owner

spender

amount

Approval

caller

assets

shares

Deposit

from

Transfer

receiver

Withdraw

DOMAIN_SEPARATOR

allowance

approve

asset

balanceOf

convertToAssets

convertToShares

decimals

deposit

maxDeposit

maxMint

maxRedeem

maxWithdraw

mint

name

nonces

value

deadline

permit

previewDeposit

previewMint

previewRedeem

previewWithdraw

redeem

symbol

totalAssets

totalSupply

transfer

transferFrom

withdraw

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../tokens/ERC20.sol";
import {SafeTransferLib} from "../utils/SafeTransferLib.sol";
import {FixedPointMathLib} from "../utils/FixedPointMathLib.sol";

/// @notice Minimal ERC4626 tokenized Vault implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/mixins/ERC4626.sol)
abstract contract ERC4626 is ERC20 {
    using SafeTransferLib for ERC20;
    using FixedPointMathLib for uint256;

    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Deposit(address indexed caller, address indexed owner, uint256 assets, uint256 shares);

    event Withdraw(
        address indexed caller,
        address indexed receiver,
        address indexed owner,
        uint256 assets,
        uint256 shares
    );

    /*//////////////////////////////////////////////////////////////
                               IMMUTABLES
    //////////////////////////////////////////////////////////////*/

    ERC20 public immutable asset;

    constructor(
        ERC20 _asset,
        string memory _name,
        string memory _symbol
    ) ERC20(_name, _symbol, _asset.decimals()) {
        asset = _asset;
    }

    /*//////////////////////////////////////////////////////////////
                        DEPOSIT/WITHDRAWAL LOGIC
    //////////////////////////////////////////////////////////////*/

    function deposit(uint256 assets, address receiver) public virtual returns (uint256 shares) {
        // Check for rounding error since we round down in previewDeposit.
        require((shares = previewDeposit(assets)) != 0, "ZERO_SHARES");

        // Need to transfer before minting or ERC777s could reenter.
        asset.safeTransferFrom(msg.sender, address(this), assets);

        _mint(receiver, shares);

        emit Deposit(msg.sender, receiver, assets, shares);

        afterDeposit(assets, shares);
    }

    function mint(uint256 shares, address receiver) public virtual returns (uint256 assets) {
        assets = previewMint(shares); // No need to check for rounding error, previewMint rounds up.

        // Need to transfer before minting or ERC777s could reenter.
        asset.safeTransferFrom(msg.sender, address(this), assets);

        _mint(receiver, shares);

        emit Deposit(msg.sender, receiver, assets, shares);

        afterDeposit(assets, shares);
    }

    function withdraw(
        uint256 assets,
        address receiver,
        address owner
    ) public virtual returns (uint256 shares) {
        shares = previewWithdraw(assets); // No need to check for rounding error, previewWithdraw rounds up.

        if (msg.sender != owner) {
            uint256 allowed = allowance[owner][msg.sender]; // Saves gas for limited approvals.

            if (allowed != type(uint256).max) allowance[owner][msg.sender] = allowed - shares;
        }

        beforeWithdraw(assets, shares);

        _burn(owner, shares);

        emit Withdraw(msg.sender, receiver, owner, assets, shares);

        asset.safeTransfer(receiver, assets);
    }

    function redeem(
        uint256 shares,
        address receiver,
        address owner
    ) public virtual returns (uint256 assets) {
        if (msg.sender != owner) {
            uint256 allowed = allowance[owner][msg.sender]; // Saves gas for limited approvals.

            if (allowed != type(uint256).max) allowance[owner][msg.sender] = allowed - shares;
        }

        // Check for rounding error since we round down in previewRedeem.
        require((assets = previewRedeem(shares)) != 0, "ZERO_ASSETS");

        beforeWithdraw(assets, shares);

        _burn(owner, shares);

        emit Withdraw(msg.sender, receiver, owner, assets, shares);

        asset.safeTransfer(receiver, assets);
    }

    /*//////////////////////////////////////////////////////////////
                            ACCOUNTING LOGIC
    //////////////////////////////////////////////////////////////*/

    function totalAssets() public view virtual returns (uint256);

    function convertToShares(uint256 assets) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? assets : assets.mulDivDown(supply, totalAssets());
    }

    function convertToAssets(uint256 shares) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? shares : shares.mulDivDown(totalAssets(), supply);
    }

    function previewDeposit(uint256 assets) public view virtual returns (uint256) {
        return convertToShares(assets);
    }

    function previewMint(uint256 shares) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? shares : shares.mulDivUp(totalAssets(), supply);
    }

    function previewWithdraw(uint256 assets) public view virtual returns (uint256) {
        uint256 supply = totalSupply; // Saves an extra SLOAD if totalSupply is non-zero.

        return supply == 0 ? assets : assets.mulDivUp(supply, totalAssets());
    }

    function previewRedeem(uint256 shares) public view virtual returns (uint256) {
        return convertToAssets(shares);
    }

    /*//////////////////////////////////////////////////////////////
                     DEPOSIT/WITHDRAWAL LIMIT LOGIC
    //////////////////////////////////////////////////////////////*/

    function maxDeposit(address) public view virtual returns (uint256) {
        return type(uint256).max;
    }

    function maxMint(address) public view virtual returns (uint256) {
        return type(uint256).max;
    }

    function maxWithdraw(address owner) public view virtual returns (uint256) {
        return convertToAssets(balanceOf[owner]);
    }

    function maxRedeem(address owner) public view virtual returns (uint256) {
        return balanceOf[owner];
    }

    /*//////////////////////////////////////////////////////////////
                          INTERNAL HOOKS LOGIC
    //////////////////////////////////////////////////////////////*/

    function beforeWithdraw(uint256 assets, uint256 shares) internal virtual {}

    function afterDeposit(uint256 assets, uint256 shares) internal virtual {}
}


This smart contract is an extension of the ERC20 standard. It allows users to deposit and withdraw assets, mint and redeem shares, and perform accounting calculations. It also includes hooks for additional logic before withdrawals and after deposits.

// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Modern and gas efficient ERC20 + EIP-2612 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC20.sol)
/// @author Modified from Uniswap (https://github.com/Uniswap/uniswap-v2-core/blob/master/contracts/UniswapV2ERC20.sol)
/// @dev Do not manually set balances without updating totalSupply, as the sum of all user balances must not exceed it.
abstract contract ERC20 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*//////////////////////////////////////////////////////////////
                            METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public name;

    string public symbol;

    uint8 public immutable decimals;

    /*//////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

    /*//////////////////////////////////////////////////////////////
                            EIP-2612 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 internal immutable INITIAL_CHAIN_ID;

    bytes32 internal immutable INITIAL_DOMAIN_SEPARATOR;

    mapping(address => uint256) public nonces;

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

    constructor(
        string memory _name,
        string memory _symbol,
        uint8 _decimals
    ) {
        name = _name;
        symbol = _symbol;
        decimals = _decimals;

        INITIAL_CHAIN_ID = block.chainid;
        INITIAL_DOMAIN_SEPARATOR = computeDomainSeparator();
    }

    /*//////////////////////////////////////////////////////////////
                               ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 amount) public virtual returns (bool) {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);

        return true;
    }

    function transfer(address to, uint256 amount) public virtual returns (bool) {
        balanceOf[msg.sender] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(msg.sender, to, amount);

        return true;
    }

    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual returns (bool) {
        uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.

        if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;

        balanceOf[from] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(from, to, amount);

        return true;
    }

    /*//////////////////////////////////////////////////////////////
                             EIP-2612 LOGIC
    //////////////////////////////////////////////////////////////*/

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual {
        require(deadline >= block.timestamp, "PERMIT_DEADLINE_EXPIRED");

        // Unchecked because the only math done is incrementing
        // the owner's nonce which cannot realistically overflow.
        unchecked {
            address recoveredAddress = ecrecover(
                keccak256(
                    abi.encodePacked(
                        "\x19\x01",
                        DOMAIN_SEPARATOR(),
                        keccak256(
                            abi.encode(
                                keccak256(
                                    "Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"
                                ),
                                owner,
                                spender,
                                value,
                                nonces[owner]++,
                                deadline
                            )
                        )
                    )
                ),
                v,
                r,
                s
            );

            require(recoveredAddress != address(0) && recoveredAddress == owner, "INVALID_SIGNER");

            allowance[recoveredAddress][spender] = value;
        }

        emit Approval(owner, spender, value);
    }

    function DOMAIN_SEPARATOR() public view virtual returns (bytes32) {
        return block.chainid == INITIAL_CHAIN_ID ? INITIAL_DOMAIN_SEPARATOR : computeDomainSeparator();
    }

    function computeDomainSeparator() internal view virtual returns (bytes32) {
        return
            keccak256(
                abi.encode(
                    keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                    keccak256(bytes(name)),
                    keccak256("1"),
                    block.chainid,
                    address(this)
                )
            );
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(address to, uint256 amount) internal virtual {
        totalSupply += amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(address(0), to, amount);
    }

    function _burn(address from, uint256 amount) internal virtual {
        balanceOf[from] -= amount;

        // Cannot underflow because a user's balance
        // will never be larger than the total supply.
        unchecked {
            totalSupply -= amount;
        }

        emit Transfer(from, address(0), amount);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../tokens/ERC20.sol";

/// @notice Safe ETH and ERC20 transfer library that gracefully handles missing return values.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeTransferLib.sol)
/// @dev Use with caution! Some functions in this library knowingly create dirty bits at the destination of the free memory pointer.
/// @dev Note that none of the functions in this library check that a token has code at all! That responsibility is delegated to the caller.
library SafeTransferLib {
    /*//////////////////////////////////////////////////////////////
                             ETH OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function safeTransferETH(address to, uint256 amount) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Transfer the ETH and store if it succeeded or not.
            success := call(gas(), to, amount, 0, 0, 0, 0)
        }

        require(success, "ETH_TRANSFER_FAILED");
    }

    /*//////////////////////////////////////////////////////////////
                            ERC20 OPERATIONS
    //////////////////////////////////////////////////////////////*/

    function safeTransferFrom(
        ERC20 token,
        address from,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0x23b872dd00000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(from, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "from" argument.
            mstore(add(freeMemoryPointer, 36), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 68), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 100 because the length of our calldata totals up like so: 4 + 32 * 3.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 100, 0, 32)
            )
        }

        require(success, "TRANSFER_FROM_FAILED");
    }

    function safeTransfer(
        ERC20 token,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0xa9059cbb00000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 68, 0, 32)
            )
        }

        require(success, "TRANSFER_FAILED");
    }

    function safeApprove(
        ERC20 token,
        address to,
        uint256 amount
    ) internal {
        bool success;

        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            let freeMemoryPointer := mload(0x40)

            // Write the abi-encoded calldata into memory, beginning with the function selector.
            mstore(freeMemoryPointer, 0x095ea7b300000000000000000000000000000000000000000000000000000000)
            mstore(add(freeMemoryPointer, 4), and(to, 0xffffffffffffffffffffffffffffffffffffffff)) // Append and mask the "to" argument.
            mstore(add(freeMemoryPointer, 36), amount) // Append the "amount" argument. Masking not required as it's a full 32 byte type.

            success := and(
                // Set success to whether the call reverted, if not we check it either
                // returned exactly 1 (can't just be non-zero data), or had no return data.
                or(and(eq(mload(0), 1), gt(returndatasize(), 31)), iszero(returndatasize())),
                // We use 68 because the length of our calldata totals up like so: 4 + 32 * 2.
                // We use 0 and 32 to copy up to 32 bytes of return data into the scratch space.
                // Counterintuitively, this call must be positioned second to the or() call in the
                // surrounding and() call or else returndatasize() will be zero during the computation.
                call(gas(), token, 0, freeMemoryPointer, 68, 0, 32)
            )
        }

        require(success, "APPROVE_FAILED");
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
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: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Provides a flexible and updatable auth pattern which is completely separate from application logic.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/Auth.sol)
/// @author Modified from Dappsys (https://github.com/dapphub/ds-auth/blob/master/src/auth.sol)
abstract contract Auth {
    event OwnershipTransferred(address indexed user, address indexed newOwner);

    event AuthorityUpdated(address indexed user, Authority indexed newAuthority);

    address public owner;

    Authority public authority;

    constructor(address _owner, Authority _authority) {
        owner = _owner;
        authority = _authority;

        emit OwnershipTransferred(msg.sender, _owner);
        emit AuthorityUpdated(msg.sender, _authority);
    }

    modifier requiresAuth() virtual {
        require(isAuthorized(msg.sender, msg.sig), "UNAUTHORIZED");

        _;
    }

    function isAuthorized(address user, bytes4 functionSig) internal view virtual returns (bool) {
        Authority auth = authority; // Memoizing authority saves us a warm SLOAD, around 100 gas.

        // Checking if the caller is the owner only after calling the authority saves gas in most cases, but be
        // aware that this makes protected functions uncallable even to the owner if the authority is out of order.
        return (address(auth) != address(0) && auth.canCall(user, address(this), functionSig)) || user == owner;
    }

    function setAuthority(Authority newAuthority) public virtual {
        // We check if the caller is the owner first because we want to ensure they can
        // always swap out the authority even if it's reverting or using up a lot of gas.
        require(msg.sender == owner || authority.canCall(msg.sender, address(this), msg.sig));

        authority = newAuthority;

        emit AuthorityUpdated(msg.sender, newAuthority);
    }

    function transferOwnership(address newOwner) public virtual requiresAuth {
        owner = newOwner;

        emit OwnershipTransferred(msg.sender, newOwner);
    }
}

/// @notice A generic interface for a contract which provides authorization data to an Auth instance.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/Auth.sol)
/// @author Modified from Dappsys (https://github.com/dapphub/ds-auth/blob/master/src/auth.sol)
interface Authority {
    function canCall(
        address user,
        address target,
        bytes4 functionSig
    ) external view returns (bool);
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Simple single owner authorization mixin.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/Owned.sol)
abstract contract Owned {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

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

    /*//////////////////////////////////////////////////////////////
                            OWNERSHIP STORAGE
    //////////////////////////////////////////////////////////////*/

    address public owner;

    modifier onlyOwner() virtual {
        require(msg.sender == owner, "UNAUTHORIZED");

        _;
    }

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

    constructor(address _owner) {
        owner = _owner;

        emit OwnershipTransferred(address(0), _owner);
    }

    /*//////////////////////////////////////////////////////////////
                             OWNERSHIP LOGIC
    //////////////////////////////////////////////////////////////*/

    function transferOwnership(address newOwner) public virtual onlyOwner {
        owner = newOwner;

        emit OwnershipTransferred(msg.sender, newOwner);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Auth, Authority} from "../Auth.sol";

/// @notice Flexible and target agnostic role based Authority that supports up to 256 roles.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/authorities/MultiRolesAuthority.sol)
contract MultiRolesAuthority is Auth, Authority {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event UserRoleUpdated(address indexed user, uint8 indexed role, bool enabled);

    event PublicCapabilityUpdated(bytes4 indexed functionSig, bool enabled);

    event RoleCapabilityUpdated(uint8 indexed role, bytes4 indexed functionSig, bool enabled);

    event TargetCustomAuthorityUpdated(address indexed target, Authority indexed authority);

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

    constructor(address _owner, Authority _authority) Auth(_owner, _authority) {}

    /*//////////////////////////////////////////////////////////////
                     CUSTOM TARGET AUTHORITY STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(address => Authority) public getTargetCustomAuthority;

    /*//////////////////////////////////////////////////////////////
                            ROLE/USER STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(address => bytes32) public getUserRoles;

    mapping(bytes4 => bool) public isCapabilityPublic;

    mapping(bytes4 => bytes32) public getRolesWithCapability;

    function doesUserHaveRole(address user, uint8 role) public view virtual returns (bool) {
        return (uint256(getUserRoles[user]) >> role) & 1 != 0;
    }

    function doesRoleHaveCapability(uint8 role, bytes4 functionSig) public view virtual returns (bool) {
        return (uint256(getRolesWithCapability[functionSig]) >> role) & 1 != 0;
    }

    /*//////////////////////////////////////////////////////////////
                           AUTHORIZATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function canCall(
        address user,
        address target,
        bytes4 functionSig
    ) public view virtual override returns (bool) {
        Authority customAuthority = getTargetCustomAuthority[target];

        if (address(customAuthority) != address(0)) return customAuthority.canCall(user, target, functionSig);

        return
            isCapabilityPublic[functionSig] || bytes32(0) != getUserRoles[user] & getRolesWithCapability[functionSig];
    }

    /*///////////////////////////////////////////////////////////////
               CUSTOM TARGET AUTHORITY CONFIGURATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function setTargetCustomAuthority(address target, Authority customAuthority) public virtual requiresAuth {
        getTargetCustomAuthority[target] = customAuthority;

        emit TargetCustomAuthorityUpdated(target, customAuthority);
    }

    /*//////////////////////////////////////////////////////////////
                  PUBLIC CAPABILITY CONFIGURATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function setPublicCapability(bytes4 functionSig, bool enabled) public virtual requiresAuth {
        isCapabilityPublic[functionSig] = enabled;

        emit PublicCapabilityUpdated(functionSig, enabled);
    }

    /*//////////////////////////////////////////////////////////////
                       USER ROLE ASSIGNMENT LOGIC
    //////////////////////////////////////////////////////////////*/

    function setUserRole(
        address user,
        uint8 role,
        bool enabled
    ) public virtual requiresAuth {
        if (enabled) {
            getUserRoles[user] |= bytes32(1 << role);
        } else {
            getUserRoles[user] &= ~bytes32(1 << role);
        }

        emit UserRoleUpdated(user, role, enabled);
    }

    /*//////////////////////////////////////////////////////////////
                   ROLE CAPABILITY CONFIGURATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function setRoleCapability(
        uint8 role,
        bytes4 functionSig,
        bool enabled
    ) public virtual requiresAuth {
        if (enabled) {
            getRolesWithCapability[functionSig] |= bytes32(1 << role);
        } else {
            getRolesWithCapability[functionSig] &= ~bytes32(1 << role);
        }

        emit RoleCapabilityUpdated(role, functionSig, enabled);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Auth, Authority} from "../Auth.sol";

/// @notice Role based Authority that supports up to 256 roles.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/auth/authorities/RolesAuthority.sol)
/// @author Modified from Dappsys (https://github.com/dapphub/ds-roles/blob/master/src/roles.sol)
contract RolesAuthority is Auth, Authority {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event UserRoleUpdated(address indexed user, uint8 indexed role, bool enabled);

    event PublicCapabilityUpdated(address indexed target, bytes4 indexed functionSig, bool enabled);

    event RoleCapabilityUpdated(uint8 indexed role, address indexed target, bytes4 indexed functionSig, bool enabled);

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

    constructor(address _owner, Authority _authority) Auth(_owner, _authority) {}

    /*//////////////////////////////////////////////////////////////
                            ROLE/USER STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(address => bytes32) public getUserRoles;

    mapping(address => mapping(bytes4 => bool)) public isCapabilityPublic;

    mapping(address => mapping(bytes4 => bytes32)) public getRolesWithCapability;

    function doesUserHaveRole(address user, uint8 role) public view virtual returns (bool) {
        return (uint256(getUserRoles[user]) >> role) & 1 != 0;
    }

    function doesRoleHaveCapability(
        uint8 role,
        address target,
        bytes4 functionSig
    ) public view virtual returns (bool) {
        return (uint256(getRolesWithCapability[target][functionSig]) >> role) & 1 != 0;
    }

    /*//////////////////////////////////////////////////////////////
                           AUTHORIZATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function canCall(
        address user,
        address target,
        bytes4 functionSig
    ) public view virtual override returns (bool) {
        return
            isCapabilityPublic[target][functionSig] ||
            bytes32(0) != getUserRoles[user] & getRolesWithCapability[target][functionSig];
    }

    /*//////////////////////////////////////////////////////////////
                   ROLE CAPABILITY CONFIGURATION LOGIC
    //////////////////////////////////////////////////////////////*/

    function setPublicCapability(
        address target,
        bytes4 functionSig,
        bool enabled
    ) public virtual requiresAuth {
        isCapabilityPublic[target][functionSig] = enabled;

        emit PublicCapabilityUpdated(target, functionSig, enabled);
    }

    function setRoleCapability(
        uint8 role,
        address target,
        bytes4 functionSig,
        bool enabled
    ) public virtual requiresAuth {
        if (enabled) {
            getRolesWithCapability[target][functionSig] |= bytes32(1 << role);
        } else {
            getRolesWithCapability[target][functionSig] &= ~bytes32(1 << role);
        }

        emit RoleCapabilityUpdated(role, target, functionSig, enabled);
    }

    /*//////////////////////////////////////////////////////////////
                       USER ROLE ASSIGNMENT LOGIC
    //////////////////////////////////////////////////////////////*/

    function setUserRole(
        address user,
        uint8 role,
        bool enabled
    ) public virtual requiresAuth {
        if (enabled) {
            getUserRoles[user] |= bytes32(1 << role);
        } else {
            getUserRoles[user] &= ~bytes32(1 << role);
        }

        emit UserRoleUpdated(user, role, enabled);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract DSInvariantTest {
    address[] private targets;

    function targetContracts() public view virtual returns (address[] memory) {
        require(targets.length > 0, "NO_TARGET_CONTRACTS");

        return targets;
    }

    function addTargetContract(address newTargetContract) internal virtual {
        targets.push(newTargetContract);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

interface Hevm {
    /// @notice Sets the block timestamp.
    function warp(uint256) external;

    /// @notice Sets the block height.
    function roll(uint256) external;

    /// @notice Sets the block base fee.
    function fee(uint256) external;

    /// @notice Loads a storage slot from an address.
    function load(address, bytes32) external returns (bytes32);

    /// @notice Stores a value to an address' storage slot.
    function store(
        address,
        bytes32,
        bytes32
    ) external;

    /// @notice Signs a digest with a private key, returns v r s.
    function sign(uint256, bytes32)
        external
        returns (
            uint8,
            bytes32,
            bytes32
        );

    /// @notice Gets address for a given private key.
    function addr(uint256) external returns (address);

    /// @notice Performs a foreign function call via a terminal call.
    function ffi(string[] calldata) external returns (bytes memory);

    /// @notice Sets the next call's msg.sender to be the input address.
    function prank(address) external;

    /// @notice Sets all subsequent calls' msg.sender to be the input address until stopPrank is called.
    function startPrank(address) external;

    /// @notice Sets the next call's msg.sender to be the input address and the tx.origin to be the second input.
    function prank(address, address) external;

    /// @notice Sets all subsequent calls' msg.sender to be the input address and
    /// sets tx.origin to be the second address inputted until stopPrank is called.
    function startPrank(address, address) external;

    /// @notice Resets msg.sender to its original value before a prank.
    function stopPrank() external;

    /// @notice Sets an address' balance.
    function deal(address, uint256) external;

    /// @notice Sets an address' code.
    function etch(address, bytes calldata) external;

    /// @notice Expects an error from the next call.
    function expectRevert(bytes calldata) external;

    /// @notice Expects a revert from the next call.
    function expectRevert(bytes4) external;

    /// @notice Record all storage reads and writes.
    function record() external;

    /// @notice Gets all accessed reads and write slots from a recording session, for a given address.
    function accesses(address) external returns (bytes32[] memory reads, bytes32[] memory writes);

    /// @notice Prepare an expected log with (bool checkTopic1, bool checkTopic2, bool checkTopic3, bool checkData).
    /// @notice Call this function, then emit an event, then call a function. Internally after the call, we check
    /// if logs were emitted in the expected order with the expected topics and data as specified by the booleans.
    function expectEmit(
        bool,
        bool,
        bool,
        bool
    ) external;

    /// @notice Mocks the behavior of a contract call, setting the input and output for a function.
    /// @notice Calldata can either be strict or a partial match, e.g. if only passed
    /// a selector to the expected calldata, then the entire function will be mocked.
    function mockCall(
        address,
        bytes calldata,
        bytes calldata
    ) external;

    /// @notice Clears all mocked calls.
    function clearMockedCalls() external;

    /// @notice Expect a call to an address with the specified calldata.
    /// @notice Calldata can either be strict or a partial match.
    function expectCall(address, bytes calldata) external;

    /// @notice Fetches the contract bytecode from its artifact file.
    function getCode(string calldata) external returns (bytes memory);

    /// @notice Label an address in test traces.
    function label(address addr, string calldata label) external;

    /// @notice When fuzzing, generate new inputs if the input conditional is not met.
    function assume(bool) external;
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Auth, Authority} from "../../../auth/Auth.sol";

contract MockAuthChild is Auth(msg.sender, Authority(address(0))) {
    bool public flag;

    function updateFlag() public virtual requiresAuth {
        flag = true;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Authority} from "../../../auth/Auth.sol";

contract MockAuthority is Authority {
    bool immutable allowCalls;

    constructor(bool _allowCalls) {
        allowCalls = _allowCalls;
    }

    function canCall(
        address,
        address,
        bytes4
    ) public view override returns (bool) {
        return allowCalls;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC1155} from "../../../tokens/ERC1155.sol";

contract MockERC1155 is ERC1155 {
    function uri(uint256) public pure virtual override returns (string memory) {}

    function mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public virtual {
        _mint(to, id, amount, data);
    }

    function batchMint(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual {
        _batchMint(to, ids, amounts, data);
    }

    function burn(
        address from,
        uint256 id,
        uint256 amount
    ) public virtual {
        _burn(from, id, amount);
    }

    function batchBurn(
        address from,
        uint256[] memory ids,
        uint256[] memory amounts
    ) public virtual {
        _batchBurn(from, ids, amounts);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../../../tokens/ERC20.sol";

contract MockERC20 is ERC20 {
    constructor(
        string memory _name,
        string memory _symbol,
        uint8 _decimals
    ) ERC20(_name, _symbol, _decimals) {}

    function mint(address to, uint256 value) public virtual {
        _mint(to, value);
    }

    function burn(address from, uint256 value) public virtual {
        _burn(from, value);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC20} from "../../../tokens/ERC20.sol";
import {ERC4626} from "../../../mixins/ERC4626.sol";

contract MockERC4626 is ERC4626 {
    uint256 public beforeWithdrawHookCalledCounter = 0;
    uint256 public afterDepositHookCalledCounter = 0;

    constructor(
        ERC20 _underlying,
        string memory _name,
        string memory _symbol
    ) ERC4626(_underlying, _name, _symbol) {}

    function totalAssets() public view override returns (uint256) {
        return asset.balanceOf(address(this));
    }

    function beforeWithdraw(uint256, uint256) internal override {
        beforeWithdrawHookCalledCounter++;
    }

    function afterDeposit(uint256, uint256) internal override {
        afterDepositHookCalledCounter++;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {ERC721} from "../../../tokens/ERC721.sol";

contract MockERC721 is ERC721 {
    constructor(string memory _name, string memory _symbol) ERC721(_name, _symbol) {}

    function tokenURI(uint256) public pure virtual override returns (string memory) {}

    function mint(address to, uint256 tokenId) public virtual {
        _mint(to, tokenId);
    }

    function burn(uint256 tokenId) public virtual {
        _burn(tokenId);
    }

    function safeMint(address to, uint256 tokenId) public virtual {
        _safeMint(to, tokenId);
    }

    function safeMint(
        address to,
        uint256 tokenId,
        bytes memory data
    ) public virtual {
        _safeMint(to, tokenId, data);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Owned} from "../../../auth/Owned.sol";

contract MockOwned is Owned(msg.sender) {
    bool public flag;

    function updateFlag() public virtual onlyOwner {
        flag = true;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract MissingReturnToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "MissingReturnToken";

    string public constant symbol = "MRT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 amount) public virtual {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);
    }

    function transfer(address to, uint256 amount) public virtual {
        balanceOf[msg.sender] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(msg.sender, to, amount);
    }

    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual {
        uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.

        if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;

        balanceOf[from] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(from, to, amount);
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract ReturnsFalseToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "ReturnsFalseToken";

    string public constant symbol = "RFT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address, uint256) public virtual returns (bool) {
        return false;
    }

    function transfer(address, uint256) public virtual returns (bool) {
        return false;
    }

    function transferFrom(
        address,
        address,
        uint256
    ) public virtual returns (bool) {
        return false;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract ReturnsGarbageToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "ReturnsGarbageToken";

    string public constant symbol = "RGT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

    /*///////////////////////////////////////////////////////////////
                              MOCK STORAGE
    //////////////////////////////////////////////////////////////*/

    bytes garbage;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 amount) public virtual {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);

        bytes memory _garbage = garbage;

        assembly {
            return(add(_garbage, 32), mload(_garbage))
        }
    }

    function transfer(address to, uint256 amount) public virtual {
        balanceOf[msg.sender] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(msg.sender, to, amount);

        bytes memory _garbage = garbage;

        assembly {
            return(add(_garbage, 32), mload(_garbage))
        }
    }

    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual {
        uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.

        if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;

        balanceOf[from] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(from, to, amount);

        bytes memory _garbage = garbage;

        assembly {
            return(add(_garbage, 32), mload(_garbage))
        }
    }

    /*///////////////////////////////////////////////////////////////
                              MOCK LOGIC
    //////////////////////////////////////////////////////////////*/

    function setGarbage(bytes memory _garbage) public virtual {
        garbage = _garbage;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract ReturnsTooLittleToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "ReturnsTooLittleToken";

    string public constant symbol = "RTLT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address, uint256) public virtual {
        assembly {
            mstore(0, 0x0100000000000000000000000000000000000000000000000000000000000000)
            return(0, 8)
        }
    }

    function transfer(address, uint256) public virtual {
        assembly {
            mstore(0, 0x0100000000000000000000000000000000000000000000000000000000000000)
            return(0, 8)
        }
    }

    function transferFrom(
        address,
        address,
        uint256
    ) public virtual {
        assembly {
            mstore(0, 0x0100000000000000000000000000000000000000000000000000000000000000)
            return(0, 8)
        }
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract ReturnsTooMuchToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "ReturnsTooMuchToken";

    string public constant symbol = "RTMT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 amount) public virtual {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);

        assembly {
            mstore(0, 1)
            return(0, 4096)
        }
    }

    function transfer(address to, uint256 amount) public virtual {
        balanceOf[msg.sender] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(msg.sender, to, amount);

        assembly {
            mstore(0, 1)
            return(0, 4096)
        }
    }

    function transferFrom(
        address from,
        address to,
        uint256 amount
    ) public virtual {
        uint256 allowed = allowance[from][msg.sender]; // Saves gas for limited approvals.

        if (allowed != type(uint256).max) allowance[from][msg.sender] = allowed - amount;

        balanceOf[from] -= amount;

        // Cannot overflow because the sum of all user
        // balances can't exceed the max uint256 value.
        unchecked {
            balanceOf[to] += amount;
        }

        emit Transfer(from, to, amount);

        assembly {
            mstore(0, 1)
            return(0, 4096)
        }
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract ReturnsTwoToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "ReturnsFalseToken";

    string public constant symbol = "RTT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address, uint256) public virtual returns (uint256) {
        return 2;
    }

    function transfer(address, uint256) public virtual returns (uint256) {
        return 2;
    }

    function transferFrom(
        address,
        address,
        uint256
    ) public virtual returns (uint256) {
        return 2;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

contract RevertingToken {
    /*///////////////////////////////////////////////////////////////
                                  EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 amount);

    event Approval(address indexed owner, address indexed spender, uint256 amount);

    /*///////////////////////////////////////////////////////////////
                             METADATA STORAGE
    //////////////////////////////////////////////////////////////*/

    string public constant name = "RevertingToken";

    string public constant symbol = "RT";

    uint8 public constant decimals = 18;

    /*///////////////////////////////////////////////////////////////
                              ERC20 STORAGE
    //////////////////////////////////////////////////////////////*/

    uint256 public totalSupply;

    mapping(address => uint256) public balanceOf;

    mapping(address => mapping(address => uint256)) public allowance;

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

    constructor() {
        totalSupply = type(uint256).max;
        balanceOf[msg.sender] = type(uint256).max;
    }

    /*///////////////////////////////////////////////////////////////
                              ERC20 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address, uint256) public virtual {
        revert();
    }

    function transfer(address, uint256) public virtual {
        revert();
    }

    function transferFrom(
        address,
        address,
        uint256
    ) public virtual {
        revert();
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Minimalist and gas efficient standard ERC1155 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC1155.sol)
abstract contract ERC1155 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event TransferSingle(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256 id,
        uint256 amount
    );

    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] amounts
    );

    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    event URI(string value, uint256 indexed id);

    /*//////////////////////////////////////////////////////////////
                             ERC1155 STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(address => mapping(uint256 => uint256)) public balanceOf;

    mapping(address => mapping(address => bool)) public isApprovedForAll;

    /*//////////////////////////////////////////////////////////////
                             METADATA LOGIC
    //////////////////////////////////////////////////////////////*/

    function uri(uint256 id) public view virtual returns (string memory);

    /*//////////////////////////////////////////////////////////////
                              ERC1155 LOGIC
    //////////////////////////////////////////////////////////////*/

    function setApprovalForAll(address operator, bool approved) public virtual {
        isApprovedForAll[msg.sender][operator] = approved;

        emit ApprovalForAll(msg.sender, operator, approved);
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes calldata data
    ) public virtual {
        require(msg.sender == from || isApprovedForAll[from][msg.sender], "NOT_AUTHORIZED");

        balanceOf[from][id] -= amount;
        balanceOf[to][id] += amount;

        emit TransferSingle(msg.sender, from, to, id, amount);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155Received(msg.sender, from, id, amount, data) ==
                    ERC1155TokenReceiver.onERC1155Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata amounts,
        bytes calldata data
    ) public virtual {
        require(ids.length == amounts.length, "LENGTH_MISMATCH");

        require(msg.sender == from || isApprovedForAll[from][msg.sender], "NOT_AUTHORIZED");

        // Storing these outside the loop saves ~15 gas per iteration.
        uint256 id;
        uint256 amount;

        for (uint256 i = 0; i < ids.length; ) {
            id = ids[i];
            amount = amounts[i];

            balanceOf[from][id] -= amount;
            balanceOf[to][id] += amount;

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, from, to, ids, amounts);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155BatchReceived(msg.sender, from, ids, amounts, data) ==
                    ERC1155TokenReceiver.onERC1155BatchReceived.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function balanceOfBatch(address[] calldata owners, uint256[] calldata ids)
        public
        view
        virtual
        returns (uint256[] memory balances)
    {
        require(owners.length == ids.length, "LENGTH_MISMATCH");

        balances = new uint256[](owners.length);

        // Unchecked because the only math done is incrementing
        // the array index counter which cannot possibly overflow.
        unchecked {
            for (uint256 i = 0; i < owners.length; ++i) {
                balances[i] = balanceOf[owners[i]][ids[i]];
            }
        }
    }

    /*//////////////////////////////////////////////////////////////
                              ERC165 LOGIC
    //////////////////////////////////////////////////////////////*/

    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return
            interfaceId == 0x01ffc9a7 || // ERC165 Interface ID for ERC165
            interfaceId == 0xd9b67a26 || // ERC165 Interface ID for ERC1155
            interfaceId == 0x0e89341c; // ERC165 Interface ID for ERC1155MetadataURI
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        balanceOf[to][id] += amount;

        emit TransferSingle(msg.sender, address(0), to, id, amount);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155Received(msg.sender, address(0), id, amount, data) ==
                    ERC1155TokenReceiver.onERC1155Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _batchMint(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        uint256 idsLength = ids.length; // Saves MLOADs.

        require(idsLength == amounts.length, "LENGTH_MISMATCH");

        for (uint256 i = 0; i < idsLength; ) {
            balanceOf[to][ids[i]] += amounts[i];

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, address(0), to, ids, amounts);

        require(
            to.code.length == 0
                ? to != address(0)
                : ERC1155TokenReceiver(to).onERC1155BatchReceived(msg.sender, address(0), ids, amounts, data) ==
                    ERC1155TokenReceiver.onERC1155BatchReceived.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _batchBurn(
        address from,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual {
        uint256 idsLength = ids.length; // Saves MLOADs.

        require(idsLength == amounts.length, "LENGTH_MISMATCH");

        for (uint256 i = 0; i < idsLength; ) {
            balanceOf[from][ids[i]] -= amounts[i];

            // An array can't have a total length
            // larger than the max uint256 value.
            unchecked {
                ++i;
            }
        }

        emit TransferBatch(msg.sender, from, address(0), ids, amounts);
    }

    function _burn(
        address from,
        uint256 id,
        uint256 amount
    ) internal virtual {
        balanceOf[from][id] -= amount;

        emit TransferSingle(msg.sender, from, address(0), id, amount);
    }
}

/// @notice A generic interface for a contract which properly accepts ERC1155 tokens.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC1155.sol)
abstract contract ERC1155TokenReceiver {
    function onERC1155Received(
        address,
        address,
        uint256,
        uint256,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155Received.selector;
    }

    function onERC1155BatchReceived(
        address,
        address,
        uint256[] calldata,
        uint256[] calldata,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC1155TokenReceiver.onERC1155BatchReceived.selector;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Modern, minimalist, and gas efficient ERC-721 implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721 {
    /*//////////////////////////////////////////////////////////////
                                 EVENTS
    //////////////////////////////////////////////////////////////*/

    event Transfer(address indexed from, address indexed to, uint256 indexed id);

    event Approval(address indexed owner, address indexed spender, uint256 indexed id);

    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /*//////////////////////////////////////////////////////////////
                         METADATA STORAGE/LOGIC
    //////////////////////////////////////////////////////////////*/

    string public name;

    string public symbol;

    function tokenURI(uint256 id) public view virtual returns (string memory);

    /*//////////////////////////////////////////////////////////////
                      ERC721 BALANCE/OWNER STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(uint256 => address) internal _ownerOf;

    mapping(address => uint256) internal _balanceOf;

    function ownerOf(uint256 id) public view virtual returns (address owner) {
        require((owner = _ownerOf[id]) != address(0), "NOT_MINTED");
    }

    function balanceOf(address owner) public view virtual returns (uint256) {
        require(owner != address(0), "ZERO_ADDRESS");

        return _balanceOf[owner];
    }

    /*//////////////////////////////////////////////////////////////
                         ERC721 APPROVAL STORAGE
    //////////////////////////////////////////////////////////////*/

    mapping(uint256 => address) public getApproved;

    mapping(address => mapping(address => bool)) public isApprovedForAll;

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

    constructor(string memory _name, string memory _symbol) {
        name = _name;
        symbol = _symbol;
    }

    /*//////////////////////////////////////////////////////////////
                              ERC721 LOGIC
    //////////////////////////////////////////////////////////////*/

    function approve(address spender, uint256 id) public virtual {
        address owner = _ownerOf[id];

        require(msg.sender == owner || isApprovedForAll[owner][msg.sender], "NOT_AUTHORIZED");

        getApproved[id] = spender;

        emit Approval(owner, spender, id);
    }

    function setApprovalForAll(address operator, bool approved) public virtual {
        isApprovedForAll[msg.sender][operator] = approved;

        emit ApprovalForAll(msg.sender, operator, approved);
    }

    function transferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        require(from == _ownerOf[id], "WRONG_FROM");

        require(to != address(0), "INVALID_RECIPIENT");

        require(
            msg.sender == from || isApprovedForAll[from][msg.sender] || msg.sender == getApproved[id],
            "NOT_AUTHORIZED"
        );

        // Underflow of the sender's balance is impossible because we check for
        // ownership above and the recipient's balance can't realistically overflow.
        unchecked {
            _balanceOf[from]--;

            _balanceOf[to]++;
        }

        _ownerOf[id] = to;

        delete getApproved[id];

        emit Transfer(from, to, id);
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id
    ) public virtual {
        transferFrom(from, to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        bytes calldata data
    ) public virtual {
        transferFrom(from, to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, from, id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    /*//////////////////////////////////////////////////////////////
                              ERC165 LOGIC
    //////////////////////////////////////////////////////////////*/

    function supportsInterface(bytes4 interfaceId) public view virtual returns (bool) {
        return
            interfaceId == 0x01ffc9a7 || // ERC165 Interface ID for ERC165
            interfaceId == 0x80ac58cd || // ERC165 Interface ID for ERC721
            interfaceId == 0x5b5e139f; // ERC165 Interface ID for ERC721Metadata
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL MINT/BURN LOGIC
    //////////////////////////////////////////////////////////////*/

    function _mint(address to, uint256 id) internal virtual {
        require(to != address(0), "INVALID_RECIPIENT");

        require(_ownerOf[id] == address(0), "ALREADY_MINTED");

        // Counter overflow is incredibly unrealistic.
        unchecked {
            _balanceOf[to]++;
        }

        _ownerOf[id] = to;

        emit Transfer(address(0), to, id);
    }

    function _burn(uint256 id) internal virtual {
        address owner = _ownerOf[id];

        require(owner != address(0), "NOT_MINTED");

        // Ownership check above ensures no underflow.
        unchecked {
            _balanceOf[owner]--;
        }

        delete _ownerOf[id];

        delete getApproved[id];

        emit Transfer(owner, address(0), id);
    }

    /*//////////////////////////////////////////////////////////////
                        INTERNAL SAFE MINT LOGIC
    //////////////////////////////////////////////////////////////*/

    function _safeMint(address to, uint256 id) internal virtual {
        _mint(to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, "") ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }

    function _safeMint(
        address to,
        uint256 id,
        bytes memory data
    ) internal virtual {
        _mint(to, id);

        require(
            to.code.length == 0 ||
                ERC721TokenReceiver(to).onERC721Received(msg.sender, address(0), id, data) ==
                ERC721TokenReceiver.onERC721Received.selector,
            "UNSAFE_RECIPIENT"
        );
    }
}

/// @notice A generic interface for a contract which properly accepts ERC721 tokens.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/ERC721.sol)
abstract contract ERC721TokenReceiver {
    function onERC721Received(
        address,
        address,
        uint256,
        bytes calldata
    ) external virtual returns (bytes4) {
        return ERC721TokenReceiver.onERC721Received.selector;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

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

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

/// @notice Minimalist and modern Wrapped Ether implementation.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/tokens/WETH.sol)
/// @author Inspired by WETH9 (https://github.com/dapphub/ds-weth/blob/master/src/weth9.sol)
contract WETH is ERC20("Wrapped Ether", "WETH", 18) {
    using SafeTransferLib for address;

    event Deposit(address indexed from, uint256 amount);

    event Withdrawal(address indexed to, uint256 amount);

    function deposit() public payable virtual {
        _mint(msg.sender, msg.value);

        emit Deposit(msg.sender, msg.value);
    }

    function withdraw(uint256 amount) public virtual {
        _burn(msg.sender, amount);

        emit Withdrawal(msg.sender, amount);

        msg.sender.safeTransferETH(amount);
    }

    receive() external payable virtual {
        deposit();
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Library for converting between addresses and bytes32 values.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/Bytes32AddressLib.sol)
library Bytes32AddressLib {
    function fromLast20Bytes(bytes32 bytesValue) internal pure returns (address) {
        return address(uint160(uint256(bytesValue)));
    }

    function fillLast12Bytes(address addressValue) internal pure returns (bytes32) {
        return bytes32(bytes20(addressValue));
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

import {Bytes32AddressLib} from "./Bytes32AddressLib.sol";

/// @notice Deploy to deterministic addresses without an initcode factor.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/CREATE3.sol)
/// @author Modified from 0xSequence (https://github.com/0xSequence/create3/blob/master/contracts/Create3.sol)
library CREATE3 {
    using Bytes32AddressLib for bytes32;

    //--------------------------------------------------------------------------------//
    // Opcode     | Opcode + Arguments    | Description      | Stack View             //
    //--------------------------------------------------------------------------------//
    // 0x36       |  0x36                 | CALLDATASIZE     | size                   //
    // 0x3d       |  0x3d                 | RETURNDATASIZE   | 0 size                 //
    // 0x3d       |  0x3d                 | RETURNDATASIZE   | 0 0 size               //
    // 0x37       |  0x37                 | CALLDATACOPY     |                        //
    // 0x36       |  0x36                 | CALLDATASIZE     | size                   //
    // 0x3d       |  0x3d                 | RETURNDATASIZE   | 0 size                 //
    // 0x34       |  0x34                 | CALLVALUE        | value 0 size           //
    // 0xf0       |  0xf0                 | CREATE           | newContract            //
    //--------------------------------------------------------------------------------//
    // Opcode     | Opcode + Arguments    | Description      | Stack View             //
    //--------------------------------------------------------------------------------//
    // 0x67       |  0x67XXXXXXXXXXXXXXXX | PUSH8 bytecode   | bytecode               //
    // 0x3d       |  0x3d                 | RETURNDATASIZE   | 0 bytecode             //
    // 0x52       |  0x52                 | MSTORE           |                        //
    // 0x60       |  0x6008               | PUSH1 08         | 8                      //
    // 0x60       |  0x6018               | PUSH1 18         | 24 8                   //
    // 0xf3       |  0xf3                 | RETURN           |                        //
    //--------------------------------------------------------------------------------//
    bytes internal constant PROXY_BYTECODE = hex"67_36_3d_3d_37_36_3d_34_f0_3d_52_60_08_60_18_f3";

    bytes32 internal constant PROXY_BYTECODE_HASH = keccak256(PROXY_BYTECODE);

    function deploy(
        bytes32 salt,
        bytes memory creationCode,
        uint256 value
    ) internal returns (address deployed) {
        bytes memory proxyChildBytecode = PROXY_BYTECODE;

        address proxy;
        /// @solidity memory-safe-assembly
        assembly {
            // Deploy a new contract with our pre-made bytecode via CREATE2.
            // We start 32 bytes into the code to avoid copying the byte length.
            proxy := create2(0, add(proxyChildBytecode, 32), mload(proxyChildBytecode), salt)
        }
        require(proxy != address(0), "DEPLOYMENT_FAILED");

        deployed = getDeployed(salt);
        (bool success, ) = proxy.call{value: value}(creationCode);
        require(success && deployed.code.length != 0, "INITIALIZATION_FAILED");
    }

    function getDeployed(bytes32 salt) internal view returns (address) {
        address proxy = keccak256(
            abi.encodePacked(
                // Prefix:
                bytes1(0xFF),
                // Creator:
                address(this),
                // Salt:
                salt,
                // Bytecode hash:
                PROXY_BYTECODE_HASH
            )
        ).fromLast20Bytes();

        return
            keccak256(
                abi.encodePacked(
                    // 0xd6 = 0xc0 (short RLP prefix) + 0x16 (length of: 0x94 ++ proxy ++ 0x01)
                    // 0x94 = 0x80 + 0x14 (0x14 = the length of an address, 20 bytes, in hex)
                    hex"d6_94",
                    proxy,
                    hex"01" // Nonce of the proxy contract (1)
                )
            ).fromLast20Bytes();
    }
}


// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/// @notice Efficient library for creating string representations of integers.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/LibString.sol)
/// @author Modified from Solady (https://github.com/Vectorized/solady/blob/main/src/utils/LibString.sol)
library LibString {
    function toString(int256 value) internal pure returns (string memory str) {
        if (value >= 0) return toString(uint256(value));

        unchecked {
            str = toString(uint256(-value));

            /// @solidity memory-safe-assembly
            assembly {
                // Note: This is only safe because we over-allocate memory
                // and write the string from right to left in toString(uint256),
                // and thus can be sure that sub(str, 1) is an unused memory location.

                let length := mload(str) // Load the string length.
                // Put the - character at the start of the string contents.
                mstore(str, 45) // 45 is the ASCII code for the - character.
                str := sub(str, 1) // Move back the string pointer by a byte.
                mstore(str, add(length, 1)) // Update the string length.
            }
        }
    }

    function toString(uint256 value) internal pure returns (string memory str) {
        /// @solidity memory-safe-assembly
        assembly {
            // The maximum value of a uint256 contains 78 digits (1 byte per digit), but we allocate 160 bytes
            // to keep the free memory pointer word aligned. We'll need 1 word for the length, 1 word for the
            // trailing zeros padding, and 3 other words for a max of 78 digits. In total: 5 * 32 = 160 bytes.
            let newFreeMemoryPointer := add(mload(0x40), 160)

            // Update the free memory pointer to avoid overriding our string.
            mstore(0x40, newFreeMemoryPointer)

            // Assign str to the end of the zone of newly allocated memory.
            str := sub(newFreeMemoryPointer, 32)

            // Clean the last word of memory it may not be overwritten.
            mstore(str, 0)

            // Cache the end of the memory to calculate the length later.
            let end := str

            // We write the string from rightmost digit to leftmost digit.
            // The following is essentially a do-while loop that also handles the zero case.
            // prettier-ignore
            for { let temp := value } 1 {} {
                // Move the pointer 1 byte to the left.
                str := sub(str, 1)

                // Write the character to the pointer.
                // The ASCII index of the '0' character is 48.
                mstore8(str, add(48, mod(temp, 10)))

                // Keep dividing temp until zero.
                temp := div(temp, 10)

                 // prettier-ignore
                if iszero(temp) { break }
            }

            // Compute and cache the final total length of the string.
            let length := sub(end, str)

            // Move the pointer 32 bytes leftwards to make room for the length.
            str := sub(str, 32)

            // Store the string's length at the start of memory allocated for our string.
            mstore(str, length)
        }
    }
}


// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/// @notice Gas optimized merkle proof verification library.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/MerkleProofLib.sol)
/// @author Modified from Solady (https://github.com/Vectorized/solady/blob/main/src/utils/MerkleProofLib.sol)
library MerkleProofLib {
    function verify(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool isValid) {
        /// @solidity memory-safe-assembly
        assembly {
            if proof.length {
                // Left shifting by 5 is like multiplying by 32.
                let end := add(proof.offset, shl(5, proof.length))

                // Initialize offset to the offset of the proof in calldata.
                let offset := proof.offset

                // Iterate over proof elements to compute root hash.
                // prettier-ignore
                for {} 1 {} {
                    // Slot where the leaf should be put in scratch space. If
                    // leaf > calldataload(offset): slot 32, otherwise: slot 0.
                    let leafSlot := shl(5, gt(leaf, calldataload(offset)))

                    // Store elements to hash contiguously in scratch space.
                    // The xor puts calldataload(offset) in whichever slot leaf
                    // is not occupying, so 0 if leafSlot is 32, and 32 otherwise.
                    mstore(leafSlot, leaf)
                    mstore(xor(leafSlot, 32), calldataload(offset))

                    // Reuse leaf to store the hash to reduce stack operations.
                    leaf := keccak256(0, 64) // Hash both slots of scratch space.

                    offset := add(offset, 32) // Shift 1 word per cycle.

                    // prettier-ignore
                    if iszero(lt(offset, end)) { break }
                }
            }

            isValid := eq(leaf, root) // The proof is valid if the roots match.
        }
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Gas optimized reentrancy protection for smart contracts.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/ReentrancyGuard.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/security/ReentrancyGuard.sol)
abstract contract ReentrancyGuard {
    uint256 private locked = 1;

    modifier nonReentrant() virtual {
        require(locked == 1, "REENTRANCY");

        locked = 2;

        _;

        locked = 1;
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Read and write to persistent storage at a fraction of the cost.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SSTORE2.sol)
/// @author Modified from 0xSequence (https://github.com/0xSequence/sstore2/blob/master/contracts/SSTORE2.sol)
library SSTORE2 {
    uint256 internal constant DATA_OFFSET = 1; // We skip the first byte as it's a STOP opcode to ensure the contract can't be called.

    /*//////////////////////////////////////////////////////////////
                               WRITE LOGIC
    //////////////////////////////////////////////////////////////*/

    function write(bytes memory data) internal returns (address pointer) {
        // Prefix the bytecode with a STOP opcode to ensure it cannot be called.
        bytes memory runtimeCode = abi.encodePacked(hex"00", data);

        bytes memory creationCode = abi.encodePacked(
            //---------------------------------------------------------------------------------------------------------------//
            // Opcode  | Opcode + Arguments  | Description  | Stack View                                                     //
            //---------------------------------------------------------------------------------------------------------------//
            // 0x60    |  0x600B             | PUSH1 11     | codeOffset                                                     //
            // 0x59    |  0x59               | MSIZE        | 0 codeOffset                                                   //
            // 0x81    |  0x81               | DUP2         | codeOffset 0 codeOffset                                        //
            // 0x38    |  0x38               | CODESIZE     | codeSize codeOffset 0 codeOffset                               //
            // 0x03    |  0x03               | SUB          | (codeSize - codeOffset) 0 codeOffset                           //
            // 0x80    |  0x80               | DUP          | (codeSize - codeOffset) (codeSize - codeOffset) 0 codeOffset   //
            // 0x92    |  0x92               | SWAP3        | codeOffset (codeSize - codeOffset) 0 (codeSize - codeOffset)   //
            // 0x59    |  0x59               | MSIZE        | 0 codeOffset (codeSize - codeOffset) 0 (codeSize - codeOffset) //
            // 0x39    |  0x39               | CODECOPY     | 0 (codeSize - codeOffset)                                      //
            // 0xf3    |  0xf3               | RETURN       |                                                                //
            //---------------------------------------------------------------------------------------------------------------//
            hex"60_0B_59_81_38_03_80_92_59_39_F3", // Returns all code in the contract except for the first 11 (0B in hex) bytes.
            runtimeCode // The bytecode we want the contract to have after deployment. Capped at 1 byte less than the code size limit.
        );

        /// @solidity memory-safe-assembly
        assembly {
            // Deploy a new contract with the generated creation code.
            // We start 32 bytes into the code to avoid copying the byte length.
            pointer := create(0, add(creationCode, 32), mload(creationCode))
        }

        require(pointer != address(0), "DEPLOYMENT_FAILED");
    }

    /*//////////////////////////////////////////////////////////////
                               READ LOGIC
    //////////////////////////////////////////////////////////////*/

    function read(address pointer) internal view returns (bytes memory) {
        return readBytecode(pointer, DATA_OFFSET, pointer.code.length - DATA_OFFSET);
    }

    function read(address pointer, uint256 start) internal view returns (bytes memory) {
        start += DATA_OFFSET;

        return readBytecode(pointer, start, pointer.code.length - start);
    }

    function read(
        address pointer,
        uint256 start,
        uint256 end
    ) internal view returns (bytes memory) {
        start += DATA_OFFSET;
        end += DATA_OFFSET;

        require(pointer.code.length >= end, "OUT_OF_BOUNDS");

        return readBytecode(pointer, start, end - start);
    }

    /*//////////////////////////////////////////////////////////////
                          INTERNAL HELPER LOGIC
    //////////////////////////////////////////////////////////////*/

    function readBytecode(
        address pointer,
        uint256 start,
        uint256 size
    ) private view returns (bytes memory data) {
        /// @solidity memory-safe-assembly
        assembly {
            // Get a pointer to some free memory.
            data := mload(0x40)

            // Update the free memory pointer to prevent overriding our data.
            // We use and(x, not(31)) as a cheaper equivalent to sub(x, mod(x, 32)).
            // Adding 31 to size and running the result through the logic above ensures
            // the memory pointer remains word-aligned, following the Solidity convention.
            mstore(0x40, add(data, and(add(add(size, 32), 31), not(31))))

            // Store the size of the data in the first 32 byte chunk of free memory.
            mstore(data, size)

            // Copy the code into memory right after the 32 bytes we used to store the size.
            extcodecopy(pointer, add(data, 32), start, size)
        }
    }
}


// SPDX-License-Identifier: AGPL-3.0-only
pragma solidity >=0.8.0;

/// @notice Safe unsigned integer casting library that reverts on overflow.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SafeCastLib.sol)
/// @author Modified from OpenZeppelin (https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/math/SafeCast.sol)
library SafeCastLib {
    function safeCastTo248(uint256 x) internal pure returns (uint248 y) {
        require(x < 1 << 248);

        y = uint248(x);
    }

    function safeCastTo240(uint256 x) internal pure returns (uint240 y) {
        require(x < 1 << 240);

        y = uint240(x);
    }

    function safeCastTo232(uint256 x) internal pure returns (uint232 y) {
        require(x < 1 << 232);

        y = uint232(x);
    }

    function safeCastTo224(uint256 x) internal pure returns (uint224 y) {
        require(x < 1 << 224);

        y = uint224(x);
    }

    function safeCastTo216(uint256 x) internal pure returns (uint216 y) {
        require(x < 1 << 216);

        y = uint216(x);
    }

    function safeCastTo208(uint256 x) internal pure returns (uint208 y) {
        require(x < 1 << 208);

        y = uint208(x);
    }

    function safeCastTo200(uint256 x) internal pure returns (uint200 y) {
        require(x < 1 << 200);

        y = uint200(x);
    }

    function safeCastTo192(uint256 x) internal pure returns (uint192 y) {
        require(x < 1 << 192);

        y = uint192(x);
    }

    function safeCastTo184(uint256 x) internal pure returns (uint184 y) {
        require(x < 1 << 184);

        y = uint184(x);
    }

    function safeCastTo176(uint256 x) internal pure returns (uint176 y) {
        require(x < 1 << 176);

        y = uint176(x);
    }

    function safeCastTo168(uint256 x) internal pure returns (uint168 y) {
        require(x < 1 << 168);

        y = uint168(x);
    }

    function safeCastTo160(uint256 x) internal pure returns (uint160 y) {
        require(x < 1 << 160);

        y = uint160(x);
    }

    function safeCastTo152(uint256 x) internal pure returns (uint152 y) {
        require(x < 1 << 152);

        y = uint152(x);
    }

    function safeCastTo144(uint256 x) internal pure returns (uint144 y) {
        require(x < 1 << 144);

        y = uint144(x);
    }

    function safeCastTo136(uint256 x) internal pure returns (uint136 y) {
        require(x < 1 << 136);

        y = uint136(x);
    }

    function safeCastTo128(uint256 x) internal pure returns (uint128 y) {
        require(x < 1 << 128);

        y = uint128(x);
    }

    function safeCastTo120(uint256 x) internal pure returns (uint120 y) {
        require(x < 1 << 120);

        y = uint120(x);
    }

    function safeCastTo112(uint256 x) internal pure returns (uint112 y) {
        require(x < 1 << 112);

        y = uint112(x);
    }

    function safeCastTo104(uint256 x) internal pure returns (uint104 y) {
        require(x < 1 << 104);

        y = uint104(x);
    }

    function safeCastTo96(uint256 x) internal pure returns (uint96 y) {
        require(x < 1 << 96);

        y = uint96(x);
    }

    function safeCastTo88(uint256 x) internal pure returns (uint88 y) {
        require(x < 1 << 88);

        y = uint88(x);
    }

    function safeCastTo80(uint256 x) internal pure returns (uint80 y) {
        require(x < 1 << 80);

        y = uint80(x);
    }

    function safeCastTo72(uint256 x) internal pure returns (uint72 y) {
        require(x < 1 << 72);

        y = uint72(x);
    }

    function safeCastTo64(uint256 x) internal pure returns (uint64 y) {
        require(x < 1 << 64);

        y = uint64(x);
    }

    function safeCastTo56(uint256 x) internal pure returns (uint56 y) {
        require(x < 1 << 56);

        y = uint56(x);
    }

    function safeCastTo48(uint256 x) internal pure returns (uint48 y) {
        require(x < 1 << 48);

        y = uint48(x);
    }

    function safeCastTo40(uint256 x) internal pure returns (uint40 y) {
        require(x < 1 << 40);

        y = uint40(x);
    }

    function safeCastTo32(uint256 x) internal pure returns (uint32 y) {
        require(x < 1 << 32);

        y = uint32(x);
    }

    function safeCastTo24(uint256 x) internal pure returns (uint24 y) {
        require(x < 1 << 24);

        y = uint24(x);
    }

    function safeCastTo16(uint256 x) internal pure returns (uint16 y) {
        require(x < 1 << 16);

        y = uint16(x);
    }

    function safeCastTo8(uint256 x) internal pure returns (uint8 y) {
        require(x < 1 << 8);

        y = uint8(x);
    }
}


// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;

/// @notice Signed 18 decimal fixed point (wad) arithmetic library.
/// @author Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/SignedWadMath.sol)
/// @author Modified from Remco Bloemen (https://xn--2-umb.com/22/exp-ln/index.html)

/// @dev Will not revert on overflow, only use where overflow is not possible.
function toWadUnsafe(uint256 x) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18.
        r := mul(x, 1000000000000000000)
    }
}

/// @dev Takes an integer amount of seconds and converts it to a wad amount of days.
/// @dev Will not revert on overflow, only use where overflow is not possible.
/// @dev Not meant for negative second amounts, it assumes x is positive.
function toDaysWadUnsafe(uint256 x) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18 and then divide it by 86400.
        r := div(mul(x, 1000000000000000000), 86400)
    }
}

/// @dev Takes a wad amount of days and converts it to an integer amount of seconds.
/// @dev Will not revert on overflow, only use where overflow is not possible.
/// @dev Not meant for negative day amounts, it assumes x is positive.
function fromDaysWadUnsafe(int256 x) pure returns (uint256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 86400 and then divide it by 1e18.
        r := div(mul(x, 86400), 1000000000000000000)
    }
}

/// @dev Will not revert on overflow, only use where overflow is not possible.
function unsafeWadMul(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by y and divide by 1e18.
        r := sdiv(mul(x, y), 1000000000000000000)
    }
}

/// @dev Will return 0 instead of reverting if y is zero and will
/// not revert on overflow, only use where overflow is not possible.
function unsafeWadDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Multiply x by 1e18 and divide it by y.
        r := sdiv(mul(x, 1000000000000000000), y)
    }
}

function wadMul(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Store x * y in r for now.
        r := mul(x, y)

        // Combined overflow check (`x == 0 || (x * y) / x == y`) and edge case check
        // where x == -1 and y == type(int256).min, for y == -1 and x == min int256,
        // the second overflow check will catch this.
        // See: https://secure-contracts.com/learn_evm/arithmetic-checks.html#arithmetic-checks-for-int256-multiplication
        // Combining into 1 expression saves gas as resulting bytecode will only have 1 `JUMPI`
        // rather than 2.
        if iszero(
            and(
                or(iszero(x), eq(sdiv(r, x), y)),
                or(lt(x, not(0)), sgt(y, 0x8000000000000000000000000000000000000000000000000000000000000000))
            )
        ) {
            revert(0, 0)
        }

        // Scale the result down by 1e18.
        r := sdiv(r, 1000000000000000000)
    }
}

function wadDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Store x * 1e18 in r for now.
        r := mul(x, 1000000000000000000)

        // Equivalent to require(y != 0 && ((x * 1e18) / 1e18 == x))
        if iszero(and(iszero(iszero(y)), eq(sdiv(r, 1000000000000000000), x))) {
            revert(0, 0)
        }

        // Divide r by y.
        r := sdiv(r, y)
    }
}

/// @dev Will not work with negative bases, only use when x is positive.
function wadPow(int256 x, int256 y) pure returns (int256) {
    // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
    return wadExp((wadLn(x) * y) / 1e18); // Using ln(x) means x must be greater than 0.
}

function wadExp(int256 x) pure returns (int256 r) {
    unchecked {
        // When the result is < 0.5 we return zero. This happens when
        // x <= floor(log(0.5e18) * 1e18) ~ -42e18
        if (x <= -42139678854452767551) return 0;

        // When the result is > (2**255 - 1) / 1e18 we can not represent it as an
        // int. This happens when x >= floor(log((2**255 - 1) / 1e18) * 1e18) ~ 135.
        if (x >= 135305999368893231589) revert("EXP_OVERFLOW");

        // x is now in the range (-42, 136) * 1e18. Convert to (-42, 136) * 2**96
        // for more intermediate precision and a binary basis. This base conversion
        // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
        x = (x << 78) / 5**18;

        // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
        // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
        // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
        int256 k = ((x << 96) / 54916777467707473351141471128 + 2**95) >> 96;
        x = x - k * 54916777467707473351141471128;

        // k is in the range [-61, 195].

        // Evaluate using a (6, 7)-term rational approximation.
        // p is made monic, we'll multiply by a scale factor later.
        int256 y = x + 1346386616545796478920950773328;
        y = ((y * x) >> 96) + 57155421227552351082224309758442;
        int256 p = y + x - 94201549194550492254356042504812;
        p = ((p * y) >> 96) + 28719021644029726153956944680412240;
        p = p * x + (4385272521454847904659076985693276 << 96);

        // We leave p in 2**192 basis so we don't need to scale it back up for the division.
        int256 q = x - 2855989394907223263936484059900;
        q = ((q * x) >> 96) + 50020603652535783019961831881945;
        q = ((q * x) >> 96) - 533845033583426703283633433725380;
        q = ((q * x) >> 96) + 3604857256930695427073651918091429;
        q = ((q * x) >> 96) - 14423608567350463180887372962807573;
        q = ((q * x) >> 96) + 26449188498355588339934803723976023;

        /// @solidity memory-safe-assembly
        assembly {
            // Div in assembly because solidity adds a zero check despite the unchecked.
            // The q polynomial won't have zeros in the domain as all its roots are complex.
            // No scaling is necessary because p is already 2**96 too large.
            r := sdiv(p, q)
        }

        // r should be in the range (0.09, 0.25) * 2**96.

        // We now need to multiply r by:
        // * the scale factor s = ~6.031367120.
        // * the 2**k factor from the range reduction.
        // * the 1e18 / 2**96 factor for base conversion.
        // We do this all at once, with an intermediate result in 2**213
        // basis, so the final right shift is always by a positive amount.
        r = int256((uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k));
    }
}

function wadLn(int256 x) pure returns (int256 r) {
    unchecked {
        require(x > 0, "UNDEFINED");

        // We want to convert x from 10**18 fixed point to 2**96 fixed point.
        // We do this by multiplying by 2**96 / 10**18. But since
        // ln(x * C) = ln(x) + ln(C), we can simply do nothing here
        // and add ln(2**96 / 10**18) at the end.

        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }

        // Reduce range of x to (1, 2) * 2**96
        // ln(2^k * x) = k * ln(2) + ln(x)
        int256 k = r - 96;
        x <<= uint256(159 - k);
        x = int256(uint256(x) >> 159);

        // Evaluate using a (8, 8)-term rational approximation.
        // p is made monic, we will multiply by a scale factor later.
        int256 p = x + 3273285459638523848632254066296;
        p = ((p * x) >> 96) + 24828157081833163892658089445524;
        p = ((p * x) >> 96) + 43456485725739037958740375743393;
        p = ((p * x) >> 96) - 11111509109440967052023855526967;
        p = ((p * x) >> 96) - 45023709667254063763336534515857;
        p = ((p * x) >> 96) - 14706773417378608786704636184526;
        p = p * x - (795164235651350426258249787498 << 96);

        // We leave p in 2**192 basis so we don't need to scale it back up for the division.
        // q is monic by convention.
        int256 q = x + 5573035233440673466300451813936;
        q = ((q * x) >> 96) + 71694874799317883764090561454958;
        q = ((q * x) >> 96) + 283447036172924575727196451306956;
        q = ((q * x) >> 96) + 401686690394027663651624208769553;
        q = ((q * x) >> 96) + 204048457590392012362485061816622;
        q = ((q * x) >> 96) + 31853899698501571402653359427138;
        q = ((q * x) >> 96) + 909429971244387300277376558375;
        /// @solidity memory-safe-assembly
        assembly {
            // Div in assembly because solidity adds a zero check despite the unchecked.
            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already 2**96 too large.
            r := sdiv(p, q)
        }

        // r is in the range (0, 0.125) * 2**96

        // Finalization, we need to:
        // * multiply by the scale factor s = 5.549…
        // * add ln(2**96 / 10**18)
        // * add k * ln(2)
        // * multiply by 10**18 / 2**96 = 5**18 >> 78

        // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
        r *= 1677202110996718588342820967067443963516166;
        // add ln(2) * k * 5e18 * 2**192
        r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
        // add ln(2**96 / 10**18) * 5e18 * 2**192
        r += 600920179829731861736702779321621459595472258049074101567377883020018308;
        // base conversion: mul 2**18 / 2**192
        r >>= 174;
    }
}

/// @dev Will return 0 instead of reverting if y is zero.
function unsafeDiv(int256 x, int256 y) pure returns (int256 r) {
    /// @solidity memory-safe-assembly
    assembly {
        // Divide x by y.
        r := sdiv(x, y)
    }
}
