Token

Contract Source Code (Solidity Standard Json-Input format)Audit Report

IDE

• Blockscan IDE
• 🤖 Code ReaderBeta
• Remix IDE

More Options

• Similar
• Sol2Uml
• Submit Audit
• Compare

// SPDX-License-Identifier: UNLICENSED
pragma solidity ^0.8.17;

/***********************************************************************************************************************
        ..:^~!?YPB&&@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
7                   .:~JP#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
&            !:            :7G@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@G           J@@#GY7~^..       ^P@@@@@@@@@@@@@Y!YYYYJG@@@@@@@77YYYJP@@@@@@@@&!&@@@@@@@@JP@@@@@@@@7#@@@@@@@G7&@@@@@@@G!&@
@@J           7@@@@@@@@@@&GJ^     ?@@@@@@@@@@@^J@@@@@@@@@@@@@.P@@@@@@@@@@@@@& ~?&@@@@@@~J@@@@@@@@.G@@@@@@@@#!?@@@@#!?&@@
@@@J        ~P#@@@@@@@@@@@@@@&!     B@@@@@@@@@~J@@@@@@@@@@@@@:P@@@@@@@@@@@@@&.@B~Y@@@@@~J@@@@@@@@:G@@@@@@@@@@G~P&?!&@@@@
@@@@G    ~G@@@@@@@@@@@@@@@@@@@@Y     G@@@@@@@@~^YYYP@@@@@@@@@:~YYYG@@@@@@@@@&.@@@P~P@@@~J@@@@@@@@:G@@@@@@@@@@@&. !@@@@@@
@@@@@&^^&@@@@@@@@@@@@@@@@@@@@@@@:     @@@@@@@@~Y@@@@@@@@@@@@@:G@@@@@@@@@@@@@&.@@@@@Y~B@!J@@@@@@@@:G@@@@@@@@@@Y~B@Y~B@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@&5!^^!P~     G@@@@@@@~J@@@@@@@@@@@@@:G@@@@@@@@@@@@@&.@@@@@@&?7.J@@@@@@@@.G@@@@@@@@P~P@@@@&7!&@@
@@@@@@@@@@@@@@@@@@@@@@@@Y             B@@@@@@@!5@@@@@@@@@@@@@^!5555Y#@@@@@@@&:@@@@@@@@&^Y@@@@@@@@^B@@@@@@&!J@@@@@@@@#!Y@
@@@@@@@@@@@@@@@@@@@@@@@&             ~@@@@@@@@@@@@@@@@@@@@@@@@@&&&&&@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@&@
@@@@@@@@@@@@@@@@@@@@@@@@7           J@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@#7.    .^Y&@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
***********************************************************************************************************************/

import { UD60x18, convert, wrap, unwrap, ud, E, ZERO } from "@prb/math/UD60x18.sol";
import { ERC20 } from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import { IERC165 } from "@openzeppelin/contracts/interfaces/IERC165.sol";
import { IBurnableToken } from "xen-crypto/interfaces/IBurnableToken.sol";
import { IBurnRedeemable } from "xen-crypto/interfaces/IBurnRedeemable.sol";

enum Status {
    ACTIVE,
    DEFER,
    END
}

struct Stake {
    Status status;
    uint40 startTs;
    uint40 deferralTs;
    uint40 endTs;
    uint16 term;
    uint256 fenix;
    uint256 shares;
    uint256 payout;
}

struct Reward {
    uint40 id;
    uint40 rewardTs;
    uint256 fenix;
    address caller;
}

///----------------------------------------------------------------------------------------------------------------
/// Events
///----------------------------------------------------------------------------------------------------------------
library FenixError {
    error WrongCaller(address caller);
    error AddressZero();
    error BalanceZero();
    error TermZero();
    error TermGreaterThanMax();
    error StakeNotActive();
    error StakeNotEnded();
    error StakeLate();
    error CooldownActive();
    error StakeStatusAlreadySet(Status status);
    error SizeGreaterThanMax();
}

/// @title FENIX pays you to hold your own crypto
/// @author Joe Blau <[email protected]>
/// @notice FENIX pays you to hold your own crypto
/// @dev Fenix is an ERC20 token that pays you to hold your own crypto.
contract Fenix is IBurnRedeemable, IERC165, ERC20("FENIX", "FENIX") {
    ///----------------------------------------------------------------------------------------------------------------
    /// Constants
    ///----------------------------------------------------------------------------------------------------------------

    address public constant XEN_ADDRESS = 0x06450dEe7FD2Fb8E39061434BAbCFC05599a6Fb8;

    uint256 public constant XEN_BURN_RATIO = 10_000;

    uint256 public constant MAX_STAKE_LENGTH_DAYS = 7_777;

    uint256 internal constant UINT256_MAX = type(uint256).max;
    uint256 internal constant ONE_DAY_TS = 86_400; // (1 day)
    uint256 internal constant ONE_EIGHTY_DAYS_TS = 15_552_000; // 86_400 * 180 (180 days)
    uint256 internal constant REWARD_COOLDOWN_TS = 7_862_400; // 86_400 * 7 * 13  (13 weeks)
    uint256 internal constant REWARD_LAUNCH_COOLDOWN_TS = 1_814_400; // 86_400 * 7 * 3 (3 weeks)

    UD60x18 public constant ANNUAL_INFLATION_RATE = UD60x18.wrap(0.016180339887498948e18);
    UD60x18 internal constant ONE = UD60x18.wrap(1e18);
    UD60x18 internal constant ONE_YEAR_DAYS = UD60x18.wrap(365);

    ///----------------------------------------------------------------------------------------------------------------
    /// Variables
    ///----------------------------------------------------------------------------------------------------------------

    uint40 public immutable genesisTs;
    uint256 public cooldownUnlockTs;
    uint256 public rewardPoolSupply = 0;

    uint256 public shareRate = 1e18;

    uint256 public equityPoolSupply = 0;
    uint256 public equityPoolTotalShares = 0;

    mapping(address => Stake[]) internal stakes;
    Reward[] internal rewards;

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

    /// @notice Stake has been started
    /// @dev Size and Time bonus have been calculated to burn FENIX in exchnge for equity to start stake
    /// @param _stake the stake object
    event StartStake(Stake indexed _stake);

    /// @notice Stake has been deferred
    /// @dev Remove the stake and it's equity from the pool
    /// @param _stake the stake object
    event DeferStake(Stake indexed _stake);

    /// @notice Stake has been ended
    /// @dev Remove the stake from the users stakes and mint the payout into the stakers wallet
    /// @param _stake the stake object
    event EndStake(Stake indexed _stake);

    /// @notice Reward Pool has been flushed
    /// @dev Flushed reward pool into staker pool
    event FlushRewardPool(Reward indexed reward);

    /// @notice Share rate has been updated
    /// @dev Share rate has been updated
    /// @param _shareRate the new share rate
    event UpdateShareRate(uint256 indexed _shareRate);

    ///----------------------------------------------------------------------------------------------------------------
    /// Contract
    ///----------------------------------------------------------------------------------------------------------------

    constructor() {
        genesisTs = uint40(block.timestamp);
        cooldownUnlockTs = block.timestamp + REWARD_LAUNCH_COOLDOWN_TS;
    }

    /// @notice Evaluate if the contract supports the interface
    /// @dev Evaluate if the contract supports burning tokens
    /// @param interfaceId the interface to evaluate
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IBurnRedeemable).interfaceId || interfaceId == this.supportsInterface.selector;
    }

    /// @notice Mint FENIX tokens
    /// @dev Mint FENIX tokens to the user address
    /// @param user the address of the user to mint FENIX tokens for
    /// @param amount the amount of FENIX tokens to mint
    function onTokenBurned(address user, uint256 amount) external {
        if (_msgSender() != XEN_ADDRESS) revert FenixError.WrongCaller(_msgSender());
        if (user == address(0)) revert FenixError.AddressZero();
        if (amount == 0) revert FenixError.BalanceZero();

        uint256 fenix = amount / XEN_BURN_RATIO;
        rewardPoolSupply += fenix;
        _mint(user, fenix);
        emit Redeemed(user, XEN_ADDRESS, address(this), amount, fenix);
    }

    /// @notice Burn XEN tokens
    /// @dev Execute proof of burn on remote contract to burn XEN tokens
    /// @param xen the amount of XEN to burn from the current wallet address
    function burnXEN(uint256 xen) public {
        IBurnableToken(XEN_ADDRESS).burn(_msgSender(), xen);
    }

    /// @notice Starts a stake
    /// @dev Initialize a stake for the current wallet address
    /// @param fenix the amount of fenix to stake
    /// @param term the number of days to stake
    function startStake(uint256 fenix, uint256 term) public {
        if (fenix == 0) revert FenixError.BalanceZero();
        if (term == 0) revert FenixError.TermZero();

        uint40 startTs = uint40(block.timestamp);
        uint40 endTs = uint40(block.timestamp + (term * ONE_DAY_TS));

        uint256 bonus = calculateBonus(fenix, term);
        uint256 shares = calculateShares(bonus);

        UD60x18 time = ud(term).div(ONE_YEAR_DAYS);
        uint256 inflatedSupply = unwrap(ud(fenix).mul((ONE.add(ANNUAL_INFLATION_RATE)).pow(time)));

        uint256 newShares = unwrap(ud(shares).mul(ud(inflatedSupply)));

        equityPoolSupply += inflatedSupply;
        equityPoolTotalShares += newShares;

        Stake memory _stake = Stake(Status.ACTIVE, startTs, 0, endTs, uint16(term), fenix, newShares, 0);
        stakes[_msgSender()].push(_stake);

        _burn(_msgSender(), fenix);
        emit StartStake(_stake);
    }

    /// @notice Defer stake until future date
    /// @dev Defer a stake by removing the supply allocated to the stake from the pool
    /// @param stakeIndex the index of the stake to defer
    /// @param stakerAddress the address of the stake owner that will be deferred
    function deferStake(uint256 stakeIndex, address stakerAddress) public {
        if (stakes[stakerAddress].length <= stakeIndex) revert FenixError.StakeNotActive();
        Stake memory _stake = stakes[stakerAddress][stakeIndex];

        if (_stake.status != Status.ACTIVE) return;

        if (block.timestamp < _stake.endTs && _msgSender() != stakerAddress)
            revert FenixError.WrongCaller(_msgSender());

        UD60x18 rewardPercent = ZERO;
        if (block.timestamp > _stake.endTs) {
            rewardPercent = ud(calculateLatePayout(_stake));
        } else {
            rewardPercent = ud(calculateEarlyPayout(_stake));
        }

        UD60x18 poolSharePercent = ud(_stake.shares).div(ud(equityPoolTotalShares));
        UD60x18 stakerPoolSupplyPercent = poolSharePercent.mul(rewardPercent);

        uint256 equitySupply = unwrap(ud(equityPoolSupply).mul(stakerPoolSupplyPercent));

        Stake memory deferredStake = Stake(
            Status.DEFER,
            _stake.startTs,
            uint40(block.timestamp),
            _stake.endTs,
            _stake.term,
            _stake.fenix,
            _stake.shares,
            equitySupply
        );

        stakes[stakerAddress][stakeIndex] = deferredStake;

        equityPoolTotalShares -= _stake.shares;
        equityPoolSupply -= equitySupply;

        emit DeferStake(deferredStake);
    }

    /// @notice End a stake
    /// @dev End a stake by allocating the stake supply to the stakers wallet
    /// @param stakeIndex the index of the stake to end
    function endStake(uint256 stakeIndex) public {
        deferStake(stakeIndex, _msgSender());

        Stake memory _stake = stakes[_msgSender()][stakeIndex];
        if (_stake.status == Status.END) revert FenixError.StakeStatusAlreadySet(Status.END);

        _mint(_msgSender(), _stake.payout);

        uint256 returnOnStake = unwrap(ud(_stake.payout).div(ud(_stake.fenix)));

        if (returnOnStake > shareRate) {
            shareRate = returnOnStake;
            emit UpdateShareRate(shareRate);
        }

        Stake memory endedStake = Stake(
            Status.END,
            _stake.startTs,
            _stake.deferralTs,
            _stake.endTs,
            _stake.term,
            _stake.fenix,
            _stake.shares,
            _stake.payout
        );

        stakes[_msgSender()][stakeIndex] = endedStake;
        emit EndStake(endedStake);
    }

    /// @notice Calculate bonus
    /// @dev Use fenix amount and term to calculate size and time bonus used for pool equity stake
    /// @param fenix the amount of fenix used to calculate the equity stake
    /// @param term the term of the stake in days used to calculate the pool equity stake
    /// @return bonus the bonus for pool equity stake
    function calculateBonus(uint256 fenix, uint256 term) public pure returns (uint256) {
        UD60x18 sizeBonus = ud(calculateSizeBonus(fenix));
        UD60x18 timeBonus = ud(calculateTimeBonus(term));
        UD60x18 bonus = sizeBonus.mul(E.pow(timeBonus));
        return unwrap(bonus);
    }

    /// @notice Calculate size bonus
    /// @dev Use fenix amount to calculate the size bonus used for pool equity stake
    /// @param fenix the amount of fenix used to calculate the equity stake
    /// @return bonus the size bonus for pool equity stake
    function calculateSizeBonus(uint256 fenix) public pure returns (uint256) {
        if (fenix >= (UINT256_MAX - 3)) revert FenixError.SizeGreaterThanMax();
        return unwrap(ONE.sub((ud(fenix).add(ONE)).inv()));
    }

    /// @notice Calculate time bonus
    /// @dev Use term to calculate the time bonus used for pool equity stake
    /// @param term the term of the stake in days used to calculate the pool equity stake
    /// @return bonus the time bonus for pool equity stake
    function calculateTimeBonus(uint256 term) public pure returns (uint256) {
        if (term > MAX_STAKE_LENGTH_DAYS) revert FenixError.TermGreaterThanMax();
        UD60x18 timeBonus = ONE.add(ud(term).div(ud(MAX_STAKE_LENGTH_DAYS)));
        return unwrap(timeBonus);
    }

    /// @notice Calculate shares
    /// @dev Use bonus to calculate the number of shares to be issued to the staker
    /// @param bonus the bonus to calculate the shares from
    /// @return shares the number of shares to be issued to the staker
    function calculateShares(uint256 bonus) public view returns (uint256) {
        UD60x18 shares = ud(bonus).div(ud(shareRate));
        return unwrap(shares);
    }

    /// @notice Calculate the early end stake penalty
    /// @dev Calculates the early end stake penality to be split between the pool and the staker
    /// @param stake the stake to calculate the penalty for
    /// @return reward the reward percentage for the stake
    function calculateEarlyPayout(Stake memory stake) public view returns (uint256) {
        if (block.timestamp < stake.startTs || stake.status != Status.ACTIVE) revert FenixError.StakeNotActive();
        if (block.timestamp > stake.endTs) revert FenixError.StakeLate();
        uint256 termDelta = block.timestamp - stake.startTs;
        uint256 scaleTerm = stake.term * ONE_DAY_TS;
        UD60x18 reward = (convert(termDelta).div(convert(scaleTerm))).powu(2);
        return unwrap(reward);
    }

    /// @notice Calculate the late end stake penalty
    /// @dev Calculates the late end stake penality to be split between the pool and the staker
    /// @param stake a parameter just like in doxygen (must be followed by parameter name)
    /// @return reward the reward percentage for the stake
    function calculateLatePayout(Stake memory stake) public view returns (uint256) {
        if (block.timestamp < stake.startTs || stake.status != Status.ACTIVE) revert FenixError.StakeNotActive();
        if (block.timestamp < stake.endTs) revert FenixError.StakeNotEnded();

        uint256 lateTs = block.timestamp - stake.endTs;
        if (lateTs > ONE_EIGHTY_DAYS_TS) return 0;

        UD60x18 penalty = ud(lateTs).div(ud(ONE_EIGHTY_DAYS_TS)).powu(3);
        UD60x18 reward = ONE.sub(penalty);
        return unwrap(reward);
    }

    /// @notice Flush reward pool
    /// @dev Flush reward pool to stake pool
    function flushRewardPool() public {
        if (block.timestamp < cooldownUnlockTs) revert FenixError.CooldownActive();
        uint256 cooldownPeriods = (block.timestamp - cooldownUnlockTs) / REWARD_COOLDOWN_TS;
        equityPoolSupply += rewardPoolSupply;
        cooldownUnlockTs += REWARD_COOLDOWN_TS + (cooldownPeriods * REWARD_COOLDOWN_TS);

        Reward memory reward = Reward(uint40(rewards.length), uint40(block.timestamp), rewardPoolSupply, _msgSender());

        rewardPoolSupply = 0;
        rewards.push(reward);
        emit FlushRewardPool(reward);
    }

    /// @notice Get stake for address at index
    /// @dev Read stake from stakes mapping stake array
    /// @param stakerAddress address of stake owner
    /// @param stakeIndex index of stake to read
    /// @return stake
    function stakeFor(address stakerAddress, uint256 stakeIndex) public view returns (Stake memory) {
        return stakes[stakerAddress][stakeIndex];
    }

    /// @notice Get stake count for address
    /// @dev Read stake count from stakes mapping
    /// @param stakerAddress address of stake owner
    /// @return stake count
    function stakeCount(address stakerAddress) public view returns (uint256) {
        return stakes[stakerAddress].length;
    }

    /// @notice Get reward for index
    /// @dev Read reward from rewards array
    /// @param index index of reward to read
    /// @return reward
    function rewardFor(uint256 index) public view returns (Reward memory) {
        return rewards[index];
    }

    /// @notice Get reward count
    /// @dev Read reward count from rewards array
    /// @return reward count
    function rewardCount() public view returns (uint256) {
        return rewards.length;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IBurnRedeemable {
    event Redeemed(
        address indexed user,
        address indexed xenContract,
        address indexed tokenContract,
        uint256 xenAmount,
        uint256 tokenAmount
    );

    function onTokenBurned(address user, uint256 amount) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IBurnableToken {
    function burn(address user, uint256 amount) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (interfaces/IERC165.sol)

pragma solidity ^0.8.0;

import "../utils/introspection/IERC165.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

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

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

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

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

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

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

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

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

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

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

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

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

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

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

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

        return true;
    }

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

        _beforeTokenTransfer(from, to, amount);

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

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

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

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

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

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

// Common.sol
//
// Common mathematical functions needed by both SD59x18 and UD60x18. Note that these global functions do not
// always operate with SD59x18 and UD60x18 numbers.

/*//////////////////////////////////////////////////////////////////////////
                                CUSTOM ERRORS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Thrown when the resultant value in {mulDiv} overflows uint256.
error PRBMath_MulDiv_Overflow(uint256 x, uint256 y, uint256 denominator);

/// @notice Thrown when the resultant value in {mulDiv18} overflows uint256.
error PRBMath_MulDiv18_Overflow(uint256 x, uint256 y);

/// @notice Thrown when one of the inputs passed to {mulDivSigned} is `type(int256).min`.
error PRBMath_MulDivSigned_InputTooSmall();

/// @notice Thrown when the resultant value in {mulDivSigned} overflows int256.
error PRBMath_MulDivSigned_Overflow(int256 x, int256 y);

/*//////////////////////////////////////////////////////////////////////////
                                    CONSTANTS
//////////////////////////////////////////////////////////////////////////*/

/// @dev The maximum value a uint128 number can have.
uint128 constant MAX_UINT128 = type(uint128).max;

/// @dev The maximum value a uint40 number can have.
uint40 constant MAX_UINT40 = type(uint40).max;

/// @dev The unit number, which the decimal precision of the fixed-point types.
uint256 constant UNIT = 1e18;

/// @dev The unit number inverted mod 2^256.
uint256 constant UNIT_INVERSE = 78156646155174841979727994598816262306175212592076161876661_508869554232690281;

/// @dev The the largest power of two that divides the decimal value of `UNIT`. The logarithm of this value is the least significant
/// bit in the binary representation of `UNIT`.
uint256 constant UNIT_LPOTD = 262144;

/*//////////////////////////////////////////////////////////////////////////
                                    FUNCTIONS
//////////////////////////////////////////////////////////////////////////*/

/// @notice Calculates the binary exponent of x using the binary fraction method.
/// @dev Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
/// @param x The exponent as an unsigned 192.64-bit fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function exp2(uint256 x) pure returns (uint256 result) {
    unchecked {
        // Start from 0.5 in the 192.64-bit fixed-point format.
        result = 0x800000000000000000000000000000000000000000000000;

        // The following logic multiplies the result by $\sqrt{2^{-i}}$ when the bit at position i is 1. Key points:
        //
        // 1. Intermediate results will not overflow, as the starting point is 2^191 and all magic factors are under 2^65.
        // 2. The rationale for organizing the if statements into groups of 8 is gas savings. If the result of performing
        // a bitwise AND operation between x and any value in the array [0x80; 0x40; 0x20; 0x10; 0x08; 0x04; 0x02; 0x01] is 1,
        // we know that `x & 0xFF` is also 1.
        if (x & 0xFF00000000000000 > 0) {
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
        }

        if (x & 0xFF000000000000 > 0) {
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
        }

        if (x & 0xFF0000000000 > 0) {
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
        }

        if (x & 0xFF00000000 > 0) {
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
        }

        if (x & 0xFF000000 > 0) {
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
        }

        if (x & 0xFF0000 > 0) {
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
        }

        if (x & 0xFF00 > 0) {
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
        }

        if (x & 0xFF > 0) {
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
        }

        // In the code snippet below, two operations are executed simultaneously:
        //
        // 1. The result is multiplied by $(2^n + 1)$, where $2^n$ represents the integer part, and the additional 1
        // accounts for the initial guess of 0.5. This is achieved by subtracting from 191 instead of 192.
        // 2. The result is then converted to an unsigned 60.18-decimal fixed-point format.
        //
        // The underlying logic is based on the relationship $2^{191-ip} = 2^{ip} / 2^{191}$, where $ip$ denotes the,
        // integer part, $2^n$.
        result *= UNIT;
        result >>= (191 - (x >> 64));
    }
}

/// @notice Finds the zero-based index of the first 1 in the binary representation of x.
///
/// @dev See the note on "msb" in this Wikipedia article: https://en.wikipedia.org/wiki/Find_first_set
///
/// Each step in this implementation is equivalent to this high-level code:
///
/// ```solidity
/// if (x >= 2 ** 128) {
///     x >>= 128;
///     result += 128;
/// }
/// ```
///
/// Where 128 is replaced with each respective power of two factor. See the full high-level implementation here:
/// https://gist.github.com/PaulRBerg/f932f8693f2733e30c4d479e8e980948
///
/// The Yul instructions used below are:
///
/// - "gt" is "greater than"
/// - "or" is the OR bitwise operator
/// - "shl" is "shift left"
/// - "shr" is "shift right"
///
/// @param x The uint256 number for which to find the index of the most significant bit.
/// @return result The index of the most significant bit as a uint256.
/// @custom:smtchecker abstract-function-nondet
function msb(uint256 x) pure returns (uint256 result) {
    // 2^128
    assembly ("memory-safe") {
        let factor := shl(7, gt(x, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^64
    assembly ("memory-safe") {
        let factor := shl(6, gt(x, 0xFFFFFFFFFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^32
    assembly ("memory-safe") {
        let factor := shl(5, gt(x, 0xFFFFFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^16
    assembly ("memory-safe") {
        let factor := shl(4, gt(x, 0xFFFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^8
    assembly ("memory-safe") {
        let factor := shl(3, gt(x, 0xFF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^4
    assembly ("memory-safe") {
        let factor := shl(2, gt(x, 0xF))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^2
    assembly ("memory-safe") {
        let factor := shl(1, gt(x, 0x3))
        x := shr(factor, x)
        result := or(result, factor)
    }
    // 2^1
    // No need to shift x any more.
    assembly ("memory-safe") {
        let factor := gt(x, 0x1)
        result := or(result, factor)
    }
}

/// @notice Calculates floor(x*y÷denominator) with 512-bit precision.
///
/// @dev Credits to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
///
/// Notes:
/// - The result is rounded down.
///
/// Requirements:
/// - The denominator must not be zero.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as a uint256.
/// @param y The multiplier as a uint256.
/// @param denominator The divisor as a uint256.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function mulDiv(uint256 x, uint256 y, uint256 denominator) pure returns (uint256 result) {
    // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
    // use the Chinese Remainder Theorem to reconstruct the 512-bit result. The result is stored in two 256
    // variables such that product = prod1 * 2^256 + prod0.
    uint256 prod0; // Least significant 256 bits of the product
    uint256 prod1; // Most significant 256 bits of the product
    assembly ("memory-safe") {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    // Handle non-overflow cases, 256 by 256 division.
    if (prod1 == 0) {
        unchecked {
            return prod0 / denominator;
        }
    }

    // Make sure the result is less than 2^256. Also prevents denominator == 0.
    if (prod1 >= denominator) {
        revert PRBMath_MulDiv_Overflow(x, y, denominator);
    }

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

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

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

    unchecked {
        // Calculate the largest power of two divisor of the denominator using the unary operator ~. This operation cannot overflow
        // because the denominator cannot be zero at this point in the function execution. The result is always >= 1.
        // For more detail, see https://cs.stackexchange.com/q/138556/92363.
        uint256 lpotdod = denominator & (~denominator + 1);
        uint256 flippedLpotdod;

        assembly ("memory-safe") {
            // Factor powers of two out of denominator.
            denominator := div(denominator, lpotdod)

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

            // Get the flipped value `2^256 / lpotdod`. If the `lpotdod` is zero, the flipped value is one.
            // `sub(0, lpotdod)` produces the two's complement version of `lpotdod`, which is equivalent to flipping all the bits.
            // However, `div` interprets this value as an unsigned value: https://ethereum.stackexchange.com/q/147168/24693
            flippedLpotdod := add(div(sub(0, lpotdod), lpotdod), 1)
        }

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

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

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

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

/// @notice Calculates floor(x*y÷1e18) with 512-bit precision.
///
/// @dev A variant of {mulDiv} with constant folding, i.e. in which the denominator is hard coded to 1e18.
///
/// Notes:
/// - The body is purposely left uncommented; to understand how this works, see the documentation in {mulDiv}.
/// - The result is rounded down.
/// - We take as an axiom that the result cannot be `MAX_UINT256` when x and y solve the following system of equations:
///
/// $$
/// \begin{cases}
///     x * y = MAX\_UINT256 * UNIT \\
///     (x * y) \% UNIT \geq \frac{UNIT}{2}
/// \end{cases}
/// $$
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - The result must fit in uint256.
///
/// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
/// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
/// @return result The result as an unsigned 60.18-decimal fixed-point number.
/// @custom:smtchecker abstract-function-nondet
function mulDiv18(uint256 x, uint256 y) pure returns (uint256 result) {
    uint256 prod0;
    uint256 prod1;
    assembly ("memory-safe") {
        let mm := mulmod(x, y, not(0))
        prod0 := mul(x, y)
        prod1 := sub(sub(mm, prod0), lt(mm, prod0))
    }

    if (prod1 == 0) {
        unchecked {
            return prod0 / UNIT;
        }
    }

    if (prod1 >= UNIT) {
        revert PRBMath_MulDiv18_Overflow(x, y);
    }

    uint256 remainder;
    assembly ("memory-safe") {
        remainder := mulmod(x, y, UNIT)
        result :=
            mul(
                or(
                    div(sub(prod0, remainder), UNIT_LPOTD),
                    mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, UNIT_LPOTD), UNIT_LPOTD), 1))
                ),
                UNIT_INVERSE
            )
    }
}

/// @notice Calculates floor(x*y÷denominator) with 512-bit precision.
///
/// @dev This is an extension of {mulDiv} for signed numbers, which works by computing the signs and the absolute values separately.
///
/// Notes:
/// - Unlike {mulDiv}, the result is rounded toward zero.
///
/// Requirements:
/// - Refer to the requirements in {mulDiv}.
/// - None of the inputs can be `type(int256).min`.
/// - The result must fit in int256.
///
/// @param x The multiplicand as an int256.
/// @param y The multiplier as an int256.
/// @param denominator The divisor as an int256.
/// @return result The result as an int256.
/// @custom:smtchecker abstract-function-nondet
function mulDivSigned(int256 x, int256 y, int256 denominator) pure returns (int256 result) {
    if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
        revert PRBMath_MulDivSigned_InputTooSmall();
    }

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

    // Compute the absolute value of x*y÷denominator. The result must fit in int256.
    uint256 resultAbs = mulDiv(xAbs, yAbs, dAbs);
    if (resultAbs > uint256(type(int256).max)) {
        revert PRBMath_MulDivSigned_Overflow(x, y);
    }

    // Get the signs of x, y and the denominator.
    uint256 sx;
    uint256 sy;
    uint256 sd;
    assembly ("memory-safe") {
        // This works thanks to two's complement.
        // "sgt" stands for "signed greater than" and "sub(0,1)" is max uint256.
        sx := sgt(x, sub(0, 1))
        sy := sgt(y, sub(0, 1))
        sd := sgt(denominator, sub(0, 1))
    }

    // XOR over sx, sy and sd. What this does is to check whether there are 1 or 3 negative signs in the inputs.
    // If there are, the result should be negative. Otherwise, it should be positive.
    unchecked {
        result = sx ^ sy ^ sd == 0 ? -int256(resultAbs) : int256(resultAbs);
    }
}

/// @notice Calculates the square root of x using the Babylonian method.
///
/// @dev See https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
///
/// Notes:
/// - If x is not a perfect square, the result is rounded down.
/// - Credits to OpenZeppelin for the explanations in comments below.
///
/// @param x The uint256 number for which to calculate the square root.
/// @return result The result as a uint256.
/// @custom:smtchecker abstract-function-nondet
function sqrt(uint256 x) pure returns (uint256 result) {
    if (x == 0) {
        return 0;
    }

    // For our first guess, we calculate the biggest power of 2 which is smaller than the square root of x.
    //
    // We know that the "msb" (most significant bit) of x is a power of 2 such that we have:
    //
    // $$
    // msb(x) <= x <= 2*msb(x)$
    // $$
    //
    // We write $msb(x)$ as $2^k$, and we get:
    //
    // $$
    // k = log_2(x)
    // $$
    //
    // Thus, we can write the initial inequality as:
    //
    // $$
    // 2^{log_2(x)} <= x <= 2*2^{log_2(x)+1} \\
    // sqrt(2^k) <= sqrt(x) < sqrt(2^{k+1}) \\
    // 2^{k/2} <= sqrt(x) < 2^{(k+1)/2} <= 2^{(k/2)+1}
    // $$
    //
    // Consequently, $2^{log_2(x) /2} is a good first approximation of sqrt(x) with at least one correct bit.
    uint256 xAux = uint256(x);
    result = 1;
    if (xAux >= 2 ** 128) {
        xAux >>= 128;
        result <<= 64;
    }
    if (xAux >= 2 ** 64) {
        xAux >>= 64;
        result <<= 32;
    }
    if (xAux >= 2 ** 32) {
        xAux >>= 32;
        result <<= 16;
    }
    if (xAux >= 2 ** 16) {
        xAux >>= 16;
        result <<= 8;
    }
    if (xAux >= 2 ** 8) {
        xAux >>= 8;
        result <<= 4;
    }
    if (xAux >= 2 ** 4) {
        xAux >>= 4;
        result <<= 2;
    }
    if (xAux >= 2 ** 2) {
        result <<= 1;
    }

    // At this point, `result` is an estimation with at least one bit of precision. We know the true value has at
    // most 128 bits, since  it is the square root of a uint256. Newton's method converges quadratically (precision
    // doubles at every iteration). We thus need at most 7 iteration to turn our partial result with one bit of
    // precision into the expected uint128 result.
    unchecked {
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;
        result = (result + x / result) >> 1;

        // If x is not a perfect square, round down the result.
        uint256 roundedDownResult = x / result;
        if (result >= roundedDownResult) {
            result = roundedDownResult;
        }
    }
}

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

/*

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

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

*/

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

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

import "../Common.sol" as Common;
import "./Errors.sol" as CastingErrors;
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { SD1x18 } from "./ValueType.sol";

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

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

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

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

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

/// @notice Casts an SD1x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD1x18 x) pure returns (uint40 result) {
    int64 xInt = SD1x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Underflow(x);
    }
    if (xInt > int64(uint64(Common.MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD1x18_ToUint40_Overflow(x);
    }
    result = uint40(uint64(xInt));
}

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

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

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

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

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

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

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

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

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

/// @dev The unit number, which gives the decimal precision of SD1x18.
SD1x18 constant UNIT = SD1x18.wrap(1e18);
int256 constant uUNIT = 1e18;

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

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

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

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

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

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

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

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

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

import "./Casting.sol" as Casting;

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

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

using {
    Casting.intoSD59x18,
    Casting.intoUD2x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for SD1x18 global;

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

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

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

/// @notice Casts an SD59x18 number into SD1x18.
/// @dev Requirements:
/// - x must be greater than or equal to `uMIN_SD1x18`.
/// - x must be less than or equal to `uMAX_SD1x18`.
function intoSD1x18(SD59x18 x) pure returns (SD1x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < uMIN_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Underflow(x);
    }
    if (xInt > uMAX_SD1x18) {
        revert CastingErrors.PRBMath_SD59x18_IntoSD1x18_Overflow(x);
    }
    result = SD1x18.wrap(int64(xInt));
}

/// @notice Casts an SD59x18 number into UD2x18.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UD2x18`.
function intoUD2x18(SD59x18 x) pure returns (UD2x18 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Underflow(x);
    }
    if (xInt > int256(uint256(uMAX_UD2x18))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUD2x18_Overflow(x);
    }
    result = UD2x18.wrap(uint64(uint256(xInt)));
}

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

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

/// @notice Casts an SD59x18 number into uint128.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `uMAX_UINT128`.
function intoUint128(SD59x18 x) pure returns (uint128 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT128))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint128_Overflow(x);
    }
    result = uint128(uint256(xInt));
}

/// @notice Casts an SD59x18 number into uint40.
/// @dev Requirements:
/// - x must be positive.
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(SD59x18 x) pure returns (uint40 result) {
    int256 xInt = SD59x18.unwrap(x);
    if (xInt < 0) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Underflow(x);
    }
    if (xInt > int256(uint256(MAX_UINT40))) {
        revert CastingErrors.PRBMath_SD59x18_IntoUint40_Overflow(x);
    }
    result = uint40(uint256(xInt));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/// @notice Thrown when trying to cast a UD60x18 number that doesn't fit in uint40.
error PRBMath_SD59x18_IntoUint40_Underflow(SD59x18 x);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        // Calculate the integer part of the logarithm and add it to the result and finally calculate $y = x * 2^{-n}$.
        uint256 n = Common.msb(uint256(xInt / uUNIT));

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

import "../Common.sol" as Common;
import "./Errors.sol" as Errors;
import { uMAX_SD1x18 } from "../sd1x18/Constants.sol";
import { SD1x18 } from "../sd1x18/ValueType.sol";
import { SD59x18 } from "../sd59x18/ValueType.sol";
import { UD2x18 } from "../ud2x18/ValueType.sol";
import { UD60x18 } from "../ud60x18/ValueType.sol";
import { UD2x18 } from "./ValueType.sol";

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/// @dev The unit number, which gives the decimal precision of UD2x18.
uint256 constant uUNIT = 1e18;
UD2x18 constant UNIT = UD2x18.wrap(1e18);

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

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

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

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

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

import "./Casting.sol" as Casting;

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

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

using {
    Casting.intoSD1x18,
    Casting.intoSD59x18,
    Casting.intoUD60x18,
    Casting.intoUint256,
    Casting.intoUint128,
    Casting.intoUint40,
    Casting.unwrap
} for UD2x18 global;

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

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

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

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

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

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

/// @notice Casts a UD60x18 number into uint128.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT128`.
function intoUint128(UD60x18 x) pure returns (uint128 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT128) {
        revert CastingErrors.PRBMath_UD60x18_IntoUint128_Overflow(x);
    }
    result = uint128(xUint);
}

/// @notice Casts a UD60x18 number into uint40.
/// @dev Requirements:
/// - x must be less than or equal to `MAX_UINT40`.
function intoUint40(UD60x18 x) pure returns (uint40 result) {
    uint256 xUint = UD60x18.unwrap(x);
    if (xUint > MAX_UINT40) {
        revert CastingErrors.PRBMath_UD60x18_IntoUint40_Overflow(x);
    }
    result = uint40(xUint);
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/// @notice Thrown when taking the logarithm of a number less than 1.
error PRBMath_UD60x18_Log_InputTooSmall(UD60x18 x);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        // Equivalent to `x + delta * (remainder > 0 ? 1 : 0)`.
        result := add(x, mul(delta, gt(remainder, 0)))
    }
}

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

/// @notice Calculates the natural exponent of x using the following formula:
///
/// $$
/// e^x = 2^{x * log_2{e}}
/// $$
///
/// @dev Requirements:
/// - x must be less than 133_084258667509499441.
///
/// @param x The exponent as a UD60x18 number.
/// @return result The result as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function exp(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

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

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

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

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

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

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

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

        // Equivalent to `x - remainder * (remainder > 0 ? 1 : 0)`.
        result := sub(x, mul(remainder, gt(remainder, 0)))
    }
}

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

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

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

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

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

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

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

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

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

/// @notice Calculates the binary logarithm of x using the iterative approximation algorithm.
///
/// For $0 \leq x < 1$, the logarithm is calculated as:
///
/// $$
/// log_2{x} = -log_2{\frac{1}{x}}
/// $$
///
/// @dev See https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
///
/// Notes:
/// - Due to the lossy precision of the iterative approximation, the results are not perfectly accurate to the last decimal.
///
/// Requirements:
/// - x must be greater than zero.
///
/// @param x The UD60x18 number for which to calculate the binary logarithm.
/// @return result The binary logarithm as a UD60x18 number.
/// @custom:smtchecker abstract-function-nondet
function log2(UD60x18 x) pure returns (UD60x18 result) {
    uint256 xUint = x.unwrap();

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

    unchecked {
        // Calculate the integer part of the logarithm, add it to the result and finally calculate $y = x * 2^{-n}$.
        uint256 n = Common.msb(xUint / uUNIT);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{
  "remappings": [
    "@atomize/=src/",
    "@openzeppelin/=lib/openzeppelin-contracts/",
    "@prb/math/=lib/prb-math/src/",
    "@prb/test/=lib/prb-test/src/",
    "XEN-crypto/=lib/XEN-crypto/contracts/",
    "abdk-libraries-solidity/=lib/abdk-libraries-solidity/",
    "ds-test/=lib/forge-std/lib/ds-test/src/",
    "forge-std/=lib/forge-std/src/",
    "prb-math/=lib/prb-math/src/",
    "prb-test/=lib/prb-test/src/",
    "xen-crypto/=lib/XEN-crypto/contracts/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 10000
  },
  "metadata": {
    "bytecodeHash": "none",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "london",
  "libraries": {}
}

• Certik - Apr 13th, 2023 - Security Audit Report

[{"inputs":[],"stateMutability":"nonpayable","type":"constructor"},{"inputs":[],"name":"AddressZero","type":"error"},{"inputs":[],"name":"BalanceZero","type":"error"},{"inputs":[],"name":"CooldownActive","type":"error"},{"inputs":[{"internalType":"uint256","name":"x","type":"uint256"},{"internalType":"uint256","name":"y","type":"uint256"}],"name":"PRBMath_MulDiv18_Overflow","type":"error"},{"inputs":[{"internalType":"uint256","name":"x","type":"uint256"},{"internalType":"uint256","name":"y","type":"uint256"},{"internalType":"uint256","name":"denominator","type":"uint256"}],"name":"PRBMath_MulDiv_Overflow","type":"error"},{"inputs":[{"internalType":"uint256","name":"x","type":"uint256"}],"name":"PRBMath_UD60x18_Convert_Overflow","type":"error"},{"inputs":[{"internalType":"UD60x18","name":"x","type":"uint256"}],"name":"PRBMath_UD60x18_Exp2_InputTooBig","type":"error"},{"inputs":[{"internalType":"UD60x18","name":"x","type":"uint256"}],"name":"PRBMath_UD60x18_Log_InputTooSmall","type":"error"},{"inputs":[],"name":"SizeGreaterThanMax","type":"error"},{"inputs":[],"name":"StakeLate","type":"error"},{"inputs":[],"name":"StakeNotActive","type":"error"},{"inputs":[],"name":"StakeNotEnded","type":"error"},{"inputs":[{"internalType":"enum Status","name":"status","type":"uint8"}],"name":"StakeStatusAlreadySet","type":"error"},{"inputs":[],"name":"TermGreaterThanMax","type":"error"},{"inputs":[],"name":"TermZero","type":"error"},{"inputs":[{"internalType":"address","name":"caller","type":"address"}],"name":"WrongCaller","type":"error"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"owner","type":"address"},{"indexed":true,"internalType":"address","name":"spender","type":"address"},{"indexed":false,"internalType":"uint256","name":"value","type":"uint256"}],"name":"Approval","type":"event"},{"anonymous":false,"inputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"indexed":true,"internalType":"struct Stake","name":"_stake","type":"tuple"}],"name":"DeferStake","type":"event"},{"anonymous":false,"inputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"indexed":true,"internalType":"struct Stake","name":"_stake","type":"tuple"}],"name":"EndStake","type":"event"},{"anonymous":false,"inputs":[{"components":[{"internalType":"uint40","name":"id","type":"uint40"},{"internalType":"uint40","name":"rewardTs","type":"uint40"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"address","name":"caller","type":"address"}],"indexed":true,"internalType":"struct Reward","name":"reward","type":"tuple"}],"name":"FlushRewardPool","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"user","type":"address"},{"indexed":true,"internalType":"address","name":"xenContract","type":"address"},{"indexed":true,"internalType":"address","name":"tokenContract","type":"address"},{"indexed":false,"internalType":"uint256","name":"xenAmount","type":"uint256"},{"indexed":false,"internalType":"uint256","name":"tokenAmount","type":"uint256"}],"name":"Redeemed","type":"event"},{"anonymous":false,"inputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"indexed":true,"internalType":"struct Stake","name":"_stake","type":"tuple"}],"name":"StartStake","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"address","name":"from","type":"address"},{"indexed":true,"internalType":"address","name":"to","type":"address"},{"indexed":false,"internalType":"uint256","name":"value","type":"uint256"}],"name":"Transfer","type":"event"},{"anonymous":false,"inputs":[{"indexed":true,"internalType":"uint256","name":"_shareRate","type":"uint256"}],"name":"UpdateShareRate","type":"event"},{"inputs":[],"name":"ANNUAL_INFLATION_RATE","outputs":[{"internalType":"UD60x18","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"MAX_STAKE_LENGTH_DAYS","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"XEN_ADDRESS","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"XEN_BURN_RATIO","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"owner","type":"address"},{"internalType":"address","name":"spender","type":"address"}],"name":"allowance","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"approve","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"account","type":"address"}],"name":"balanceOf","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"xen","type":"uint256"}],"name":"burnXEN","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"term","type":"uint256"}],"name":"calculateBonus","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"pure","type":"function"},{"inputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"internalType":"struct Stake","name":"stake","type":"tuple"}],"name":"calculateEarlyPayout","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"internalType":"struct Stake","name":"stake","type":"tuple"}],"name":"calculateLatePayout","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"bonus","type":"uint256"}],"name":"calculateShares","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"fenix","type":"uint256"}],"name":"calculateSizeBonus","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"pure","type":"function"},{"inputs":[{"internalType":"uint256","name":"term","type":"uint256"}],"name":"calculateTimeBonus","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"pure","type":"function"},{"inputs":[],"name":"cooldownUnlockTs","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"decimals","outputs":[{"internalType":"uint8","name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"subtractedValue","type":"uint256"}],"name":"decreaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"stakeIndex","type":"uint256"},{"internalType":"address","name":"stakerAddress","type":"address"}],"name":"deferStake","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"uint256","name":"stakeIndex","type":"uint256"}],"name":"endStake","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"equityPoolSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"equityPoolTotalShares","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"flushRewardPool","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"genesisTs","outputs":[{"internalType":"uint40","name":"","type":"uint40"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"addedValue","type":"uint256"}],"name":"increaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"name","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"user","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"onTokenBurned","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"rewardCount","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"index","type":"uint256"}],"name":"rewardFor","outputs":[{"components":[{"internalType":"uint40","name":"id","type":"uint40"},{"internalType":"uint40","name":"rewardTs","type":"uint40"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"address","name":"caller","type":"address"}],"internalType":"struct Reward","name":"","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"rewardPoolSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"shareRate","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"stakerAddress","type":"address"}],"name":"stakeCount","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"stakerAddress","type":"address"},{"internalType":"uint256","name":"stakeIndex","type":"uint256"}],"name":"stakeFor","outputs":[{"components":[{"internalType":"enum Status","name":"status","type":"uint8"},{"internalType":"uint40","name":"startTs","type":"uint40"},{"internalType":"uint40","name":"deferralTs","type":"uint40"},{"internalType":"uint40","name":"endTs","type":"uint40"},{"internalType":"uint16","name":"term","type":"uint16"},{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"shares","type":"uint256"},{"internalType":"uint256","name":"payout","type":"uint256"}],"internalType":"struct Stake","name":"","type":"tuple"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"fenix","type":"uint256"},{"internalType":"uint256","name":"term","type":"uint256"}],"name":"startStake","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"bytes4","name":"interfaceId","type":"bytes4"}],"name":"supportsInterface","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"symbol","outputs":[{"internalType":"string","name":"","type":"string"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"totalSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"to","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transfer","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"from","type":"address"},{"internalType":"address","name":"to","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transferFrom","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"}]

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

0x608060405234801561001057600080fd5b50600436106102925760003560e01c8063615a89a311610160578063a457c2d7116100d8578063dd62ed3e1161008c578063e3af6d0a11610071578063e3af6d0a146105f2578063e6c2cbb11461062f578063fb802a651461064257600080fd5b8063dd62ed3e14610599578063e1e48eb3146105df57600080fd5b8063ae94d2b5116100bd578063ae94d2b514610547578063bc1d089a14610550578063d8af78fc1461059057600080fd5b8063a457c2d714610521578063a9059cbb1461053457600080fd5b80637862affa1161012f5780639159e862116101145780639159e862146104a457806395d89b41146104ad578063a1472b15146104b557600080fd5b80637862affa14610489578063790854251461049c57600080fd5b8063615a89a31461041a5780636630a05e1461042d5780636f72fd201461044057806370a082311461045357600080fd5b806323b872dd1161020e57806339509351116101c25780633ec16194116101a75780633ec16194146103ec578063543746b1146103ff5780635cdc12f81461041257600080fd5b806339509351146103d0578063397b3378146103e357600080fd5b80633027e3c7116101f35780633027e3c714610382578063313ce5671461038b57806333060d901461039a57600080fd5b806323b872dd1461034f5780632ee409081461036257600080fd5b80630da63e3f1161026557806318160ddd1161024a57806318160ddd1461032b5780631a6cef14146103335780631c3fd1671461033c57600080fd5b80630da63e3f146102fc578063128bfcae1461031857600080fd5b806301ffc9a71461029757806306fdde03146102bf578063095ea7b3146102d45780630cbe28d6146102e7575b600080fd5b6102aa6102a5366004613494565b61064b565b60405190151581526020015b60405180910390f35b6102c76106e4565b6040516102b691906134d6565b6102aa6102e236600461356b565b610776565b6102fa6102f5366004613595565b61078e565b005b61030a66397beef356e6c481565b6040519081526020016102b6565b6102fa6103263660046135ae565b610bb7565b60025461030a565b61030a61271081565b6102fa61034a3660046135d0565b610f0f565b6102aa61035d3660046135fc565b61142b565b61037561037036600461356b565b611451565b6040516102b691906136a2565b61030a60085481565b604051601281526020016102b6565b61030a6103a8366004613715565b73ffffffffffffffffffffffffffffffffffffffff166000908152600a602052604090205490565b6102aa6103de36600461356b565b61158b565b61030a60065481565b61030a6103fa366004613595565b6115d7565b6102fa61040d36600461356b565b6115f4565b6102fa61173c565b61030a610428366004613766565b6119a3565b6102fa61043b366004613595565b611ab2565b61030a61044e3660046135ae565b611b55565b61030a610461366004613715565b73ffffffffffffffffffffffffffffffffffffffff1660009081526020819052604090205490565b61030a610497366004613595565b611b9e565b600b5461030a565b61030a611e6181565b6102c7611bfd565b6104c86104c3366004613595565b611c0c565b6040516102b69190600060808201905064ffffffffff808451168352806020850151166020840152506040830151604083015273ffffffffffffffffffffffffffffffffffffffff606084015116606083015292915050565b6102aa61052f36600461356b565b611caf565b6102aa61054236600461356b565b611d8b565b61030a60055481565b61056b7306450dee7fd2fb8e39061434babcfc05599a6fb881565b60405173ffffffffffffffffffffffffffffffffffffffff90911681526020016102b6565b61030a60095481565b61030a6105a7366004613840565b73ffffffffffffffffffffffffffffffffffffffff918216600090815260016020908152604080832093909416825291909152205490565b61030a6105ed366004613595565b611d99565b6106197f00000000000000000000000000000000000000000000000000000000645fc30b81565b60405164ffffffffff90911681526020016102b6565b61030a61063d366004613766565b611e2d565b61030a60075481565b60007fffffffff0000000000000000000000000000000000000000000000000000000082167f543746b10000000000000000000000000000000000000000000000000000000014806106de57507fffffffff0000000000000000000000000000000000000000000000000000000082167f01ffc9a700000000000000000000000000000000000000000000000000000000145b92915050565b6060600380546106f39061386a565b80601f016020809104026020016040519081016040528092919081815260200182805461071f9061386a565b801561076c5780601f106107415761010080835404028352916020019161076c565b820191906000526020600020905b81548152906001019060200180831161074f57829003601f168201915b5050505050905090565b600033610784818585611f2f565b5060019392505050565b6107988133610f0f565b336000908152600a602052604081208054839081106107b9576107b96138bd565b600091825260209091206040805161010081019091526004909202018054829060ff1660028111156107ed576107ed613638565b60028111156107fe576107fe613638565b8152815464ffffffffff61010082048116602084015266010000000000008204811660408401526b010000000000000000000000820416606083015261ffff700100000000000000000000000000000000909104166080820152600182015460a082015260028083015460c083015260039092015460e0909101529091508151600281111561088f5761088f613638565b036108d25760026040517fe04981d90000000000000000000000000000000000000000000000000000000081526004016108c991906138ec565b60405180910390fd5b6108e0338260e001516120e3565b60006109026108ff6108f38460a0015190565b60e08501515b906121d6565b90565b905060075481111561093f57600781905560405181907f371aff3c55ca45101819dbd6486bc608c1fe30cd77bd8ffef45a5429b024576090600090a25b6040805161010081019091526000908060028152602001846020015164ffffffffff168152602001846040015164ffffffffff168152602001846060015164ffffffffff168152602001846080015161ffff1681526020018460a0015181526020018460c0015181526020018460e00151815250905080600a60006109c13390565b73ffffffffffffffffffffffffffffffffffffffff1673ffffffffffffffffffffffffffffffffffffffff1681526020019081526020016000208581548110610a0c57610a0c6138bd565b600091825260209091208251600490920201805490919082907fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00166001836002811115610a5b57610a5b613638565b0217905550602082015181546040808501516060860151608087015161ffff16700100000000000000000000000000000000027fffffffffffffffffffffffffffff0000ffffffffffffffffffffffffffffffff64ffffffffff9283166b01000000000000000000000002167fffffffffffffffffffffffffffff00000000000000ffffffffffffffffffffff9383166601000000000000027fffffffffffffffffffffffffffffffffffffffffff0000000000ffffffffffff9390971661010002929092167fffffffffffffffffffffffffffffffffffffffffff00000000000000000000ff9095169490941794909417169290921717825560a0830151600183015560c0830151600283015560e09092015160039091015551610b819082906138fa565b604051908190038120907fd862f5fdbfa9636a4c1666d8348a7ae982c2350cc4c2894d901687f57c59c75b90600090a250505050565b81600003610bf1576040517f836fd8a700000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b80600003610c2b576040517fb38ff31300000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b426000610c3b62015180846139a2565b610c4590426139b9565b90506000610c538585611b55565b90506000610c60826115d7565b90506000610c7061016d876108f9565b90506000610ca56108ff610c9d84610c97670de0b6b3a764000066397beef356e6c46121ee565b906121fd565b8a5b9061230f565b90506000610cb66108ff8386610c9f565b90508160086000828254610cca91906139b9565b925050819055508060096000828254610ce391906139b9565b90915550506040805161010081018252600080825264ffffffffff8a8116602080850191909152838501839052908a16606084015261ffff8c16608084015260a083018d905260c0830185905260e08301829052338252600a81529281208054600180820183559183529390912082516004909402018054929384939192909183917fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0090911690836002811115610d9c57610d9c613638565b02179055506020820151815460408401516060850151608086015161ffff16700100000000000000000000000000000000027fffffffffffffffffffffffffffff0000ffffffffffffffffffffffffffffffff64ffffffffff9283166b01000000000000000000000002167fffffffffffffffffffffffffffff00000000000000ffffffffffffffffffffff9383166601000000000000027fffffffffffffffffffffffffffffffffffffffffff0000000000ffffffffffff9390961661010002929092167fffffffffffffffffffffffffffffffffffffffffff00000000000000000000ff9094169390931793909317169190911717815560a0820151600182015560c0820151600282015560e090910151600390910155610ec5610ebf3390565b8b61231e565b80604051610ed391906138fa565b604051908190038120907f49735babbf75685a1d5f3d305826f3c9df6d8cc12b0f9de5867f95675ac38c3a90600090a250505050505050505050565b73ffffffffffffffffffffffffffffffffffffffff81166000908152600a60205260409020548210610f6d576040517fb0dd466e00000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b73ffffffffffffffffffffffffffffffffffffffff81166000908152600a60205260408120805484908110610fa457610fa46138bd565b600091825260209091206040805161010081019091526004909202018054829060ff166002811115610fd857610fd8613638565b6002811115610fe957610fe9613638565b8152815464ffffffffff61010082048116602084015266010000000000008204811660408401526b010000000000000000000000820416606083015261ffff700100000000000000000000000000000000909104166080820152600182015460a0820152600282015460c082015260039091015460e090910152905060008151600281111561107a5761107a613638565b1461108457505050565b806060015164ffffffffff16421080156110b457503373ffffffffffffffffffffffffffffffffffffffff831614155b1561110657335b6040517f29507dbf00000000000000000000000000000000000000000000000000000000815273ffffffffffffffffffffffffffffffffffffffff90911660048201526024016108c9565b6000816060015164ffffffffff1642111561112e576111276108ff83611e2d565b905061113d565b61113a6108ff836119a3565b90505b600061115561114b60095490565b60c08501516108f9565b90506000611163828461230f565b905060006111776108ff83610c9f60085490565b905060006040518061010001604052806001600281111561119a5761119a613638565b8152602001876020015164ffffffffff1681526020014264ffffffffff168152602001876060015164ffffffffff168152602001876080015161ffff1681526020018760a0015181526020018760c00151815260200183815250905080600a60008973ffffffffffffffffffffffffffffffffffffffff1673ffffffffffffffffffffffffffffffffffffffff1681526020019081526020016000208981548110611247576112476138bd565b600091825260209091208251600490920201805490919082907fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0016600183600281111561129657611296613638565b02179055506020820151815460408401516060850151608086015161ffff16700100000000000000000000000000000000027fffffffffffffffffffffffffffff0000ffffffffffffffffffffffffffffffff64ffffffffff9283166b01000000000000000000000002167fffffffffffffffffffffffffffff00000000000000ffffffffffffffffffffff9383166601000000000000027fffffffffffffffffffffffffffffffffffffffffff0000000000ffffffffffff9390961661010002929092167fffffffffffffffffffffffffffffffffffffffffff00000000000000000000ff9094169390931793909317169190911717815560a0820151600182015560c080830151600283015560e090920151600390910155860151600980546000906113c59084906139cc565b9250508190555081600860008282546113de91906139cc565b90915550506040516113f19082906138fa565b604051908190038120907f9e6e56d0de3dd1d5b1ecba216b5e45e232e331aafcec0799fe0221b2b4e0ec6790600090a25050505050505050565b6000336114398582856124da565b6114448585856125b1565b60019150505b9392505050565b604080516101008101825260008082526020808301829052828401829052606083018290526080830182905260a0830182905260c0830182905260e0830182905273ffffffffffffffffffffffffffffffffffffffff86168252600a9052919091208054839081106114c5576114c56138bd565b600091825260209091206040805161010081019091526004909202018054829060ff1660028111156114f9576114f9613638565b600281111561150a5761150a613638565b81528154610100810464ffffffffff908116602084015266010000000000008204811660408401526b0100000000000000000000008204166060830152700100000000000000000000000000000000900461ffff166080820152600182015460a0820152600282015460c082015260039091015460e0909101529392505050565b33600081815260016020908152604080832073ffffffffffffffffffffffffffffffffffffffff8716845290915281205490919061078490829086906115d29087906139b9565b611f2f565b6000806115ec6115e660075490565b846108f9565b90508061144a565b337306450dee7fd2fb8e39061434babcfc05599a6fb81461161557336110bb565b73ffffffffffffffffffffffffffffffffffffffff8216611662576040517f9fabe1c100000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b8060000361169c576040517f836fd8a700000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b60006116aa61271083613a0e565b905080600660008282546116be91906139b9565b909155506116ce905083826120e3565b604080518381526020810183905230917306450dee7fd2fb8e39061434babcfc05599a6fb89173ffffffffffffffffffffffffffffffffffffffff8716917fda4c370e4f539b8e19d66144cad73d70fbf440a544e56ff38e28e38ed47801a8910160405180910390a4505050565b600554421015611778576040517faa9a98df00000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b60006277f8806005544261178c91906139cc565b6117969190613a0e565b9050600654600860008282546117ac91906139b9565b909155506117bf90506277f880826139a2565b6117cc906277f8806139b9565b600560008282546117dd91906139b9565b9250508190555060006040518060800160405280600b8054905064ffffffffff1681526020014264ffffffffff168152602001600654815260200161181f3390565b73ffffffffffffffffffffffffffffffffffffffff90811690915260006006819055600b8054600181018255915282517f0175b7a638427703f0dbe7bb9bbf987a2551717b34e79f33b5b1008d1fa01db9600390920291820180546020808701805164ffffffffff9586167fffffffffffffffffffffffffffffffffffffffffffff000000000000000000009094168417650100000000009187169190910217909355604080880180517f0175b7a638427703f0dbe7bb9bbf987a2551717b34e79f33b5b1008d1fa01dba8801556060808a0180517f0175b7a638427703f0dbe7bb9bbf987a2551717b34e79f33b5b1008d1fa01dbb90990180547fffffffffffffffffffffffff000000000000000000000000000000000000000016998b16999099179098558251948552945190951691830191909152925192810192909252915190921690820152909150608001604051908190038120907f4d21482c1d529d00b9e27bc6452492f43bb15630fbb706690945731858edae0f90600090a25050565b6000816020015164ffffffffff164210806119d157506000825160028111156119ce576119ce613638565b14155b15611a08576040517fb0dd466e00000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b816060015164ffffffffff16421115611a4d576040517fe3b243e200000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b6000826020015164ffffffffff1642611a6691906139cc565b9050600062015180846080015161ffff16611a8191906139a2565b90506000611aa56002611a9f611a9685612820565b6108f987612820565b9061289e565b9050805b95945050505050565b7306450dee7fd2fb8e39061434babcfc05599a6fb8639dc29fac336040517fffffffff0000000000000000000000000000000000000000000000000000000060e084901b16815273ffffffffffffffffffffffffffffffffffffffff909116600482015260248101849052604401600060405180830381600087803b158015611b3a57600080fd5b505af1158015611b4e573d6000803e3d6000fd5b5050505050565b600080611b646108ff85611d99565b90506000611b746108ff85611b9e565b90506000611b94611b8d6725b946ebc0b36173846121fd565b849061230f565b9695505050505050565b6000611e61821115611bdc576040517fe44ae5b500000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b60006115ec611bee611e615b856108f9565b670de0b6b3a7640000906121ee565b6060600480546106f39061386a565b604080516080810182526000808252602082018190529181018290526060810191909152600b8281548110611c4357611c436138bd565b6000918252602091829020604080516080810182526003909302909101805464ffffffffff808216855265010000000000909104169383019390935260018301549082015260029091015473ffffffffffffffffffffffffffffffffffffffff16606082015292915050565b33600081815260016020908152604080832073ffffffffffffffffffffffffffffffffffffffff8716845290915281205490919083811015611d73576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602560248201527f45524332303a2064656372656173656420616c6c6f77616e63652062656c6f7760448201527f207a65726f00000000000000000000000000000000000000000000000000000060648201526084016108c9565b611d808286868403611f2f565b506001949350505050565b6000336107848185856125b1565b6000611dc660037fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff6139cc565b8210611dfe576040517f2d493f1300000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b6106de6108ff611e1e611e1985670de0b6b3a76400006121ee565b6128fe565b670de0b6b3a764000090612925565b6000816020015164ffffffffff16421080611e5b5750600082516002811115611e5857611e58613638565b14155b15611e92576040517fb0dd466e00000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b816060015164ffffffffff16421015611ed7576040517f0f3f8ebf00000000000000000000000000000000000000000000000000000000815260040160405180910390fd5b6000826060015164ffffffffff1642611ef091906139cc565b905062ed4e00811115611f065750600092915050565b6000611f196003611a9f62ed4e00611be8565b90506000611aa5670de0b6b3a764000083612925565b73ffffffffffffffffffffffffffffffffffffffff8316611fd1576040517f08c379a0000000000000000000000000000000000000000000000000000000008152602060048201526024808201527f45524332303a20617070726f76652066726f6d20746865207a65726f2061646460448201527f726573730000000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff8216612074576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602260248201527f45524332303a20617070726f766520746f20746865207a65726f20616464726560448201527f737300000000000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff83811660008181526001602090815260408083209487168084529482529182902085905590518481527f8c5be1e5ebec7d5bd14f71427d1e84f3dd0314c0f7b2291e5b200ac8c7c3b92591015b60405180910390a3505050565b73ffffffffffffffffffffffffffffffffffffffff8216612160576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152601f60248201527f45524332303a206d696e7420746f20746865207a65726f20616464726573730060448201526064016108c9565b806002600082825461217291906139b9565b909155505073ffffffffffffffffffffffffffffffffffffffff8216600081815260208181526040808320805486019055518481527fddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef910160405180910390a35050565b600061144a6108ff84670de0b6b3a764000085612934565b600061144a6108ff83856139b9565b6000828281830361222857801561221557600061221f565b670de0b6b3a76400005b925050506106de565b670de0b6b3a7640000820361224957670de0b6b3a7640000925050506106de565b8060000361226357670de0b6b3a7640000925050506106de565b670de0b6b3a7640000810361227c5784925050506106de565b670de0b6b3a76400008211156122ad576122a66122a161229b87612a3f565b8661230f565b612ba2565b9250612307565b60006122cb6108ff846ec097ce7bc90715b34b9f1000000000613a0e565b905060006122e46122a16122de84612a3f565b8861230f565b90506123026108ff826ec097ce7bc90715b34b9f1000000000613a0e565b945050505b505092915050565b600061144a6108ff8484612c19565b73ffffffffffffffffffffffffffffffffffffffff82166123c1576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602160248201527f45524332303a206275726e2066726f6d20746865207a65726f2061646472657360448201527f730000000000000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff821660009081526020819052604090205481811015612477576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602260248201527f45524332303a206275726e20616d6f756e7420657863656564732062616c616e60448201527f636500000000000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff83166000818152602081815260408083208686039055600280548790039055518581529192917fddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef91016120d6565b73ffffffffffffffffffffffffffffffffffffffff8381166000908152600160209081526040808320938616835292905220547fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff81146125ab578181101561259e576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152601d60248201527f45524332303a20696e73756666696369656e7420616c6c6f77616e636500000060448201526064016108c9565b6125ab8484848403611f2f565b50505050565b73ffffffffffffffffffffffffffffffffffffffff8316612654576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602560248201527f45524332303a207472616e736665722066726f6d20746865207a65726f20616460448201527f647265737300000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff82166126f7576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602360248201527f45524332303a207472616e7366657220746f20746865207a65726f206164647260448201527f657373000000000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff8316600090815260208190526040902054818110156127ad576040517f08c379a000000000000000000000000000000000000000000000000000000000815260206004820152602660248201527f45524332303a207472616e7366657220616d6f756e742065786365656473206260448201527f616c616e6365000000000000000000000000000000000000000000000000000060648201526084016108c9565b73ffffffffffffffffffffffffffffffffffffffff848116600081815260208181526040808320878703905593871680835291849020805487019055925185815290927fddf252ad1be2c89b69c2b068fc378daa952ba7f163c4a11628f55a4df523b3ef910160405180910390a36125ab565b6000612854670de0b6b3a76400007fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff613a0e565b821115612890576040517f1cd951a7000000000000000000000000000000000000000000000000000000008152600481018390526024016108c9565b50670de0b6b3a76400000290565b60008281600184166128b857670de0b6b3a76400006128ba565b815b9050600184901c93505b83156128f8576128d48283612c19565b915060018416156128ec576128e98183612c19565b90505b600184901c93506128c4565b80611aa9565b60006106de826ec097ce7bc90715b34b9f100000000081612921576129216139df565b0490565b600061144a6108ff83856139cc565b600080807fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8587098587029250828110838203039150508060000361298c57838281612982576129826139df565b049250505061144a565b8381106129d6576040517f63a057780000000000000000000000000000000000000000000000000000000081526004810187905260248101869052604481018590526064016108c9565b60008486880960026001871981018816978890046003810283188082028403028082028403028082028403028082028403028082028403029081029092039091026000889003889004909101858311909403939093029303949094049190911702949350505050565b600081670de0b6b3a7640000811015612a87576040517f36d32ef0000000000000000000000000000000000000000000000000000000008152600481018490526024016108c9565b6000612b13670de0b6b3a7640000830460016fffffffffffffffffffffffffffffffff821160071b91821c67ffffffffffffffff811160061b90811c63ffffffff811160051b90811c61ffff811160041b90811c60ff8111600390811b91821c600f811160021b90811c918211871b91821c969096119490961792909217171791909117919091171790565b9050670de0b6b3a7640000810282821c7ffffffffffffffffffffffffffffffffffffffffffffffffff21f494c589c00008101612b535750949350505050565b671bc16d674ec800006706f05b59d3b200005b8015612b9657670de0b6b3a7640000838002049250818310612b8e579283019260019290921c915b60011c612b66565b50919695505050505050565b600081680a688906bd8affffff811115612beb576040517fb3b6ba1f000000000000000000000000000000000000000000000000000000008152600481018490526024016108c9565b6000612c03670de0b6b3a7640000604084901b613a0e565b9050612c116108ff82612d20565b949350505050565b600080807fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff84860984860292508281108382030391505080600003612c6b5750670de0b6b3a7640000900490506106de565b670de0b6b3a76400008110612cb6576040517f5173648d00000000000000000000000000000000000000000000000000000000815260048101869052602481018590526044016108c9565b6000670de0b6b3a7640000858709620400008185030493109091037d40000000000000000000000000000000000000000000000000000000000002919091177faccb18165bd6fe31ae1cf318dc5b51eee0e1ba569b88cd74c1773b91fac106690291505092915050565b7780000000000000000000000000000000000000000000000067ff00000000000000821615612e4157678000000000000000821615612d685768016a09e667f3bcc9090260401c5b674000000000000000821615612d87576801306fe0a31b7152df0260401c5b672000000000000000821615612da6576801172b83c7d517adce0260401c5b671000000000000000821615612dc55768010b5586cf9890f62a0260401c5b670800000000000000821615612de4576801059b0d31585743ae0260401c5b670400000000000000821615612e0357680102c9a3e778060ee70260401c5b670200000000000000821615612e225768010163da9fb33356d80260401c5b670100000000000000821615612e4157680100b1afa5abcbed610260401c5b66ff000000000000821615612f40576680000000000000821615612e6e5768010058c86da1c09ea20260401c5b6640000000000000821615612e8c576801002c605e2e8cec500260401c5b6620000000000000821615612eaa57680100162f3904051fa10260401c5b6610000000000000821615612ec8576801000b175effdc76ba0260401c5b6608000000000000821615612ee657680100058ba01fb9f96d0260401c5b6604000000000000821615612f045768010002c5cc37da94920260401c5b6602000000000000821615612f22576801000162e525ee05470260401c5b6601000000000000821615612f405768010000b17255775c040260401c5b65ff00000000008216156130365765800000000000821615612f6b576801000058b91b5bc9ae0260401c5b65400000000000821615612f8857680100002c5c89d5ec6d0260401c5b65200000000000821615612fa55768010000162e43f4f8310260401c5b65100000000000821615612fc257680100000b1721bcfc9a0260401c5b65080000000000821615612fdf5768010000058b90cf1e6e0260401c5b65040000000000821615612ffc576801000002c5c863b73f0260401c5b6502000000000082161561301957680100000162e430e5a20260401c5b65010000000000821615613036576801000000b1721835510260401c5b64ff000000008216156131235764800000000082161561305f57680100000058b90c0b490260401c5b64400000000082161561307b5768010000002c5c8601cc0260401c5b642000000000821615613097576801000000162e42fff00260401c5b6410000000008216156130b35768010000000b17217fbb0260401c5b6408000000008216156130cf576801000000058b90bfce0260401c5b6404000000008216156130eb57680100000002c5c85fe30260401c5b6402000000008216156131075768010000000162e42ff10260401c5b64010000000082161561312357680100000000b17217f80260401c5b63ff00000082161561320757638000000082161561314a5768010000000058b90bfc0260401c5b6340000000821615613165576801000000002c5c85fe0260401c5b632000000082161561318057680100000000162e42ff0260401c5b631000000082161561319b576801000000000b17217f0260401c5b63080000008216156131b657680100000000058b90c00260401c5b63040000008216156131d15768010000000002c5c8600260401c5b63020000008216156131ec576801000000000162e4300260401c5b63010000008216156132075768010000000000b172180260401c5b62ff00008216156132e2576280000082161561322c576801000000000058b90c0260401c5b6240000082161561324657680100000000002c5c860260401c5b622000008216156132605768010000000000162e430260401c5b6210000082161561327a57680100000000000b17210260401c5b620800008216156132945768010000000000058b910260401c5b620400008216156132ae576801000000000002c5c80260401c5b620200008216156132c857680100000000000162e40260401c5b620100008216156132e2576801000000000000b1720260401c5b61ff008216156133b45761800082161561330557680100000000000058b90260401c5b61400082161561331e5768010000000000002c5d0260401c5b612000821615613337576801000000000000162e0260401c5b6110008216156133505768010000000000000b170260401c5b610800821615613369576801000000000000058c0260401c5b61040082161561338257680100000000000002c60260401c5b61020082161561339b57680100000000000001630260401c5b6101008216156133b457680100000000000000b10260401c5b60ff82161561347d5760808216156133d557680100000000000000590260401c5b60408216156133ed576801000000000000002c0260401c5b602082161561340557680100000000000000160260401c5b601082161561341d576801000000000000000b0260401c5b600882161561343557680100000000000000060260401c5b600482161561344d57680100000000000000030260401c5b600282161561346557680100000000000000010260401c5b600182161561347d57680100000000000000010260401c5b670de0b6b3a76400000260409190911c60bf031c90565b6000602082840312156134a657600080fd5b81357fffffffff000000000000000000000000000000000000000000000000000000008116811461144a57600080fd5b600060208083528351808285015260005b81811015613503578581018301518582016040015282016134e7565b5060006040828601015260407fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0601f8301168501019250505092915050565b803573ffffffffffffffffffffffffffffffffffffffff8116811461356657600080fd5b919050565b6000806040838503121561357e57600080fd5b61358783613542565b946020939093013593505050565b6000602082840312156135a757600080fd5b5035919050565b600080604083850312156135c157600080fd5b50508035926020909101359150565b600080604083850312156135e357600080fd5b823591506135f360208401613542565b90509250929050565b60008060006060848603121561361157600080fd5b61361a84613542565b925061362860208501613542565b9150604084013590509250925092565b7f4e487b7100000000000000000000000000000000000000000000000000000000600052602160045260246000fd5b6003811061369e577f4e487b7100000000000000000000000000000000000000000000000000000000600052602160045260246000fd5b9052565b6000610100820190506136b6828451613667565b602083015164ffffffffff8082166020850152806040860151166040850152806060860151166060850152505061ffff608084015116608083015260a083015160a083015260c083015160c083015260e083015160e083015292915050565b60006020828403121561372757600080fd5b61144a82613542565b80356003811061356657600080fd5b803564ffffffffff8116811461356657600080fd5b803561ffff8116811461356657600080fd5b600061010080838503121561377a57600080fd5b6040519081019067ffffffffffffffff821181831017156137c4577f4e487b7100000000000000000000000000000000000000000000000000000000600052604160045260246000fd5b816040526137d184613730565b81526137df6020850161373f565b60208201526137f06040850161373f565b60408201526138016060850161373f565b606082015261381260808501613754565b608082015260a084013560a082015260c084013560c082015260e084013560e0820152809250505092915050565b6000806040838503121561385357600080fd5b61385c83613542565b91506135f360208401613542565b600181811c9082168061387e57607f821691505b6020821081036138b7577f4e487b7100000000000000000000000000000000000000000000000000000000600052602260045260246000fd5b50919050565b7f4e487b7100000000000000000000000000000000000000000000000000000000600052603260045260246000fd5b602081016106de8284613667565b613905818351613667565b600064ffffffffff8060208501511660208401528060408501511660408401528060608501511660608401525061ffff608084015116608083015260a083015160a083015260c083015160c083015261396860e0830160e0850151815260200190565b505061010001919050565b7f4e487b7100000000000000000000000000000000000000000000000000000000600052601160045260246000fd5b80820281158282048414176106de576106de613973565b808201808211156106de576106de613973565b818103818111156106de576106de613973565b7f4e487b7100000000000000000000000000000000000000000000000000000000600052601260045260246000fd5b600082613a44577f4e487b7100000000000000000000000000000000000000000000000000000000600052601260045260246000fd5b50049056fea164736f6c6343000813000a