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// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.24;

// Interfaces
import {IERC20, SafeERC20} from "@openzeppelin/[email protected]/token/ERC20/utils/SafeERC20.sol";
import {CurveTricryptoOptimizedWETH} from "@napier/v1-pool/src/interfaces/external/CurveTricryptoOptimizedWETH.sol";
import {IWETH9} from "@napier/v1-tranche/src/interfaces/IWETH9.sol";
import {INapierPool} from "@napier/v1-pool/src/interfaces/INapierPool.sol";
import {ITranche} from "@napier/v1-tranche/src/interfaces/ITranche.sol";
import {Twocrypto} from "./interfaces/external/Twocrypto.sol";
import {IVault} from "./interfaces/external/balancer/IVault.sol";
import {IFlashLoanRecipient} from "./interfaces/external/balancer/IFlashLoanRecipient.sol";
import {MetapoolFactory} from "./MetapoolFactory.sol";

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

// Libraries
import {TransientStorage} from "./TransientStorage.sol";
import {Math} from "@openzeppelin/[email protected]/utils/math/Math.sol";
import {TrancheMathHelper} from "@napier/v1-pool/src/libs/TrancheMathHelper.sol";
import {ApproxParams} from "@napier/v1-pool/src/interfaces/ApproxParams.sol";
import {Errors} from "./Errors.sol";

// Inherits
import {ReentrancyGuard} from "@openzeppelin/[email protected]/security/ReentrancyGuard.sol";

/// @title MetapoolRouter - A contract for swapping between PT, YT, and ETH on the 3LST NapierPool, 3LST-PT tricrypto, and Twocrypto metapools
contract MetapoolRouter is ReentrancyGuard, IFlashLoanRecipient, IMetapoolRouter {
    /// @dev Constants for the Twocrypto metapool indexes
    /// coins(0) is the pegged token (PT) and coins(1) is the base pool token (triLST-PT Tricrypto)
    uint128 constant PEGGED_PT_INDEX = 0;
    uint128 constant BASE_POOL_INDEX = 1;

    /// @dev Transient storage slots
    uint256 constant TSLOT_0 = 0; // Authorization flag for `receiveFlashLoan`
    uint256 constant TSLOT_1 = 1; // Temporary storage for `swapETHForYt` function return value
    uint256 constant TSLOT_CB_DATA_METAPOOL = 2; // `FlashLoanData.metapool` slot for `receiveFlashLoan` callback data
    uint256 constant TSLOT_CB_DATA_PT = 3; // `FlashLoanData.pt` slot for `receiveFlashLoan` callback data
    uint256 constant TSLOT_CB_DATA_SENDER = 4; // `FlashLoanData.sender` slot for `receiveFlashLoan` callback data
    uint256 constant TSLOT_CB_DATA_VALUE = 5; // `FlashLoanData.msgValue` slot for `receiveFlashLoan` callback data
    uint256 constant TSLOT_CB_DATA_MAX_ETH_SPENT = 6; // `FlashLoanData.maxEthSpent` slot for `receiveFlashLoan` callback data
    uint256 constant TSLOT_CB_DATA_RECEIPIENT = 7; // `FlashLoanData.recipient` slot for `receiveFlashLoan` callback data

    /// @notice The WETH9 contract
    IWETH9 public immutable WETH9;

    /// @notice The Factory contract for the Principal Token metapools
    MetapoolFactory public immutable metapoolFactory;

    /// @notice The rETH-PT<>stETH-PT<>sfrxETH-PT Curve TricryptoNG pool (triLST-PT Tricrypto)
    CurveTricryptoOptimizedWETH public immutable tricryptoLST;

    /// @notice The triLST-PT<>WETH NapierPool
    INapierPool public immutable triLSTPool;

    /// @notice The Balancer Vault contract for flash loans
    IVault public immutable vault;

    /// @dev The approval slot of (`token`, `spender`) is given by:
    /// ```
    ///     mstore(0x20, spender)
    ///     mstore(0x0c, _IS_APPROVED_SLOT_SEED)
    ///     mstore(0x00, token)
    ///     let allowanceSlot := keccak256(0x0c, 0x34)
    /// ```
    /// @dev Optimized storage slot for approval flags
    /// `mapping (address token => mapping (address spender => uint256 approved)) _isApproved;`
    uint256 private constant _IS_APPROVED_SLOT_SEED = 0xa8fe4407;

    /// @notice If the transaction is too old, revert.
    /// @param deadline Transaction deadline in unix timestamp
    modifier checkDeadline(uint256 deadline) {
        if (block.timestamp > deadline) revert Errors.MetapoolRouterTransactionTooOld();
        _;
    }

    /// @notice If the metapool is not a TwoCrypto with Principal Token, revert.
    modifier checkMetapool(address metapool) {
        if (!metapoolFactory.isPtMetapool(metapool)) revert Errors.MetapoolRouterInvalidMetapool();
        _;
    }

    receive() external payable {
        if (msg.sender != address(WETH9)) revert Errors.NotWETH();
    }

    constructor(MetapoolFactory _metapoolFactory, INapierPool _triLSTPool, IVault _vault) {
        metapoolFactory = _metapoolFactory;
        triLSTPool = _triLSTPool;
        vault = _vault;
        WETH9 = IWETH9(_metapoolFactory.WETH9());
        tricryptoLST = _triLSTPool.tricrypto();

        (bool s, bytes memory data) = CurveTricryptoOptimizedWETH(tricryptoLST).factory().staticcall(
            abi.encodeWithSignature("get_coins(address)", tricryptoLST)
        );
        require(s);
        address[3] memory coins = abi.decode(data, (address[3]));
        // Approve rETH-PT<>stETH-PT<>sfrxETH-PT Curve TricryptoNG pool (triLST-PT Tricrypto) to spend meta tokens
        IERC20(coins[0]).approve(address(tricryptoLST), type(uint256).max);
        IERC20(coins[1]).approve(address(tricryptoLST), type(uint256).max);
        IERC20(coins[2]).approve(address(tricryptoLST), type(uint256).max);
        // Approve triLST-PT<>WETH NapierPool to spend WETH9
        SafeERC20.forceApprove(IWETH9(WETH9), address(triLSTPool), type(uint256).max);
        // Approve triLST-PT<>WETH NapierPool to spend tricryptoLST
        SafeERC20.forceApprove(tricryptoLST, address(triLSTPool), type(uint256).max);
    }

    /// @notice Swap ETH for PT
    /// @notice A caller must send ETH enough greater than the `maxEthSpent`. Remaining ETH will be sent back to the caller.
    /// @dev This function can't swap ETH for the exact amount of PT because of precision loss. So, `minPtOut` must be specified by the caller.
    /// @param metapool The address of the Twocrypto metapool
    /// @param ptAmount The amount of PT tokens to receive
    /// @param maxEthSpent The maximum amount of ETH to spend in the swap
    /// @param minPtOut The minimum amount of PT tokens to receive
    /// @param recipient The address to receive the swapped PT tokens
    /// @param deadline The timestamp after which the transaction will be reverted
    /// @return ethSpent The amount of ETH spent in the swap
    function swapETHForPt(
        address metapool,
        uint256 ptAmount,
        uint256 maxEthSpent,
        uint256 minPtOut, // TODO: really need this?
        address recipient,
        uint256 deadline
    ) external payable nonReentrant checkDeadline(deadline) checkMetapool(metapool) returns (uint256 ethSpent) {
        // Steps:
        // 1. Quote swap PT -> base pool token on triLST-PT Tricrypto (get_dx)
        // 2. Swap ETH -> base pool token on triLST-PT<>WETH NapierPool
        // 3. Swap base pool token -> PT on twocrypto metapool
        // 4. Send remaining ETH to the recipient

        // Calculate the amount of base pool token required for the specified PT amount
        uint256 basePoolTokenAmount = Twocrypto(metapool).get_dx({i: BASE_POOL_INDEX, j: PEGGED_PT_INDEX, dy: ptAmount});

        // Wrap the received ETH into WETH
        if (maxEthSpent > msg.value) revert Errors.MetapoolRouterInsufficientETHReceived();
        _wrapETH(msg.value);

        // Swap the received WETH for the required amount of base pool token on the NapierPool
        /// @dev Txn may revert if the triLSTPool tries to swap more than the received ETH.
        ethSpent = triLSTPool.swapUnderlyingForExactBaseLpToken({baseLpOut: basePoolTokenAmount, recipient: metapool});

        // Swap the received base pool token for PT on the Curve metapool
        Twocrypto(metapool).exchange_received({
            i: BASE_POOL_INDEX,
            j: PEGGED_PT_INDEX,
            dx: basePoolTokenAmount,
            // `get_dx` has a precision loss, so the actual amount of PT received may be less than `ptAmount`.
            min_dy: minPtOut,
            receiver: recipient
        });

        if (ethSpent > maxEthSpent) revert Errors.MetapoolRouterExceededLimitETHIn();

        // Send the remaining WETH back to the sender
        uint256 remainingWeth = msg.value - ethSpent;
        if (remainingWeth > 0) _unwrapWETH(msg.sender, remainingWeth);

        return ethSpent;
    }

    /// @notice Swap PT for ETH on the Curve metapool through the 3LST-PT<>ETH NapierPool
    /// @param metapool The address of the Twocrypto metapool
    /// @param ptAmount The amount of PT to swap
    /// @param minEthOut The minimum amount of ETH to receive
    /// @param recipient The address to receive the ETH
    /// @param deadline The timestamp after which the transaction will be reverted
    function swapPtForETH(address metapool, uint256 ptAmount, uint256 minEthOut, address recipient, uint256 deadline)
        external
        nonReentrant
        checkDeadline(deadline)
        checkMetapool(metapool)
        returns (uint256 ethOut)
    {
        // Steps:
        // 1. Exchange PT for the base pool token on twoCrypto metapool
        // 2. Swap the received base pool token -> ETH on triLST-PT<>WETH NapierPool
        // 3. Send remaining ETH to the recipient

        // Swap PT for the base pool token on the Curve metapool
        SafeERC20.safeTransferFrom(IERC20(Twocrypto(metapool).coins(PEGGED_PT_INDEX)), msg.sender, metapool, ptAmount);
        uint256 basePoolTokenAmount =
            Twocrypto(metapool).exchange_received(PEGGED_PT_INDEX, BASE_POOL_INDEX, ptAmount, 0, address(this));

        // Swap the received base pool token for ETH on the 3LST-PT<>ETH NapierPool
        ethOut =
            triLSTPool.swapExactBaseLpTokenForUnderlying({baseLptIn: basePoolTokenAmount, recipient: address(this)});

        // Check slippage
        if (minEthOut > ethOut) revert Errors.MetapoolRouterInsufficientETHOut();

        // Send native ETH to the recipient
        _unwrapWETH(recipient, ethOut);

        return ethOut;
    }

    /// @notice Swap Ethereum (ETH) for Yield Tokens (YT)
    /// @dev This function first issues PT and YT using ETH, then swaps the PT for the base pool token on the Curve metapool,
    ///      and finally swaps the received base pool token for ETH on the NapierPool.
    /// @notice Caller must send enough ETH equal to the `maxEthSpent` and the remaining ETH will be sent back to the caller.
    /// @dev `recipient` will receive at least `ytAmount` YTs and at most `ytAmount * (1 + approx.eps / 1e18)` YTs.
    /// @param metapool The address of the Curve metapool contract
    /// @param ytAmount The amount of YT tokens to receive
    /// @param maxEthSpent The maximum amount of ETH to spend in the swap
    /// @param recipient The address to receive the swapped YT tokens
    /// @param deadline The timestamp after which the transaction will be reverted
    /// @return ethSpent The amount of ETH spent in the swap
    function swapETHForYt(
        address metapool,
        uint256 ytAmount,
        uint256 maxEthSpent,
        address recipient,
        uint256 deadline,
        ApproxParams calldata approx
    ) external payable nonReentrant checkDeadline(deadline) checkMetapool(metapool) returns (uint256 ethSpent) {
        // Steps:
        // 1. Estimate the amount of WETH required to issue the PT and YT
        // 2. Issue PT and YT using the WETH
        // 3. Swap PT -> Base pool token on the Twocrypto metapool
        // 4. Swap Base pool token -> ETH on the NapierPool
        // 5. Refund the remaining WETH to the sender

        ITranche pt = ITranche(Twocrypto(metapool).coins(PEGGED_PT_INDEX));

        if (maxEthSpent > msg.value) revert Errors.MetapoolRouterInsufficientETHReceived();

        // Estimate the amount of WETH required to issue the PT and YT
        // Bisection method is used to find the approximate amount of WETH needed, which ensures the at least `ytAmount` YT tokens are issued.
        uint256 wethDeposit =
            TrancheMathHelper.getApproxUnderlyingNeededByYt({pt: pt, ytDesired: ytAmount, approx: approx});

        // Authorize access to `receiveFlashLoan` at the last step (flag=address(this))
        assembly {
            // Note: This slot should be used only for authorization purpose and should be cleared after use
            tstore(TSLOT_0, address())
        }

        IERC20[] memory tokens = new IERC20[](1);
        uint256[] memory amounts = new uint256[](1);
        tokens[0] = WETH9;
        amounts[0] = wethDeposit;
        // Record the flash loan data in the transient storage
        // Note: Based on try-and-error, passing userData directly is more expensive than using transient storage.
        assembly {
            tstore(TSLOT_CB_DATA_METAPOOL, metapool)
            tstore(TSLOT_CB_DATA_PT, shr(96, shl(96, pt)))
            tstore(TSLOT_CB_DATA_SENDER, caller())
            tstore(TSLOT_CB_DATA_VALUE, callvalue())
            tstore(TSLOT_CB_DATA_MAX_ETH_SPENT, maxEthSpent)
            tstore(TSLOT_CB_DATA_RECEIPIENT, recipient)
        }

        _wrapETH(msg.value);
        vault.flashLoan(this, tokens, amounts, ""); // call receiveFlashLoan

        assembly {
            ethSpent := tload(TSLOT_1)
            tstore(TSLOT_1, 0) // clear transitient storage
        }

        return ethSpent;
    }

    /// @notice Receive the flash loan and run operations to swap ETH for YT
    /// @dev Revert if the call is not initiated by the `swapETHForYt` function.
    /// @custom:param userData - Data structure for the flash loan callback data.
    /// @dev Those members are stored in the transient storage slots with prefix `TSLOT_CB_DATA_`.
    /// ```
    /// struct UserData {
    ///     address _metapool;
    ///     address _pt;
    ///     address _sender; // The address of the caller of `swapETHForYt`
    ///     uint256 _msgValue; // The amount of ETH sent with the call to `swapETHForYt`
    ///     uint256 _maxEthSpent;
    ///     address _recipient;
    /// }
    /// ```
    function receiveFlashLoan(
        IERC20[] calldata, /* tokens */
        uint256[] calldata amounts,
        uint256[] calldata feeAmounts,
        bytes calldata /* userData */
    ) external {
        // CHECK
        // Note: Call only through `swapETHForYt` && from the Vault should be allowed.
        // This ensures that the function call is invoked by `swapETHForYt` entry point.
        // Checking `msg.sender == address(vault)` may not be sufficient as the call may be initiated by other contracts and pass arbitrary data.
        assembly {
            let ctx := tload(TSLOT_0)
            tstore(TSLOT_0, 0) // Delete the authorization (flag=address(0))
            if iszero(eq(ctx, address())) {
                mstore(0x00, 0x5c501941) // `MetapoolRouterUnauthorized()`
                revert(0x1c, 0x04)
            }
        }

        address pt = TransientStorage.tloadAddress(TSLOT_CB_DATA_PT);
        address metapool = TransientStorage.tloadAddress(TSLOT_CB_DATA_METAPOOL);

        // Issue PT tokens using the WETH
        if (!_isApproved(address(WETH9), pt)) {
            _setApproval(address(WETH9), pt);
            WETH9.approve(pt, type(uint256).max);
        }
        uint256 wethDeposit = amounts[0];
        uint256 pyIssued = ITranche(pt).issue(address(this), wethDeposit);

        // Swap the PT for the base pool token on the Curve metapool
        ITranche(pt).transfer(metapool, pyIssued);
        uint256 basePoolTokenOut =
            Twocrypto(metapool).exchange_received(PEGGED_PT_INDEX, BASE_POOL_INDEX, pyIssued, 0, address(this));

        // Swap the received base pool token for ETH on the NapierPool
        uint256 wethReceived = triLSTPool.swapExactBaseLpTokenForUnderlying(basePoolTokenOut, address(this));

        // Unreasonable situation: Received more WETH than sold
        if (wethReceived > wethDeposit) revert Errors.MetapoolRouterNonSituationSwapETHForYt();

        // Calculate the amount of ETH spent in the swap
        uint256 repayAmount = wethDeposit + feeAmounts[0];
        uint256 spent = repayAmount - wethReceived; // wethDeposit + feeAmounts[0] - wethReceived

        // Revert if the ETH spent exceeds the specified maximum
        if (spent > TransientStorage.tloadU256(TSLOT_CB_DATA_MAX_ETH_SPENT)) {
            revert Errors.MetapoolRouterExceededLimitETHIn();
        }

        // Temporarily store a return value of `swapETHForYt` function across the call context
        assembly {
            tstore(TSLOT_1, spent)
        }

        // Transfer the YT tokens to the recipient
        IERC20(ITranche(pt).yieldToken()).transfer(TransientStorage.tloadAddress(TSLOT_CB_DATA_RECEIPIENT), pyIssued);

        // Repay the flash loan
        WETH9.transfer(msg.sender, repayAmount);

        // Unwrap and send the remaining WETH back to the sender
        // The next line will not underflow due to the `msg.value >= maxEthSpent` check in `swapETHForYt`
        uint256 refundAmount = TransientStorage.tloadU256(TSLOT_CB_DATA_VALUE) - spent;
        _unwrapWETH(TransientStorage.tloadAddress(TSLOT_CB_DATA_SENDER), refundAmount);
    }

    /// @notice Add liquidity to the Curve metapool using native ETH and receive LP tokens and YT
    /// @dev Revert if timestamp exceeds the maturity date.
    /// @param metapool The address of the Curve metapool contract
    /// @param minLiquidity The minimum amount of LP tokens to receive
    /// @param minYt The minimum amount of YT to receive
    /// @param recipient The address to receive the LP tokens and YT
    /// @param deadline The timestamp after which the transaction will be reverted
    function addLiquidityOneETHKeepYt(
        address metapool,
        uint256 minLiquidity,
        uint256 minYt,
        address recipient,
        uint256 deadline
    ) external payable nonReentrant checkDeadline(deadline) checkMetapool(metapool) returns (uint256 liquidity) {
        // Steps:
        // 1. Issue PT and YT using the received ETH
        // 2. Add liquidity to the Curve metapool
        // 3. Send the received LP token and YT to the recipient

        // Wrap the received ETH into WETH
        _wrapETH(msg.value);

        ITranche pt = ITranche(Twocrypto(metapool).coins(PEGGED_PT_INDEX));
        // Issue PT and YT using the received ETH
        if (!_isApproved(address(WETH9), address(pt))) {
            _setApproval(address(WETH9), address(pt));
            WETH9.approve(address(pt), type(uint256).max);
        }
        uint256 pyAmount = pt.issue({to: address(this), underlyingAmount: msg.value});
        if (pyAmount < minYt) revert Errors.MetapoolRouterInsufficientYtOut();

        // Add liquidity to the Curve metapool
        if (!_isApproved(address(pt), metapool)) {
            _setApproval(address(pt), metapool);
            pt.approve(metapool, type(uint256).max);
        }
        liquidity = Twocrypto(metapool).add_liquidity({
            amounts: [pyAmount, 0],
            min_mint_amount: minLiquidity,
            receiver: recipient
        });

        IERC20(pt.yieldToken()).transfer(recipient, pyAmount);
    }

    /// @notice Remove liquidity from the Curve twocrypto (metapool) and receive native ETH
    /// @notice Before the maturity date of PT, the PT is not redeemable, so the PT is swapped for the Base pool Token
    /// @param metapool The address of the Curve metapool contract
    /// @param liquidity The amount of LP tokens to remove from the Curve twocrypto (metapool)
    /// @param minEthOut The minimum amount of ETH to receive
    /// @param recipient The address to receive the ETH
    /// @param deadline The timestamp after which the transaction will be reverted
    function removeLiquidityOneETH(
        address metapool,
        uint256 liquidity,
        uint256 minEthOut,
        address recipient,
        uint256 deadline
    ) external nonReentrant checkDeadline(deadline) checkMetapool(metapool) returns (uint256 ethOut) {
        // Steps:
        // If PT is matured, redemption of PT is allowed:
        // 1. Remove liquidity from the Curve metapool and withdraw one PT
        // 2. Redeem the PT for ETH

        // If PT is not matured: redemption of PT is not allowed yet:
        // 1. Remove liquidity from the Curve metapool and withdraw one base pool token
        // 2. Swap the received base pool token for ETH on the NapierPool

        ITranche pt = ITranche(Twocrypto(metapool).coins(PEGGED_PT_INDEX));

        SafeERC20.safeTransferFrom(Twocrypto(metapool), msg.sender, address(this), liquidity);

        if (block.timestamp >= pt.maturity()) {
            // If PT is matured, we can directly redeem the PT for ETH
            uint256 ptAmount = Twocrypto(metapool).remove_liquidity_one_coin(liquidity, PEGGED_PT_INDEX, 0);
            ethOut = pt.redeem({principalAmount: ptAmount, to: address(this), from: address(this)});
        } else {
            // Otherwise, redemption of PT is not allowed, so we need to swap the base pool token for ETH
            uint256 basePoolTokenAmount = Twocrypto(metapool).remove_liquidity_one_coin(liquidity, BASE_POOL_INDEX, 0);
            ethOut = triLSTPool.swapExactBaseLpTokenForUnderlying(basePoolTokenAmount, address(this));
        }

        if (minEthOut > ethOut) revert Errors.MetapoolRouterInsufficientETHOut();

        _unwrapWETH(recipient, ethOut);
    }

    //// Helper functions ////

    /// @dev Get the approval status of the spender for the token. Return true if approved, 0 otherwise.
    function _isApproved(address token, address spender) internal view returns (bool approved) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x20, spender)
            mstore(0x0c, _IS_APPROVED_SLOT_SEED)
            mstore(0x00, token)
            approved := sload(keccak256(0x0c, 0x34))
        }
    }

    /// @dev Set the approval status to 1 for the spender for the token.
    function _setApproval(address token, address spender) internal {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute the approval slot and store the amount.
            mstore(0x20, spender)
            mstore(0x0c, _IS_APPROVED_SLOT_SEED)
            mstore(0x00, token)
            sstore(keccak256(0x0c, 0x34), 1)
        }
    }

    function _wrapETH(uint256 value) internal {
        WETH9.deposit{value: value}();
    }

    function _unwrapWETH(address recipient, uint256 value) internal {
        WETH9.withdraw(value);
        _safeTransferETH(recipient, value);
    }

    /// @notice transfer ether safely
    function _safeTransferETH(address to, uint256 value) internal {
        (bool success,) = to.call{value: value}(new bytes(0));
        if (!success) revert Errors.FailedToSendEther();
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.3) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/IERC20Permit.sol";
import "../../../utils/Address.sol";

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

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

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

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

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

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, oldAllowance - value));
        }
    }

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

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

    /**
     * @dev Use a ERC-2612 signature to set the `owner` approval toward `spender` on `token`.
     * Revert on invalid signature.
     */
    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

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

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        require(returndata.length == 0 || abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
    }

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

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

// https://github.com/curvefi/tricrypto-ng/blob/0bc1191b6097c8854e4f09e385f6c2c79a5bb773/contracts/main/CurveTricryptoOptimizedWETH.vy

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";

interface CurveTricryptoOptimizedWETH is IERC20 {
    /// @notice Exchange using wrapped native token by default
    /// @param i Index value for the input coin
    /// @param j Index value for the output coin
    /// @param dx Amount of input coin being swapped in
    /// @param min_dy Minimum amount of output coin to receive
    /// @param use_eth True if the input coin is native token, False otherwise
    /// @param receiver Address to send the output coin to. Default is msg.sender
    /// @return uint256 Amount of tokens at index j received by the `receiver
    function exchange(uint256 i, uint256 j, uint256 dx, uint256 min_dy, bool use_eth, address receiver)
        external
        payable
        returns (uint256);

    /// @notice Exchange with callback method.
    /// @dev This method does not allow swapping in native token, but does allow
    /// swaps that transfer out native token from the pool.
    /// @dev Does not allow flashloans
    /// @dev One use-case is to reduce the number of redundant ERC20 token
    /// transfers in zaps.
    /// @param i Index value for the input coin
    /// @param j Index value for the output coin
    /// @param dx Amount of input coin being swapped in
    /// @param min_dy Minimum amount of output coin to receive
    /// @param use_eth True if output is native token, False otherwise
    /// @param sender Address to transfer input coin from
    /// @param receiver Address to send the output coin to
    /// @param cb Callback signature
    /// @return uint256 Amount of tokens at index j received by the `receiver`
    function exchange_extended(
        uint256 i,
        uint256 j,
        uint256 dx,
        uint256 min_dy,
        bool use_eth,
        address sender,
        address receiver,
        bytes32 cb
    ) external returns (uint256);

    /// @notice Adds liquidity into the pool.
    /// @param amounts Amounts of each coin to add.
    /// @param min_mint_amount Minimum amount of LP to mint.
    function add_liquidity(uint256[3] calldata amounts, uint256 min_mint_amount) external payable returns (uint256);

    /// @notice Adds liquidity into the pool.
    /// @param amounts Amounts of each coin to add.
    /// @param min_mint_amount Minimum amount of LP to mint.
    /// @return uint256 Amount of LP tokens received by the `receiver
    /// @param use_eth True if native token is being added to the pool.
    /// @param receiver Address to send the LP tokens to. Default is msg.sender
    function add_liquidity(uint256[3] calldata amounts, uint256 min_mint_amount, bool use_eth, address receiver)
        external
        payable
        returns (uint256);

    /// @notice This withdrawal method is very safe, does no complex math since
    ///         tokens are withdrawn in balanced proportions. No fees are charged.
    /// @param amount Amount of LP tokens to burn
    /// @param min_amounts Minimum amounts of tokens to withdraw
    /// @param use_eth Whether to withdraw ETH or not
    /// @param receiver Address to send the withdrawn tokens to
    /// @param claim_admin_fees If True, call self._claim_admin_fees(). Default is True.
    /// @return uint256[3] Amount of pool tokens received by the `receiver`
    function remove_liquidity(
        uint256 amount,
        uint256[3] calldata min_amounts,
        bool use_eth,
        address receiver,
        bool claim_admin_fees
    ) external returns (uint256[3] memory);

    /// @notice Withdraw liquidity in a single token.
    /// Involves fees (lower than swap fees).
    /// @dev This operation also involves an admin fee claim.
    /// @param token_amount Amount of LP tokens to burn
    /// @param i Index of the token to withdraw
    /// @param min_amount Minimum amount of token to withdraw.
    /// @param use_eth Whether to withdraw ETH or not
    /// @param receiver Address to send the withdrawn tokens to
    /// @return Amount of tokens at index i received by the `receiver`
    function remove_liquidity_one_coin(
        uint256 token_amount,
        uint256 i,
        uint256 min_amount,
        bool use_eth,
        address receiver
    ) external returns (uint256);

    ///////////////////////////////////////////////////////////
    // View methods
    ///////////////////////////////////////////////////////////

    /// @notice Returns the balance of the coin at index `i`
    function balances(uint256 i) external view returns (uint256);

    /// @notice Calculate LP tokens minted or to be burned for depositing or
    ///         removing `amounts` of coins
    /// @dev Includes fee.
    /// @param amounts Amounts of tokens being deposited or withdrawn
    /// @param deposit True if it is a deposit action, False if withdrawn.
    /// @return uint256 Amount of LP tokens deposited or withdrawn.
    function calc_token_amount(uint256[3] calldata amounts, bool deposit) external view returns (uint256);

    function get_dy(uint256 i, uint256 j, uint256 dx) external view returns (uint256);

    function get_dx(uint256 i, uint256 j, uint256 dy) external view returns (uint256);

    /// @notice Calculates the current price of the LP token with respect to the coin at the 0th index
    /// @dev This function should be implemented to return the LP price
    /// @return The current LP price as a uint256
    function lp_price() external view returns (uint256);

    /// @notice calculate the current virtual price of the pool's LP token (in 18 decimals)
    /// @dev Non read-reenrant.
    /// @dev https://docs.curve.fi/cryptoswap-exchange/tricrypto-ng/pools/tricrypto/?h=virtual#get_virtual_price
    function get_virtual_price() external view returns (uint256);

    /// @notice Returns the oracle price of the coin at index `k` with respect to the coin at index 0
    /// @dev The oracle is an exponential moving average, with a periodicity determined internally.
    ///      The aggregated prices are cached state prices (dy/dx) calculated AFTER the latest trade.
    /// @param k The index of the coin for which the oracle price is needed (k = 0 or 1)
    /// @return The oracle price of the coin at index `k` as a uint256
    function price_oracle(uint256 k) external view returns (uint256);

    /// @notice Calculates output tokens with fee
    /// @param token_amount LP Token amount to burn
    /// @param i token in which liquidity is withdrawn
    /// @return uint256 Amount of ith tokens received for burning token_amount LP tokens.
    function calc_withdraw_one_coin(uint256 token_amount, uint256 i) external view returns (uint256);

    function calc_token_fee(uint256[3] calldata amounts, uint256[3] calldata xp) external view returns (uint256);

    function fee_calc(uint256[3] calldata xp) external view returns (uint256);

    /// @notice Returns i-th coin address.
    /// @param i Index of the coin. i must be 0, 1 or 2.
    function coins(uint256 i) external view returns (address);

    /// @dev Returns the address of the factory that created the pool.
    /// @return address The factory address.
    function factory() external view returns (address);

    function D() external view returns (uint256);

    /// @dev Returns the cached virtual price of the pool.
    function virtual_price() external view returns (uint256);

    /// @dev Returns the current pool amplification parameter.
    /// @return uint256 The A parameter.
    function A() external view returns (uint256);

    /// @dev Returns the current pool gamma parameter.
    /// @return uint256 The gamma parameter.
    function gamma() external view returns (uint256);

    ///////////////////////////////////////////////////////////
    // Protected methods
    ///////////////////////////////////////////////////////////

    /// @notice Initialise Ramping A and gamma parameter values linearly.
    /// @dev Only accessible by factory admin, and only
    /// @param future_A The future A value.
    /// @param future_gamma The future gamma value.
    /// @param future_time The timestamp at which the ramping will end.
    function ramp_A_gamma(uint256 future_A, uint256 future_gamma, uint256 future_time) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";

/// @notice WETH9 interface
interface IWETH9 is IERC20 {
    function deposit() external payable;

    function withdraw(uint256 wad) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";
import {CurveTricryptoOptimizedWETH} from "./external/CurveTricryptoOptimizedWETH.sol";

import {PoolState} from "../libs/PoolMath.sol";

interface INapierPool {
    event Mint(address indexed receiver, uint256 liquidity, uint256 underlyingUsed, uint256 baseLptUsed);

    event Burn(address indexed receiver, uint256 liquidity, uint256 underlyingOut, uint256 baseLptOut);

    event Swap(
        address indexed caller,
        address indexed receiver,
        int256 netUnderlying,
        uint256 index,
        int256 netPt,
        uint256 swapFee,
        uint256 protocolFee
    );

    event SwapBaseLpt(
        address indexed caller,
        address indexed receiver,
        int256 netUnderlying,
        int256 netBaseLpt,
        uint256 swapFee,
        uint256 protocolFee
    );

    event UpdateLnImpliedRate(uint256 lnImpliedRate);

    /**
     * @notice Add liquidity to the pool with Underlying and base lp token.
     * Caller have to transfer tokens to this contract before calling this function.
     * @param underlyingInDesired The desired amount of underlying asset to add.
     * @param baseLptInDesired The desired amount of base lp token to add.
     * @param recipient The recipient of the liquidity tokens.
     * @param data Additional data for callback.
     * @return The amount of liquidity tokens received.
     */
    function addLiquidity(uint256 underlyingInDesired, uint256 baseLptInDesired, address recipient, bytes memory data)
        external
        returns (uint256);

    /**
     * @notice Remove liquidity from the pool.
     * Caller have to transfer Lp token to this contract before calling this function.
     * @param recipient The recipient of the assets.
     * @return The amounts of base lp token and underlying asset received.
     */
    function removeLiquidity(address recipient) external returns (uint256, uint256);

    /**
     * @notice Swap exact amount of PT for Underlying asset.
     * It supports flash swap by specifying the callback data.
     * Flash swap enables user to receive Underlying asset before paying PT.
     * If the pool contract received enough PT after the callback, the swap is successful. Otherwise, the swap is reverted.
     * @param index The index of the PT.
     * @param ptIn The amount of PT to swap.
     * @param recipient The recipient of the swapped underlying asset.
     * @param data Additional data for the flash swap.
     * @return The amount of underlying asset received.
     */
    function swapPtForUnderlying(uint256 index, uint256 ptIn, address recipient, bytes calldata data)
        external
        returns (uint256);

    /**
     * @notice Swap Underlying asset for exact amount of PT.
     * It supports flash swap by specifying the callback data.
     * It enables user to receive PT before paying Underlying asset.
     * if the pool contract received enough Underlying asset after the callback, the swap is successful. Otherwise, the swap is reverted.
     * @param index The index of the PT.
     * @param ptOut The desired amount of PT to receive.
     * @param recipient The recipient of the PT.
     * @param data Additional data for the flash swap.
     * @return The amount of PT received.
     */
    function swapUnderlyingForPt(uint256 index, uint256 ptOut, address recipient, bytes calldata data)
        external
        returns (uint256);

    /**
     * @notice Swap Underlying asset for exact amount of Base LP token.
     * @param baseLpOut The desired amount of Base LP token to receive.
     * @param recipient The recipient of the Base LP token.
     */
    function swapUnderlyingForExactBaseLpToken(uint256 baseLpOut, address recipient) external returns (uint256);

    /**
     * @notice Swap exact amount of Base LP token for Underlying asset.
     * @param recipient The recipient of the Underlying asset.
     */
    function swapExactBaseLpTokenForUnderlying(uint256 baseLptIn, address recipient) external returns (uint256);

    /**
     * @notice Maturity of the pool, in unix timestamp.
     * @dev Maturity is same as the maturity of Principal Token in the pool.
     */
    function maturity() external view returns (uint256);

    function totalUnderlying() external view returns (uint128);

    function totalBaseLpt() external view returns (uint128);

    function getAssets() external view returns (address, address);

    /**
     * @notice State of the pool.
     * @dev This function is not expected to be called on-chain.
     */
    function readState() external view returns (PoolState memory);

    function tricrypto() external view returns (CurveTricryptoOptimizedWETH);

    function principalTokens() external view returns (IERC20[3] memory);

    function lastLnImpliedRate() external view returns (uint256);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import {IERC5095} from "./IERC5095.sol";

/// @notice Tranche interface
/// @dev Tranche divides a yield-bearing token into two tokens: Principal and Yield tokens
///      Unspecific types: Simply avoiding dependencies on other interfaces from our interfaces
interface ITranche is IERC5095 {
    /* ==================== ERRORS ===================== */

    error TimestampBeforeMaturity();
    error TimestampAfterMaturity();
    error ProtectedToken();
    error Unauthorized();
    error OnlyYT();
    error ReentrancyGuarded();
    error ZeroAddress();
    error NoAccruedYield();

    /* ==================== EVENTS ===================== */

    /// @param adapter the address of the adapter
    /// @param maturity timestamp of maturity (seconds since Unix epoch)
    /// @param issuanceFee fee for issuing PT and YT
    event SeriesCreated(address indexed adapter, uint256 indexed maturity, uint256 issuanceFee);

    /// @param from the sender of the underlying token
    /// @param to the recipient of the PT and YT
    /// @param underlyingUsed the amount of underlying token used to issue PT and YT
    /// @param sharesUsed the amount of target token used to issue PT and YT (before deducting issuance fee)
    event Issue(address indexed from, address indexed to, uint256 underlyingUsed, uint256 sharesUsed);

    /// @param owner the address of the owner of the PT and YT (address that called collect())
    /// @param shares the amount of Target token collected
    event Collect(address indexed owner, uint256 shares);

    /// @param owner the address of the owner of the PT and YT
    /// @param to the recipient of the underlying token redeemed
    /// @param underlyingRedeemed the amount of underlying token redeemed
    event RedeemWithYT(address indexed owner, address indexed to, uint256 underlyingRedeemed);

    /* ==================== STRUCTS ===================== */

    /// @notice Series is a struct that contains all the information about a series.
    /// @param underlying the address of the underlying token
    /// @param target the address of the target token
    /// @param yt the address of the Yield Token
    /// @param adapter the address of the adapter
    /// @param mscale scale value at maturity
    /// @param maxscale max scale value from this series' lifetime
    /// @param issuanceFee fee for issuing PT and YT
    /// @param maturity timestamp of maturity (seconds since Unix epoch)
    struct Series {
        address underlying;
        address target;
        address yt;
        address adapter;
        uint256 mscale;
        uint256 maxscale;
        uint64 issuanceFee;
        uint64 maturity;
    }

    /// @notice GlobalScales is a struct that contains scale values that are used in multiple functions throughout the Tranche contract.
    /// @param mscale scale value at maturity. before maturity and settlement, this value is 0.
    /// @param maxscale max scale value from this series' lifetime.
    struct GlobalScales {
        uint128 mscale;
        uint128 maxscale;
    }

    /* ================== MUTATIVE METHODS =================== */

    /// @notice deposit an `underlyingAmount` of underlying token into the yield source, receiving PT and YT.
    ///         amount of PT and YT issued are the same.
    /// @param   to the address to receive PT and YT
    /// @param   underlyingAmount the amount of underlying token to deposit
    /// @return  principalAmount the amount of PT and YT issued
    function issue(address to, uint256 underlyingAmount) external returns (uint256 principalAmount);

    /// @notice redeem an `principalAmount` of PT and YT for underlying token.
    /// @param from the address to burn PT and YT from
    /// @param to the address to receive underlying token
    /// @param pyAmount the amount of PT and YT to redeem
    /// @return underlyingAmount the amount of underlying token redeemed
    function redeemWithYT(address from, address to, uint256 pyAmount) external returns (uint256 underlyingAmount);

    /// @notice collect interest for `msg.sender` and transfer accrued interest to `msg.sender`
    /// NOTE: if the maturity has passed, all the YT balance of `msg.sender` is burned.
    /// @dev anyone can call this function to collect interest for themselves
    /// @return collected collected interest in Underlying token
    function collect() external returns (uint256 collected);

    /* ================== PERMISSIONED METHODS =================== */

    /// @notice collect interest from the yield source and distribute it
    ///         every YT transfer, this function is triggered by the Yield Token contract.
    ///         only the Yield Token contract can call this function.
    ///         NOTE: YT is not burned in this function even if the maturity has passed.
    /// @param from address to transfer the Yield Token from. i.e. the user who collects the interest.
    /// @param to address to transfer the Yield Token to (MUST NOT be zero address, CAN be the same as `from`)
    /// @param value amount of Yield Token transferred to `to` (CAN be 0)
    function updateUnclaimedYield(address from, address to, uint256 value) external;

    /* ================== VIEW METHODS =================== */

    /// @notice get the address of Yield Token associated with this Tranche.
    function yieldToken() external view returns (address);

    /// @notice get Series struct
    function getSeries() external view returns (Series memory);

    /// @notice get an accrued yield that can be claimed by `account` (in unis of Target token)
    /// @dev this is reset to 0 when `account` claims the yield.
    /// @param account the address to check
    /// @return accruedInTarget
    function unclaimedYields(address account) external view returns (uint256 accruedInTarget);

    /// @notice get an accrued yield that can be claimed by `account` (in unis of Underlying token)
    /// @param account the address to check
    /// @return accruedInUnderlying accrued yield in underlying token
    function previewCollect(address account) external view returns (uint256 accruedInUnderlying);
}

// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";

interface Twocrypto is IERC20 {
    function balances(uint256 i) external view returns (uint256);

    /// @notice Exchange using wrapped native token by default
    /// @param i Index value for the input coin
    /// @param j Index value for the output coin
    /// @param dx Amount of input coin being swapped in
    /// @param min_dy Minimum amount of output coin to receive
    /// @param receiver Address to send the output coin to, defaults to msg.sender
    /// @return Amount of tokens at index j received by the `receiver`
    function exchange(uint256 i, uint256 j, uint256 dx, uint256 min_dy, address receiver) external returns (uint256);

    /// @notice Exchange: but user must transfer dx amount of coin[i] tokens to pool first.
    ///         Pool will not call transferFrom and will only check if a surplus of
    ///         coins[i] is greater than or equal to `dx`.
    /// @dev Use-case is to reduce the number of redundant ERC20 token
    ///      transfers in zaps. Primarily for dex-aggregators/arbitrageurs/searchers.
    ///      Note for users: please transfer + exchange_received in 1 tx.
    /// @param i Index value for the input coin
    /// @param j Index value for the output coin
    /// @param dx Amount of input coin being swapped in
    /// @param min_dy Minimum amount of output coin to receive
    /// @param receiver Address to send the output coin to
    /// @return Amount of tokens at index j received by the `receiver`
    function exchange_received(uint256 i, uint256 j, uint256 dx, uint256 min_dy, address receiver)
        external
        returns (uint256);

    /// @notice Adds liquidity into the pool.
    /// @param amounts Amounts of each coin to add
    /// @param min_mint_amount Minimum amount of LP to mint
    /// @param receiver Address to send the LP tokens to, defaults to msg.sender
    /// @return Amount of LP tokens received by the `receiver`
    function add_liquidity(uint256[2] calldata amounts, uint256 min_mint_amount, address receiver)
        external
        returns (uint256);

    /// @notice This withdrawal method is very safe, does no complex math since
    ///         tokens are withdrawn in balanced proportions. No fees are charged.
    /// @param _amount Amount of LP tokens to burn
    /// @param min_amounts Minimum amounts of tokens to withdraw
    /// @param receiver Address to send the withdrawn tokens to
    /// @return Amounts of pool tokens received by the `receiver`
    function remove_liquidity(uint256 _amount, uint256[2] calldata min_amounts, address receiver)
        external
        returns (uint256[2] memory);

    /// @notice Withdraw liquidity in a single token.
    ///         Involves fees (lower than swap fees).
    /// @dev This operation also involves an admin fee claim.
    /// @param token_amount Amount of LP tokens to burn
    /// @param i Index of the token to withdraw
    /// @param min_amount Minimum amount of token to withdraw
    /// @param receiver Address to send the withdrawn tokens to
    /// @return Amount of tokens at index i received by the `receiver`
    function remove_liquidity_one_coin(uint256 token_amount, uint256 i, uint256 min_amount, address receiver)
        external
        returns (uint256);

    function remove_liquidity_one_coin(uint256 token_amount, uint256 i, uint256 min_amount)
        external
        returns (uint256);

    /// @notice Calculate LP tokens minted or to be burned for depositing or removing `amounts` of coins
    /// @dev Includes fee.
    /// @param amounts Amounts of tokens being deposited or withdrawn
    /// @param deposit True if it is a deposit action, False if withdrawn.
    /// @return Amount of LP tokens deposited or withdrawn.
    function calc_token_amount(uint256[2] calldata amounts, bool deposit) external view returns (uint256);

    /// @notice Get amount of coin[j] tokens received for swapping in dx amount of coin[i]
    /// @dev Includes fee.
    /// @param i index of input token. Check pool.coins(i) to get coin address at ith index
    /// @param j index of output token
    /// @param dx amount of input coin[i] tokens
    /// @return Exact amount of output j tokens for dx amount of i input tokens.
    function get_dy(uint256 i, uint256 j, uint256 dx) external view returns (uint256);

    /// @notice Get amount of coin[i] tokens to input for swapping out dy amount of coin[j]
    /// @dev This is an approximate method, and returns estimates close to the input amount. Expensive to call on-chain.
    /// @param i index of input token. Check pool.coins(i) to get coin address at ith index
    /// @param j index of output token
    /// @param dy amount of input coin[j] tokens received
    /// @return Approximate amount of input i tokens to get dy amount of j tokens.
    function get_dx(uint256 i, uint256 j, uint256 dy) external view returns (uint256);

    /// @notice Calculates the current price of the LP token w.r.t coin at the 0th index
    /// @return LP price.
    function lp_price() external view returns (uint256);

    /// @notice Calculates the current virtual price of the pool LP token.
    /// @dev Not to be confused with `self.virtual_price` which is a cached virtual price.
    /// @return Virtual Price.
    function get_virtual_price() external view returns (uint256);

    /// @notice Returns the oracle price of the coin at index `k` w.r.t the coin at index 0.
    /// @dev The oracle is an exponential moving average, with a periodicity determined by `self.ma_time`.
    /// @return Price oracle value of kth coin.
    function price_oracle() external view returns (uint256);

    /// @notice Returns the oracle value for xcp.
    /// @dev The oracle is an exponential moving average, with a periodicity determined by `self.xcp_ma_time`.
    /// @return Oracle value of xcp.
    function xcp_oracle() external view returns (uint256);

    /// @notice Returns the price scale of the coin at index `k` w.r.t the coin at index 0.
    /// @dev Price scale determines the price band around which liquidity is concentrated.
    /// @return Price scale of coin.
    function price_scale() external view returns (uint256);

    /// @notice Returns the fee charged by the pool at current state.
    /// @dev Not to be confused with the fee charged at liquidity action.
    /// @return fee bps.
    function fee() external view returns (uint256);

    /// @notice Calculates output tokens with fee for withdrawing one coin
    /// @param token_amount LP Token amount to burn
    /// @param i token in which liquidity is withdrawn
    /// @return Amount of ith tokens received for burning token_amount LP tokens.
    function calc_withdraw_one_coin(uint256 token_amount, uint256 i) external view returns (uint256);

    /// @notice Returns the fee charged on the given amounts for add_liquidity.
    /// @param amounts The amounts of coins being added to the pool.
    /// @param xp The current balances of the pool multiplied by coin precisions.
    /// @return Fee charged.
    function calc_token_fee(uint256[] calldata amounts, uint256[] calldata xp) external view returns (uint256);

    /// @notice Returns the current pool amplification parameter.
    /// @return A param.
    function A() external view returns (uint256);

    /// @notice Returns the current pool gamma parameter.
    /// @return gamma param.
    function gamma() external view returns (uint256);

    /// @notice Returns the current mid fee
    /// @return mid_fee value.
    function mid_fee() external view returns (uint256);

    /// @notice Returns the current out fee
    /// @return out_fee value.
    function out_fee() external view returns (uint256);

    /// @notice Returns the current fee gamma
    /// @return fee_gamma value.
    function fee_gamma() external view returns (uint256);

    /// @notice Returns the current allowed extra profit
    /// @return allowed_extra_profit value.
    function allowed_extra_profit() external view returns (uint256);

    /// @notice Returns the current adjustment step
    /// @return adjustment_step value.
    function adjustment_step() external view returns (uint256);

    /// @notice Returns the current moving average time in seconds
    /// @dev To get time in seconds, the parameter is multiplied by ln(2).
    /// @return ma_time value.
    function ma_time() external view returns (uint256);

    function coins(uint256 i) external view returns (address);

    function initial_A_gamma() external view returns (uint256);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.10;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";
import {IFlashLoanRecipient} from "./IFlashLoanRecipient.sol";
import {IProtocolFeesCollector} from "./IProtocolFeesCollector.sol";

interface IVault {
    /**
     * @dev Performs a 'flash loan', sending tokens to `recipient`, executing the `receiveFlashLoan` hook on it,
     * and then reverting unless the tokens plus a proportional protocol fee have been returned.
     *
     * The `tokens` and `amounts` arrays must have the same length, and each entry in these indicates the loan amount
     * for each token contract. `tokens` must be sorted in ascending order.
     *
     * The 'userData' field is ignored by the Vault, and forwarded as-is to `recipient` as part of the
     * `receiveFlashLoan` call.
     *
     * Emits `FlashLoan` events.
     */
    function flashLoan(
        IFlashLoanRecipient recipient,
        IERC20[] memory tokens,
        uint256[] memory amounts,
        bytes memory userData
    ) external;

    /**
     * @dev Returns the protocol fees collector contract.
     */
    function getProtocolFeesCollector() external view returns (IProtocolFeesCollector);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.10;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";

interface IFlashLoanRecipient {
    /**
     * @dev When `flashLoan` is called on the Vault, it invokes the `receiveFlashLoan` hook on the recipient.
     *
     * At the time of the call, the Vault will have transferred `amounts` for `tokens` to the recipient. Before this
     * call returns, the recipient must have transferred `amounts` plus `feeAmounts` for each token back to the
     * Vault, or else the entire flash loan will revert.
     *
     * `userData` is the same value passed in the `IVault.flashLoan` call.
     */
    function receiveFlashLoan(
        IERC20[] calldata tokens,
        uint256[] calldata amounts,
        uint256[] calldata feeAmounts,
        bytes calldata userData
    ) external;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.24;

import {INapierPool} from "@napier/v1-pool/src/interfaces/INapierPool.sol";
import {ITranche} from "@napier/v1-tranche/src/interfaces/ITranche.sol";
import {TwocryptoFactory} from "./interfaces/external/TwocryptoFactory.sol";

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

import {Ownable2Step} from "@openzeppelin/[email protected]/access/Ownable2Step.sol";

/// @notice A factory contract for deploying TwoCrypto metapools (Technically it is just regular twocrypto pool with PT and tricrypto LP token)
/// @dev It's a wrapper around the TwocryptoFactory contract with additional checks
contract MetapoolFactory is Ownable2Step {
    /// @notice The TwocryptoFactory contract
    TwocryptoFactory public immutable twocryptoFactory;

    /// @notice The WETH9 address
    address public immutable WETH9;

    /// @notice Mapping (metapool -> deployed by this factory). True if the metapool was deployed by this factory
    mapping(address metapool => bool) public isPtMetapool;

    event MetapoolDeployed(address metapool, address pt, address napierPool);

    /// @notice A parameter struct for deploying a metapool
    struct TwocryptoParams {
        uint256 A;
        uint256 gamma;
        uint256 mid_fee;
        uint256 out_fee;
        uint256 fee_gamma;
        uint256 allowed_extra_profit;
        uint256 adjustment_step;
        uint256 ma_time;
        uint256 initial_price;
    }

    constructor(address owner, address _WETH9, TwocryptoFactory _twocryptoFactory) {
        WETH9 = _WETH9;
        twocryptoFactory = _twocryptoFactory;

        _transferOwnership(owner);
    }

    /// @notice Deploys a TwocryptoNG from Factory contract
    /// NOTE: This metapool is not typical metapool, Technically it is just a pool with 2 volatile coins,
    /// where one of the coins is PT, and the other is triLST-PT tricrypto LP token (like rETH-PT, sfrxETH-PT, stETH-PT)
    /// @dev Reverts if:
    /// - The NapierPool's underlying is not WETH
    /// - The PT's underlying is not WETH
    /// - Maturity of the PT is longer than the maturity of the NapierPool
    /// - Name or symbol are too long
    /// @param pt The Principal Token address
    /// @param pool The NapierPool address for the metapool to use (Underlying token of those PTs must be WETH)
    /// @custom:param implementation_idx The index of the implementation to use
    /// @param name The name of the metapool
    /// @param symbol The symbol of the metapool
    /// @param params The metapool parameters
    /// @return metapool The address of the deployed metapool (coin0 is PT, coin1 is tricrypto LP token)
    function deployMetapool(
        address pt,
        address pool,
        uint256, /* implementation_idx */
        string calldata name,
        string calldata symbol,
        TwocryptoParams calldata params
    ) external onlyOwner returns (address metapool) {
        (address underlying, address tricrypto) = INapierPool(pool).getAssets();

        /// CHECK
        if (underlying != WETH9) revert Errors.MetapoolFactoryWETHMismatch();
        if (ITranche(pt).underlying() != WETH9) revert Errors.MetapoolFactoryWETHMismatch();
        if (ITranche(pt).maturity() > INapierPool(pool).maturity()) revert Errors.MetapoolFactoryMaturityTooLong();

        // Deploy twocrypto
        address[2] memory coins = [pt, tricrypto];
        uint256 implementation_idx;
        // Workaround for stack too deep error
        assembly { implementation_idx := calldataload(0x44) }// forgefmt: disable-line
        bytes memory data = abi.encodeWithSelector(
            TwocryptoFactory.deploy_pool.selector,
            name, // name
            symbol, // symbol
            coins, // coins
            implementation_idx, // implementation_idx
            // Avoid stack too deep error by passing params as a struct instead of individual parameters
            // Note: the order of members in the struct must match the order of the parameters in the function
            params
        );
        (bool success, bytes memory ret) = address(twocryptoFactory).call(data);
        if (!success) revert Errors.MetapoolFactoryFailedToDeployMetapool();
        metapool = abi.decode(ret, (address));
        isPtMetapool[metapool] = true;
        // Workaround for stack too deep error
        emit MetapoolDeployed(metapool, calldataLoadAddress(0x04), calldataLoadAddress(0x24));
    }

    function calldataLoadAddress(uint256 offset) private pure returns (address value) {
        assembly {
            value := calldataload(offset)
        }
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.10;

import {ApproxParams} from "@napier/v1-pool/src/interfaces/ApproxParams.sol";

interface IMetapoolRouter {
    function swapETHForPt(
        address metapool,
        uint256 ptAmount,
        uint256 maxEthSpent,
        uint256 minPtOut,
        address recipient,
        uint256 deadline
    ) external payable returns (uint256 ethSpent);

    function swapPtForETH(address metapool, uint256 ptAmount, uint256 minEthOut, address recipient, uint256 deadline)
        external
        returns (uint256 ethOut);

    function swapETHForYt(
        address metapool,
        uint256 ytAmount,
        uint256 maxEthSpent,
        address recipient,
        uint256 deadline,
        ApproxParams calldata approx
    ) external payable returns (uint256 ethSpent);

    function addLiquidityOneETHKeepYt(
        address metapool,
        uint256 minLiquidity,
        uint256 minYt,
        address recipient,
        uint256 deadline
    ) external payable returns (uint256 liquidity);

    function removeLiquidityOneETH(
        address metapool,
        uint256 liquidity,
        uint256 minEthOut,
        address recipient,
        uint256 deadline
    ) external returns (uint256 ethOut);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.24;

/// @notice Transient storage utility functions
library TransientStorage {
    function tloadU256(uint256 slot) internal view returns (uint256 value) {
        assembly {
            value := tload(slot)
        }
    }

    /// @notice The return value may contain dirty upper bits
    function tloadAddress(uint256 slot) internal view returns (address value) {
        assembly {
            value := tload(slot)
        }
    }
}

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

pragma solidity ^0.8.0;

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

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

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

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

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

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

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

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

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

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

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

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

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

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

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

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

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

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

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

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

import {ERC20} from "@openzeppelin/[email protected]/token/ERC20/ERC20.sol";
import {ITranche} from "@napier/v1-tranche/src/interfaces/ITranche.sol";
import {IBaseAdapter} from "@napier/v1-tranche/src/interfaces/IBaseAdapter.sol";
import {ApproxParams} from "..//interfaces/ApproxParams.sol";

import {FixedPointMathLib} from "@napier/v1-tranche/src/utils/FixedPointMathLib.sol";
import {Math} from "@openzeppelin/[email protected]/utils/math/Math.sol";
import {SafeCast} from "@openzeppelin/[email protected]/utils/math/SafeCast.sol";
import {MAX_BPS} from "@napier/v1-tranche/src/Constants.sol";
import {Errors} from "./Errors.sol";

library TrancheMathHelper {
    using SafeCast for uint256;

    uint256 constant DEFAULT_MAX_ITERATION = 100;
    uint256 constant MAX_ISSUANCE_FEE_BPS = 500; // 5%

    function getApproxUnderlyingNeededByYt(ITranche pt, uint256 ytDesired) internal view returns (uint256) {
        return getApproxUnderlyingNeededByYt(pt, ytDesired, ApproxParams(0, 0, 0, 0));
    }

    /// @notice This section of code aims to calculate the amount of underlying asset (`uDeposit`) required to issue a specific amount of PT and YT (`ytOutDesired`).
    /// The calculations are based on the formula used in the `Tranche.issue` function.
    function getApproxUnderlyingNeededByYt(ITranche pt, uint256 ytDesired, ApproxParams memory approx)
        internal
        view
        returns (uint256)
    {
        // Default approx parameters if not set
        if (approx.guessMax < approx.guessMin) revert Errors.ApproxBinarySearchInputInvalid();
        if (approx.eps == 0) approx.eps = 0.05 * 1e18; // 5%
        if (approx.maxIteration == 0) approx.maxIteration = DEFAULT_MAX_ITERATION;

        ITranche.Series memory series = pt.getSeries();
        uint256 cscale = IBaseAdapter(series.adapter).scale();
        IssueParams memory params = IssueParams({
            decimals: ERC20(address(pt)).decimals(),
            cscale: cscale,
            maxscale: Math.max(series.maxscale, cscale), // Update maxscale if current scale is greater than maxscale
            issuanceFeeBps: series.issuanceFee
        });
        // Variable Definitions:
        // - `uDeposit`: The amount of underlying asset that needs to be deposited to issue PT and YT.
        // - `ytOutDesired`: The desired amount of PT and YT to be issued.
        // - `cscale`: Current scale of the Tranche.
        // - `maxscale`: Maximum scale of the Tranche (denoted as 'S' in the formula).
        // - `issuanceFee`: Issuance fee in basis points. (10000 =100%).
        // `uDeposit` amount of underlying should issue at least `ytOutDesired` amount of PT and YT.
        // Issuance fee is charged in units of underlying token.
        // Formula for `Tranche.issue`:
        // ```
        // fee = uDeposit * issuanceFeeBps
        // shares = (uDeposit - fee) / s
        // pyIssue = shares * S
        // ```
        // Solving for `uDeposit`:
        // ```
        // uDeposit = pyIssue * s / S / (1 - issuanceFeeBps)
        //          => pyIssue * s * MAX_BPS / (S * (MAX_BPS - issuanceFeeBps))
        // ```
        // However, we can't get correct `uDeposit` due to the precision loss, probably indirectly caused by the issuance fee mechanism.

        // Estimate the maximum amount of underlying token
        uint256 uDepositMax = FixedPointMathLib.mulDivUp(
            // cscale is basically a share price which is usually rounded down.
            // So, we need to add 1 to cscale to round up the share price
            ytDesired * (cscale + 1),
            MAX_BPS,
            params.maxscale * (MAX_BPS - MAX_ISSUANCE_FEE_BPS)
        );
        // We use bisection as a workaround.
        return
            _bisectUnderlyingNeeded({params: params, ytDesired: ytDesired, uDepositGuess: uDepositMax, approx: approx});
    }

    /// @notice Variables to be cached
    struct IssueParams {
        uint256 decimals;
        uint256 cscale;
        uint256 maxscale;
        uint256 issuanceFeeBps;
    }

    /// @notice This function uses bisection to find [uDeposit] such that `Tranche::issue` would mint at least `ytDesired` YT.
    /// @param params - Variables to be cached for gas saving
    /// @param ytDesired - A desired amount of YT to issue
    /// @param uDepositGuess - An amount of underlying token that would issue less than `ytDesired` YT.
    function _bisectUnderlyingNeeded(
        IssueParams memory params,
        uint256 ytDesired,
        uint256 uDepositGuess,
        ApproxParams memory approx
    ) internal pure returns (uint256) {
        uint256 stepSize = 10 ** params.decimals; // 1 Underlying token
        uint256 a = FixedPointMathLib.mulDivUp(ytDesired, params.cscale, params.maxscale);
        uint256 b = uDepositGuess + stepSize; // upper bound

        if (approx.guessMin != 0) a = Math.max(approx.guessMin, a);
        if (approx.guessMax != 0) b = Math.min(approx.guessMax, b);

        // Try to find an min amount of underlying token such that the issuing at least `ytDesired`.
        // Bisect the interval [a, b].
        uint256 midpoint;
        for (uint256 i = 0; i != approx.maxIteration;) {
            midpoint = (a + b) / 2;
            uint256 preview = _previewIssue(params, midpoint);
            int256 err_mid = 1e18 - (preview * 1e18 / ytDesired).toInt256(); // v_desired - v_approx
            // Check if the relative error is less than the tolerance
            if (preview >= ytDesired && -(approx.eps).toInt256() < err_mid) {
                return midpoint;
            }
            // a == b ---> midpoint is `b` forever
            // a+1 == b ---> midpoint is `b` forever
            // Exit the loop if midpoin doesn't change
            if (a == b || (a + 1 == b)) break;

            if (err_mid > 0) {
                // bound interval [midpoint, b]
                a = midpoint;
            } else {
                // bound interval [a, midpoint]
                b = midpoint;
            }
            unchecked {
                ++i;
            }
        }
        // If the function hasn't returned by now, it means it didn't find a solution within the tolerance.
        // Try changing the tolerance.
        revert Errors.ApproxFail();
    }

    /// @notice A copy of `Tranche::issue` math
    function _previewIssue(IssueParams memory params, uint256 underlyingAmount) internal pure returns (uint256) {
        uint256 fee = FixedPointMathLib.mulDivUp(underlyingAmount, params.issuanceFeeBps, MAX_BPS);
        uint256 shares = FixedPointMathLib.divWadDown(underlyingAmount - fee, params.cscale);
        return FixedPointMathLib.mulWadDown(shares, params.maxscale);
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

// Taken from: Pendle finance v2

/// @notice Parameters for controlling the approximation process
/// @dev The approximation process is a binary search algorithm that finds the value that satisfies the provided function `f`.
/// By default, NapierPool defines swap formula in terms of Principal token (Base Pool LP token). To swap a given amount of Underlying token,
/// it's necessary to run an approximation algorithm to find the corresponding amount of Principal token to swap in/out
/// because computing inverse of the swap function is very hard.
/// The approximation algorithm will run as follows:
/// Let f(x) be the function that calculates difference between the desired value and the computed value for a given x (the amount of Base pool LP token to swap in/out)
/// The algorithm will find the value x that satisfies f(x) ~= ε, where ε is the relative error tolerance.
/// for a given range [a, b],
/// ```
///     mid = (a + b) / 2
///     error_mid = f(mid)
///     if error_mid <= eps
///         return mid
///     if error_mid > 0
///         a = mid
///     else
///         b = mid
/// ```
/// The algorithm will run for `maxIteration` times, or until the relative error tolerance `eps` is satisfied.
/// @param guessMin The lower bound of the guess range
/// @param guessMax The upper bound of the guess range
/// @param maxIteration The maximum number of iterations to run the approximation algorithm
/// @param eps The maximum relative error tolerance (in 18 decimals) between the desired value and the computed value. 0.1% = 1e15 (1e18/1000)
struct ApproxParams {
    uint256 guessMin;
    uint256 guessMax;
    uint256 maxIteration;
    uint256 eps;
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

library Errors {
    // Generic
    error FailedToSendEther();
    error NotWETH();

    // Factory
    error MetapoolFactoryFailedToDeployMetapool();
    error MetapoolFactoryMaturityTooLong();
    error MetapoolFactoryWETHMismatch();

    // Router
    error MetapoolRouterUnauthorized();
    error MetapoolRouterInvalidMetapool();
    error MetapoolRouterTransactionTooOld();
    error MetapoolRouterInsufficientETHOut();
    error MetapoolRouterInsufficientYtOut();
    error MetapoolRouterExceededLimitETHIn();
    error MetapoolRouterInsufficientETHReceived();
    error MetapoolRouterNonSituationSwapETHForYt();
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

/**
 * @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 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].
 */
abstract contract ReentrancyGuard {
    // 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;

    uint256 private _status;

    constructor() {
        _status = _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();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

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

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

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

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

    /**
     * @dev Moves `amount` 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 amount) 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 `amount` 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 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` 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 amount) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

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

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

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

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

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

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

/// @notice This library contains the math used in NapierPool.
/// @dev Taken and modified from Pendle V2: https://github.com/pendle-finance/pendle-core-v2-public/blob/163783b09014e515b645b83936fec32c5731d092/contracts/core/Market/MarketMathCore.sol
/// @dev Taken and modified from Notional : https://github.com/notional-finance/contracts-v2/blob/1845605ab0d9eec9b5dd374cf7c246957b534f85/contracts/internal/markets/Market.sol
/// @dev Naming convention:
/// - `pt` => baseLpt: BasePool LP token
/// - `asset` => `underlying`: underlying asset
/// - `totalPt` => `totalBaseLptTimesN`: total BasePool LP token reserve in the pool multiplied by 3 * virtual_price where virtual_price is the share price of the Tricrypto LP token
/// See NapierPool.sol for more details.
/// - `totalAsset` => `totalUnderlying`: total underlying asset reserve in the pool
/// - `executeTradeCore` function =>  `executeSwap` function
/// - `calculateTrade` function => `calculateSwap` function
/// - `getMarketPreCompute` function => `computeAmmParameters` function
/// - `setNewMarketStateTrade` function => `_setPostPoolState` function
/// @dev All functions in this library are view functions.
/// @dev Changes:
///  1) Math library dependency from LogExpMath to PRBMath etc.
///  2) Swap functions multiply the parameter `exactPtToAccount` by N(=3) to make it equivalent to the amount of PT being swapped.
///  3) Swap functions divide the computed underlying swap result by N.
///  3) Remove some redundant checks (e.g. check for maturity)
///  4) Remove some redundant variables (e.g. `totalAsset` in `MarketPreCompute`)
///  5) Remove some redundant functions (`addLiquidity` and `removeLiquidity`)

// libraries
import {Math} from "@openzeppelin/[email protected]/utils/math/Math.sol";
import {SafeCast} from "@openzeppelin/[email protected]/utils/math/SafeCast.sol";
import {FixedPointMathLib} from "@napier/v1-tranche/src/utils/FixedPointMathLib.sol";
import {SignedMath} from "./SignedMath.sol";
import {sd, ln, intoInt256} from "@prb/math/SD59x18.sol"; // used for logarithm operation
import {ud, exp, intoUint256} from "@prb/math/UD60x18.sol"; // used for exp operation
import {Errors} from "./Errors.sol";

/// @param totalBaseLptTimesN - Reserve Curve v2 Tricrypto 3PrincipalToken Pool LP token x times N(=# of Curve v2 Pool assets) in 18 decimals
/// @param totalUnderlying18 - Reserve underlying asset in 18 decimals
/// @param scalarRoot - Scalar root for NapierPool (See whitepaper)
/// @param maturity - Expiry of NapierPool (Unix timestamp)
/// @param lnFeeRateRoot - Logarithmic fee rate root
/// @param protocolFeePercent - Protocol fee percent (base 100)
/// @param lastLnImpliedRate - Last ln implied rate
struct PoolState {
    uint256 totalBaseLptTimesN;
    uint256 totalUnderlying18;
    // Tricrypto pool LP token virtual price
    uint256 virtualPrice;
    /// immutable variables ///
    uint256 scalarRoot;
    uint256 maturity;
    /// fee data ///
    uint256 lnFeeRateRoot;
    uint256 protocolFeePercent; // 100=100%
    /// last trade data ///
    uint256 lastLnImpliedRate;
}

/// @notice Variables that are used to compute the swap result
/// @dev params that are expensive to compute, therefore we pre-compute them
struct PoolPreCompute {
    int256 rateScalar;
    int256 rateAnchor;
    int256 feeRate;
}

/// @title PoolMath - library for calculating swaps
/// @notice Taken and modified from Pendle V2: https://github.com/pendle-finance/pendle-core-v2-public/blob/163783b09014e515b645b83936fec32c5731d092/contracts/core/Market/MarketMathCore.sol
/// @dev Swaps take place between the BasePool LP token and the underlying asset.
/// The BasePool LP token is basket of 3 principal tokens.
/// @dev The AMM formula is defined in terms of the amount of PT being swapped.
/// @dev The math assumes two tokens (pt and underlying) have same decimals. Need to convert if they have different decimals.
/// @dev All functions in this library are view functions.
library PoolMath {
    /// @notice Minimum liquidity in the pool
    uint256 internal constant MINIMUM_LIQUIDITY = 10 ** 3;
    /// @notice Percentage base (100=100%)
    int256 internal constant FULL_PERCENTAGE = 100;
    /// @notice Day in seconds in Unix timestamp
    uint256 internal constant DAY = 86400;
    /// @notice Year in seconds in Unix timestamp
    uint256 internal constant IMPLIED_RATE_TIME = 365 * DAY;

    /// @notice Max proportion of BasePool LP token / (BasePool LP token + underlying asset) in the pool
    uint256 internal constant MAX_POOL_PROPORTION = 0.96 * 1e18; // 96%

    int256 internal constant N_COINS = 3;

    using FixedPointMathLib for uint256;
    using SignedMath for int256;
    using SignedMath for uint256;
    using SafeCast for uint256;
    using SafeCast for int256;

    /// @param pool State - pool state of the pool
    /// @param exactBaseLptIn - exact amount of Base Pool LP tokens to be swapped in
    /// @return underlyingOut18 - underlying tokens to be swapped out (18 decimals)
    /// @return swapFee18 - swap fee in underlying (18 decimals)
    /// @return protocolFee18 - protocol fee in underlying (18 decimals)
    function swapExactBaseLpTokenForUnderlying(PoolState memory pool, uint256 exactBaseLptIn)
        internal
        view
        returns (uint256 underlyingOut18, uint256 swapFee18, uint256 protocolFee18)
    {
        (int256 _netUnderlyingToAccount18, int256 _netUnderlyingFee18, int256 _netUnderlyingToProtocol18) = executeSwap(
            pool,
            // Note: sign is defined from the perspective of the swapper.
            // negative because the swapper is selling pt
            // Note: Here we are multiplying by virtualPrice * N_COINS because the swap formula is defined in terms of the amount of PT being swapped.
            // Basically BaseLpt is equivalent to more than 3 times the amount of PT due to the initial deposit of 1:1:1:1=pt1:pt2:pt3:Lp share in Curve pool.
            // The LP token accrues trade fees on the Tricrypto pool and the virtual price’s value would increase over time.
            FixedPointMathLib.mulWadDown(exactBaseLptIn, pool.virtualPrice * uint256(N_COINS)).neg() // user would get smaller amount of underlying due to the rounding down
        );

        underlyingOut18 = _netUnderlyingToAccount18.toUint256();
        swapFee18 = _netUnderlyingFee18.toUint256();
        protocolFee18 = _netUnderlyingToProtocol18.toUint256();
    }

    /// @param pool State - pool state of the pool
    /// @param exactBaseLptOut exact amount of Base Pool LP tokens to be swapped out
    /// @return underlyingIn18 - underlying tokens to be swapped in (18 decimals)
    /// @return swapFee18 - swap fee in underlying (18 decimals)
    /// @return protocolFee18 - protocol fee in underlying (18 decimals)
    function swapUnderlyingForExactBaseLpToken(PoolState memory pool, uint256 exactBaseLptOut)
        internal
        view
        returns (uint256 underlyingIn18, uint256 swapFee18, uint256 protocolFee18)
    {
        (int256 _netUnderlyingToAccount18, int256 _netUnderlyingFee18, int256 _netUnderlyingToProtocol18) = executeSwap(
            pool,
            // Note: sign is defined from the perspective of the swapper.
            // positive because the swapper is buying pt
            FixedPointMathLib.mulWadUp(exactBaseLptOut, pool.virtualPrice * uint256(N_COINS)).toInt256() // user would need to pay more underlying due to the rounding up
        );

        underlyingIn18 = _netUnderlyingToAccount18.neg().toUint256();
        swapFee18 = _netUnderlyingFee18.toUint256();
        protocolFee18 = _netUnderlyingToProtocol18.toUint256();
    }

    /// @notice Compute swap result given the amount of base pool LP tokens to be swapped in.
    /// @dev This function is used to compute the swap result before the swap is executed.
    /// @param pool State - pool state of the pool
    /// @param netBaseLptToAccount (int256) amount of base pool LP tokens to be swapped in (negative if selling pt) multiplied by the number of BasePool assets
    /// Note: sign is defined from the perspective of the swapper. positive if the swapper is buying pt.
    /// @return netUnderlyingToAccount18 (int256) amount of underlying tokens to be swapped out
    /// @return netUnderlyingFee18 (int256) total fee. including protocol fee.
    /// `netUnderlyingFee18 - netUnderlyingToProtocol` will be distributed to LP holders.
    /// @return netUnderlyingToProtocol18 (int256) Protocol fee
    function executeSwap(PoolState memory pool, int256 netBaseLptToAccount)
        internal
        view
        returns (int256 netUnderlyingToAccount18, int256 netUnderlyingFee18, int256 netUnderlyingToProtocol18)
    {
        if (pool.totalBaseLptTimesN.toInt256() <= netBaseLptToAccount) {
            revert Errors.PoolInsufficientBaseLptForTrade();
        }

        /// ------------------------------------------------------------
        /// MATH
        /// ------------------------------------------------------------
        PoolPreCompute memory comp = computeAmmParameters(pool);

        (netUnderlyingToAccount18, netUnderlyingFee18, netUnderlyingToProtocol18) =
            calculateSwap(pool, comp, netBaseLptToAccount);
        /// ------------------------------------------------------------
        /// WRITE
        /// ------------------------------------------------------------
        _setPostPoolState(pool, comp, netBaseLptToAccount, netUnderlyingToAccount18, netUnderlyingToProtocol18);
    }

    /// @notice Compute the pseudo invariant of the pool.
    /// @dev The pseudo invariant is computed every swap before the swap is executed.
    /// @param pool State - pool state of the pool
    function computeAmmParameters(PoolState memory pool) internal view returns (PoolPreCompute memory cache) {
        uint256 timeToExpiry = pool.maturity - block.timestamp;

        cache.rateScalar = _getRateScalar(pool, timeToExpiry);
        cache.rateAnchor = _getRateAnchor(
            pool.totalBaseLptTimesN, pool.lastLnImpliedRate, pool.totalUnderlying18, cache.rateScalar, timeToExpiry
        );
        cache.feeRate = _getExchangeRateFromImpliedRate(pool.lnFeeRateRoot, timeToExpiry);
    }

    /// @notice Calculate the new `RateAnchor(t)` based on the pre-trade implied rate, `lastImpliedRate`, before the swap.
    /// To ensure interest rate continuity, we adjust the `rateAnchor(t)` such that the pre-trade implied rate at t* remains the same as `lastImpliedRate`.
    ///
    /// Formulas for `rateAnchor(t)`:
    /// ----------------------------
    /// yearsToExpiry(t) = timeToExpiry / 365 days
    ///
    /// portion(t*) = totalBaseLptTimesN / (totalBaseLptTimesN + totalUnderlying18)
    ///
    /// extRate(t*) = lastImpliedRate^(yearsToExpiry(t))
    ///              = e^(ln(lastImpliedRate) * yearsToExpiry(t))
    ///
    /// rateAnchor(t) = extRate(t*) - ln(portion(t*)) / rateScalar(t)
    /// ----------------------------
    /// Where `portion(t*)` represents the portion of the pool that is BasePool LP token at t* and `extRate(t*)` is the exchange rate at t*.
    ///
    /// @param totalBaseLptTimesN total Base Lp token in the pool
    /// @param lastLnImpliedRate the implied rate for the last trade that occurred at t_last.
    /// @param totalUnderlying18 total underlying in the pool
    /// @param rateScalar a parameter of swap formula. Calculated as  `scalarRoot` divided by `yearsToExpiry`
    /// @param timeToExpiry time to maturity in seconds
    /// @return rateAnchor the new rate anchor
    function _getRateAnchor(
        uint256 totalBaseLptTimesN,
        uint256 lastLnImpliedRate,
        uint256 totalUnderlying18,
        int256 rateScalar,
        uint256 timeToExpiry
    ) internal pure returns (int256 rateAnchor) {
        // `extRate(t*) = e^(lastLnImpliedRate * yearsToExpiry(t))`
        // Get pre-trade exchange rate with zero-fee
        int256 preTradeExchangeRate = _getExchangeRateFromImpliedRate(lastLnImpliedRate, timeToExpiry);
        // exchangeRate should not be below 1.
        // But it is mathematically almost impossible to happen because `exp(x) < 1` is satisfied for all `x < 0`.
        // Here x = lastLnImpliedRate * yearsToExpiry(t), which is very unlikely to be negative.(or
        // more accurately the natural log rounds down to zero). `lastLnImpliedRate` is guaranteed to be positive when it is set
        // and `yearsToExpiry(t)` is guaranteed to be positive because swap can only happen before maturity.
        // We still check for this case to be safe.
        require(preTradeExchangeRate >= SignedMath.WAD);
        uint256 proportion = totalBaseLptTimesN.divWadDown(totalBaseLptTimesN + totalUnderlying18);
        int256 lnProportion = _logProportion(proportion);

        // Compute `rateAnchor(t) = extRate(t*) - ln(portion(t*)) / rateScalar(t)`
        rateAnchor = preTradeExchangeRate - lnProportion.divWadDown(rateScalar);
    }

    /// @notice Converts an implied rate to an exchange rate given a time to maturity. The
    /// @dev Formula: `E = e^rt`
    /// @return exchangeRate the price of underlying token in Base LP token. Guaranteed to be positive or zero.
    function _getExchangeRateFromImpliedRate(uint256 lnImpliedRate, uint256 timeToExpiry)
        internal
        pure
        returns (int256 exchangeRate)
    {
        uint256 rt = (lnImpliedRate * timeToExpiry) / IMPLIED_RATE_TIME;
        exchangeRate = exp(ud(rt)).intoUint256().toInt256();
    }

    /// @notice Compute swap result given the delta of baseLpt an swapper wants to swap.
    /// @param pool State - pool state of the pool
    /// @param comp PreCompute - pre-computed values of the pool
    /// @param netBaseLptToAccount the delta of baseLpt the swapper wants to swap.
    /// @dev Note: Ensure that abs(`netBaseLptToAccount`) is not greater than `totalBaseLptTimesN`.
    /// @return netUnderlyingToAccount18 the amount of underlying the swapper will receive
    /// negative if the swapper is selling BaseLpt and positive if the swapper is buying BaseLpt.
    /// @return underlyingFee18 the amount of underlying charged as swap fee
    /// this includes `underlyingToProtocol18`
    /// @return underlyingToProtocol18 the amount of underlying the Pool fee recipient will receive as fee
    /// Protocol accrues fee in underlying.
    function calculateSwap(
        PoolState memory pool,
        PoolPreCompute memory comp,
        int256 netBaseLptToAccount // d_pt
    ) internal pure returns (int256, int256, int256) {
        // Calculates the exchange rate from underlying to baseLpt before any fees are applied
        // Note: The exchange rate is int type but it must be always strictly gt 1.
        // Note: `netBaseLptToAccount` should be checked prior to calling this function
        int256 preFeeExchangeRate = _getExchangeRate(
            pool.totalBaseLptTimesN, pool.totalUnderlying18, comp.rateScalar, comp.rateAnchor, netBaseLptToAccount
        ).toInt256();

        // Basically swap formula is:
        //                                 netBaseLptToAccount
        // netUnderlyingToAccount18 = -1 * ────────────────────────
        //                                       extRate
        // where `netBaseLptToAccount` is the delta of baseLpt (`d_pt`) and `netUnderlyingToAccount18` is the delta of underlying (`d_u`).
        // because if `d_pt > 0`, then `d_u < 0` and vice versa.
        // fees can be applied to the `extRate`.
        // `postFeeExchangeRate = preFeeExchangeRate / feeRate` if `netBaseLptToAccount > 0` else `postFeeExchangeRate = preFeeExchangeRate * feeRate`
        int256 netUnderlying18 = netBaseLptToAccount.divWadDown(preFeeExchangeRate).neg();

        // See whitepaper for the formula:
        // fee is calculated as the difference between the underlying amount before and after the fee is applied:
        // fee = underlyingNoFee - underlyingWithFee
        // where `underlyingNoFee = - (ptToAccount / preFeeExchangeRate)`
        // and `underlyingWithFee = - (ptToAccount / postFeeExchangeRate)`
        //
        // Therefore:
        // fee = - (ptToAccount / preFeeExchangeRate) + (ptToAccount / postFeeExchangeRate)
        int256 underlyingFee18;
        if (netBaseLptToAccount > 0) {
            // User swap underlying for baseLpt
            // Exchange rate after fee is applied is:
            //  `postFeeExchangeRate := preFeeExchangeRate / feeRate`
            //  `postFeeExchangeRate` must be strictly gt 1.
            // It's possible that the fee pushes the implied rate into negative territory. This is not allowed.
            int256 postFeeExchangeRate = preFeeExchangeRate.divWadDown(comp.feeRate);
            if (postFeeExchangeRate < SignedMath.WAD) revert Errors.PoolExchangeRateBelowOne(postFeeExchangeRate);

            // fee = - (ptToAccount / preFeeExchangeRate) + (ptToAccount / postFeeExchangeRate)
            //     = (ptToAccount / preFeeExchangeRate) * (feeRate - 1)
            //     = netUnderlying18 * (feeRate - 1)
            underlyingFee18 = netUnderlying18.mulWadDown(SignedMath.WAD - comp.feeRate);
        } else {
            // User swap baseLpt for underlying
            // Exchange rate after fee is applied is:
            //  `postFeeExchangeRate := preFeeExchangeRate * feeRate`
            // In this case, `postFeeExchangeRate` can't be below 1 unlike the case above.

            // fee = - (ptToAccount / preFeeExchangeRate) + (ptToAccount / postFeeExchangeRate)
            //     = - (ptToAccount / preFeeExchangeRate) + (ptToAccount / (preFeeExchangeRate * feeRate))
            //     = - (ptToAccount / preFeeExchangeRate) * (1 - 1 / feeRate)
            //     = - (ptToAccount / preFeeExchangeRate) * (feeRate - 1) / feeRate
            // Note: ptToAccount is negative in this branch so we negate it to ensure that fee is a positive number
            underlyingFee18 = ((netUnderlying18 * (SignedMath.WAD - comp.feeRate)) / comp.feeRate).neg();
        }

        // Subtract swap fee
        // underlyingWithFee = underlyingNoFee - fee
        int256 netUnderlyingToAccount18 = netUnderlying18 - underlyingFee18;
        // Charge protocol fee on swap fee
        // This underlying will be removed from the pool reserve
        int256 underlyingToProtocol18 = (underlyingFee18 * pool.protocolFeePercent.toInt256()) / FULL_PERCENTAGE;

        return (netUnderlyingToAccount18, underlyingFee18, underlyingToProtocol18);
    }

    /// @notice Update pool state cache after swap is executed
    /// @param pool pool state of the pool
    /// @param comp swap formula pre-computed values
    /// @param netBaseLptToAccount net Base Lpt to account. negative if the swapper is selling BaseLpt
    /// @param netUnderlyingToAccount18 net underlying to account. positive if the swapper is selling BaseLpt.
    /// @param netUnderlyingToProtocol18 should be removed from the pool reserve `totalUnderlying18`. must be positive
    function _setPostPoolState(
        PoolState memory pool,
        PoolPreCompute memory comp,
        int256 netBaseLptToAccount,
        int256 netUnderlyingToAccount18,
        int256 netUnderlyingToProtocol18
    ) internal view {
        // update pool state
        // Note safe because pre-trade check ensures totalBaseLptTimesN >= netBaseLptToAccount
        pool.totalBaseLptTimesN = (pool.totalBaseLptTimesN.toInt256() - netBaseLptToAccount).toUint256();
        pool.totalUnderlying18 = (pool.totalUnderlying18).toInt256().subNoNeg(
            netUnderlyingToAccount18 + netUnderlyingToProtocol18
        ).toUint256();
        // compute post-trade implied rate
        // this will be used to compute the new rateAnchor for the next trade
        uint256 timeToExpiry = pool.maturity - block.timestamp;
        pool.lastLnImpliedRate = _getLnImpliedRate(
            pool.totalBaseLptTimesN, pool.totalUnderlying18, comp.rateScalar, comp.rateAnchor, timeToExpiry
        );
        // It's technically unlikely that the implied rate is actually exactly zero but we will still fail
        // in this case.
        if (pool.lastLnImpliedRate == 0) revert Errors.PoolZeroLnImpliedRate();
    }

    /// @notice Get rate scalar given the pool state and time to maturity.
    /// @dev Formula: `scalarRoot * ONE_YEAR / yearsToExpiry`
    function _getRateScalar(PoolState memory pool, uint256 timeToExpiry) internal pure returns (int256) {
        uint256 rateScalar = (pool.scalarRoot * IMPLIED_RATE_TIME) / timeToExpiry;
        if (rateScalar == 0) revert Errors.PoolRateScalarZero();
        return rateScalar.toInt256();
    }

    /// @notice Calculates the current pool implied rate.
    /// ln(extRate) * ONE_YEAR / timeToExpiry
    /// @return lnImpliedRate the implied rate
    function _getLnImpliedRate(
        uint256 totalBaseLptTimesN,
        uint256 totalUnderlying18,
        int256 rateScalar,
        int256 rateAnchor,
        uint256 timeToExpiry
    ) internal pure returns (uint256 lnImpliedRate) {
        // This should ensure that exchange rate < FixedPointMathLib.WAD
        int256 exchangeRate =
            _getExchangeRate(totalBaseLptTimesN, totalUnderlying18, rateScalar, rateAnchor, 0).toInt256();

        // exchangeRate >= 1 so its ln(extRate) >= 0
        int256 lnRate = ln(sd(exchangeRate)).intoInt256();

        lnImpliedRate = (uint256(lnRate) * IMPLIED_RATE_TIME) / timeToExpiry;
    }

    /// @notice Calculates exchange rate given the total baseLpt and total underlying.
    ///     (1 / rateScalar) * ln(proportion / (1 - proportion)) + rateAnchor
    /// where:
    ///     proportion = totalPt / (totalPt + totalUnderlying)
    ///
    /// @dev Revert if the exchange rate is below 1. Prevent users from swapping when 1 baseLpt is worth more than 1 underlying.
    /// @dev Revert if the proportion of baseLpt to total is greater than MAX_POOL_PROPORTION.
    /// @param totalBaseLptTimesN the total baseLpt in the pool
    /// @param totalUnderlying18 the total underlying in the pool
    /// @param rateScalar the scalar used to compute the exchange rate
    /// @param rateAnchor the anchor used to compute the exchange rate
    /// @param netBaseLptToAccount the net baseLpt to the account (negative if account is swapping baseLpt for underlying)
    /// @return exchangeRate the price of underlying token in terms of Base LP token
    function _getExchangeRate(
        uint256 totalBaseLptTimesN,
        uint256 totalUnderlying18,
        int256 rateScalar,
        int256 rateAnchor,
        int256 netBaseLptToAccount
    ) internal pure returns (uint256) {
        // Revert if there is not enough baseLpt to support this swap.
        // Note: Ensure that abs(`netBaseLptToAccount`) is not greater than `totalBaseLptTimesN` before calling this function
        uint256 numerator = (totalBaseLptTimesN.toInt256() - netBaseLptToAccount).toUint256();
        uint256 proportion = numerator.divWadDown(totalBaseLptTimesN + totalUnderlying18);

        if (proportion > MAX_POOL_PROPORTION) {
            revert Errors.PoolProportionTooHigh();
        }

        int256 lnProportion = _logProportion(proportion);

        int256 exchangeRate = lnProportion.divWadDown(rateScalar) + rateAnchor;
        if (exchangeRate < int256(FixedPointMathLib.WAD)) revert Errors.PoolExchangeRateBelowOne(exchangeRate);
        return exchangeRate.toUint256();
    }

    /// @notice Compute Logit function (log(p/(1-p)) given a proportion `p`.
    /// @param proportion the proportion of baseLpt to (baseLpt + underlying) (0 <= proportion <= 1e18)
    function _logProportion(uint256 proportion) internal pure returns (int256 logitP) {
        if (proportion == FixedPointMathLib.WAD) revert Errors.PoolProportionMustNotEqualOne();

        // input = p/(1-p)
        int256 input = proportion.divWadDown(FixedPointMathLib.WAD - proportion).toInt256();
        // logit(p) = log(input) = ln(p/(1-p))
        logitP = ln(sd(input)).intoInt256();
    }

    /// @notice Compute the initial implied rate of the pool.
    /// @dev This function is expected to be called only once when initial liquidity is added.
    /// @param pool pool state of the pool
    /// @param initialAnchor initial anchor of the pool
    /// @return initialLnImpliedRate the initial implied rate
    function computeInitialLnImpliedRate(PoolState memory pool, int256 initialAnchor) internal view returns (uint256) {
        uint256 timeToExpiry = pool.maturity - block.timestamp;
        int256 rateScalar = _getRateScalar(pool, timeToExpiry);

        return
            _getLnImpliedRate(pool.totalBaseLptTimesN, pool.totalUnderlying18, rateScalar, initialAnchor, timeToExpiry);
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

import {IERC20} from "@openzeppelin/[email protected]/token/ERC20/IERC20.sol";

/// @notice Principal tokens (zero-coupon tokens) are redeemable for a single underlying EIP-20 token at a future timestamp.
///         https://eips.ethereum.org/EIPS/eip-5095
interface IERC5095 is IERC20 {
    event Redeem(address indexed from, address indexed to, uint256 underlyingAmount);

    /// @dev Asset that is returned on redemption.
    function underlying() external view returns (address underlyingAddress);

    /// @dev Unix time at which redemption of fyToken for underlying are possible
    function maturity() external view returns (uint256 timestamp);

    /// @dev Converts a specified amount of principal to underlying
    function convertToUnderlying(uint256 principalAmount) external view returns (uint256 underlyingAmount);

    /// @dev Converts a specified amount of underlying to principal
    function convertToPrincipal(uint256 underlyingAmount) external view returns (uint256 principalAmount);

    /// @dev Gives the maximum amount an address holder can redeem in terms of the principal
    function maxRedeem(address holder) external view returns (uint256 maxPrincipalAmount);

    /// @dev Gives the amount in terms of underlying that the princiapl amount can be redeemed for plus accrual
    function previewRedeem(uint256 principalAmount) external view returns (uint256 underlyingAmount);

    /// @dev Burn fyToken after maturity for an amount of principal.
    function redeem(uint256 principalAmount, address to, address from) external returns (uint256 underlyingAmount);

    /// @dev Gives the maximum amount an address holder can withdraw in terms of the underlying
    function maxWithdraw(address holder) external view returns (uint256 maxUnderlyingAmount);

    /// @dev Gives the amount in terms of principal that the underlying amount can be withdrawn for plus accrual
    function previewWithdraw(uint256 underlyingAmount) external view returns (uint256 principalAmount);

    /// @dev Burn fyToken after maturity for an amount of underlying.
    function withdraw(uint256 underlyingAmount, address to, address from) external returns (uint256 principalAmount);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.10;

/**
 * Taken from: https://github.com/balancer/balancer-v2-monorepo/blob/ac63d64018c6331248c7d77b9f317a06cced0243/pkg/vault/contracts/ProtocolFeesCollector.sol
 * @dev This an auxiliary contract to the Vault, deployed by it during construction. It offloads some of the tasks the
 * Vault performs to reduce its overall bytecode size.
 *
 * The current values for all protocol fee percentages are stored here, and any tokens charged as protocol fees are
 * sent to this contract, where they may be withdrawn by authorized entities. All authorization tasks are delegated
 * to the Vault's own authorizer.
 */
interface IProtocolFeesCollector {
    function getFlashLoanFeePercentage() external view returns (uint256);
}

// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.0;

pragma solidity ^0.8.0;

interface TwocryptoFactory {
    /// @notice Deploy a new pool
    /// @param _name Name of the new plain pool
    /// @param _symbol Symbol for the new plain pool - will be concatenated with factory symbol
    /// @param _coins Addresses of the coins in the pool
    /// @param implementation_id ID of the pool implementation
    /// @param A Amplification coefficient
    /// @param gamma Swap fee coefficient
    /// @param mid_fee Fee for stable swaps
    /// @param out_fee Fee for volatile swaps
    /// @param fee_gamma Adjustment coefficient for fees
    /// @param allowed_extra_profit Extra profit limit for adjusting swap fees
    /// @param adjustment_step Step size for fee adjustment
    /// @param ma_exp_time Moving average expiration time
    /// @param initial_price Initial price for the pool
    /// @return Address of the deployed pool
    function deploy_pool(
        string calldata _name,
        string calldata _symbol,
        address[2] calldata _coins,
        uint256 implementation_id,
        uint256 A,
        uint256 gamma,
        uint256 mid_fee,
        uint256 out_fee,
        uint256 fee_gamma,
        uint256 allowed_extra_profit,
        uint256 adjustment_step,
        uint256 ma_exp_time,
        uint256 initial_price
    ) external returns (address);

    /// @notice Set pool implementation
    /// @dev Set to address(0) to prevent deployment of new pools
    /// @param _pool_implementation Address of the new pool implementation
    /// @param _implementation_index Index of the pool implementation
    function set_pool_implementation(address _pool_implementation, uint256 _implementation_index) external;

    /// @notice Set gauge implementation
    /// @dev Set to address(0) to prevent deployment of new gauges
    /// @param _gauge_implementation Address of the new gauge implementation
    function set_gauge_implementation(address _gauge_implementation) external;

    /// @notice Set views contract implementation
    /// @param _views_implementation Address of the new views contract
    function set_views_implementation(address _views_implementation) external;

    /// @notice Set math implementation
    /// @param _math_implementation Address of the new math contract
    function set_math_implementation(address _math_implementation) external;

    function initialise_ownership(address fee_receiver, address admin) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.0;

import "./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.
 *
 * By default, the owner account will be the one that deploys the contract. 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.
     */
    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();
        require(pendingOwner() == sender, "Ownable2Step: caller is not the new owner");
        _transferOwnership(sender);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead returning `false` on failure. This behavior is nonetheless
 * conventional and does not conflict with the expectations of ERC20
 * applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping(address => uint256) private _balances;

    mapping(address => mapping(address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the default value returned by this function, unless
     * it's overridden.
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address from, address to, uint256 amount) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, amount);
        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        address owner = _msgSender();
        _approve(owner, spender, allowance(owner, spender) + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        address owner = _msgSender();
        uint256 currentAllowance = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `from` to `to`.
     *
     * This internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(address from, address to, uint256 amount) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.0;

interface IBaseAdapter {
    /* ============== MUTATIVE METHODS =============== */

    /// @notice update adapter's scale value and return it
    ///         Underlying decimals: `u`, Target decimals: `t`, Target conversion rate: 10^u / 10^t
    ///         => Scale = 10^(u-t) * 10^18 = 10^(u-t+18)
    ///         e.g. WstETH (t=18,u=18) price: 1.2 WETH => scale = 1.2*10^18
    ///              eUSDC (t=18,u=6) price: 1.01 USDC => scale = 1.01*10^(6-18+18) = 1.01*10^6
    /// @dev For interest-bearing token, such as cTokens, this is simply the conversion rate
    /// @dev For other Targets, such as AMM LP shares, specialized logic will be required
    /// @return scale in units of underlying token
    function scale() external view returns (uint256);

    /// @notice deposit Underlying in return for Target.
    /// @dev no funds should be left in the contract after this call.
    ///      the caller must transfer Underlying to this contract before calling this function.
    /// @return underlyingUsed amount of Underlying used
    /// @return sharesMinted amount of Target minted
    function prefundedDeposit() external returns (uint256 underlyingUsed, uint256 sharesMinted);

    /// @notice redeem Target and receive Underlying in return.
    /// @dev no funds should be left in the contract after this call
    ///      the caller must transfer Target to this contract before calling this function.
    /// @param to recipient of Underlying
    /// @return underlyingWithdrawn amount of Underlying returned
    /// @return sharesRedeemed amount of Target redeemed
    function prefundedRedeem(address to) external returns (uint256 underlyingWithdrawn, uint256 sharesRedeemed);

    /* =============== VIEW METHODS ================ */

    /// @notice return Underlying token address (eg USDC, DAI)
    /// @return Underlying address
    function underlying() external view returns (address);

    /// @notice return yield-bearing token address (eg cUSDC, wstETH, AMM LP shares)
    /// @return Target address (yield-bearing token)
    function target() external view returns (address);
}

// SPDX-License-Identifier: AGPL-3.0-only
/// @notice Taken from: https://github.com/transmissions11/solmate/blob/2001af43aedb46fdc2335d2a7714fb2dae7cfcd1/src/utils/FixedPointMathLib.sol

pragma solidity >=0.8.0;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    uint256 internal constant MAX_UINT256 = 2 ** 256 - 1;

    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.

    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }

    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }

    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }

    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }

    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function mulDivDown(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                revert(0, 0)
            }

            // Divide x * y by the denominator.
            z := div(mul(x, y), denominator)
        }
    }

    function mulDivUp(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to require(denominator != 0 && (y == 0 || x <= type(uint256).max / y))
            if iszero(mul(denominator, iszero(mul(y, gt(x, div(MAX_UINT256, y)))))) {
                revert(0, 0)
            }

            // If x * y modulo the denominator is strictly greater than 0,
            // 1 is added to round up the division of x * y by the denominator.
            z := add(gt(mod(mul(x, y), denominator), 0), div(mul(x, y), denominator))
        }
    }

    function rpow(uint256 x, uint256 n, uint256 scalar) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }

                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)

                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }

                    // Store x squared.
                    let xx := mul(x, x)

                    // Round to the nearest number.
                    let xxRound := add(xx, half)

                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }

                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)

                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)

                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }

                        // Round to the nearest number.
                        let zxRound := add(zx, half)

                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }

                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }

    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/

    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.

            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, z)
            }

            // Goal was to get z*z*y within a small factor of x. More iterations could
            // get y in a tighter range. Currently, we will have y in [256, 256*2^16).
            // We ensured y >= 256 so that the relative difference between y and y+1 is small.
            // That's not possible if x < 256 but we can just verify those cases exhaustively.

            // Now, z*z*y <= x < z*z*(y+1), and y <= 2^(16+8), and either y >= 256, or x < 256.
            // Correctness can be checked exhaustively for x < 256, so we assume y >= 256.
            // Then z*sqrt(y) is within sqrt(257)/sqrt(256) of sqrt(x), or about 20bps.

            // For s in the range [1/256, 256], the estimate f(s) = (181/1024) * (s+1) is in the range
            // (1/2.84 * sqrt(s), 2.84 * sqrt(s)), with largest error when s = 1 and when s = 256 or 1/256.

            // Since y is in [256, 256*2^16), let a = y/65536, so that a is in [1/256, 256). Then we can estimate
            // sqrt(y) using sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2^18.

            // There is no overflow risk here since y < 2^136 after the first branch above.
            z := shr(18, mul(z, add(y, 65536))) // A mul() is saved from starting z at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If x+1 is a perfect square, the Babylonian method cycles between
            // floor(sqrt(x)) and ceil(sqrt(x)). This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }

    function unsafeMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Mod x by y. Note this will return
            // 0 instead of reverting if y is zero.
            z := mod(x, y)
        }
    }

    function unsafeDiv(uint256 x, uint256 y) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // Divide x by y. Note this will return
            // 0 instead of reverting if y is zero.
            r := div(x, y)
        }
    }

    function unsafeDivUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Add 1 to x * y if x % y > 0. Note this will
            // return 0 instead of reverting if y is zero.
            z := add(gt(mod(x, y), 0), div(x, y))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        require(value <= type(uint248).max, "SafeCast: value doesn't fit in 248 bits");
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        require(value <= type(uint240).max, "SafeCast: value doesn't fit in 240 bits");
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        require(value <= type(uint232).max, "SafeCast: value doesn't fit in 232 bits");
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.2._
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        require(value <= type(uint216).max, "SafeCast: value doesn't fit in 216 bits");
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        require(value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        require(value <= type(uint200).max, "SafeCast: value doesn't fit in 200 bits");
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        require(value <= type(uint192).max, "SafeCast: value doesn't fit in 192 bits");
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        require(value <= type(uint184).max, "SafeCast: value doesn't fit in 184 bits");
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        require(value <= type(uint176).max, "SafeCast: value doesn't fit in 176 bits");
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        require(value <= type(uint168).max, "SafeCast: value doesn't fit in 168 bits");
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        require(value <= type(uint160).max, "SafeCast: value doesn't fit in 160 bits");
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        require(value <= type(uint152).max, "SafeCast: value doesn't fit in 152 bits");
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        require(value <= type(uint144).max, "SafeCast: value doesn't fit in 144 bits");
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        require(value <= type(uint136).max, "SafeCast: value doesn't fit in 136 bits");
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v2.5._
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        require(value <= type(uint120).max, "SafeCast: value doesn't fit in 120 bits");
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        require(value <= type(uint112).max, "SafeCast: value doesn't fit in 112 bits");
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        require(value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.2._
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        require(value <= type(uint88).max, "SafeCast: value doesn't fit in 88 bits");
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        require(value <= type(uint80).max, "SafeCast: value doesn't fit in 80 bits");
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        require(value <= type(uint72).max, "SafeCast: value doesn't fit in 72 bits");
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v2.5._
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        require(value <= type(uint56).max, "SafeCast: value doesn't fit in 56 bits");
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        require(value <= type(uint48).max, "SafeCast: value doesn't fit in 48 bits");
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        require(value <= type(uint40).max, "SafeCast: value doesn't fit in 40 bits");
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v2.5._
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        require(value <= type(uint24).max, "SafeCast: value doesn't fit in 24 bits");
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v2.5._
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v2.5._
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     *
     * _Available since v3.0._
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 248 bits");
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 240 bits");
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 232 bits");
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.7._
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 224 bits");
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 216 bits");
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 208 bits");
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 200 bits");
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 192 bits");
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 184 bits");
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 176 bits");
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 168 bits");
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 160 bits");
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 152 bits");
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 144 bits");
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 136 bits");
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 128 bits");
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 120 bits");
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 112 bits");
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 104 bits");
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.7._
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 96 bits");
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 88 bits");
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 80 bits");
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 72 bits");
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 64 bits");
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 56 bits");
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 48 bits");
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 40 bits");
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 32 bits");
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 24 bits");
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 16 bits");
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        require(downcasted == value, "SafeCast: value doesn't fit in 8 bits");
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     *
     * _Available since v3.0._
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

uint256 constant WAD = 1e18;

// @notice 100% in basis points. 10_000 = 100%s
uint256 constant MAX_BPS = 10_000;

/* =============== ADDRESSES ================ */

// @notice WETH address on mainnet
address constant WETH = 0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2;

// @notice stETH address on mainnet
address constant STETH = 0xae7ab96520DE3A18E5e111B5EaAb095312D7fE84;

// @notice wstETH address on mainnet
address constant WSTETH = 0x7f39C581F595B53c5cb19bD0b3f8dA6c935E2Ca0;

// @notice WithdrawalQueueERC721 of LIDO address on mainnet
address constant LIDO_WITHDRAWAL_QUEUE = 0x889edC2eDab5f40e902b864aD4d7AdE8E412F9B1;

// @notice rETH address on mainnet
address constant RETH = 0xae78736Cd615f374D3085123A210448E74Fc6393;

// @notice eETH address on mainnet
address constant EETH = 0x35fA164735182de50811E8e2E824cFb9B6118ac2;

// @notice cETH address on mainnet
address constant CETH = 0x4Ddc2D193948926D02f9B1fE9e1daa0718270ED5;

// @notice CDAI address on mainnet
address constant CDAI = 0x5d3a536E4D6DbD6114cc1Ead35777bAB948E3643;

// @notice DAI address on mainnet
address constant DAI = 0x6B175474E89094C44Da98b954EedeAC495271d0F;

// @notice COMPTROLLER address on mainnet
address constant COMPTROLLER = 0x3d9819210A31b4961b30EF54bE2aeD79B9c9Cd3B;

// @notice COMP address on mainnet
address constant COMP = 0xc00e94Cb662C3520282E6f5717214004A7f26888;

// @notice AWETH address on mainnet
address constant AWETH = 0x4d5F47FA6A74757f35C14fD3a6Ef8E3C9BC514E8;

// @notice LendingAAVEV3_POOL_ADDRESSES_PROVIDER address on mainnet
address constant AAVEV3_POOL_ADDRESSES_PROVIDER = 0x2f39d218133AFaB8F2B819B1066c7E434Ad94E9e;

// @notice ma3WETH ERC 4626 Vault address on mainnet
address constant MA3WETH = 0x39Dd7790e75C6F663731f7E1FdC0f35007D3879b;

// @notice Morpho Aave v3 optimizer contract address on mainnet
address constant MORPHO_AAVE_V3 = 0x33333aea097c193e66081E930c33020272b33333;

// @notice MORPHO token address on mainnet
address constant MORPHO = 0x9994E35Db50125E0DF82e4c2dde62496CE330999;

// @notice Frax Ether address on mainnet
address constant FRXETH = 0x5E8422345238F34275888049021821E8E08CAa1f;

// @notice Staked Frax Ether address on mainnet
address constant STAKED_FRXETH = 0xac3E018457B222d93114458476f3E3416Abbe38F;

// @notice EtherFi LiquidityPool
address constant ETHERFI_LP = 0x308861A430be4cce5502d0A12724771Fc6DaF216;

// @notice EtherFi WETH
address constant ETHERFI_WEETH = 0xCd5fE23C85820F7B72D0926FC9b05b43E359b7ee;

// @notice EtherFi WithdrawRequestNFT
address constant ETHERFI_WITHDRAW_REQUEST = 0x7d5706f6ef3F89B3951E23e557CDFBC3239D4E2c;

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

library Errors {
    // Approx
    error ApproxFail();
    error ApproxBinarySearchInputInvalid();

    // Quoter
    error ApproxFailWithHint(bytes hint);

    // Factory
    error FactoryPoolAlreadyExists();
    error FactoryUnderlyingMismatch();
    error FactoryMaturityMismatch();

    // Pool
    error PoolOnlyOwner();
    error PoolInvalidParamName();
    error PoolUnauthorizedCallback();
    error PoolExpired();
    error PoolInvariantViolated();
    error PoolZeroAmountsInput();
    error PoolZeroAmountsOutput();
    error PoolZeroLnImpliedRate();
    error PoolInsufficientBaseLptForTrade();
    error PoolInsufficientBaseLptReceived();
    error PoolInsufficientUnderlyingReceived();
    error PoolExchangeRateBelowOne(int256 exchangeRate);
    error PoolProportionMustNotEqualOne();
    error PoolRateScalarZero();
    error PoolProportionTooHigh();

    // Router
    error RouterInsufficientWETH();
    error RouterInconsistentWETHPayment();
    error RouterPoolNotFound();
    error RouterTransactionTooOld();
    error RouterInsufficientLpOut();
    error RouterInsufficientTokenBalance();
    error RouterInsufficientUnderlyingOut();
    error RouterExceededLimitUnderlyingIn();
    error RouterInsufficientUnderlyingRepay();
    error RouterInsufficientPtRepay();
    error RouterCallbackNotNapierPool();
    error RouterNonSituationSwapUnderlyingForYt();
    error RouterInsufficientPyIssue();

    // Generic
    error FailedToSendEther();
    error NotWETH();

    // Config
    error LnFeeRateRootTooHigh();
    error ProtocolFeePercentTooHigh();
    error InitialAnchorTooLow();
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity ^0.8.19;

import {SafeCast} from "@openzeppelin/[email protected]/utils/math/SafeCast.sol";

library SignedMath {
    int256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.

    function mulDivDown(int256 x, int256 y, int256 z) internal pure returns (int256) {
        int256 xy = x * y;
        unchecked {
            return xy / z;
        }
    }

    function subNoNeg(int256 a, int256 b) internal pure returns (int256) {
        require(a >= b, "negative");
        return a - b; // no unchecked since if b is very negative, a - b might overflow
    }

    function mulWadDown(int256 a, int256 b) internal pure returns (int256) {
        return mulDivDown(a, b, WAD);
    }

    function divWadDown(int256 a, int256 b) internal pure returns (int256) {
        return mulDivDown(a, WAD, b);
    }

    function neg(int256 x) internal pure returns (int256) {
        return x * (-1);
    }

    function neg(uint256 x) internal pure returns (int256) {
        return SafeCast.toInt256(x) * (-1);
    }
}

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

/*

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

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

*/

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

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

/*

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

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

*/

import "./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
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../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.
 *
 * By default, the owner account will be the one that deploys the contract. 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;

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @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 {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @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 {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _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 v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @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;
    }
}

// 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_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/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 must be greater than or equal to `uMIN_SD1x18`.
/// - x must be less than or equal to `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 UD2x18.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `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 UD60x18.
/// @dev Requirements:
/// - x must be positive.
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 must be positive.
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 must be positive.
/// - x must be less than or equal to `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 must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

import { uMAX_SD59x18, uMIN_SD59x18, uUNIT } from "./Constants.sol";
import { PRBMath_SD59x18_Convert_Overflow, PRBMath_SD59x18_Convert_Underflow } from "./Errors.sol";
import { SD59x18 } from "./ValueType.sol";

/// @notice Converts a simple integer to SD59x18 by multiplying it by `UNIT`.
///
/// @dev Requirements:
/// - x must be greater than or equal to `MIN_SD59x18 / UNIT`.
/// - x must be less than or equal to `MAX_SD59x18 / UNIT`.
///
/// @param x The basic integer to convert.
/// @param result The same number converted to SD59x18.
function convert(int256 x) pure returns (SD59x18 result) {
    if (x < uMIN_SD59x18 / uUNIT) {
        revert PRBMath_SD59x18_Convert_Underflow(x);
    }
    if (x > uMAX_SD59x18 / uUNIT) {
        revert PRBMath_SD59x18_Convert_Overflow(x);
    }
    unchecked {
        result = SD59x18.wrap(x * uUNIT);
    }
}

/// @notice Converts an SD59x18 number to a simple integer by dividing it by `UNIT`.
/// @dev The result is rounded toward zero.
/// @param x The SD59x18 number to convert.
/// @return result The same number as a simple integer.
function convert(SD59x18 x) pure returns (int256 result) {
    result = SD59x18.unwrap(x) / uUNIT;
}

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

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

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

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

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

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

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

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

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

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

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

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

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

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in SD1x18.
error PRBMath_SD59x18_IntoSD1x18_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in UD2x18.
error PRBMath_SD59x18_IntoUD2x18_Underflow(SD59x18 x);

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

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint128.
error PRBMath_SD59x18_IntoUint128_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint256.
error PRBMath_SD59x18_IntoUint256_Underflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Overflow(SD59x18 x);

/// @notice Thrown when trying to cast a UD60x18 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 hte intermediary absolute result overflows SD59x18.
error PRBMath_SD59x18_Powu_Overflow(SD59x18 x, uint256 y);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import {
    uEXP_MAX_INPUT,
    uEXP2_MAX_INPUT,
    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 must be greater than `MIN_SD59x18`.
///
/// @param x The SD59x18 number for which to calculate the absolute value.
/// @param 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 must be less than or equal to `MAX_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to ceil.
/// @param 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.
/// @param 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 must be less than 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();

    // 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 is less than -59_794705707972522261, the result is zero.
///
/// Requirements:
/// - x must be less than 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 this is truncated to zero.
        if (xInt < -59_794705707972522261) {
            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 must be greater than or equal to `MIN_WHOLE_SD59x18`.
///
/// @param x The SD59x18 number to floor.
/// @param 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.
/// @param 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 must be greater than zero.
///
/// @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 cannot be negative, since complex numbers are not supported.
/// - x must be less than `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 "./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.intoUD2x18,
    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 "./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_SD59x18 } from "../sd59x18/Constants.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { uMAX_UD2x18 } from "../ud2x18/Constants.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "./ValueType.sol";

/// @notice Casts a UD60x18 number into SD1x18.
/// @dev Requirements:
/// - x must be less than or equal to `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 UD2x18.
/// @dev Requirements:
/// - x must be less than or equal to `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 SD59x18.
/// @dev Requirements:
/// - x must be less than or equal to `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 must be less than or equal to `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 must be less than or equal to `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 must be less than or equal to `MAX_UD60x18 / UNIT`.
///
/// @param x The basic integer to convert.
/// @param 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 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 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 1.
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 must be less than or equal to `MAX_WHOLE_UD60x18`.
///
/// @param x The UD60x18 number to ceil.
/// @param 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.
/// @param 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 must be less than 133_084258667509499441.
///
/// @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 must be less than 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.
/// @param 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.
/// @param 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 must be greater than zero.
///
/// @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 greater than `UNIT`, use the standard formula.
    if (xUint > uUNIT) {
        result = exp2(mul(log2(x), y));
    }
    // Conversely, if x is less than `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 must be less than `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.intoUD2x18,
    Casting.intoSD59x18,
    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 needed by 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 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 maximum 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);
int256 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.intoUD2x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for SD1x18 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.
uint256 constant uUNIT = 1e18;
UD2x18 constant UNIT = UD2x18.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.intoSD1x18,
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for UD2x18 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 { UD2x18 } from "../ud2x18/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 the domain of SD1x18 is a subset of SD59x18.
function intoSD59x18(SD1x18 x) pure returns (SD59x18 result) {
    result = SD59x18.wrap(int256(SD1x18.unwrap(x)));
}

/// @notice Casts an SD1x18 number into UD2x18.
/// - x must be positive.
function intoUD2x18(SD1x18 x) pure returns (UD2x18 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUD2x18_Underflow(x);
    }
    result = UD2x18.wrap(uint64(xInt));
}

/// @notice Casts an SD1x18 number into UD60x18.
/// @dev Requirements:
/// - x must be positive.
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 uint256.
/// @dev Requirements:
/// - x must be positive.
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 uint128.
/// @dev Requirements:
/// - x must be positive.
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 uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `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 Errors;
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

/// @notice Casts a UD2x18 number into SD1x18.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(UD2x18 x) pure returns (SD1x18 result) {
    uint64 xUint = UD2x18.unwrap(x);
    if (xUint > uint64(uMAX_SD1x18)) {
        revert Errors.PRBMath_UD2x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xUint));
}

/// @notice Casts a UD2x18 number into SD59x18.
/// @dev There is no overflow check because the domain of UD2x18 is a subset of 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 the domain of UD2x18 is a subset of 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 the domain of UD2x18 is a subset of 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 the domain of UD2x18 is a subset of uint256.
function intoUint256(UD2x18 x) pure returns (uint256 result) {
    result = uint256(UD2x18.unwrap(x));
}

/// @notice Casts a UD2x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `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 { SD1x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a SD1x18 number that doesn't fit in UD2x18.
error PRBMath_SD1x18_ToUD2x18_Underflow(SD1x18 x);

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

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

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

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

/// @notice Thrown when trying to cast a 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 { UD2x18 } from "./ValueType.sol";

/// @notice Thrown when trying to cast a UD2x18 number that doesn't fit in SD1x18.
error PRBMath_UD2x18_IntoSD1x18_Overflow(UD2x18 x);

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

{
  "remappings": [
    "@napier/v1-pool/=lib/v1-pool/",
    "forge-std/=lib/forge-std/src/",
    "@napier/v1-tranche/=lib/v1-pool/lib/napier-v1/",
    "@openzeppelin/[email protected]/=lib/v1-pool/lib/openzeppelin-contracts/contracts/",
    "@prb/math/=lib/v1-pool/lib/prb-math/src/",
    "@prb/test/=lib/v1-pool/lib/prb-math/lib/prb-test/src/",
    "ds-test/=lib/forge-std/lib/ds-test/src/",
    "erc4626-tests/=lib/v1-pool/lib/openzeppelin-contracts/lib/erc4626-tests/",
    "forge-std/=lib/forge-std/src/",
    "foundry-vyper/=lib/v1-pool/lib/foundry-vyper/src/",
    "hardhat-deployer/=lib/v1-pool/lib/hardhat-deployer/src/",
    "napier-v1/=lib/v1-pool/lib/napier-v1/",
    "openzeppelin-contracts/=lib/v1-pool/lib/openzeppelin-contracts/",
    "openzeppelin/=lib/v1-pool/lib/openzeppelin-contracts/contracts/",
    "prb-math/=lib/v1-pool/lib/prb-math/src/",
    "prb-test/=lib/v1-pool/lib/prb-math/lib/prb-test/src/",
    "tricrypto-ng/=lib/v1-pool/lib/tricrypto-ng/contracts/",
    "v1-pool/=lib/v1-pool/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 10000000
  },
  "metadata": {
    "useLiteralContent": false,
    "bytecodeHash": "none",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "cancun",
  "viaIR": false,
  "libraries": {}
}

• No Contract Security Audit Submitted- Submit Audit Here

[{"inputs":[{"internalType":"contract MetapoolFactory","name":"_metapoolFactory","type":"address"},{"internalType":"contract INapierPool","name":"_triLSTPool","type":"address"},{"internalType":"contract IVault","name":"_vault","type":"address"}],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[],"name":"ApproxBinarySearchInputInvalid","type":"error"},{"inputs":[],"name":"ApproxFail","type":"error"},{"inputs":[],"name":"FailedToSendEther","type":"error"},{"inputs":[],"name":"MetapoolRouterExceededLimitETHIn","type":"error"},{"inputs":[],"name":"MetapoolRouterInsufficientETHOut","type":"error"},{"inputs":[],"name":"MetapoolRouterInsufficientETHReceived","type":"error"},{"inputs":[],"name":"MetapoolRouterInsufficientYtOut","type":"error"},{"inputs":[],"name":"MetapoolRouterInvalidMetapool","type":"error"},{"inputs":[],"name":"MetapoolRouterNonSituationSwapETHForYt","type":"error"},{"inputs":[],"name":"MetapoolRouterTransactionTooOld","type":"error"},{"inputs":[],"name":"NotWETH","type":"error"},{"inputs":[],"name":"WETH9","outputs":[{"internalType":"contract IWETH9","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"metapool","type":"address"},{"internalType":"uint256","name":"minLiquidity","type":"uint256"},{"internalType":"uint256","name":"minYt","type":"uint256"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"}],"name":"addLiquidityOneETHKeepYt","outputs":[{"internalType":"uint256","name":"liquidity","type":"uint256"}],"stateMutability":"payable","type":"function"},{"inputs":[],"name":"metapoolFactory","outputs":[{"internalType":"contract MetapoolFactory","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"contract IERC20[]","name":"","type":"address[]"},{"internalType":"uint256[]","name":"amounts","type":"uint256[]"},{"internalType":"uint256[]","name":"feeAmounts","type":"uint256[]"},{"internalType":"bytes","name":"","type":"bytes"}],"name":"receiveFlashLoan","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"metapool","type":"address"},{"internalType":"uint256","name":"liquidity","type":"uint256"},{"internalType":"uint256","name":"minEthOut","type":"uint256"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"}],"name":"removeLiquidityOneETH","outputs":[{"internalType":"uint256","name":"ethOut","type":"uint256"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"metapool","type":"address"},{"internalType":"uint256","name":"ptAmount","type":"uint256"},{"internalType":"uint256","name":"maxEthSpent","type":"uint256"},{"internalType":"uint256","name":"minPtOut","type":"uint256"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"}],"name":"swapETHForPt","outputs":[{"internalType":"uint256","name":"ethSpent","type":"uint256"}],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"address","name":"metapool","type":"address"},{"internalType":"uint256","name":"ytAmount","type":"uint256"},{"internalType":"uint256","name":"maxEthSpent","type":"uint256"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"},{"components":[{"internalType":"uint256","name":"guessMin","type":"uint256"},{"internalType":"uint256","name":"guessMax","type":"uint256"},{"internalType":"uint256","name":"maxIteration","type":"uint256"},{"internalType":"uint256","name":"eps","type":"uint256"}],"internalType":"struct ApproxParams","name":"approx","type":"tuple"}],"name":"swapETHForYt","outputs":[{"internalType":"uint256","name":"ethSpent","type":"uint256"}],"stateMutability":"payable","type":"function"},{"inputs":[{"internalType":"address","name":"metapool","type":"address"},{"internalType":"uint256","name":"ptAmount","type":"uint256"},{"internalType":"uint256","name":"minEthOut","type":"uint256"},{"internalType":"address","name":"recipient","type":"address"},{"internalType":"uint256","name":"deadline","type":"uint256"}],"name":"swapPtForETH","outputs":[{"internalType":"uint256","name":"ethOut","type":"uint256"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"triLSTPool","outputs":[{"internalType":"contract INapierPool","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"tricryptoLST","outputs":[{"internalType":"contract CurveTricryptoOptimizedWETH","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"vault","outputs":[{"internalType":"contract IVault","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"stateMutability":"payable","type":"receive"}]

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000000000000000000000000d5a7bf70bc6135d1a9df914ce364b1765460e6750000000000000000000000005a2d321ed5c525e52a3b8d295c6d097a3c78b821000000000000000000000000ba12222222228d8ba445958a75a0704d566bf2c8

-----Decoded View---------------
Arg [0] : _metapoolFactory (address): 0xd5a7bF70BC6135D1A9dF914ce364b1765460E675
Arg [1] : _triLSTPool (address): 0x5a2d321eD5C525e52A3b8d295c6D097a3c78B821
Arg [2] : _vault (address): 0xBA12222222228d8Ba445958a75a0704d566BF2C8

-----Encoded View---------------
3 Constructor Arguments found :
Arg [0] : 000000000000000000000000d5a7bf70bc6135d1a9df914ce364b1765460e675
Arg [1] : 0000000000000000000000005a2d321ed5c525e52a3b8d295c6d097a3c78b821
Arg [2] : 000000000000000000000000ba12222222228d8ba445958a75a0704d566bf2c8