxPrices_.length) {
            revert ArrayLengthMismatch();
        }

        // Validate batch size does not exceed maximum.
        if (listingIds_.length > MAX_BATCH_SIZE) {
            revert BatchSizeTooLarge();
        }

        // Settle each listing.
        for (uint256 i; i < listingIds_.length; ++i) {
            settle(listingIds_[i], maxPrices_[i]);
        }
    }

    // -------------------------------------------------------------------------
    // Internal Functions
    // -------------------------------------------------------------------------

    /// @notice Internal helper to create a listing.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price in ETH (auction start price).
    /// @param minPrice_ The minimum price in ETH (auction floor price).
    /// @param proceedsRecipient_ Address to receive settlement proceeds.
    /// @return listingId_ The ID of the created listing.
    function _createListing(
        address nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_,
        address proceedsRecipient_
    ) internal returns (uint256 listingId_) {
        // 1. Validate inputs (nftContract, maxPrice, minPrice).
        if (nftContract_ == address(0)) revert InvalidAddress();
        if (maxPrice_ == 0 || minPrice_ == 0) revert InvalidAmount();
        if (maxPrice_ < minPrice_) revert InvalidAmount();

        // 1b. Check collection whitelist.
        // DutchVault can list any collection (protocol-owned NFTs).
        if (
            _collectionWhitelistEnabled
                && !_isCollectionAllowed[nftContract_]
                && msg.sender != _dutchVaultAddress
        ) {
            revert CollectionNotWhitelisted();
        }

        // 2. Verify NFT ownership.
        address owner_ = IERC721(nftContract_).ownerOf(tokenId_);
        if (owner_ != msg.sender) revert NotNFTOwner();

        // 3. Verify marketplace approval.
        if (
            !IERC721(nftContract_).isApprovedForAll(msg.sender, address(this))
                && IERC721(nftContract_).getApproved(tokenId_) != address(this)
        ) {
            revert NotApproved();
        }

        // 4. Check if NFT already has an active listing.
        uint256 existingListingId_ = _nftToListingId[nftContract_][tokenId_];
        if (existingListingId_ < _listingIdCounter) {
            Listing storage existingListing_ = _listings[existingListingId_];
            // Verify this is actually a listing for this NFT (not just default mapping value 0).
            if (
                existingListing_.nftContract == nftContract_
                    && existingListing_.tokenId == tokenId_
            ) {
                if (!existingListing_.settled && !existingListing_.cancelled) {
                    revert NFTAlreadyListed();
                }
                // If existing listing is settled or cancelled, allow new listing (mapping will be overwritten).
            }
        }

        // 5. Calculate and collect listing fee (skip if protocol or vault).
        if (proceedsRecipient_ != BURN_ADDRESS && msg.sender != _dutchVaultAddress) {
            // Normal user listing: charge fee.
            uint256 listingFee_ = _calculateListingFee(minPrice_);
            if (msg.value != listingFee_) revert InvalidAmount();
            _distributeListingFee(listingFee_);
        } else {
            // Protocol or DutchVault listings: no fee required.
            if (msg.value != 0) revert NoFeeRequired();
        }

        // 6. Create listing.
        listingId_ = _listingIdCounter;
        _listings[listingId_] = Listing({
            seller: msg.sender,
            nftContract: nftContract_,
            tokenId: tokenId_,
            maxPrice: maxPrice_,
            minPrice: minPrice_,
            startTime: block.timestamp,
            duration: _auctionDuration,
            settled: false,
            cancelled: false,
            proceedsRecipient: proceedsRecipient_
        });

        // 7. Update counters.
        _listingIdCounter++;
        _totalListings++;

        // 8. Store NFT to listing ID mapping.
        _nftToListingId[nftContract_][tokenId_] = listingId_;

        // 9. Emit event.
        emit ListingCreated(
            listingId_,
            msg.sender,
            nftContract_,
            tokenId_,
            maxPrice_,
            minPrice_,
            block.timestamp,
            _auctionDuration
        );
    }

    /// @notice Calculate listing fee.
    /// @param minPrice_ The minimum price in ETH.
    /// @return fee_ The listing fee in ETH.
    function _calculateListingFee(uint256 minPrice_)
        internal
        view
        returns (uint256 fee_)
    {
        // Fee = Math.min(minPrice * listingFeeBps, maxListingFee).
        uint256 percentageFee_ = (minPrice_ * _sellerListingFee)
            / BPS_DENOMINATOR;
        fee_ = percentageFee_ > _maxListingFee
            ? _maxListingFee
            : percentageFee_;
    }

    /// @notice Distribute listing fee between Dutch Vault and Ops Wallet.
    /// @param feeAmount_ The fee amount in ETH.
    function _distributeListingFee(uint256 feeAmount_) internal {
        // Split between Dutch Vault and Ops Wallet according to configured
        // basis point shares.
        uint256 vaultAmount_ =
            (feeAmount_ * _listingVaultSplitBps) / BPS_DENOMINATOR;
        uint256 opsAmount_ = feeAmount_ - vaultAmount_;

        // Transfer to Dutch Vault.
        (bool success1_,) =
            payable(_dutchVaultAddress).call{value: vaultAmount_}("");
        if (!success1_) revert ETHTransferFailed();

        // Transfer to Ops Wallet.
        (bool success2_,) =
            payable(_opsWallet).call{value: opsAmount_}("");
        if (!success2_) revert ETHTransferFailed();
    }

    /// @notice Internal settlement logic shared by settle() and settleWithETH().
    /// @dev Assumes listing is valid and DUTCH tokens are in marketplace.
    /// @param listingId_ The ID of the listing to settle.
    /// @param currentPriceInDUTCH_ The current price in DUTCH tokens.
    /// @param buyer_ The address of the buyer.
    function _settleInternal(
        uint256 listingId_,
        uint256 currentPriceInETH_,
        uint256 currentPriceInDUTCH_,
        address buyer_
    ) internal {
        Listing storage listing_ = _listings[listingId_];

        // Handle proceeds based on listing type.
        if (listing_.proceedsRecipient == BURN_ADDRESS) {
            // Protocol listing: burn all proceeds (no fees).
            _dutchToken.userBurn(currentPriceInDUTCH_);
        } else if (listing_.seller == _dutchVaultAddress) {
            // Protocol listing, just transfer proceeds to recipient (no fees).
            IERC20(address(_dutchToken)).safeTransfer(
                listing_.proceedsRecipient, currentPriceInDUTCH_
            );
        } else {
            // Third-party listing: charge seller fee and pay seller.
            uint256 fee_ =
                (currentPriceInDUTCH_ * _sellerFeeOnSettled) / BPS_DENOMINATOR;

            // Distribute seller fee according to configurable splits.
            uint256 vaultFee_ =
                (fee_ * _sellerFeeOnSettledVaultSplitBps) / BPS_DENOMINATOR;
            uint256 opsFee_ =
                (fee_ * _sellerFeeOnSettledOpsSplitBps) / BPS_DENOMINATOR;
            uint256 burnFee_ = fee_ - vaultFee_ - opsFee_;

            if (vaultFee_ != 0) {
                IERC20(address(_dutchToken)).safeTransfer(
                    _dutchVaultAddress, vaultFee_
                );
            }

            if (opsFee_ != 0) {
                IERC20(address(_dutchToken)).safeTransfer(
                    _opsWallet, opsFee_
                );
            }

            if (burnFee_ != 0) {
                _dutchToken.userBurn(burnFee_);
            }

            // Transfer proceeds to recipient (typically seller).
            uint256 proceeds_ = currentPriceInDUTCH_ - fee_;
            IERC20(address(_dutchToken)).safeTransfer(
                listing_.proceedsRecipient, proceeds_
            );
        }

        // Transfer NFT from seller to buyer.
        IERC721(listing_.nftContract).transferFrom(
            listing_.seller, buyer_, listing_.tokenId
        );

        if (IERC721(listing_.nftContract).ownerOf(listing_.tokenId) != buyer_) {
            revert NFTTransferFailed();
        }

        // Notify DutchVault if it's the seller (automatic settlement).
        if (listing_.seller == _dutchVaultAddress) {
            IDutchVault(_dutchVaultAddress).onListingSettled(
                listingId_, buyer_, currentPriceInETH_, currentPriceInDUTCH_
            );
        }

        // Emit event.
        emit ListingSettled(listingId_, buyer_, currentPriceInETH_, currentPriceInDUTCH_);
    }

    /// @notice Convert an ETH‑denominated price into a DUTCH token amount
    ///         using the current bonding curve spot price.
    /// @param ethAmount_ The amount of ETH (18 decimals).
    /// @return dutchAmount_ The corresponding DUTCH amount (18 decimals).
    function _convertETHToDUTCH(uint256 ethAmount_)
        internal
        view
        returns (uint256 dutchAmount_)
    {
        if (ethAmount_ == 0) {
            return 0;
        }

        // If bonding curve is not set, return 0 for DUTCH price.
        if (address(_bondingCurve) == address(0)) {
            return 0;
        }

        // Spot price from bonding curve: WETH per 1 DUTCH (18 decimals).
        uint256 dutchPrice_ = _bondingCurve.getCurrentPrice();
        if (dutchPrice_ == 0) {
            revert InvalidAmount();
        }

        // dutchAmount = ethAmount / price, both 18‑decimals.
        dutchAmount_ = (ethAmount_ * 1e18) / dutchPrice_;
    }

    // -------------------------------------------------------------------------
    // Receive Function
    // -------------------------------------------------------------------------

    /// @notice Allow contract to receive ETH refunds from bonding hook.
    /// @dev Required for settleWithETH() when bonding hook refunds excess ETH.
    receive() external payable {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Contract module which provides access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * This extension of the {Ownable} contract includes a two-step mechanism to transfer
 * ownership, where the new owner must call {acceptOwnership} in order to replace the
 * old one. This can help prevent common mistakes, such as transfers of ownership to
 * incorrect accounts, or to contracts that are unable to interact with the
 * permission system.
 *
 * The initial owner is specified at deployment time in the constructor for `Ownable`. This
 * can later be changed with {transferOwnership} and {acceptOwnership}.
 *
 * This module is used through inheritance. It will make available all functions
 * from parent (Ownable).
 */
abstract contract Ownable2Step is Ownable {
    address private _pendingOwner;

    event OwnershipTransferStarted(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Returns the address of the pending owner.
     */
    function pendingOwner() public view virtual returns (address) {
        return _pendingOwner;
    }

    /**
     * @dev Starts the ownership transfer of the contract to a new account. Replaces the pending transfer if there is one.
     * Can only be called by the current owner.
     *
     * Setting `newOwner` to the zero address is allowed; this can be used to cancel an initiated ownership transfer.
     */
    function transferOwnership(address newOwner) public virtual override onlyOwner {
        _pendingOwner = newOwner;
        emit OwnershipTransferStarted(owner(), newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`) and deletes any pending owner.
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual override {
        delete _pendingOwner;
        super._transferOwnership(newOwner);
    }

    /**
     * @dev The new owner accepts the ownership transfer.
     */
    function acceptOwnership() public virtual {
        address sender = _msgSender();
        if (pendingOwner() != sender) {
            revert OwnableUnauthorizedAccount(sender);
        }
        _transferOwnership(sender);
    }
}

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

pragma solidity ^0.8.20;

import {Context} from "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * The initial owner is set to the address provided by the deployer. This can
 * later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    constructor(address initialOwner) {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

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

pragma solidity ^0.8.20;

import {Context} from "../utils/Context.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract Pausable is Context {
    bool private _paused;

    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    /**
     * @dev The operation failed because the contract is paused.
     */
    error EnforcedPause();

    /**
     * @dev The operation failed because the contract is not paused.
     */
    error ExpectedPause();

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        _requireNotPaused();
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        _requirePaused();
        _;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Throws if the contract is paused.
     */
    function _requireNotPaused() internal view virtual {
        if (paused()) {
            revert EnforcedPause();
        }
    }

    /**
     * @dev Throws if the contract is not paused.
     */
    function _requirePaused() internal view virtual {
        if (!paused()) {
            revert ExpectedPause();
        }
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        _paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        _paused = false;
        emit Unpaused(_msgSender());
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.5.0) (utils/ReentrancyGuard.sol)

pragma solidity ^0.8.20;

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

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If EIP-1153 (transient storage) is available on the chain you're deploying at,
 * consider using {ReentrancyGuardTransient} instead.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 *
 * IMPORTANT: Deprecated. This storage-based reentrancy guard will be removed and replaced
 * by the {ReentrancyGuardTransient} variant in v6.0.
 *
 * @custom:stateless
 */
abstract contract ReentrancyGuard {
    using StorageSlot for bytes32;

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.ReentrancyGuard")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant REENTRANCY_GUARD_STORAGE =
        0x9b779b17422d0df92223018b32b4d1fa46e071723d6817e2486d003becc55f00;

    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant NOT_ENTERED = 1;
    uint256 private constant ENTERED = 2;

    /**
     * @dev Unauthorized reentrant call.
     */
    error ReentrancyGuardReentrantCall();

    constructor() {
        _reentrancyGuardStorageSlot().getUint256Slot().value = NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    /**
     * @dev A `view` only version of {nonReentrant}. Use to block view functions
     * from being called, preventing reading from inconsistent contract state.
     *
     * CAUTION: This is a "view" modifier and does not change the reentrancy
     * status. Use it only on view functions. For payable or non-payable functions,
     * use the standard {nonReentrant} modifier instead.
     */
    modifier nonReentrantView() {
        _nonReentrantBeforeView();
        _;
    }

    function _nonReentrantBeforeView() private view {
        if (_reentrancyGuardEntered()) {
            revert ReentrancyGuardReentrantCall();
        }
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be NOT_ENTERED
        _nonReentrantBeforeView();

        // Any calls to nonReentrant after this point will fail
        _reentrancyGuardStorageSlot().getUint256Slot().value = ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _reentrancyGuardStorageSlot().getUint256Slot().value = NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _reentrancyGuardStorageSlot().getUint256Slot().value == ENTERED;
    }

    function _reentrancyGuardStorageSlot() internal pure virtual returns (bytes32) {
        return REENTRANCY_GUARD_STORAGE;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC20/IERC20.sol)

pragma solidity >=0.4.16;

/**
 * @dev Interface of the ERC-20 standard as defined in the ERC.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.5.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";
import {IERC1363} from "../../../interfaces/IERC1363.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC-20 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 {
    /**
     * @dev An operation with an ERC-20 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 {
        if (!_safeTransfer(token, to, value, true)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @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 {
        if (!_safeTransferFrom(token, from, to, value, true)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Variant of {safeTransfer} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransfer(IERC20 token, address to, uint256 value) internal returns (bool) {
        return _safeTransfer(token, to, value, false);
    }

    /**
     * @dev Variant of {safeTransferFrom} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransferFrom(IERC20 token, address from, address to, uint256 value) internal returns (bool) {
        return _safeTransferFrom(token, from, to, value, false);
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    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.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    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.
     *
     * NOTE: If the token implements ERC-7674, this function will not modify any temporary allowance. This function
     * only sets the "standard" allowance. Any temporary allowance will remain active, in addition to the value being
     * set here.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        if (!_safeApprove(token, spender, value, false)) {
            if (!_safeApprove(token, spender, 0, true)) revert SafeERC20FailedOperation(address(token));
            if (!_safeApprove(token, spender, value, true)) revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferAndCall, with a fallback to the simple {ERC20} transfer if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that relies on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            safeTransfer(token, to, value);
        } else if (!token.transferAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferFromAndCall, with a fallback to the simple {ERC20} transferFrom if the target
     * has no code. This can be used to implement an {ERC721}-like safe transfer that relies on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferFromAndCallRelaxed(
        IERC1363 token,
        address from,
        address to,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length == 0) {
            safeTransferFrom(token, from, to, value);
        } else if (!token.transferFromAndCall(from, to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} approveAndCall, with a fallback to the simple {ERC20} approve if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * NOTE: When the recipient address (`to`) has no code (i.e. is an EOA), this function behaves as {forceApprove}.
     * Oppositely, when the recipient address (`to`) has code, this function only attempts to call {ERC1363-approveAndCall}
     * once without retrying, and relies on the returned value to be true.
     *
     * Reverts if the returned value is other than `true`.
     */
    function approveAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            forceApprove(token, to, value);
        } else if (!token.approveAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity `token.transfer(to, value)` call, 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 to The recipient of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeTransfer(IERC20 token, address to, uint256 value, bool bubble) private returns (bool success) {
        bytes4 selector = IERC20.transfer.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(to, shr(96, not(0))))
            mstore(0x24, value)
            success := call(gas(), token, 0, 0x00, 0x44, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
        }
    }

    /**
     * @dev Imitates a Solidity `token.transferFrom(from, to, value)` call, 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 from The sender of the tokens
     * @param to The recipient of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value,
        bool bubble
    ) private returns (bool success) {
        bytes4 selector = IERC20.transferFrom.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(from, shr(96, not(0))))
            mstore(0x24, and(to, shr(96, not(0))))
            mstore(0x44, value)
            success := call(gas(), token, 0, 0x00, 0x64, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
            mstore(0x60, 0)
        }
    }

    /**
     * @dev Imitates a Solidity `token.approve(spender, value)` call, 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 spender The spender of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeApprove(IERC20 token, address spender, uint256 value, bool bubble) private returns (bool success) {
        bytes4 selector = IERC20.approve.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(spender, shr(96, not(0))))
            mstore(0x24, value)
            success := call(gas(), token, 0, 0x00, 0x44, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC721/IERC721.sol)

pragma solidity >=0.6.2;

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

/**
 * @dev Required interface of an ERC-721 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 ERC-721 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 ERC-721
     * 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: BSL-1.1
pragma solidity 0.8.26;

/// @title IDUTCHToken
/// @notice Interface for DUTCH token bonding curve interactions.
interface IDUTCHToken {
    /// @notice Mints tokens to a specified address.
    /// @dev Only callable by the bonding curve contract.
    /// @param to_ The address to mint tokens to.
    /// @param amount_ The amount of tokens to mint.
    function mint(address to_, uint256 amount_) external;

    /// @notice Burns tokens from a specified address.
    /// @dev Only callable by the bonding curve contract.
    /// @param from_ The address to burn tokens from.
    /// @param amount_ The amount of tokens to burn.
    function burn(address from_, uint256 amount_) external;

    /// @notice Returns the current bonding curve supply.
    /// @return The bonding curve supply.
    function bondingCurveSupply() external view returns (uint256);

    /// @notice Returns the total amount of tokens burned by users.
    /// @return The total user burned tokens.
    function getTotalUserBurned() external view returns (uint256);

    /// @notice Allows users to voluntarily burn their tokens.
    /// @dev Transfers tokens to burn address without decreasing supply.
    /// @param amount_ The amount of tokens to burn.
    function userBurn(uint256 amount_) external;
}

// SPDX-License-Identifier: BSL-1.1
pragma solidity 0.8.26;

/// @title IDutchVault
/// @notice Interface for DutchVault contract.
interface IDutchVault {
    /// @notice Returns the base price for a collection.
    /// @param collection_ The collection address.
    /// @return price_ The base price in wei.
    function getBasePrice(address collection_)
        external
        view
        returns (uint256 price_);

    /// @notice Returns the allocation for a collection.
    /// @param collection_ The collection address.
    /// @return allocationBPS_ The allocation in basis points.
    function getCollectionAllocation(address collection_)
        external
        view
        returns (uint16 allocationBPS_);

    /// @notice Receives a contribution from AuctionAssist.
    /// @param collection_ The collection to contribute to.
    /// @param contributor_ The contributor address.
    function receiveContribution(address collection_, address contributor_)
        external
        payable;

    /// @notice Returns contribution to AuctionAssist for user withdrawal.
    /// @param collection_ The collection to return contribution from.
    /// @param amount_ The amount to return.
    function returnContribution(address collection_, uint256 amount_)
        external;

    /// @notice Called by marketplace when a vault listing is settled.
    /// @param listingId_ The marketplace listing ID.
    /// @param buyer_ The buyer address.
    /// @param salePriceETH_ The final sale price in ETH.
    /// @param salePriceDUTCH_ The final sale price in DUTCH.
    function onListingSettled(
        uint256 listingId_,
        address buyer_,
        uint256 salePriceETH_,
        uint256 salePriceDUTCH_
    ) external;
}

// SPDX-License-Identifier: BSL-1.1
pragma solidity 0.8.26;

import {UD60x18, ud} from "@prb/math/src/UD60x18.sol";

import {IWETH9} from "@uniswap/v4-periphery/src/interfaces/external/IWETH9.sol";

import {Ownable2Step} from "@openzeppelin/contracts/access/Ownable2Step.sol";
import {Ownable} from "@openzeppelin/contracts/access/Ownable.sol";
import {Pausable} from "@openzeppelin/contracts/utils/Pausable.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/utils/ReentrancyGuard.sol";

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

/**
 * @title BondingCurve
 * @notice Polynomial bonding curve for DUTCH token with configurable taxes
 * @dev Implements buy and sell operations with tax distribution
 *      Price formula: P(supply) = C × supply^1.5
 *      Where C = 500_000_000 (5.0E-10 ETH)
 */
contract BondingCurve is Ownable2Step, ReentrancyGuard, Pausable {

    // -------------------------------------------------------------------------
    // Errors
    // -------------------------------------------------------------------------

    /// @notice Thrown when caller is not authorized for liquidity operations.
    error Unauthorized();

    /// @notice Thrown when swap amount is zero.
    error InvalidAmount();

    /// @notice Thrown when hook's WETH reserves are insufficient for sell.
    error InsufficientReserves();

    /// @notice Thrown when calculated output is less than minimum expected.
    error SlippageExceeded(uint256 expected, uint256 actual);

    /// @notice Thrown when invalid address provided (zero address).
    error InvalidAddress();

    /// @notice Thrown when invalid BPS value (exceeds 10000).
    error InvalidBPS();

    /// @notice Thrown when tax split percentages don't sum to 100%.
    error InvalidSplitConfig();

    /// @notice Thrown when insufficient excess reserve is available.
    error InsufficientExcessReserve();

    /// @notice Thrown when attempting to initialize a second pool.
    error PoolAlreadyInitialized();

    /// @notice Thrown when pool has incorrect token pair.
    error InvalidTokenPair();

    /// @notice Thrown when attempting operations before pool initialization.
    error PoolNotInitialized();

    /// @notice Thrown when attempting to buy before presale ends.
    error PresaleNotEnded();

    // -------------------------------------------------------------------------
    // Events
    // -------------------------------------------------------------------------

    /// @notice Emitted when DUTCH tokens are minted via buy swap.
    /// @param wethAmount_ Amount of WETH spent (including tax).
    /// @param tokenAmount_ Amount of DUTCH tokens minted.
    /// @param taxAmount_ Amount of tax collected.
    /// @param currentPrice_ Spot price after mint.
    event Minted(
        uint256 wethAmount_,
        uint256 tokenAmount_,
        uint256 taxAmount_,
        uint256 currentPrice_
    );

    /// @notice Emitted when DUTCH tokens are burned via sell swap.
    /// @param tokenAmount_ Amount of DUTCH tokens burned.
    /// @param wethAmount_ Amount of WETH refunded (net after tax).
    /// @param taxAmount_ Amount of tax collected.
    /// @param currentPrice_ Spot price after burn.
    event Burned(
        uint256 tokenAmount_,
        uint256 wethAmount_,
        uint256 taxAmount_,
        uint256 currentPrice_
    );

    /// @notice Emitted when buy tax rate is updated.
    /// @param oldBps_ Previous buy tax in basis points.
    /// @param newBps_ New buy tax in basis points.
    event BuyTaxUpdated(uint256 oldBps_, uint256 newBps_);

    /// @notice Emitted when sell tax rate is updated.
    /// @param oldBps_ Previous sell tax in basis points.
    /// @param newBps_ New sell tax in basis points.
    event SellTaxUpdated(uint256 oldBps_, uint256 newBps_);

    /// @notice Emitted when buy tax split configuration is updated.
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops wallet share in basis points.
    event BuySplitUpdated(uint256 vaultBps_, uint256 opsBps_);

    /// @notice Emitted when sell tax split configuration is updated.
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops wallet share in basis points.
    event SellSplitUpdated(uint256 vaultBps_, uint256 opsBps_);

    /// @notice Emitted when DutchVault address is updated.
    /// @param oldVault_ Previous vault address.
    /// @param newVault_ New vault address.
    event DutchVaultUpdated(address oldVault_, address newVault_);

    /// @notice Emitted when OpsWallet address is updated.
    /// @param oldWallet_ Previous wallet address.
    /// @param newWallet_ New wallet address.
    event OpsWalletUpdated(address oldWallet_, address newWallet_);

    /// @notice Emitted when excess reserve is withdrawn.
    /// @param amount_ Amount of WETH withdrawn.
    /// @param dutchVault_ DutchVault that received the WETH.
    event ExcessReserveWithdrawn(uint256 amount_, address dutchVault_);

    /// @notice Emitted when tax exemption status changes.
    /// @param account_ Address whose exemption status changed.
    /// @param exempt_ New exemption status.
    event TaxExemptionSet(address indexed account_, bool exempt_);

    // -------------------------------------------------------------------------
    // Immutables
    // -------------------------------------------------------------------------

    /// @notice DUTCH token contract.
    IDUTCHToken public immutable dutchToken;

    /// @notice WETH currency for pool interactions.
    IWETH9 private immutable _weth;

    // -------------------------------------------------------------------------
    // Constants - Bonding Curve
    // -------------------------------------------------------------------------

    /// @notice Curve constant: 5.0E-10 ETH (500,000,000 wei).
    UD60x18 private constant CURVE_CONSTANT = UD60x18.wrap(500_000_000);

    /// @notice Price exponent: 1.5.
    UD60x18 private constant EXPONENT = UD60x18.wrap(1_500000000000000000);

    /// @notice Integral exponent: 2.5 (EXPONENT + 1).
    UD60x18 private constant EXPONENT_PLUS_ONE = UD60x18.wrap(2_500000000000000000);

    // -------------------------------------------------------------------------
    // Constants - Tax Configuration
    // -------------------------------------------------------------------------

    /// @notice Basis points denominator (100%).
    uint256 private constant BPS_DENOMINATOR = 10000;

    // -------------------------------------------------------------------------
    // State - Addresses
    // -------------------------------------------------------------------------

    /// @notice DutchVault address receiving vault share of taxes.
    address private _dutchVault;

    /// @notice Operations wallet receiving ops share of taxes.
    address private _opsWallet;

    /// @notice DutchAuctionMarketplace address (tax-exempt, set at deploy).
    address private _marketplace;

    /// @notice Presale contract address; first call to buyDutchExactIn/Out must be from this. Tax-exempt.
    address private _presale;

    // -------------------------------------------------------------------------
    // State - Tax Configuration
    // -------------------------------------------------------------------------

    /// @notice Buy tax rate in basis points (default: 1000 = 10%).
    uint256 private _buyTaxBps;

    /// @notice Sell tax rate in basis points (default: 1000 = 10%).
    uint256 private _sellTaxBps;

    /// @notice Buy tax: Vault share in basis points (default: 7500 = 75%).
    uint256 private _buyVaultSplitBps;

    /// @notice Buy tax: Ops share in basis points (default: 2500 = 25%).
    uint256 private _buyOpsSplitBps;

    /// @notice Sell tax: Vault share in basis points (default: 7500 = 75%).
    uint256 private _sellVaultSplitBps;

    /// @notice Sell tax: Ops share in basis points (default: 2500 = 25%).
    uint256 private _sellOpsSplitBps;

    /// @notice Mapping of tax-exempt addresses (e.g., marketplace).
    mapping(address account => bool isExempt) private _taxExempt;

    // -------------------------------------------------------------------------
    // State - Accounting
    // -------------------------------------------------------------------------

    /// @notice WETH reserve balance backing bonding curve.
    uint256 private _wethReserve;

    /// @notice Cumulative DUTCH tokens minted through bonding curve.
    uint256 private _totalMinted;

    /// @notice Cumulative DUTCH tokens burned through bonding curve.
    uint256 private _totalBurned;

    /// @notice Cumulative WETH added to reserve (after buy tax).
    uint256 private _wethInflow;

    /// @notice Cumulative WETH removed from reserve (before sell tax).
    uint256 private _wethOutflow;

    /// @notice Total number of mint operations (buy swaps).
    uint256 private _totalMintOperations;

    /// @notice Total number of burn operations (sell swaps).
    uint256 private _totalBurnOperations;

    /// @notice Total excess WETH withdrawn from burned token range.
    uint256 private _totalExcessWithdrawn;

    /// @notice Flag indicating if the presale has ended.
    bool private _isPresaleEnded;

    constructor(
        address wethAddress_,
        address dutchToken_,
        address dutchVault_,
        address opsWallet_,
        address marketplace_,
        address presale_,
        address owner_
    ) Ownable(owner_) {
        // Validate addresses.
        if (wethAddress_ == address(0)) revert InvalidAddress();
        if (dutchToken_ == address(0)) revert InvalidAddress();
        if (dutchVault_ == address(0)) revert InvalidAddress();
        if (opsWallet_ == address(0)) revert InvalidAddress();
        if (marketplace_ == address(0)) revert InvalidAddress();
        if (presale_ == address(0)) revert InvalidAddress();
        
        dutchToken = IDUTCHToken(dutchToken_);
        _dutchVault = dutchVault_;
        _opsWallet = opsWallet_;
        _marketplace = marketplace_;
        _presale = presale_;

        // Initialize WETH
        _weth = IWETH9(wethAddress_);

        // Initialize tax configuration with defaults (configurable)
        _buyTaxBps = 1000;          // 10%.
        _sellTaxBps = 1000;         // 10%.
        _buyVaultSplitBps = 7500;   // 75%.
        _buyOpsSplitBps = 2500;     // 25%.
        _sellVaultSplitBps = 7500;  // 75%.
        _sellOpsSplitBps = 2500;    // 25%.
        
        // Mark marketplace as tax-exempt.
        _taxExempt[marketplace_] = true;
    }

    // -------------------------------------------------------------------------
    // Admin Functions
    // -------------------------------------------------------------------------

    /// @notice Updates the buy tax rate.
    /// @dev Only callable by owner.
    /// @param newBps_ New buy tax in basis points (max 10000).
    function setBuyTaxBps(uint256 newBps_) external onlyOwner {
        if (newBps_ >= BPS_DENOMINATOR) revert InvalidBPS();
        
        uint256 oldBps_ = _buyTaxBps;
        _buyTaxBps = newBps_;
        
        emit BuyTaxUpdated(oldBps_, newBps_);
    }

    /// @notice Updates the sell tax rate.
    /// @dev Only callable by owner.
    /// @param newBps_ New sell tax in basis points (max 10000).
    function setSellTaxBps(uint256 newBps_) external onlyOwner {
        if (newBps_ >= BPS_DENOMINATOR) revert InvalidBPS();
        
        uint256 oldBps_ = _sellTaxBps;
        _sellTaxBps = newBps_;
        
        emit SellTaxUpdated(oldBps_, newBps_);
    }

    /// @notice Updates the buy tax split configuration.
    /// @dev Only callable by owner. Splits must sum to 100% (10000 BPS).
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops wallet share in basis points.
    function setBuySplitConfig(uint256 vaultBps_, uint256 opsBps_)
        external
        onlyOwner
    {
        if (vaultBps_ + opsBps_ != BPS_DENOMINATOR) {
            revert InvalidSplitConfig();
        }
        
        _buyVaultSplitBps = vaultBps_;
        _buyOpsSplitBps = opsBps_;
        
        emit BuySplitUpdated(vaultBps_, opsBps_);
    }

    /// @notice Updates the sell tax split configuration.
    /// @dev Only callable by owner. Splits must sum to 100% (10000 BPS).
    /// @param vaultBps_ Vault share in basis points.
    /// @param opsBps_ Ops wallet share in basis points.
    function setSellSplitConfig(uint256 vaultBps_, uint256 opsBps_)
        external
        onlyOwner
    {
        if (vaultBps_ + opsBps_ != BPS_DENOMINATOR) {
            revert InvalidSplitConfig();
        }
        
        _sellVaultSplitBps = vaultBps_;
        _sellOpsSplitBps = opsBps_;
        
        emit SellSplitUpdated(vaultBps_, opsBps_);
    }

    /// @notice Updates the DutchVault address.
    /// @dev Only callable by owner.
    /// @param newVault_ New vault address.
    function setDutchVault(address newVault_) external onlyOwner {
        if (newVault_ == address(0)) revert InvalidAddress();
        
        address oldVault_ = _dutchVault;
        _dutchVault = newVault_;
        
        emit DutchVaultUpdated(oldVault_, newVault_);
    }

    /// @notice Updates the OpsWallet address.
    /// @dev Only callable by owner.
    /// @param newWallet_ New wallet address.
    function setOpsWallet(address newWallet_) external onlyOwner {
        if (newWallet_ == address(0)) revert InvalidAddress();
        
        emit OpsWalletUpdated(_opsWallet, newWallet_);
        _opsWallet = newWallet_;
    }

    /// @notice Sets tax exemption status for an address.
    /// @dev Only callable by owner.
    /// @param account_ Address to update exemption status.
    /// @param exempt_ True to exempt from taxes, false otherwise.
    function setTaxExemption(
        address account_,
        bool exempt_
    ) external onlyOwner {
        if (account_ == address(0)) revert InvalidAddress();
        _taxExempt[account_] = exempt_;
        emit TaxExemptionSet(account_, exempt_);
    }

    /// @notice Pauses all swap operations.
    /// @dev Only callable by owner. Prevents swaps.
    function pause() external onlyOwner {
        _pause();
    }

    /// @notice Unpauses all swap operations.
    /// @dev Only callable by owner. Resumes normal swap operations.
    function unpause() external onlyOwner {
        _unpause();
    }

    // -------------------------------------------------------------------------
    // View Functions - Configuration
    // -------------------------------------------------------------------------

    /// @notice Checks if an address is tax-exempt.
    /// @param account_ Address to check.
    /// @return True if address is exempt from taxes.
    function isTaxExempt(address account_) external view returns (bool) {
        return _taxExempt[account_];
    }

    /// @notice Returns the current buy tax rate.
    /// @return Buy tax in basis points.
    function getBuyTaxBps() external view returns (uint256) {
        return _buyTaxBps;
    }

    /// @notice Returns the current sell tax rate.
    /// @return Sell tax in basis points.
    function getSellTaxBps() external view returns (uint256) {
        return _sellTaxBps;
    }

    /// @notice Returns the buy tax split configuration.
    /// @return vaultBps_ Vault share in basis points.
    /// @return opsBps_ Ops wallet share in basis points.
    function getBuySplitConfig()
        external
        view
        returns (uint256 vaultBps_, uint256 opsBps_)
    {
        return (_buyVaultSplitBps, _buyOpsSplitBps);
    }

    /// @notice Returns the sell tax split configuration.
    /// @return vaultBps_ Vault share in basis points.
    /// @return opsBps_ Ops wallet share in basis points.
    function getSellSplitConfig()
        external
        view
        returns (uint256 vaultBps_, uint256 opsBps_)
    {
        return (_sellVaultSplitBps, _sellOpsSplitBps);
    }

    /// @notice Returns whether the presale has ended.
    /// @return True if presale has ended, false otherwise.
    function isPresaleEnded() external view returns (bool) {
        return _isPresaleEnded;
    }

    /// @notice Manually sets presale ended flag (owner only).
    /// @dev Used for testing or emergency situations.
    function setPresaleEnded() external onlyOwner {
        _isPresaleEnded = true;
    }

    /// @notice Returns the DutchVault address.
    /// @return DutchVault address.
    function getDutchVault() external view returns (address) {
        return _dutchVault;
    }

    /// @notice Returns the OpsWallet address.
    /// @return OpsWallet address.
    function getOpsWallet() external view returns (address) {
        return _opsWallet;
    }

    // -------------------------------------------------------------------------
    // View Functions - Current State, Quotes
    // -------------------------------------------------------------------------

    /// @notice Calculates available excess reserve from burned tokens.
    /// @dev Excess reserve is the WETH value of burned tokens from bottom of
    ///      curve, minus any prior withdrawals.
    /// @return available_ Amount of excess WETH available to withdraw.
    function getExcessReserve() external view returns (uint256 available_) {
        uint256 burnedTokens_ = dutchToken.getTotalUserBurned();
        uint256 excessWeth_ = _calculateCostFromZero(burnedTokens_);

        available_ = excessWeth_ > _totalExcessWithdrawn
            ? excessWeth_ - _totalExcessWithdrawn
            : 0;
    }

    /// @notice Exact-in buy quote: DUTCH out for ETH in. Includes buy tax when _buyTaxBps>0.
    /// @dev Simulates buy operation with tax. Does not account for slippage or tax exemptions.
    /// @param wethIn_ Amount of WETH to spend (including tax).
    /// @return dutchOut_ Gross amount of DUTCH tokens before distribution.
    /// @return taxAmount_ Amount of WETH taken as tax.
    /// @return netDutch_ Net DUTCH tokens user receives.
    function getQuoteWETHtoDUTCH(uint256 wethIn_)
        external
        view
        returns (uint256 dutchOut_, uint256 taxAmount_, uint256 netDutch_)
    {
        if (wethIn_ == 0) return (0, 0, 0);

        // Calculate net WETH after tax.
        uint256 netWeth_;
        if (_buyTaxBps > 0) {
            netWeth_ = (wethIn_ * (BPS_DENOMINATOR - _buyTaxBps)) /
                BPS_DENOMINATOR;
            taxAmount_ = wethIn_ - netWeth_;
        } else {
            netWeth_ = wethIn_;
            taxAmount_ = 0;
        }

        // Calculate tokens from net WETH.
        dutchOut_ = _calculateTokensFromWETH(netWeth_);
        netDutch_ = dutchOut_;
    }

    /// @notice Exact-out buy quote: ETH required for exact DUTCH. Includes buy tax when _buyTaxBps>0.
    /// @dev Simulates buy operation with tax. Does not account for slippage or tax exemptions.
    /// @param exactDutchAmount_ Exact DUTCH to receive.
    /// @return totalEthRequired_ Total ETH to send (curve + tax).
    /// @return taxAmount_ ETH that would be taken as tax (0 if _buyTaxBps==0).
    function getQuoteWETHForExactDUTCH(uint256 exactDutchAmount_)
        external
        view
        returns (uint256 totalEthRequired_, uint256 taxAmount_)
    {
        if (exactDutchAmount_ == 0) return (0, 0);

        // Calculate curve cost.
        uint256 ethForCurve_ = _calculateMintCost(exactDutchAmount_);

        // Apply buy tax.
        if (_buyTaxBps == 0) {
            totalEthRequired_ = ethForCurve_;
            taxAmount_ = 0;
        } else {
            totalEthRequired_ = (ethForCurve_ * BPS_DENOMINATOR) / (BPS_DENOMINATOR - _buyTaxBps);
            taxAmount_ = totalEthRequired_ - ethForCurve_;
        }
    }

    /// @notice Sell quote: ETH out for DUTCH in. Includes sell tax when _sellTaxBps>0.
    /// @param dutchIn_ Amount of DUTCH tokens to sell.
    /// @return wethOut_ Gross WETH refund before tax.
    /// @return taxAmount_ Amount of WETH taken as tax.
    /// @return netWeth_ Net WETH user receives.
    function getQuoteDUTCHtoWETH(uint256 dutchIn_)
        external
        view
        returns (uint256 wethOut_, uint256 taxAmount_, uint256 netWeth_)
    {
        if (dutchIn_ == 0) return (0, 0, 0);

        // Calculate gross refund.
        wethOut_ = _calculateBurnRefund(dutchIn_);

        // Apply sell tax.
        if (_sellTaxBps > 0) {
            taxAmount_ = (wethOut_ * _sellTaxBps) / BPS_DENOMINATOR;
            netWeth_ = wethOut_ - taxAmount_;
        } else {
            taxAmount_ = 0;
            netWeth_ = wethOut_;
        }
    }

    //-------------------------------------------------------------------------
    // Admin Functions - Excess Reserve
    //-------------------------------------------------------------------------

    /// @notice Withdraws excess reserve from burned tokens to DutchVault.
    /// @dev Only callable by owner. Amount must not exceed available excess.
    /// @param amount_ Amount of excess WETH to withdraw.
    function withdrawExcessReserve(uint256 amount_) external onlyOwner {
        if (amount_ == 0) revert InvalidAmount();

        uint256 burnedTokens_ = dutchToken.getTotalUserBurned();
        uint256 excessWeth_ = _calculateCostFromZero(burnedTokens_);
        uint256 available_ = excessWeth_ > _totalExcessWithdrawn
            ? excessWeth_ - _totalExcessWithdrawn
            : 0;

        if (amount_ > available_) revert InsufficientExcessReserve();
        if (amount_ > _wethReserve) revert InsufficientReserves();

        _totalExcessWithdrawn += amount_;
        _wethReserve -= amount_;

        // Unwrap WETH to ETH before sending to DutchVault.
        _weth.withdraw(amount_);
        (bool success_,) = payable(_dutchVault).call{value: amount_}("");
        if (!success_) revert InvalidAddress();
        
        emit ExcessReserveWithdrawn(amount_, _dutchVault);
    }

    // -------------------------------------------------------------------------
    // Buy / Sell Functions
    // -------------------------------------------------------------------------

    /// @notice Exact-in buy: send ETH, receive DUTCH. Reverts if DUTCH out < minDutchAmount_.
    /// @dev First buy must be from _presale. Tax: 0 if _taxExempt[caller] or _buyTaxBps==0.
    /// @param minDutchAmount_ Minimum DUTCH to receive (slippage).
    /// @param recipient_ Recipient of DUTCH.
    /// @return dutchAmount_ DUTCH minted.
    /// @return ethUsed_ ETH used (always msg.value).
    /// @return taxAmount_ ETH taken as tax (0 if exempt).
    function buyDutchExactIn(uint256 minDutchAmount_, address recipient_)
        external
        payable
        whenNotPaused
        nonReentrant
        returns (uint256 dutchAmount_, uint256 ethUsed_, uint256 taxAmount_)
    {
        if (!_isPresaleEnded && msg.sender != _presale) revert PresaleNotEnded();
        if (msg.value == 0) revert InvalidAmount();
        if (recipient_ == address(0)) revert InvalidAddress();

        // 1. Tax (exempt or zero rate => no tax).
        uint256 netWeth_;
        if (_taxExempt[msg.sender] || _buyTaxBps == 0) {
            netWeth_ = msg.value;
            taxAmount_ = 0;
        } else {
            taxAmount_ = (msg.value * _buyTaxBps) / BPS_DENOMINATOR;
            netWeth_ = msg.value - taxAmount_;
        }

        // 2. Exact-in: DUTCH from net WETH.
        dutchAmount_ = _calculateTokensFromWETH(netWeth_);
        if (dutchAmount_ == 0) revert InvalidAmount();
        if (dutchAmount_ < minDutchAmount_) revert SlippageExceeded(minDutchAmount_, dutchAmount_);

        // 3. Wrap, update reserve, mint.
        _weth.deposit{value: netWeth_}();
        _wethReserve += netWeth_;
        _wethInflow += netWeth_;
        _totalMinted += dutchAmount_;
        ++_totalMintOperations;

        // 4. Distribute buy tax.
        if (taxAmount_ > 0) {
            (uint256 vaultAmount_, uint256 opsAmount_) = _calculateBuyTax(taxAmount_);
            if (vaultAmount_ > 0) {
                (bool vaultOk,) = payable(_dutchVault).call{value: vaultAmount_}("");
                if (!vaultOk) revert InvalidAddress();
            }
            if (opsAmount_ > 0) {
                (bool opsOk,) = payable(_opsWallet).call{value: opsAmount_}("");
                if (!opsOk) revert InvalidAddress();
            }
        }

        // 5. Mint DUTCH tokens to recipient.
        dutchToken.mint(recipient_, dutchAmount_);

        // 6. Mark presale as ended.
        if (!_isPresaleEnded && msg.sender == _presale) _isPresaleEnded = true;

        // 7. Emit event.
        ethUsed_ = msg.value;
        emit Minted(msg.value, dutchAmount_, taxAmount_, getCurrentPrice());
    }

    /// @notice Exact-out buy: receive exact DUTCH for ETH. Refunds msg.value - totalRequired. Reverts if msg.value < totalRequired.
    /// @dev First buy must be from _presale. Tax: 0 if _taxExempt[caller] or _buyTaxBps==0.
    /// @param exactDutchAmount_ DUTCH to receive.
    /// @param recipient_ Recipient of DUTCH.
    /// @return dutchAmount_ DUTCH minted (equals exactDutchAmount_).
    /// @return ethUsed_ ETH used (curve + tax); excess refunded to caller.
    /// @return taxAmount_ ETH taken as tax (0 if exempt).
    function buyDutchExactOut(uint256 exactDutchAmount_, address recipient_)
        external
        payable
        whenNotPaused
        nonReentrant
        returns (uint256 dutchAmount_, uint256 ethUsed_, uint256 taxAmount_)
    {
        if (!_isPresaleEnded && msg.sender != _presale) revert PresaleNotEnded();
        if (exactDutchAmount_ == 0) revert InvalidAmount();
        if (recipient_ == address(0)) revert InvalidAddress();

        // 1. Tax (exempt or zero rate => no tax). Exact-out: ethForCurve + totalRequired.
        uint256 ethForCurve_ = _calculateMintCost(exactDutchAmount_);
        uint256 totalRequired_;
        if (_taxExempt[msg.sender] || _buyTaxBps == 0) {
            totalRequired_ = ethForCurve_;
            taxAmount_ = 0;
        } else {
            totalRequired_ = (ethForCurve_ * BPS_DENOMINATOR) / (BPS_DENOMINATOR - _buyTaxBps);
            taxAmount_ = totalRequired_ - ethForCurve_;
        }

        if (msg.value < totalRequired_) revert SlippageExceeded(totalRequired_, msg.value);

        // 2. Wrap ETH, update reserve.
        _weth.deposit{value: ethForCurve_}();
        _wethReserve += ethForCurve_;
        _wethInflow += ethForCurve_;
        _totalMinted += exactDutchAmount_;
        ++_totalMintOperations;

        // 3. Distribute buy tax.
        if (taxAmount_ > 0) {
            (uint256 vaultAmount_, uint256 opsAmount_) = _calculateBuyTax(taxAmount_);
            if (vaultAmount_ > 0) {
                (bool vaultOk,) = payable(_dutchVault).call{value: vaultAmount_}("");
                if (!vaultOk) revert InvalidAddress();
            }
            if (opsAmount_ > 0) {
                (bool opsOk,) = payable(_opsWallet).call{value: opsAmount_}("");
                if (!opsOk) revert InvalidAddress();
            }
        }

        // 4. Mint DUTCH tokens to recipient.
        dutchToken.mint(recipient_, exactDutchAmount_);

        // 5. Mark presale as ended.
        if (!_isPresaleEnded && msg.sender == _presale) _isPresaleEnded = true;

        // 6. Refund excess ETH to caller.
        uint256 excess_ = msg.value - totalRequired_;
        if (excess_ > 0) {
            (bool ok,) = payable(msg.sender).call{value: excess_}("");
            if (!ok) revert InvalidAmount();
        }

        // 7. Emit event.
        dutchAmount_ = exactDutchAmount_;
        ethUsed_ = totalRequired_;
        emit Minted(totalRequired_, exactDutchAmount_, taxAmount_, getCurrentPrice());
    }

    /// @notice Sell DUTCH for ETH. Burns caller's DUTCH; sends net ETH after sell tax. Reverts if net ETH < minEthAmount_.
    /// @dev Tax: 0 if _taxExempt[caller] or _sellTaxBps==0.
    /// @param tokenAmount_ Amount of DUTCH tokens to sell.
    /// @param minEthAmount_ Minimum ETH to receive (slippage protection).
    /// @return netEth_ Net ETH returned to user after tax.
    function redeemDUTCH(
        uint256 tokenAmount_,
        uint256 minEthAmount_
    )
        external
        whenNotPaused
        nonReentrant
        returns (uint256 netEth_)
    {
        // 1. Validate input.
        if (tokenAmount_ == 0) revert InvalidAmount();

        // 2. Calculate gross refund from curve.
        uint256 grossRefund_ = _calculateBurnRefund(tokenAmount_);

        // 3. Check reserve sufficiency.
        if (_wethReserve < grossRefund_) revert InsufficientReserves();

        // 4. Calculate tax (unless caller is exempt).
        uint256 taxAmount_;
        bool isExempt_ = _taxExempt[msg.sender];
        if (isExempt_ || _sellTaxBps == 0) {
            netEth_ = grossRefund_;
            taxAmount_ = 0;
        } else {
            taxAmount_ = (grossRefund_ * _sellTaxBps) / BPS_DENOMINATOR;
            netEth_ = grossRefund_ - taxAmount_;
        }

        // 5. Slippage protection.
        if (netEth_ < minEthAmount_) {
            revert SlippageExceeded(minEthAmount_, netEth_);
        }

        // 6. Burn tokens from caller.
        dutchToken.burn(msg.sender, tokenAmount_);

        // 7. Update state.
        _wethReserve -= grossRefund_;
        _wethOutflow += grossRefund_;
        _totalBurned += tokenAmount_;
        ++_totalBurnOperations;

        // 8. Distribute sell tax if applicable.
        if (taxAmount_ > 0) {
            (uint256 vaultAmount_, uint256 opsAmount_) =
                _calculateSellTax(taxAmount_);

            // Unwrap tax amount to ETH.
            _weth.withdraw(vaultAmount_ + opsAmount_);

            // Send tax to vault and ops wallet.
            if (vaultAmount_ > 0) {
                (bool vaultSuccess_,) = payable(_dutchVault).call{value: vaultAmount_}("");
                if (!vaultSuccess_) revert InvalidAddress();
            }
            
            if (opsAmount_ > 0) {
                (bool opsSuccess_,) = payable(_opsWallet).call{value: opsAmount_}("");
                if (!opsSuccess_) revert InvalidAddress();
            }
        }

        // 9. Unwrap and send net refund to caller.
        _weth.withdraw(netEth_);
        (bool success_, ) = payable(msg.sender).call{value: netEth_}("");
        if (!success_) revert InvalidAddress();

        // 10. Emit event.
        emit Burned(tokenAmount_, netEth_, taxAmount_, getCurrentPrice());
    }

    /// @notice Allow receiving ETH
    receive() external payable {}

    // -------------------------------------------------------------------------
    // View Functions - Bonding Curve
    // -------------------------------------------------------------------------

    /// @notice Returns the current spot price for 1 token at current supply.
    /// @dev Price = C × supply^1.5.
    /// @return price_ The current price in WETH (18 decimals).
    function getCurrentPrice() public view returns (uint256 price_) {
        uint256 currentSupply_ = _totalMinted - _totalBurned;
        
        if (currentSupply_ == 0) {
            return 0;
        }
        
        UD60x18 supply_ = ud(currentSupply_);
        UD60x18 price60x18_ = CURVE_CONSTANT.mul(supply_.pow(EXPONENT));
        price_ = price60x18_.unwrap();
    }

    /// @notice Returns current bonding curve supply.
    /// @return supply_ Current supply (totalMinted - totalBurned).
    function getBondingCurveSupply() external view returns (uint256 supply_) {
        supply_ = _totalMinted - _totalBurned;
    }

    /// @notice Returns WETH reserve balance.
    /// @return reserve_ Current WETH reserve backing the curve.
    function getReserveBalance() external view returns (uint256 reserve_) {
        reserve_ = _wethReserve;
    }

    /// @notice Returns total minted tokens.
    /// @return total_ Cumulative DUTCH minted.
    function getTotalMinted() external view returns (uint256 total_) {
        total_ = _totalMinted;
    }

    /// @notice Returns total burned tokens.
    /// @return total_ Cumulative DUTCH burned.
    function getTotalBurned() external view returns (uint256 total_) {
        total_ = _totalBurned;
    }

    // -------------------------------------------------------------------------
    // Internal Functions - Bonding Curve Math
    // -------------------------------------------------------------------------

    /// @notice WETH cost to mint tokens at current supply. Integral: C×((s₁^2.5-s₀^2.5)/2.5).
    /// @param tokenAmount_ Tokens to mint.
    /// @return cost_ WETH cost (18 decimals).
    function _calculateMintCost(uint256 tokenAmount_)
        internal
        view
        returns (uint256 cost_)
    {
        uint256 currentSupply_ = _totalMinted - _totalBurned;

        // Convert to UD60x18 for PRBMath.
        UD60x18 s0_ = ud(currentSupply_);
        UD60x18 s1_ = ud(currentSupply_ + tokenAmount_);

        // Calculate s1^2.5 and s0^2.5.
        UD60x18 s1Pow_ = s1_.pow(EXPONENT_PLUS_ONE);
        UD60x18 s0Pow_ = s0_.pow(EXPONENT_PLUS_ONE);

        // Calculate integral: (s1^2.5 - s0^2.5) / 2.5.
        UD60x18 integral_ = (s1Pow_.sub(s0Pow_)).div(EXPONENT_PLUS_ONE);

        // Multiply by curve constant: C × integral.
        UD60x18 cost60x18_ = CURVE_CONSTANT.mul(integral_);

        // WETH uses 18 decimals, same as UD60x18, no conversion needed.
        cost_ = cost60x18_.unwrap();
    }

    /// @notice Calculates WETH refund for burning tokens.
    /// @dev Integral: C × ((s₀^2.5 - s₁^2.5) / 2.5).
    /// @param tokenAmount_ Tokens to burn.
    /// @return refund_ WETH refund (18 decimals).
    function _calculateBurnRefund(uint256 tokenAmount_)
        internal
        view
        returns (uint256 refund_)
    {
        uint256 currentSupply_ = _totalMinted - _totalBurned;

        // Convert to UD60x18 for PRBMath.
        UD60x18 s0_ = ud(currentSupply_);
        UD60x18 s1_ = ud(currentSupply_ - tokenAmount_);

        // Calculate s0^2.5 and s1^2.5.
        UD60x18 s0Pow_ = s0_.pow(EXPONENT_PLUS_ONE);
        UD60x18 s1Pow_ = s1_.pow(EXPONENT_PLUS_ONE);

        // Calculate integral: (s0^2.5 - s1^2.5) / 2.5.
        UD60x18 integral_ = (s0Pow_.sub(s1Pow_)).div(EXPONENT_PLUS_ONE);

        // Multiply by curve constant: C × integral.
        UD60x18 refund60x18_ = CURVE_CONSTANT.mul(integral_);

        // WETH uses 18 decimals, same as UD60x18, no conversion needed.
        refund_ = refund60x18_.unwrap();
    }

    /// @notice Tokens mintable for given WETH. Inverts mint curve: Δs = ((cost×2.5/C)+s0^2.5)^(1/2.5)-s0.
    /// @param wethAmount_ WETH to spend on curve.
    /// @return tokenAmount_ Tokens minted.
    function _calculateTokensFromWETH(uint256 wethAmount_)
        internal
        view
        returns (uint256 tokenAmount_)
    {
        uint256 currentSupply_ = _totalMinted - _totalBurned;

        // Convert to UD60x18 for PRBMath.
        UD60x18 s0_ = ud(currentSupply_);
        UD60x18 wethAmount60x18_ = ud(wethAmount_);

        // Calculate (cost × 2.5 / C).
        UD60x18 scaledCost_ =
            wethAmount60x18_.mul(EXPONENT_PLUS_ONE).div(CURVE_CONSTANT);

        // Calculate s0^2.5.
        UD60x18 s0Pow_ = s0_.pow(EXPONENT_PLUS_ONE);

        // Calculate (cost × 2.5 / C + s0^2.5).
        UD60x18 sum_ = scaledCost_.add(s0Pow_);

        // Calculate s1 = sum^(1/2.5).
        UD60x18 s1_ = sum_.pow(EXPONENT_PLUS_ONE.inv());

        // Token amount = s₁ - s₀.
        tokenAmount_ = s1_.unwrap() - currentSupply_;
    }

    /// @notice Tokens to burn for desired WETH. Inverts burn curve: Δs = s0-(s0^2.5-refund×2.5/C)^(1/2.5).
    /// @param wethAmount_ WETH desired.
    /// @return tokenAmount_ Tokens to burn.
    function _calculateTokensNeededForWETH(uint256 wethAmount_)
        internal
        view
        returns (uint256 tokenAmount_)
    {
        uint256 currentSupply_ = _totalMinted - _totalBurned;

        // Convert to UD60x18 for PRBMath.
        UD60x18 s0_ = ud(currentSupply_);
        UD60x18 wethAmount60x18_ = ud(wethAmount_);

        // Calculate (refund × 2.5 / C).
        UD60x18 scaledRefund_ =
            wethAmount60x18_.mul(EXPONENT_PLUS_ONE).div(CURVE_CONSTANT);

        // Calculate s0^2.5.
        UD60x18 s0Pow_ = s0_.pow(EXPONENT_PLUS_ONE);

        // Calculate (s0^2.5 - refund × 2.5 / C).
        UD60x18 diff_ = s0Pow_.sub(scaledRefund_);

        // Calculate s1 = diff^(1/2.5).
        UD60x18 s1_ = diff_.pow(EXPONENT_PLUS_ONE.inv());

        // Token amount = s₀ - s₁.
        tokenAmount_ = currentSupply_ - s1_.unwrap();
    }

    /// @notice WETH cost for tokens from curve bottom (0). Used for excess-reserve accounting.
    /// @param tokenAmount_ Tokens from bottom of curve.
    /// @return cost_ WETH (18 decimals).
    function _calculateCostFromZero(uint256 tokenAmount_)
        internal
        pure
        returns (uint256 cost_)
    {
        UD60x18 s1_ = ud(tokenAmount_);
        UD60x18 s1Pow_ = s1_.pow(EXPONENT_PLUS_ONE);
        UD60x18 integral_ = s1Pow_.div(EXPONENT_PLUS_ONE);
        UD60x18 cost60x18_ = CURVE_CONSTANT.mul(integral_);
        cost_ = cost60x18_.unwrap();
    }

    /// @notice Buy tax split: Vault and Ops. Ops gets rounding remainder.
    /// @param taxAmount_ Total tax.
    /// @return vaultAmount_ For DutchVault.
    /// @return opsAmount_ For OpsWallet.
    function _calculateBuyTax(uint256 taxAmount_)
        internal
        view
        returns (uint256 vaultAmount_, uint256 opsAmount_)
    {
        vaultAmount_ = (taxAmount_ * _buyVaultSplitBps) / BPS_DENOMINATOR;
        opsAmount_ = taxAmount_ - vaultAmount_;
    }

    /// @notice Sell tax split: Vault and Ops. Ops gets rounding remainder.
    /// @param taxAmount_ Total tax.
    /// @return vaultAmount_ For DutchVault.
    /// @return opsAmount_ For OpsWallet.
    function _calculateSellTax(uint256 taxAmount_)
        internal
        view
        returns (uint256 vaultAmount_, uint256 opsAmount_)
    {
        vaultAmount_ = (taxAmount_ * _sellVaultSplitBps) / BPS_DENOMINATOR;
        opsAmount_ = taxAmount_ - vaultAmount_;
    }
}

// SPDX-License-Identifier: BSL-1.1
pragma solidity 0.8.26;

/// @title IDutchAuctionMarketplace
/// @notice Interface for the Dutch Auction Marketplace contract.
interface IDutchAuctionMarketplace {
    /// @notice Create a listing with proceeds to seller.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price (auction start price).
    /// @param minPrice_ The minimum price (auction floor price).
    /// @return listingId_ The ID of the created listing.
    function createListing(
        address nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_
    ) external payable returns (uint256 listingId_);

    /// @notice Create a listing with proceeds burned.
    /// @param nftContract_ The address of the NFT contract.
    /// @param tokenId_ The token ID of the NFT.
    /// @param maxPrice_ The maximum price (auction start price).
    /// @param minPrice_ The minimum price (auction floor price).
    /// @return listingId_ The ID of the created listing.
    function createListingWithBurn(
        address nftContract_,
        uint256 tokenId_,
        uint256 maxPrice_,
        uint256 minPrice_
    ) external payable returns (uint256 listingId_);

    /// @notice Cancel a listing.
    /// @param listingId_ The ID of the listing to cancel.
    function cancelListing(uint256 listingId_) external;

    /// @notice Get seller fee on settled.
    /// @return feeBps_ The fee in basis points.
    function getSellerFeeOnSettled() external view returns (uint256 feeBps_);
}

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

pragma solidity ^0.8.20;

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns a `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC1363.sol)

pragma solidity >=0.6.2;

import {IERC20} from "./IERC20.sol";
import {IERC165} from "./IERC165.sol";

/**
 * @title IERC1363
 * @dev Interface of the ERC-1363 standard as defined in the https://eips.ethereum.org/EIPS/eip-1363[ERC-1363].
 *
 * Defines an extension interface for ERC-20 tokens that supports executing code on a recipient contract
 * after `transfer` or `transferFrom`, or code on a spender contract after `approve`, in a single transaction.
 */
interface IERC1363 is IERC20, IERC165 {
    /*
     * Note: the ERC-165 identifier for this interface is 0xb0202a11.
     * 0xb0202a11 ===
     *   bytes4(keccak256('transferAndCall(address,uint256)')) ^
     *   bytes4(keccak256('transferAndCall(address,uint256,bytes)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256,bytes)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256,bytes)'))
     */

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @param data Additional data with no specified format, sent in call to `spender`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value, bytes calldata data) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (utils/introspection/IERC165.sol)

pragma solidity >=0.4.16;

/**
 * @dev Interface of the ERC-165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[ERC].
 *
 * 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[ERC 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: MIT
pragma solidity ^0.8.0;

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

/// @title IWETH9
interface IWETH9 is IERC20 {
    /// @notice Deposit ether to get wrapped ether
    function deposit() external payable;

    /// @notice Withdraw wrapped ether to get ether
    function withdraw(uint256) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC20.sol)

pragma solidity >=0.4.16;

import {IERC20} from "../token/ERC20/IERC20.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC165.sol)

pragma solidity >=0.4.16;

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

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

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

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

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

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

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

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

import "./Casting.sol" as Casting;

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

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

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

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

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

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

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

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

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

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

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

import "./Casting.sol" as Casting;

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

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

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

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

import { SD59x18 } from "./ValueType.sol";

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

/// @dev Euler's number as an SD59x18 number.
SD59x18 constant E = SD59x18.wrap(2_718281828459045235);

/// @dev The maximum input permitted in {exp}.
int256 constant uEXP_MAX_INPUT = 133_084258667509499440;
SD59x18 constant EXP_MAX_INPUT = SD59x18.wrap(uEXP_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp}.
int256 constant uEXP_MIN_THRESHOLD = -41_446531673892822322;
SD59x18 constant EXP_MIN_THRESHOLD = SD59x18.wrap(uEXP_MIN_THRESHOLD);

/// @dev The maximum input permitted in {exp2}.
int256 constant uEXP2_MAX_INPUT = 192e18 - 1;
SD59x18 constant EXP2_MAX_INPUT = SD59x18.wrap(uEXP2_MAX_INPUT);

/// @dev Any value less than this returns 0 in {exp2}.
int256 constant uEXP2_MIN_THRESHOLD = -59_794705707972522261;
SD59x18 constant EXP2_MIN_THRESHOLD = SD59x18.wrap(uEXP2_MIN_THRESHOLD);

/// @dev Half the UNIT number.
int256 constant uHALF_UNIT = 0.5e18;
SD59x18 constant HALF_UNIT = SD59x18.wrap(uHALF_UNIT);

/// @dev $log_2(10)$ as an SD59x18 number.
int256 constant uLOG2_10 = 3_321928094887362347;
SD59x18 constant LOG2_10 = SD59x18.wrap(uLOG2_10);

/// @dev $log_2(e)$ as an SD59x18 number.
int256 constant uLOG2_E = 1_442695040888963407;
SD59x18 constant LOG2_E = SD59x18.wrap(uLOG2_E);

/// @dev The maximum value an SD59x18 number can have.
int256 constant uMAX_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_792003956564819967;
SD59x18 constant MAX_SD59x18 = SD59x18.wrap(uMAX_SD59x18);

/// @dev The maximum whole value an SD59x18 number can have.
int256 constant uMAX_WHOLE_SD59x18 = 57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MAX_WHOLE_SD59x18 = SD59x18.wrap(uMAX_WHOLE_SD59x18);

/// @dev The minimum value an SD59x18 number can have.
int256 constant uMIN_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_792003956564819968;
SD59x18 constant MIN_SD59x18 = SD59x18.wrap(uMIN_SD59x18);

/// @dev The minimum whole value an SD59x18 number can have.
int256 constant uMIN_WHOLE_SD59x18 = -57896044618658097711785492504343953926634992332820282019728_000000000000000000;
SD59x18 constant MIN_WHOLE_SD59x18 = SD59x18.wrap(uMIN_WHOLE_SD59x18);

/// @dev PI as an SD59x18 number.
SD59x18 constant PI = SD59x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of SD59x18.
int256 constant uUNIT = 1e18;
SD59x18 constant UNIT = SD59x18.wrap(1e18);

/// @dev The unit number squared.
int256 constant uUNIT_SQUARED = 1e36;
SD59x18 constant UNIT_SQUARED = SD59x18.wrap(uUNIT_SQUARED);

/// @dev Zero as an SD59x18 number.
SD59x18 constant ZERO = SD59x18.wrap(0);

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

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

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

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

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

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

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

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

using {
    Helpers.add,
    Helpers.and,
    Helpers.eq,
    Helpers.gt,
    Helpers.gte,
    Helpers.isZero,
    Helpers.lshift,
    Helpers.lt,
    Helpers.lte,
    Helpers.mod,
    Helpers.neq,
    Helpers.not,
    Helpers.or,
    Helpers.rshift,
    Helpers.sub,
    Helpers.uncheckedAdd,
    Helpers.uncheckedSub,
    Helpers.uncheckedUnary,
    Helpers.xor
} for SD59x18 global;

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

// The global "using for" directive makes it possible to use these operators on the SD59x18 type.
using {
    Helpers.add as +,
    Helpers.and2 as &,
    Math.div as /,
    Helpers.eq as ==,
    Helpers.gt as >,
    Helpers.gte as >=,
    Helpers.lt as <,
    Helpers.lte as <=,
    Helpers.mod as %,
    Math.mul as *,
    Helpers.neq as !=,
    Helpers.not as ~,
    Helpers.or as |,
    Helpers.sub as -,
    Helpers.unary as -,
    Helpers.xor as ^
} for SD59x18 global;

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

import { UD2x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD2x18 number.
UD2x18 constant E = UD2x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD2x18 number can have.
uint64 constant uMAX_UD2x18 = 18_446744073709551615;
UD2x18 constant MAX_UD2x18 = UD2x18.wrap(uMAX_UD2x18);

/// @dev PI as a UD2x18 number.
UD2x18 constant PI = UD2x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD2x18.
UD2x18 constant UNIT = UD2x18.wrap(1e18);
uint64 constant uUNIT = 1e18;

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

import { UD21x18 } from "./ValueType.sol";

/// @dev Euler's number as a UD21x18 number.
UD21x18 constant E = UD21x18.wrap(2_718281828459045235);

/// @dev The maximum value a UD21x18 number can have.
uint128 constant uMAX_UD21x18 = 340282366920938463463_374607431768211455;
UD21x18 constant MAX_UD21x18 = UD21x18.wrap(uMAX_UD21x18);

/// @dev PI as a UD21x18 number.
UD21x18 constant PI = UD21x18.wrap(3_141592653589793238);

/// @dev The unit number, which gives the decimal precision of UD21x18.
uint256 constant uUNIT = 1e18;
UD21x18 constant UNIT = UD21x18.wrap(1e18);

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

import "./Casting.sol" as Casting;

/// @notice The unsigned 2.18-decimal fixed-point number representation, which can have up to 2 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint64. This is useful when end users want to use uint64 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD2x18 is uint64;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD2x18 global;

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

import "./Casting.sol" as Casting;

/// @notice The unsigned 21.18-decimal fixed-point number representation, which can have up to 21 digits and up to 18
/// decimals. The values of this are bound by the minimum and the maximum values permitted by the underlying Solidity
/// type uint128. This is useful when end users want to use uint128 to save gas, e.g. with tight variable packing in contract
/// storage.
type UD21x18 is uint128;

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

using {
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint128,
    Casting.intoUint256,
    Casting.intoUint40,
    Casting.unwrap
} for UD21x18 global;

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

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";

/// @notice Casts an SD1x18 number into SD59x18.
/// @dev There is no overflow check because SD1x18 ⊆ SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}

/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD1x18 x) pure returns (UD60x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD1x18 x) pure returns (uint128 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint128_Underflow(x);
    }
    result = uint128(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD1x18 x) pure returns (uint256 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint256_Underflow(x);
    }
    result = uint256(uint64(xInt));
}

/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD1x18 x) pure returns (uint40 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
    }
    if (xInt > int64(uint64(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
    }
    result = uint40(uint64(xInt));
}

/// @notice Alias for {wrap}.
function sd1x18(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

/// @notice Unwraps an SD1x18 number into int64.
function unwrap(SD1x18 x) pure returns (int64 result) {
    result = SD1x18.unwrap(x);
}

/// @notice Wraps an int64 number into SD1x18.
function wrap(int64 x) pure returns (SD1x18 result) {
    result = SD1x18.wrap(x);
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD21x18 } from "./ValueType.sol";

/// @notice Casts an SD21x18 number into SD59x18.
/// @dev There is no overflow check because SD21x18 ⊆ SD59x18.
function intoSD59x18(SD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD21x18.unwrap(x)));
}

/// @notice Casts an SD21x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD21x18 x) pure returns (UD60x18 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
function intoUint128(SD21x18 x) pure returns (uint128 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint128_Underflow(x);
    }
    result = uint128(xInt);
}

/// @notice Casts an SD21x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD21x18 x) pure returns (uint256 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint256_Underflow(x);
    }
    result = uint256(uint128(xInt));
}

/// @notice Casts an SD21x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD21x18 x) pure returns (uint40 result) {
    int128 xInt = SD21x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Underflow(x);
    }
    if (xInt > int128(uint128(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD21x18_ToUint40_Overflow(x);
    }
    result = uint40(uint128(xInt));
}

/// @notice Alias for {wrap}.
function sd21x18(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

/// @notice Unwraps an SD21x18 number into int128.
function unwrap(SD21x18 x) pure returns (int128 result) {
    result = SD21x18.unwrap(x);
}

/// @notice Wraps an int128 number into SD21x18.
function wrap(int128 x) pure returns (SD21x18 result) {
    result = SD21x18.wrap(x);
}

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

import "./Errors.sol" as CastingErrors;
import { MAX_UINT128, MAX_UINT40 } from "../Common.sol";
import { uMAX_SD1x18, uMIN_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { uMAX_SD21x18, uMIN_SD21x18 } from "../sd21x18/Constants.sol";
import { SD21x18 } from "../sd21x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { uMAX_UD21x18 } from "../ud21x18/Constants.sol";
import { UD21x18 } from "../ud21x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Casts an SD59x18 number into int256.
/// @dev This is basically a functional alias for {unwrap}.
function intoInt256(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD1x18
/// - x ≤ uMAX_SD1x18
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
    }
    if (xInt > uMAX_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xInt));
}

/// @notice Casts an SD59x18 number into SD21x18.
/// @dev Requirements:
/// - x ≥ uMIN_SD21x18
/// - x ≤ uMAX_SD21x18
function intoSD21x18(SD59x18 x) pure returns (SD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Underflow(x);
    }
    if (xInt > uMAX_SD21x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD21x18_Overflow(x);
    }
    result = SD21x18.wrap(int128(xInt));
}

/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD2x18
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD2x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD21x18.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UD21x18
function intoUD21x18(SD59x18 x) pure returns (UD21x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD21x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD21x18_Overflow(x);
    }
    result = UD21x18.wrap(uint128(uint256(xInt)));
}

/// @notice Casts an SD59x18 number into UD60x18.
/// @dev Requirements:
/// - x ≥ 0
function intoUD60x18(SD59x18 x) pure returns (UD60x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD60x18_Underflow(x);
    }
    result = UD60x18.wrap(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint256.
/// @dev Requirements:
/// - x ≥ 0
function intoUint256(SD59x18 x) pure returns (uint256 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint256_Underflow(x);
    }
    result = uint256(xInt);
}

/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ uMAX_UINT128
function intoUint128(SD59x18 x) pure returns (uint128 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT128))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
    }
    result = uint128(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x ≥ 0
/// - x ≤ MAX_UINT40
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

/// @notice Alias for {wrap}.
function sd(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Alias for {wrap}.
function sd59x18(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

/// @notice Unwraps an SD59x18 number into int256.
function unwrap(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x);
}

/// @notice Wraps an int256 number into SD59x18.
function wrap(int256 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(x);
}

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

import { wrap } from "./Casting.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Implements the checked addition operation (+) in the SD59x18 type.
function add(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() + y.unwrap());
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and(SD59x18 x, int256 bits) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & bits);
}

/// @notice Implements the AND (&) bitwise operation in the SD59x18 type.
function and2(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    return wrap(x.unwrap() & y.unwrap());
}

/// @notice Implements the equal (=) operation in the SD59x18 type.
function eq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() == y.unwrap();
}

/// @notice Implements the greater than operation (>) in the SD59x18 type.
function gt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() > y.unwrap();
}

/// @notice Implements the greater than or equal to operation (>=) in the SD59x18 type.
function gte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() >= y.unwrap();
}

/// @notice Implements a zero comparison check function in the SD59x18 type.
function isZero(SD59x18 x) pure returns (bool result) {
    result = x.unwrap() == 0;
}

/// @notice Implements the left shift operation (<<) in the SD59x18 type.
function lshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() << bits);
}

/// @notice Implements the lower than operation (<) in the SD59x18 type.
function lt(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() < y.unwrap();
}

/// @notice Implements the lower than or equal to operation (<=) in the SD59x18 type.
function lte(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() <= y.unwrap();
}

/// @notice Implements the unchecked modulo operation (%) in the SD59x18 type.
function mod(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % y.unwrap());
}

/// @notice Implements the not equal operation (!=) in the SD59x18 type.
function neq(SD59x18 x, SD59x18 y) pure returns (bool result) {
    result = x.unwrap() != y.unwrap();
}

/// @notice Implements the NOT (~) bitwise operation in the SD59x18 type.
function not(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(~x.unwrap());
}

/// @notice Implements the OR (|) bitwise operation in the SD59x18 type.
function or(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() | y.unwrap());
}

/// @notice Implements the right shift operation (>>) in the SD59x18 type.
function rshift(SD59x18 x, uint256 bits) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() >> bits);
}

/// @notice Implements the checked subtraction operation (-) in the SD59x18 type.
function sub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() - y.unwrap());
}

/// @notice Implements the checked unary minus operation (-) in the SD59x18 type.
function unary(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(-x.unwrap());
}

/// @notice Implements the unchecked addition operation (+) in the SD59x18 type.
function uncheckedAdd(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() + y.unwrap());
    }
}

/// @notice Implements the unchecked subtraction operation (-) in the SD59x18 type.
function uncheckedSub(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(x.unwrap() - y.unwrap());
    }
}

/// @notice Implements the unchecked unary minus operation (-) in the SD59x18 type.
function uncheckedUnary(SD59x18 x) pure returns (SD59x18 result) {
    unchecked {
        result = wrap(-x.unwrap());
    }
}

/// @notice Implements the XOR (^) bitwise operation in the SD59x18 type.
function xor(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() ^ y.unwrap());
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
    uEXP_MAX_INPUT,
    uEXP2_MAX_INPUT,
    uEXP_MIN_THRESHOLD,
    uEXP2_MIN_THRESHOLD,
    uHALF_UNIT,
    uLOG2_10,
    uLOG2_E,
    uMAX_SD59x18,
    uMAX_WHOLE_SD59x18,
    uMIN_SD59x18,
    uMIN_WHOLE_SD59x18,
    UNIT,
    uUNIT,
    uUNIT_SQUARED,
    ZERO
} from "./Constants.sol";
import { wrap } from "./Helpers.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Calculates the absolute value of x.
///
/// @dev Requirements:
/// - x > MIN_SD59x18.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @return result The absolute value of x as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function abs(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Abs_MinSD59x18();
    }
    result = xInt < 0 ? wrap(-xInt) : x;
}

/// @notice Calculates the arithmetic average of x and y.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The arithmetic average as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function avg(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

    unchecked {
        // This operation is equivalent to `x / 2 +  y / 2`, and it can never overflow.
        int256 sum = (xInt >> 1) + (yInt >> 1);

        if (sum < 0) {
            // If at least one of x and y is odd, add 1 to the result, because shifting negative numbers to the right
            // rounds toward negative infinity. The right part is equivalent to `sum + (x % 2 == 1 || y % 2 == 1)`.
            assembly ("memory-safe") {
                result := add(sum, and(or(xInt, yInt), 1))
            }
        } else {
            // Add 1 if both x and y are odd to account for the double 0.5 remainder truncated after shifting.
            result = wrap(sum + (xInt & yInt & 1));
        }
    }
}

/// @notice Yields the smallest whole number greater than or equal to x.
///
/// @dev Optimized for fractional value inputs, because every whole value has (1e18 - 1) fractional counterparts.
/// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≤ MAX_WHOLE_SD59x18
///
/// @param x The SD59x18 number to ceil.
/// @return result The smallest whole number greater than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ceil(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt > uMAX_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Ceil_Overflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt > 0) {
                resultInt += uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Divides two SD59x18 numbers, returning a new SD59x18 number.
///
/// @dev This is an extension of {Common.mulDiv} for signed numbers, which works by computing the signs and the absolute
/// values separately.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv}.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The denominator must not be zero.
/// - The result must fit in SD59x18.
///
/// @param x The numerator as an SD59x18 number.
/// @param y The denominator as an SD59x18 number.
/// @return result The quotient as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function div(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Div_InputTooSmall();
    }

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

    // Compute the absolute value (x*UNIT÷y). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv(xAbs, uint256(uUNIT), yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Div_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}.
///
/// Requirements:
/// - Refer to the requirements in {exp2}.
/// - x < 133_084258667509499441.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();

    // Any input less than the threshold returns zero.
    // This check also prevents an overflow for very small numbers.
    if (xInt < uEXP_MIN_THRESHOLD) {
        return ZERO;
    }

    // This check prevents values greater than 192e18 from being passed to {exp2}.
    if (xInt > uEXP_MAX_INPUT) {
        revert Errors.PRBMath_SD59x18_Exp_InputTooBig(x);
    }

    unchecked {
        // Inline the fixed-point multiplication to save gas.
        int256 doubleUnitProduct = xInt * uLOG2_E;
        result = exp2(wrap(doubleUnitProduct / uUNIT));
    }
}

/// @notice Calculates the binary exponent of x using the binary fraction method using the following formula:
///
/// $$
/// 2^{-x} = \frac{1}{2^x}
/// $$
///
/// @dev See https://ethereum.stackexchange.com/q/79903/24693.
///
/// Notes:
/// - If x < -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x < 192e18.
/// - The result must fit in SD59x18.
///
/// @param x The exponent as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        // The inverse of any number less than the threshold is truncated to zero.
        if (xInt < uEXP2_MIN_THRESHOLD) {
            return ZERO;
        }

        unchecked {
            // Inline the fixed-point inversion to save gas.
            result = wrap(uUNIT_SQUARED / exp2(wrap(-xInt)).unwrap());
        }
    } else {
        // Numbers greater than or equal to 192e18 don't fit in the 192.64-bit format.
        if (xInt > uEXP2_MAX_INPUT) {
            revert Errors.PRBMath_SD59x18_Exp2_InputTooBig(x);
        }

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

            // It is safe to cast the result to int256 due to the checks above.
            result = wrap(int256(Common.exp2(x_192x64)));
        }
    }
}

/// @notice Yields the greatest whole number less than or equal to x.
///
/// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional
/// counterparts. See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
///
/// Requirements:
/// - x ≥ MIN_WHOLE_SD59x18
///
/// @param x The SD59x18 number to floor.
/// @return result The greatest whole number less than or equal to x, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function floor(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < uMIN_WHOLE_SD59x18) {
        revert Errors.PRBMath_SD59x18_Floor_Underflow(x);
    }

    int256 remainder = xInt % uUNIT;
    if (remainder == 0) {
        result = x;
    } else {
        unchecked {
            // Solidity uses C fmod style, which returns a modulus with the same sign as x.
            int256 resultInt = xInt - remainder;
            if (xInt < 0) {
                resultInt -= uUNIT;
            }
            result = wrap(resultInt);
        }
    }
}

/// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right.
/// of the radix point for negative numbers.
/// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
/// @param x The SD59x18 number to get the fractional part of.
/// @return result The fractional part of x as an SD59x18 number.
function frac(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(x.unwrap() % uUNIT);
}

/// @notice Calculates the geometric mean of x and y, i.e. $\sqrt{x * y}$.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x * y must fit in SD59x18.
/// - x * y must not be negative, since complex numbers are not supported.
///
/// @param x The first operand as an SD59x18 number.
/// @param y The second operand as an SD59x18 number.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function gm(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == 0 || yInt == 0) {
        return ZERO;
    }

    unchecked {
        // Equivalent to `xy / x != y`. Checking for overflow this way is faster than letting Solidity do it.
        int256 xyInt = xInt * yInt;
        if (xyInt / xInt != yInt) {
            revert Errors.PRBMath_SD59x18_Gm_Overflow(x, y);
        }

        // The product must not be negative, since complex numbers are not supported.
        if (xyInt < 0) {
            revert Errors.PRBMath_SD59x18_Gm_NegativeProduct(x, y);
        }

        // We don't need to multiply the result by `UNIT` here because the x*y product picked up a factor of `UNIT`
        // during multiplication. See the comments in {Common.sqrt}.
        uint256 resultUint = Common.sqrt(uint256(xyInt));
        result = wrap(int256(resultUint));
    }
}

/// @notice Calculates the inverse of x.
///
/// @dev Notes:
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x must not be zero.
///
/// @param x The SD59x18 number for which to calculate the inverse.
/// @return result The inverse as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function inv(SD59x18 x) pure returns (SD59x18 result) {
    result = wrap(uUNIT_SQUARED / x.unwrap());
}

/// @notice Calculates the natural logarithm of x using the following formula:
///
/// $$
/// ln{x} = log_2{x} / log_2{e}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
/// - The precision isn't sufficiently fine-grained to return exactly `UNIT` when the input is `E`.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the natural logarithm.
/// @return result The natural logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function ln(SD59x18 x) pure returns (SD59x18 result) {
    // Inline the fixed-point multiplication to save gas. This is overflow-safe because the maximum value that
    // {log2} can return is ~195_205294292027477728.
    result = wrap(log2(x).unwrap() * uUNIT / uLOG2_E);
}

/// @notice Calculates the common logarithm of x using the following formula:
///
/// $$
/// log_{10}{x} = log_2{x} / log_2{10}
/// $$
///
/// However, if x is an exact power of ten, a hard coded value is returned.
///
/// @dev Notes:
/// - Refer to the notes in {log2}.
///
/// Requirements:
/// - Refer to the requirements in {log2}.
///
/// @param x The SD59x18 number for which to calculate the common logarithm.
/// @return result The common logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log10(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    // Note that the `mul` in this block is the standard multiplication operation, not {SD59x18.mul}.
    // prettier-ignore
    assembly ("memory-safe") {
        switch x
        case 1 { result := mul(uUNIT, sub(0, 18)) }
        case 10 { result := mul(uUNIT, sub(1, 18)) }
        case 100 { result := mul(uUNIT, sub(2, 18)) }
        case 1000 { result := mul(uUNIT, sub(3, 18)) }
        case 10000 { result := mul(uUNIT, sub(4, 18)) }
        case 100000 { result := mul(uUNIT, sub(5, 18)) }
        case 1000000 { result := mul(uUNIT, sub(6, 18)) }
        case 10000000 { result := mul(uUNIT, sub(7, 18)) }
        case 100000000 { result := mul(uUNIT, sub(8, 18)) }
        case 1000000000 { result := mul(uUNIT, sub(9, 18)) }
        case 10000000000 { result := mul(uUNIT, sub(10, 18)) }
        case 100000000000 { result := mul(uUNIT, sub(11, 18)) }
        case 1000000000000 { result := mul(uUNIT, sub(12, 18)) }
        case 10000000000000 { result := mul(uUNIT, sub(13, 18)) }
        case 100000000000000 { result := mul(uUNIT, sub(14, 18)) }
        case 1000000000000000 { result := mul(uUNIT, sub(15, 18)) }
        case 10000000000000000 { result := mul(uUNIT, sub(16, 18)) }
        case 100000000000000000 { result := mul(uUNIT, sub(17, 18)) }
        case 1000000000000000000 { result := 0 }
        case 10000000000000000000 { result := uUNIT }
        case 100000000000000000000 { result := mul(uUNIT, 2) }
        case 1000000000000000000000 { result := mul(uUNIT, 3) }
        case 10000000000000000000000 { result := mul(uUNIT, 4) }
        case 100000000000000000000000 { result := mul(uUNIT, 5) }
        case 1000000000000000000000000 { result := mul(uUNIT, 6) }
        case 10000000000000000000000000 { result := mul(uUNIT, 7) }
        case 100000000000000000000000000 { result := mul(uUNIT, 8) }
        case 1000000000000000000000000000 { result := mul(uUNIT, 9) }
        case 10000000000000000000000000000 { result := mul(uUNIT, 10) }
        case 100000000000000000000000000000 { result := mul(uUNIT, 11) }
        case 1000000000000000000000000000000 { result := mul(uUNIT, 12) }
        case 10000000000000000000000000000000 { result := mul(uUNIT, 13) }
        case 100000000000000000000000000000000 { result := mul(uUNIT, 14) }
        case 1000000000000000000000000000000000 { result := mul(uUNIT, 15) }
        case 10000000000000000000000000000000000 { result := mul(uUNIT, 16) }
        case 100000000000000000000000000000000000 { result := mul(uUNIT, 17) }
        case 1000000000000000000000000000000000000 { result := mul(uUNIT, 18) }
        case 10000000000000000000000000000000000000 { result := mul(uUNIT, 19) }
        case 100000000000000000000000000000000000000 { result := mul(uUNIT, 20) }
        case 1000000000000000000000000000000000000000 { result := mul(uUNIT, 21) }
        case 10000000000000000000000000000000000000000 { result := mul(uUNIT, 22) }
        case 100000000000000000000000000000000000000000 { result := mul(uUNIT, 23) }
        case 1000000000000000000000000000000000000000000 { result := mul(uUNIT, 24) }
        case 10000000000000000000000000000000000000000000 { result := mul(uUNIT, 25) }
        case 100000000000000000000000000000000000000000000 { result := mul(uUNIT, 26) }
        case 1000000000000000000000000000000000000000000000 { result := mul(uUNIT, 27) }
        case 10000000000000000000000000000000000000000000000 { result := mul(uUNIT, 28) }
        case 100000000000000000000000000000000000000000000000 { result := mul(uUNIT, 29) }
        case 1000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 30) }
        case 10000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 31) }
        case 100000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 32) }
        case 1000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 33) }
        case 10000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 34) }
        case 100000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 35) }
        case 1000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 36) }
        case 10000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 37) }
        case 100000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 38) }
        case 1000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 39) }
        case 10000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 40) }
        case 100000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 41) }
        case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 42) }
        case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 43) }
        case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 44) }
        case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 45) }
        case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 46) }
        case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 47) }
        case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 48) }
        case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 49) }
        case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 50) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 51) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 52) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 53) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 54) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 55) }
        case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 56) }
        case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 57) }
        case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(uUNIT, 58) }
        default { result := uMAX_SD59x18 }
    }

    if (result.unwrap() == uMAX_SD59x18) {
        unchecked {
            // Inline the fixed-point division to save gas.
            result = wrap(log2(x).unwrap() * uUNIT / uLOG2_10);
        }
    }
}

/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm:
///
/// $$
/// log_2{x} = n + log_2{y}, \text{ where } y = x*2^{-n}, \ y \in [1, 2)
/// $$
///
/// For $0 \leq x \lt 1$, the input is inverted:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation.
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x > 0
///
/// @param x The SD59x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt <= 0) {
        revert Errors.PRBMath_SD59x18_Log_InputTooSmall(x);
    }

    unchecked {
        int256 sign;
        if (xInt >= uUNIT) {
            sign = 1;
        } else {
            sign = -1;
            // Inline the fixed-point inversion to save gas.
            xInt = uUNIT_SQUARED / xInt;
        }

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

        // This is the integer part of the logarithm as an SD59x18 number. The operation can't overflow
        // because n is at most 255, `UNIT` is 1e18, and the sign is either 1 or -1.
        int256 resultInt = int256(n) * uUNIT;

        // Calculate $y = x * 2^{-n}$.
        int256 y = xInt >> n;

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

        // Calculate the fractional part via the iterative approximation.
        // The `delta >>= 1` part is equivalent to `delta /= 2`, but shifting bits is more gas efficient.
        int256 DOUBLE_UNIT = 2e18;
        for (int256 delta = uHALF_UNIT; delta > 0; delta >>= 1) {
            y = (y * y) / uUNIT;

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

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

/// @notice Multiplies two SD59x18 numbers together, returning a new SD59x18 number.
///
/// @dev Notes:
/// - Refer to the notes in {Common.mulDiv18}.
///
/// Requirements:
/// - Refer to the requirements in {Common.mulDiv18}.
/// - None of the inputs can be `MIN_SD59x18`.
/// - The result must fit in SD59x18.
///
/// @param x The multiplicand as an SD59x18 number.
/// @param y The multiplier as an SD59x18 number.
/// @return result The product as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function mul(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();
    if (xInt == uMIN_SD59x18 || yInt == uMIN_SD59x18) {
        revert Errors.PRBMath_SD59x18_Mul_InputTooSmall();
    }

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

    // Compute the absolute value (x*y÷UNIT). The resulting value must fit in SD59x18.
    uint256 resultAbs = Common.mulDiv18(xAbs, yAbs);
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Mul_Overflow(x, y);
    }

    // Check if x and y have the same sign using two's complement representation. The left-most bit represents the sign (1 for
    // negative, 0 for positive or zero).
    bool sameSign = (xInt ^ yInt) > -1;

    // If the inputs have the same sign, the result should be positive. Otherwise, it should be negative.
    unchecked {
        result = wrap(sameSign ? int256(resultAbs) : -int256(resultAbs));
    }
}

/// @notice Raises x to the power of y using the following formula:
///
/// $$
/// x^y = 2^{log_2{x} * y}
/// $$
///
/// @dev Notes:
/// - Refer to the notes in {exp2}, {log2}, and {mul}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {exp2}, {log2}, and {mul}.
///
/// @param x The base as an SD59x18 number.
/// @param y Exponent to raise x to, as an SD59x18 number
/// @return result x raised to power y, as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function pow(SD59x18 x, SD59x18 y) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    int256 yInt = y.unwrap();

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

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

    // Calculate the result using the formula.
    result = exp2(mul(log2(x), y));
}

/// @notice Raises x (an SD59x18 number) to the power y (an unsigned basic integer) using the well-known
/// algorithm "exponentiation by squaring".
///
/// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring.
///
/// Notes:
/// - Refer to the notes in {Common.mulDiv18}.
/// - Returns `UNIT` for 0^0.
///
/// Requirements:
/// - Refer to the requirements in {abs} and {Common.mulDiv18}.
/// - The result must fit in SD59x18.
///
/// @param x The base as an SD59x18 number.
/// @param y The exponent as a uint256.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function powu(SD59x18 x, uint256 y) pure returns (SD59x18 result) {
    uint256 xAbs = uint256(abs(x).unwrap());

    // Calculate the first iteration of the loop in advance.
    uint256 resultAbs = y & 1 > 0 ? xAbs : uint256(uUNIT);

    // Equivalent to `for(y /= 2; y > 0; y /= 2)`.
    uint256 yAux = y;
    for (yAux >>= 1; yAux > 0; yAux >>= 1) {
        xAbs = Common.mulDiv18(xAbs, xAbs);

        // Equivalent to `y % 2 == 1`.
        if (yAux & 1 > 0) {
            resultAbs = Common.mulDiv18(resultAbs, xAbs);
        }
    }

    // The result must fit in SD59x18.
    if (resultAbs > uint256(uMAX_SD59x18)) {
        revert Errors.PRBMath_SD59x18_Powu_Overflow(x, y);
    }

    unchecked {
        // Is the base negative and the exponent odd? If yes, the result should be negative.
        int256 resultInt = int256(resultAbs);
        bool isNegative = x.unwrap() < 0 && y & 1 == 1;
        if (isNegative) {
            resultInt = -resultInt;
        }
        result = wrap(resultInt);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - Only the positive root is returned.
/// - The result is rounded toward zero.
///
/// Requirements:
/// - x ≥ 0, since complex numbers are not supported.
/// - x ≤ MAX_SD59x18 / UNIT
///
/// @param x The SD59x18 number for which to calculate the square root.
/// @return result The result as an SD59x18 number.
/// @custom:smtchecker abstract-function-nondet
function sqrt(SD59x18 x) pure returns (SD59x18 result) {
    int256 xInt = x.unwrap();
    if (xInt < 0) {
        revert Errors.PRBMath_SD59x18_Sqrt_NegativeInput(x);
    }
    if (xInt > uMAX_SD59x18 / uUNIT) {
        revert Errors.PRBMath_SD59x18_Sqrt_Overflow(x);
    }

    unchecked {
        // Multiply x by `UNIT` to account for the factor of `UNIT` picked up when multiplying two SD59x18 numbers.
        // In this case, the two numbers are both the square root.
        uint256 resultUint = Common.sqrt(uint256(xInt * uUNIT));
        result = wrap(int256(resultUint));
    }
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because UD2x18 ⊆ SD59x18.
function intoSD59x18(UD2x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD2x18.unwrap(x))));
}

/// @notice Casts a UD2x18 number into UD60x18.
/// @dev There is no overflow check because UD2x18 ⊆ UD60x18.
function intoUD60x18(UD2x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint128.
/// @dev There is no overflow check because UD2x18 ⊆ uint128.
function intoUint128(UD2x18 x) pure returns (uint128 result) {
    result = uint128(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint256.
/// @dev There is no overflow check because UD2x18 ⊆ uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
    result = uint256(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD2x18 x) pure returns (uint40 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD2x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud2x18(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

/// @notice Unwrap a UD2x18 number into uint64.
function unwrap(UD2x18 x) pure returns (uint64 result) {
    result = UD2x18.unwrap(x);
}

/// @notice Wraps a uint64 number into UD2x18.
function wrap(uint64 x) pure returns (UD2x18 result) {
    result = UD2x18.wrap(x);
}

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD21x18 } from "./ValueType.sol";

/// @notice Casts a UD21x18 number into SD59x18.
/// @dev There is no overflow check because UD21x18 ⊆ SD59x18.
function intoSD59x18(UD21x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(uint256(UD21x18.unwrap(x))));
}

/// @notice Casts a UD21x18 number into UD60x18.
/// @dev There is no overflow check because UD21x18 ⊆ UD60x18.
function intoUD60x18(UD21x18 x) pure returns (UD60x18 result) {
    result = UD60x18.wrap(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint128.
/// @dev This is basically an alias for {unwrap}.
function intoUint128(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Casts a UD21x18 number into uint256.
/// @dev There is no overflow check because UD21x18 ⊆ uint256.
function intoUint256(UD21x18 x) pure returns (uint256 result) {
    result = uint256(UD21x18.unwrap(x));
}

/// @notice Casts a UD21x18 number into uint40.
/// @dev Requirements:
/// - x ≤ MAX_UINT40
function intoUint40(UD21x18 x) pure returns (uint40 result) {
    uint128 xUint = UD21x18.unwrap(x);
    if (xUint > uint128(Common.MAX_UINT40)) {
        revert Errors.PRBMath_UD21x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

/// @notice Alias for {wrap}.
function ud21x18(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

/// @notice Unwrap a UD21x18 number into uint128.
function unwrap(UD21x18 x) pure returns (uint128 result) {
    result = UD21x18.unwrap(x);
}

/// @notice Wraps a uint128 number into UD21x18.
function wrap(uint128 x) pure returns (UD21x18 result) {
    result = UD21x18.wrap(x);
}

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

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

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in UD60x18.
error PRBMath_SD1x18_ToUD60x18_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint128.
error PRBMath_SD1x18_ToUint128_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint256.
error PRBMath_SD1x18_ToUint256_Underflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Overflow(SD1x18 x);

/// @notice Thrown when trying to cast an SD1x18 number that doesn't fit in uint40.
error PRBMath_SD1x18_ToUint40_Underflow(SD1x18 x);

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

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

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint128.
error PRBMath_SD21x18_ToUint128_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in UD60x18.
error PRBMath_SD21x18_ToUD60x18_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint256.
error PRBMath_SD21x18_ToUint256_Underflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Overflow(SD21x18 x);

/// @notice Thrown when trying to cast an SD21x18 number that doesn't fit in uint40.
error PRBMath_SD21x18_ToUint40_Underflow(SD21x18 x);

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

import { SD59x18 } from "./ValueType.sol";

/// @notice Thrown when taking the absolute value of `MIN_SD59x18`.
error PRBMath_SD59x18_Abs_MinSD59x18();

/// @notice Thrown when ceiling a number overflows SD59x18.
error PRBMath_SD59x18_Ceil_Overflow(SD59x18 x);

/// @notice Thrown when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMath_SD59x18_Convert_Overflow(int256 x);

/// @notice Thrown when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMath_SD59x18_Convert_Underflow(int256 x);

/// @notice Thrown when dividing two numbers and one of them is `MIN_SD59x18`.
error PRBMath_SD59x18_Div_InputTooSmall();

/// @notice Thrown when dividing two numbers and one of the intermediary unsigned results overflows SD59x18.
error PRBMath_SD59x18_Div_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the natural exponent of a base greater than 133_084258667509499441.
error PRBMath_SD59x18_Exp_InputTooBig(SD59x18 x);

/// @notice Thrown when taking the binary exponent of a base greater than 192e18.
error PRBMath_SD59x18_Exp2_InputTooBig(SD59x18 x);

/// @notice Thrown when flooring a number underflows SD59x18.
error PRBMath_SD59x18_Floor_Underflow(SD59x18 x);

/// @notice Thrown when taking the geometric mean of two numbers and their product is negative.
error PRBMath_SD59x18_Gm_NegativeProduct(SD59x18 x, SD59x18 y);

/// @notice Thrown when taking the geometric mean of two numbers and multiplying them overflows SD59x18.
error PRBMath_SD59x18_Gm_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in SD21x18.
error PRBMath_SD59x18_IntoSD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD21x18.
error PRBMath_SD59x18_IntoUD21x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in UD60x18.
error PRBMath_SD59x18_IntoUD60x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast an SD59x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);

/// @notice Thrown when taking the logarithm of a number less than or equal to zero.
error PRBMath_SD59x18_Log_InputTooSmall(SD59x18 x);

/// @notice Thrown when multiplying two numbers and one of the inputs is `MIN_SD59x18`.
error PRBMath_SD59x18_Mul_InputTooSmall();

/// @notice Thrown when multiplying two numbers and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Mul_Overflow(SD59x18 x, SD59x18 y);

/// @notice Thrown when raising a number to a power and the intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);

/// @notice Thrown when taking the square root of a negative number.
error PRBMath_SD59x18_Sqrt_NegativeInput(SD59x18 x);

/// @notice Thrown when the calculating the square root overflows SD59x18.
error PRBMath_SD59x18_Sqrt_Overflow(SD59x18 x);

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

import { UD2x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in uint40.
error PRBMath_UD2x18_IntoUint40_Overflow(UD2x18 x);

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

import { UD21x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD21x18 number that doesn't fit in uint40.
error PRBMath_UD21x18_IntoUint40_Overflow(UD21x18 x);

{
  "remappings": [
    "@openzeppelin-contracts-5/=dependencies/@openzeppelin-contracts-5.5.0/",
    "@sablier-lockup-2.0.1/=dependencies/@sablier-lockup-2.0.1/",
    "@uniswap-v4-core-4.0.0/=dependencies/@uniswap-v4-core-4.0.0/",
    "@uniswap-v4-periphery-1.0.3/=dependencies/@uniswap-v4-periphery-1.0.3/",
    "forge-std-1/=dependencies/forge-std-1.14.0/",
    "prb-math-4.1.0/=dependencies/prb-math-4.1.0/",
    "solmate-1.0.0/=dependencies/solmate-1.0.0/",
    "forge-std/=dependencies/forge-std-1.14.0/src/",
    "@openzeppelin/contracts/=dependencies/@openzeppelin-contracts-5.5.0/",
    "@uniswap/v4-core/=dependencies/@uniswap-v4-core-4.0.0/",
    "@uniswap/v4-periphery/=dependencies/@uniswap-v4-periphery-1.0.3/",
    "@sablier/lockup/=dependencies/@sablier-lockup-2.0.1/src/",
    "@prb/math/=dependencies/prb-math-4.1.0/",
    "solmate/=dependencies/solmate-1.0.0/",
    "@ensdomains/=dependencies/@uniswap-v4-core-4.0.0/node_modules/@ensdomains/",
    "@openzeppelin-contracts-5.5.0/=dependencies/@openzeppelin-contracts-5.5.0/",
    "ds-test/=dependencies/@uniswap-v4-core-4.0.0/lib/forge-std/lib/ds-test/src/",
    "forge-std-1.14.0/=dependencies/forge-std-1.14.0/src/",
    "hardhat/=dependencies/@uniswap-v4-core-4.0.0/node_modules/hardhat/",
    "openzeppelin-contracts/=dependencies/@uniswap-v4-periphery-1.0.3/lib/v4-core/lib/openzeppelin-contracts/",
    "solady/=dependencies/@sablier-lockup-2.0.1/node_modules/solady/",
    "solarray/=dependencies/@sablier-lockup-2.0.1/node_modules/solarray/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "ipfs",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "cancun",
  "viaIR": true
}

• No Contract Security Audit Submitted- Submit Audit Here

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0000000000000000000000007b2f34f323148262e145f60c3c715822a5430f0800000000000000000000000035ec3ebaaa5e471ec2b05ebc28ab3c8734c4a4b7000000000000000000000000da2cab7348bb63f4e8cf82a877ae280f0e48ed60

-----Decoded View---------------
Arg [0] : dutchToken_ (address): 0x7B2F34F323148262E145f60C3C715822a5430F08
Arg [1] : dutchVaultAddress_ (address): 0x35EC3EBaaa5E471Ec2B05EBC28ab3C8734c4a4B7
Arg [2] : opsWallet_ (address): 0xDA2CAb7348Bb63f4e8cf82a877AE280F0e48ed60

-----Encoded View---------------
3 Constructor Arguments found :
Arg [0] : 0000000000000000000000007b2f34f323148262e145f60c3c715822a5430f08
Arg [1] : 00000000000000000000000035ec3ebaaa5e471ec2b05ebc28ab3c8734c4a4b7
Arg [2] : 000000000000000000000000da2cab7348bb63f4e8cf82a877ae280f0e48ed60