Unidentified contract

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { UintUtils } from './UintUtils.sol';

library AddressUtils {
    using UintUtils for uint256;

    error AddressUtils__InsufficientBalance();
    error AddressUtils__NotContract();
    error AddressUtils__SendValueFailed();

    function toString(address account) internal pure returns (string memory) {
        return uint256(uint160(account)).toHexString(20);
    }

    function isContract(address account) internal view returns (bool) {
        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 0;
    }

    function sendValue(address payable account, uint256 amount) internal {
        (bool success, ) = account.call{ value: amount }('');
        if (!success) revert AddressUtils__SendValueFailed();
    }

    function functionCall(
        address target,
        bytes memory data
    ) internal returns (bytes memory) {
        return
            functionCall(target, data, 'AddressUtils: failed low-level call');
    }

    function functionCall(
        address target,
        bytes memory data,
        string memory error
    ) internal returns (bytes memory) {
        return _functionCallWithValue(target, data, 0, error);
    }

    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return
            functionCallWithValue(
                target,
                data,
                value,
                'AddressUtils: failed low-level call with value'
            );
    }

    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory error
    ) internal returns (bytes memory) {
        if (value > address(this).balance)
            revert AddressUtils__InsufficientBalance();
        return _functionCallWithValue(target, data, value, error);
    }

    /**
     * @notice execute arbitrary external call with limited gas usage and amount of copied return data
     * @dev derived from https://github.com/nomad-xyz/ExcessivelySafeCall (MIT License)
     * @param target recipient of call
     * @param gasAmount gas allowance for call
     * @param value native token value to include in call
     * @param maxCopy maximum number of bytes to copy from return data
     * @param data encoded call data
     * @return success whether call is successful
     * @return returnData copied return data
     */
    function excessivelySafeCall(
        address target,
        uint256 gasAmount,
        uint256 value,
        uint16 maxCopy,
        bytes memory data
    ) internal returns (bool success, bytes memory returnData) {
        returnData = new bytes(maxCopy);

        assembly {
            // execute external call via assembly to avoid automatic copying of return data
            success := call(
                gasAmount,
                target,
                value,
                add(data, 0x20),
                mload(data),
                0,
                0
            )

            // determine whether to limit amount of data to copy
            let toCopy := returndatasize()

            if gt(toCopy, maxCopy) {
                toCopy := maxCopy
            }

            // store the length of the copied bytes
            mstore(returnData, toCopy)

            // copy the bytes from returndata[0:toCopy]
            returndatacopy(add(returnData, 0x20), 0, toCopy)
        }
    }

    function _functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory error
    ) private returns (bytes memory) {
        if (!isContract(target)) revert AddressUtils__NotContract();

        (bool success, bytes memory returnData) = target.call{ value: value }(
            data
        );

        if (success) {
            return returnData;
        } else if (returnData.length > 0) {
            assembly {
                let returnData_size := mload(returnData)
                revert(add(32, returnData), returnData_size)
            }
        } else {
            revert(error);
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.9.0;

// ----------------------------------------------------------------------------
// BokkyPooBah's DateTime Library v1.01
//
// A gas-efficient Solidity date and time library
//
// https://github.com/bokkypoobah/BokkyPooBahsDateTimeLibrary
//
// Tested date range 1970/01/01 to 2345/12/31
//
// Conventions:
// Unit      | Range         | Notes
// :-------- |:-------------:|:-----
// timestamp | >= 0          | Unix timestamp, number of seconds since 1970/01/01 00:00:00 UTC
// year      | 1970 ... 2345 |
// month     | 1 ... 12      |
// day       | 1 ... 31      |
// hour      | 0 ... 23      |
// minute    | 0 ... 59      |
// second    | 0 ... 59      |
// dayOfWeek | 1 ... 7       | 1 = Monday, ..., 7 = Sunday
//
//
// Enjoy. (c) BokkyPooBah / Bok Consulting Pty Ltd 2018-2019. The MIT Licence.
// ----------------------------------------------------------------------------

library BokkyPooBahsDateTimeLibrary {

    uint constant SECONDS_PER_DAY = 24 * 60 * 60;
    uint constant SECONDS_PER_HOUR = 60 * 60;
    uint constant SECONDS_PER_MINUTE = 60;
    int constant OFFSET19700101 = 2440588;

    uint constant DOW_MON = 1;
    uint constant DOW_TUE = 2;
    uint constant DOW_WED = 3;
    uint constant DOW_THU = 4;
    uint constant DOW_FRI = 5;
    uint constant DOW_SAT = 6;
    uint constant DOW_SUN = 7;

    // ------------------------------------------------------------------------
    // Calculate the number of days from 1970/01/01 to year/month/day using
    // the date conversion algorithm from
    //   https://aa.usno.navy.mil/faq/JD_formula.html
    // and subtracting the offset 2440588 so that 1970/01/01 is day 0
    //
    // days = day
    //      - 32075
    //      + 1461 * (year + 4800 + (month - 14) / 12) / 4
    //      + 367 * (month - 2 - (month - 14) / 12 * 12) / 12
    //      - 3 * ((year + 4900 + (month - 14) / 12) / 100) / 4
    //      - offset
    // ------------------------------------------------------------------------
    function _daysFromDate(uint year, uint month, uint day) internal pure returns (uint _days) {
        require(year >= 1970);
        int _year = int(year);
        int _month = int(month);
        int _day = int(day);

        int __days = _day
          - 32075
          + 1461 * (_year + 4800 + (_month - 14) / 12) / 4
          + 367 * (_month - 2 - (_month - 14) / 12 * 12) / 12
          - 3 * ((_year + 4900 + (_month - 14) / 12) / 100) / 4
          - OFFSET19700101;

        _days = uint(__days);
    }

    // ------------------------------------------------------------------------
    // Calculate year/month/day from the number of days since 1970/01/01 using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // and adding the offset 2440588 so that 1970/01/01 is day 0
    //
    // int L = days + 68569 + offset
    // int N = 4 * L / 146097
    // L = L - (146097 * N + 3) / 4
    // year = 4000 * (L + 1) / 1461001
    // L = L - 1461 * year / 4 + 31
    // month = 80 * L / 2447
    // dd = L - 2447 * month / 80
    // L = month / 11
    // month = month + 2 - 12 * L
    // year = 100 * (N - 49) + year + L
    // ------------------------------------------------------------------------
    function _daysToDate(uint _days) internal pure returns (uint year, uint month, uint day) {
        int __days = int(_days);

        int L = __days + 68569 + OFFSET19700101;
        int N = 4 * L / 146097;
        L = L - (146097 * N + 3) / 4;
        int _year = 4000 * (L + 1) / 1461001;
        L = L - 1461 * _year / 4 + 31;
        int _month = 80 * L / 2447;
        int _day = L - 2447 * _month / 80;
        L = _month / 11;
        _month = _month + 2 - 12 * L;
        _year = 100 * (N - 49) + _year + L;

        year = uint(_year);
        month = uint(_month);
        day = uint(_day);
    }

    function timestampFromDate(uint year, uint month, uint day) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY;
    }
    function timestampFromDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + hour * SECONDS_PER_HOUR + minute * SECONDS_PER_MINUTE + second;
    }
    function timestampToDate(uint timestamp) internal pure returns (uint year, uint month, uint day) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function timestampToDateTime(uint timestamp) internal pure returns (uint year, uint month, uint day, uint hour, uint minute, uint second) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
        secs = secs % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
        second = secs % SECONDS_PER_MINUTE;
    }

    function isValidDate(uint year, uint month, uint day) internal pure returns (bool valid) {
        if (year >= 1970 && month > 0 && month <= 12) {
            uint daysInMonth = _getDaysInMonth(year, month);
            if (day > 0 && day <= daysInMonth) {
                valid = true;
            }
        }
    }
    function isValidDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (bool valid) {
        if (isValidDate(year, month, day)) {
            if (hour < 24 && minute < 60 && second < 60) {
                valid = true;
            }
        }
    }
    function isLeapYear(uint timestamp) internal pure returns (bool leapYear) {
        (uint year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        leapYear = _isLeapYear(year);
    }
    function _isLeapYear(uint year) internal pure returns (bool leapYear) {
        leapYear = ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
    }
    function isWeekDay(uint timestamp) internal pure returns (bool weekDay) {
        weekDay = getDayOfWeek(timestamp) <= DOW_FRI;
    }
    function isWeekEnd(uint timestamp) internal pure returns (bool weekEnd) {
        weekEnd = getDayOfWeek(timestamp) >= DOW_SAT;
    }
    function getDaysInMonth(uint timestamp) internal pure returns (uint daysInMonth) {
        (uint year, uint month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        daysInMonth = _getDaysInMonth(year, month);
    }
    function _getDaysInMonth(uint year, uint month) internal pure returns (uint daysInMonth) {
        if (month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
            daysInMonth = 31;
        } else if (month != 2) {
            daysInMonth = 30;
        } else {
            daysInMonth = _isLeapYear(year) ? 29 : 28;
        }
    }
    // 1 = Monday, 7 = Sunday
    function getDayOfWeek(uint timestamp) internal pure returns (uint dayOfWeek) {
        uint _days = timestamp / SECONDS_PER_DAY;
        dayOfWeek = (_days + 3) % 7 + 1;
    }

    function getYear(uint timestamp) internal pure returns (uint year) {
        (year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getMonth(uint timestamp) internal pure returns (uint month) {
        (,month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getDay(uint timestamp) internal pure returns (uint day) {
        (,,day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getHour(uint timestamp) internal pure returns (uint hour) {
        uint secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
    }
    function getMinute(uint timestamp) internal pure returns (uint minute) {
        uint secs = timestamp % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
    }
    function getSecond(uint timestamp) internal pure returns (uint second) {
        second = timestamp % SECONDS_PER_MINUTE;
    }

    function addYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year += _years;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addMonths(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        month += _months;
        year += (month - 1) / 12;
        month = (month - 1) % 12 + 1;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addDays(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _days * SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _hours * SECONDS_PER_HOUR;
        require(newTimestamp >= timestamp);
    }
    function addMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp >= timestamp);
    }
    function addSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _seconds;
        require(newTimestamp >= timestamp);
    }

    function subYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year -= _years;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subMonths(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint yearMonth = year * 12 + (month - 1) - _months;
        year = yearMonth / 12;
        month = yearMonth % 12 + 1;
        uint daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + timestamp % SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subDays(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _days * SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _hours * SECONDS_PER_HOUR;
        require(newTimestamp <= timestamp);
    }
    function subMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp <= timestamp);
    }
    function subSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _seconds;
        require(newTimestamp <= timestamp);
    }

    function diffYears(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _years) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear,,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear,,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _years = toYear - fromYear;
    }
    function diffMonths(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _months) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear, uint fromMonth,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear, uint toMonth,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _months = toYear * 12 + toMonth - fromYear * 12 - fromMonth;
    }
    function diffDays(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _days) {
        require(fromTimestamp <= toTimestamp);
        _days = (toTimestamp - fromTimestamp) / SECONDS_PER_DAY;
    }
    function diffHours(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _hours) {
        require(fromTimestamp <= toTimestamp);
        _hours = (toTimestamp - fromTimestamp) / SECONDS_PER_HOUR;
    }
    function diffMinutes(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _minutes) {
        require(fromTimestamp <= toTimestamp);
        _minutes = (toTimestamp - fromTimestamp) / SECONDS_PER_MINUTE;
    }
    function diffSeconds(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _seconds) {
        require(fromTimestamp <= toTimestamp);
        _seconds = toTimestamp - fromTimestamp;
    }
}

// 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;

// 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 { 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 { 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 ^0.8.8;

import { IERC165BaseInternal } from './IERC165BaseInternal.sol';
import { ERC165BaseStorage } from './ERC165BaseStorage.sol';

/**
 * @title ERC165 implementation
 */
abstract contract ERC165BaseInternal is IERC165BaseInternal {
    /**
     * @notice indicates whether an interface is already supported based on the interfaceId
     * @param interfaceId id of interface to check
     * @return bool indicating whether interface is supported
     */
    function _supportsInterface(
        bytes4 interfaceId
    ) internal view virtual returns (bool) {
        return ERC165BaseStorage.layout().supportedInterfaces[interfaceId];
    }

    /**
     * @notice sets status of interface support
     * @param interfaceId id of interface to set status for
     * @param status boolean indicating whether interface will be set as supported
     */
    function _setSupportsInterface(
        bytes4 interfaceId,
        bool status
    ) internal virtual {
        if (interfaceId == 0xffffffff) revert ERC165Base__InvalidInterfaceId();
        ERC165BaseStorage.layout().supportedInterfaces[interfaceId] = status;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

library ERC165BaseStorage {
    struct Layout {
        mapping(bytes4 => bool) supportedInterfaces;
    }

    bytes32 internal constant STORAGE_SLOT =
        keccak256('solidstate.contracts.storage.ERC165Base');

    function layout() internal pure returns (Layout storage l) {
        bytes32 slot = STORAGE_SLOT;
        assembly {
            l.slot := slot
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

/**
 * @title Set implementation with enumeration functions
 * @dev derived from https://github.com/OpenZeppelin/openzeppelin-contracts (MIT license)
 */
library EnumerableSet {
    error EnumerableSet__IndexOutOfBounds();

    struct Set {
        bytes32[] _values;
        // 1-indexed to allow 0 to signify nonexistence
        mapping(bytes32 => uint256) _indexes;
    }

    struct Bytes32Set {
        Set _inner;
    }

    struct AddressSet {
        Set _inner;
    }

    struct UintSet {
        Set _inner;
    }

    function at(
        Bytes32Set storage set,
        uint256 index
    ) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    function at(
        AddressSet storage set,
        uint256 index
    ) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    function at(
        UintSet storage set,
        uint256 index
    ) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    function contains(
        Bytes32Set storage set,
        bytes32 value
    ) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    function contains(
        AddressSet storage set,
        address value
    ) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    function contains(
        UintSet storage set,
        uint256 value
    ) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    function indexOf(
        Bytes32Set storage set,
        bytes32 value
    ) internal view returns (uint256) {
        return _indexOf(set._inner, value);
    }

    function indexOf(
        AddressSet storage set,
        address value
    ) internal view returns (uint256) {
        return _indexOf(set._inner, bytes32(uint256(uint160(value))));
    }

    function indexOf(
        UintSet storage set,
        uint256 value
    ) internal view returns (uint256) {
        return _indexOf(set._inner, bytes32(value));
    }

    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    function add(
        Bytes32Set storage set,
        bytes32 value
    ) internal returns (bool) {
        return _add(set._inner, value);
    }

    function add(
        AddressSet storage set,
        address value
    ) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    function remove(
        Bytes32Set storage set,
        bytes32 value
    ) internal returns (bool) {
        return _remove(set._inner, value);
    }

    function remove(
        AddressSet storage set,
        address value
    ) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    function remove(
        UintSet storage set,
        uint256 value
    ) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    function toArray(
        Bytes32Set storage set
    ) internal view returns (bytes32[] memory) {
        return set._inner._values;
    }

    function toArray(
        AddressSet storage set
    ) internal view returns (address[] memory) {
        bytes32[] storage values = set._inner._values;
        address[] storage array;

        assembly {
            array.slot := values.slot
        }

        return array;
    }

    function toArray(
        UintSet storage set
    ) internal view returns (uint256[] memory) {
        bytes32[] storage values = set._inner._values;
        uint256[] storage array;

        assembly {
            array.slot := values.slot
        }

        return array;
    }

    function _at(
        Set storage set,
        uint256 index
    ) private view returns (bytes32) {
        if (index >= set._values.length)
            revert EnumerableSet__IndexOutOfBounds();
        return set._values[index];
    }

    function _contains(
        Set storage set,
        bytes32 value
    ) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    function _indexOf(
        Set storage set,
        bytes32 value
    ) private view returns (uint256) {
        unchecked {
            return set._indexes[value] - 1;
        }
    }

    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    function _add(
        Set storage set,
        bytes32 value
    ) private returns (bool status) {
        if (!_contains(set, value)) {
            set._values.push(value);
            set._indexes[value] = set._values.length;
            status = true;
        }
    }

    function _remove(
        Set storage set,
        bytes32 value
    ) private returns (bool status) {
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            unchecked {
                bytes32 last = set._values[set._values.length - 1];

                // move last value to now-vacant index

                set._values[valueIndex - 1] = last;
                set._indexes[last] = valueIndex;
            }
            // clear last index

            set._values.pop();
            delete set._indexes[value];

            status = true;
        }
    }
}

// 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 { 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 ^0.8.8;

import { IERC165 } from './IERC165.sol';
import { IERC1155Internal } from './IERC1155Internal.sol';

/**
 * @title ERC1155 interface
 * @dev see https://eips.ethereum.org/EIPS/eip-1155
 */
interface IERC1155 is IERC1155Internal, IERC165 {
    /**
     * @notice query the balance of given token held by given address
     * @param account address to query
     * @param id token to query
     * @return token balance
     */
    function balanceOf(
        address account,
        uint256 id
    ) external view returns (uint256);

    /**
     * @notice query the balances of given tokens held by given addresses
     * @param accounts addresss to query
     * @param ids tokens to query
     * @return token balances
     */
    function balanceOfBatch(
        address[] calldata accounts,
        uint256[] calldata ids
    ) external view returns (uint256[] memory);

    /**
     * @notice query approval status of given operator with respect to given address
     * @param account address to query for approval granted
     * @param operator address to query for approval received
     * @return whether operator is approved to spend tokens held by account
     */
    function isApprovedForAll(
        address account,
        address operator
    ) external view returns (bool);

    /**
     * @notice grant approval to or revoke approval from given operator to spend held tokens
     * @param operator address whose approval status to update
     * @param status whether operator should be considered approved
     */
    function setApprovalForAll(address operator, bool status) external;

    /**
     * @notice transfer tokens between given addresses, checking for ERC1155Receiver implementation if applicable
     * @param from sender of tokens
     * @param to receiver of tokens
     * @param id token ID
     * @param amount quantity of tokens to transfer
     * @param data data payload
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes calldata data
    ) external;

    /**
     * @notice transfer batch of tokens between given addresses, checking for ERC1155Receiver implementation if applicable
     * @param from sender of tokens
     * @param to receiver of tokens
     * @param ids list of token IDs
     * @param amounts list of quantities of tokens to transfer
     * @param data data payload
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata amounts,
        bytes calldata data
    ) external;
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC1155 } from '../../../interfaces/IERC1155.sol';
import { IERC1155BaseInternal } from './IERC1155BaseInternal.sol';

/**
 * @title ERC1155 base interface
 */
interface IERC1155Base is IERC1155BaseInternal, IERC1155 {

}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC1155Internal } from '../../../interfaces/IERC1155Internal.sol';

/**
 * @title ERC1155 base interface
 */
interface IERC1155BaseInternal is IERC1155Internal {
    error ERC1155Base__ArrayLengthMismatch();
    error ERC1155Base__BalanceQueryZeroAddress();
    error ERC1155Base__NotOwnerOrApproved();
    error ERC1155Base__SelfApproval();
    error ERC1155Base__BurnExceedsBalance();
    error ERC1155Base__BurnFromZeroAddress();
    error ERC1155Base__ERC1155ReceiverRejected();
    error ERC1155Base__ERC1155ReceiverNotImplemented();
    error ERC1155Base__MintToZeroAddress();
    error ERC1155Base__TransferExceedsBalance();
    error ERC1155Base__TransferToZeroAddress();
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC1155BaseInternal } from '../base/IERC1155BaseInternal.sol';

/**
 * @title ERC1155 enumerable and aggregate function interface
 */
interface IERC1155Enumerable is IERC1155BaseInternal {
    /**
     * @notice query total minted supply of given token
     * @param id token id to query
     * @return token supply
     */
    function totalSupply(uint256 id) external view returns (uint256);

    /**
     * @notice query total number of holders for given token
     * @param id token id to query
     * @return quantity of holders
     */
    function totalHolders(uint256 id) external view returns (uint256);

    /**
     * @notice query holders of given token
     * @param id token id to query
     * @return list of holder addresses
     */
    function accountsByToken(
        uint256 id
    ) external view returns (address[] memory);

    /**
     * @notice query tokens held by given address
     * @param account address to query
     * @return list of token ids
     */
    function tokensByAccount(
        address account
    ) external view returns (uint256[] memory);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

/**
 * @title Partial ERC1155 interface needed by internal functions
 */
interface IERC1155Internal {
    event TransferSingle(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256 id,
        uint256 value
    );

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

    event ApprovalForAll(
        address indexed account,
        address indexed operator,
        bool approved
    );
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC165Internal } from './IERC165Internal.sol';

/**
 * @title ERC165 interface registration interface
 * @dev see https://eips.ethereum.org/EIPS/eip-165
 */
interface IERC165 is IERC165Internal {
    /**
     * @notice query whether contract has registered support for given interface
     * @param interfaceId interface id
     * @return bool whether interface is supported
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import { IERC165Internal } from '../../../interfaces/IERC165Internal.sol';

interface IERC165BaseInternal is IERC165Internal {
    error ERC165Base__InvalidInterfaceId();
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

/**
 * @title ERC165 interface registration interface
 */
interface IERC165Internal {

}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC20Internal } from './IERC20Internal.sol';

/**
 * @title ERC20 interface
 * @dev see https://eips.ethereum.org/EIPS/eip-20
 */
interface IERC20 is IERC20Internal {
    /**
     * @notice query the total minted token supply
     * @return token supply
     */
    function totalSupply() external view returns (uint256);

    /**
     * @notice query the token balance of given account
     * @param account address to query
     * @return token balance
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @notice query the allowance granted from given holder to given spender
     * @param holder approver of allowance
     * @param spender recipient of allowance
     * @return token allowance
     */
    function allowance(
        address holder,
        address spender
    ) external view returns (uint256);

    /**
     * @notice grant approval to spender to spend tokens
     * @dev prefer ERC20Extended functions to avoid transaction-ordering vulnerability (see https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729)
     * @param spender recipient of allowance
     * @param amount quantity of tokens approved for spending
     * @return success status (always true; otherwise function should revert)
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @notice transfer tokens to given recipient
     * @param recipient beneficiary of token transfer
     * @param amount quantity of tokens to transfer
     * @return success status (always true; otherwise function should revert)
     */
    function transfer(
        address recipient,
        uint256 amount
    ) external returns (bool);

    /**
     * @notice transfer tokens to given recipient on behalf of given holder
     * @param holder holder of tokens prior to transfer
     * @param recipient beneficiary of token transfer
     * @param amount quantity of tokens to transfer
     * @return success status (always true; otherwise function should revert)
     */
    function transferFrom(
        address holder,
        address recipient,
        uint256 amount
    ) external returns (bool);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

/**
 * @title Partial ERC20 interface needed by internal functions
 */
interface IERC20Internal {
    event Transfer(address indexed from, address indexed to, uint256 value);

    event Approval(
        address indexed owner,
        address indexed spender,
        uint256 value
    );
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { IERC20MetadataInternal } from './IERC20MetadataInternal.sol';

/**
 * @title ERC20 metadata interface
 */
interface IERC20Metadata is IERC20MetadataInternal {
    /**
     * @notice return token name
     * @return token name
     */
    function name() external view returns (string memory);

    /**
     * @notice return token symbol
     * @return token symbol
     */
    function symbol() external view returns (string memory);

    /**
     * @notice return token decimals, generally used only for display purposes
     * @return token decimals
     */
    function decimals() external view returns (uint8);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

/**
 * @title ERC20 metadata internal interface
 */
interface IERC20MetadataInternal {

}

// SPDX-License-Identifier: LGPL-3.0-or-later
// For terms and conditions regarding commercial use please see https://license.premia.blue
pragma solidity ^0.8.19;

import {UD60x18} from "lib/prb-math/src/UD60x18.sol";
import {IERC1155Base} from "@solidstate/contracts/token/ERC1155/base/IERC1155Base.sol";
import {IERC1155Enumerable} from "@solidstate/contracts/token/ERC1155/enumerable/IERC1155Enumerable.sol";

interface IOptionPS is IERC1155Base, IERC1155Enumerable {
    enum TokenType {
        Long,
        Short
    }

    error OptionPS__ExercisePeriodEnded(uint256 maturity, uint256 exercisePeriodEnd);
    error OptionPS__ExercisePeriodNotEnded(uint256 maturity, uint256 exercisePeriodEnd);
    error OptionPS__OptionMaturityNot8UTC(uint256 maturity);
    error OptionPS__OptionExpired(uint256 maturity);
    error OptionPS__OptionNotExpired(uint256 maturity);
    error OptionPS__StrikeNotMultipleOfStrikeInterval(UD60x18 strike, UD60x18 strikeInterval);

    event Exercise(
        address indexed user,
        UD60x18 strike,
        uint256 maturity,
        UD60x18 contractSize,
        UD60x18 exerciseValue,
        UD60x18 exerciseCost,
        UD60x18 exerciseFee
    );

    event Settle(
        address indexed user,
        UD60x18 contractSize,
        UD60x18 strike,
        uint256 maturity,
        UD60x18 collateralAmount,
        UD60x18 exerciseTokenAmount
    );

    event Underwrite(
        address indexed underwriter,
        address indexed longReceiver,
        UD60x18 strike,
        uint256 maturity,
        UD60x18 contractSize
    );

    event Annihilate(address indexed annihilator, UD60x18 strike, uint256 maturity, UD60x18 contractSize);

    /// @notice Returns the pair infos for this option
    function getSettings() external view returns (address base, address quote, bool isCall);

    /// @notice Returns the length of time in seconds during which long holders can exercise their options after maturity
    function getExerciseDuration() external pure returns (uint256);

    /// @notice Underwrite an option by depositing collateral
    /// @param strike the option strike price (18 decimals)
    /// @param longReceiver the address that will receive the long tokens
    /// @param maturity the option maturity timestamp
    /// @param contractSize number of long tokens to mint (18 decimals)
    function underwrite(UD60x18 strike, uint64 maturity, address longReceiver, UD60x18 contractSize) external;

    /// @notice Burn longs and shorts, to recover collateral of the option
    /// @param strike the option strike price (18 decimals)
    /// @param maturity the option maturity timestamp
    /// @param contractSize number of contracts to annihilate (18 decimals)
    function annihilate(UD60x18 strike, uint64 maturity, UD60x18 contractSize) external;

    /// @notice Exercises the long options held by the caller.
    /// @param strike the option strike price (18 decimals)
    /// @param maturity the option maturity timestamp
    /// @param contractSize number of long tokens to exercise (18 decimals)
    /// @return exerciseValue the amount of tokens transferred to the caller
    function exercise(UD60x18 strike, uint64 maturity, UD60x18 contractSize) external returns (uint256 exerciseValue);

    /// @notice Settles the short options held by the caller.
    /// @param strike the option strike price (18 decimals)
    /// @param maturity the option maturity timestamp
    /// @param contractSize number of short tokens to settle (18 decimals)
    /// @return collateralAmount the amount of collateral transferred to the caller (base for calls, quote for puts)
    /// @return exerciseTokenAmount the amount of exerciseToken transferred to the caller (quote for calls, base for puts)
    function settle(
        UD60x18 strike,
        uint64 maturity,
        UD60x18 contractSize
    ) external returns (uint256 collateralAmount, uint256 exerciseTokenAmount);

    /// @notice Returns the list of existing tokenIds with non zero balance
    /// @return tokenIds The list of existing tokenIds
    function getTokenIds() external view returns (uint256[] memory);
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

interface IProxy {
    error Proxy__ImplementationIsNotContract();

    fallback() external payable;
}

// SPDX-License-Identifier: LGPL-3.0-or-later
// For terms and conditions regarding commercial use please see https://license.premia.blue
pragma solidity ^0.8.19;

interface IProxyManager {
    event ManagedImplementationSet(address implementation);

    /// @notice Return the implementation address of the managed proxy
    function getManagedProxyImplementation() external view returns (address);

    /// @notice Set the implementation address of the managed proxy
    function setManagedProxyImplementation(address implementation) external;
}

// 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: LicenseRef-P3-DUAL
// For terms and conditions regarding commercial use please see https://license.premia.blue
pragma solidity ^0.8.19;

import {BokkyPooBahsDateTimeLibrary as DateTime} from "lib/BokkyPooBahsDateTimeLibrary/contracts/BokkyPooBahsDateTimeLibrary.sol";
import {UD60x18, ud} from "lib/prb-math/src/UD60x18.sol";
import {SD59x18} from "lib/prb-math/src/SD59x18.sol";

import {ZERO, ONE, TWO, iZERO, iONE, iTWO, iFOUR, iNINE} from "./Constants.sol";

library OptionMath {
    struct BlackScholesPriceVarsInternal {
        int256 discountFactor;
        int256 timeScaledVol;
        int256 timeScaledVar;
        int256 timeScaledRiskFreeRate;
    }

    UD60x18 internal constant INITIALIZATION_ALPHA = UD60x18.wrap(5e18);
    UD60x18 internal constant ATM_MONEYNESS = UD60x18.wrap(0.5e18);
    uint256 internal constant NEAR_TERM_TTM = 14 days;
    uint256 internal constant ONE_YEAR_TTM = 365 days;
    UD60x18 internal constant FEE_SCALAR = UD60x18.wrap(100e18);

    SD59x18 internal constant ALPHA = SD59x18.wrap(-6.37309208e18);
    SD59x18 internal constant LAMBDA = SD59x18.wrap(-0.61228883e18);
    SD59x18 internal constant S1 = SD59x18.wrap(-0.11105481e18);
    SD59x18 internal constant S2 = SD59x18.wrap(0.44334159e18);
    int256 internal constant SQRT_2PI = 2_506628274631000502;

    UD60x18 internal constant MIN_INPUT_PRICE = UD60x18.wrap(1e1);
    UD60x18 internal constant MAX_INPUT_PRICE = UD60x18.wrap(1e34);

    error OptionMath__NonPositiveVol();
    error OptionMath__OutOfBoundsPrice(UD60x18 min, UD60x18 max, UD60x18 price);
    error OptionMath__Underflow();

    /// @notice Helper function to evaluate used to compute the normal CDF approximation
    /// @param x The input to the normal CDF (18 decimals)
    /// @return result The value of the evaluated helper function (18 decimals)
    function helperNormal(SD59x18 x) internal pure returns (SD59x18 result) {
        SD59x18 a = (ALPHA / LAMBDA) * S1;
        SD59x18 b = (S1 * x + iONE).pow(LAMBDA / S1) - iONE;
        result = ((a * b + S2 * x).exp() * (-iTWO.ln())).exp();
    }

    /// @notice Approximation of the normal CDF
    /// @dev The approximation implemented is based on the paper 'Accurate RMM-Based Approximations for the CDF of the
    ///      Normal Distribution' by Haim Shore
    /// @param x input value to evaluate the normal CDF on, F(Z<=x) (18 decimals)
    /// @return result The normal CDF evaluated at x (18 decimals)
    function normalCdf(SD59x18 x) internal pure returns (SD59x18 result) {
        if (x <= -iNINE) {
            result = iZERO;
        } else if (x >= iNINE) {
            result = iONE;
        } else {
            result = ((iONE + helperNormal(-x)) - helperNormal(x)) / iTWO;
        }
    }

    /// @notice Normal Distribution Probability Density Function.
    /// @dev Equal to `Z(x) = (1 / σ√2π)e^( (-(x - µ)^2) / 2σ^2 )`. Only computes pdf of a distribution with `µ = 0` and
    ///      `σ = 1`.
    /// @custom:error Maximum error of 1.2e-7.
    /// @custom:source https://mathworld.wolfram.com/ProbabilityDensityFunction.html.
    /// @param x Number to get PDF for (18 decimals)
    /// @return z z-number (18 decimals)
    function normalPdf(SD59x18 x) internal pure returns (SD59x18 z) {
        SD59x18 e;
        int256 one = iONE.unwrap();
        uint256 two = TWO.unwrap();

        assembly {
            e := sdiv(mul(add(not(x), 1), x), two) // (-x * x) / 2.
        }
        e = e.exp();
        assembly {
            z := sdiv(mul(e, one), SQRT_2PI)
        }
    }

    /// @notice Implementation of the ReLu function `f(x)=(x)^+` to compute call / put payoffs
    /// @param x Input value (18 decimals)
    /// @return result Output of the relu function (18 decimals)
    function relu(SD59x18 x) internal pure returns (UD60x18) {
        if (x >= iZERO) {
            return x.intoUD60x18();
        }
        return ZERO;
    }

    /// @notice Returns the terms `d1` and `d2` from the Black-Scholes formula that are used to compute the price of a
    ///         call / put option.
    /// @param spot The spot price. (18 decimals)
    /// @param strike The strike price of the option. (18 decimals)
    /// @param timeToMaturity The time until the option expires. (18 decimals)
    /// @param volAnnualized The percentage volatility of the geometric Brownian motion. (18 decimals)
    /// @param riskFreeRate The rate of the risk-less asset, i.e. the risk-free interest rate. (18 decimals)
    /// @return d1 The term d1 from the Black-Scholes formula. (18 decimals)
    /// @return d2 The term d2 from the Black-Scholes formula. (18 decimals)
    function d1d2(
        UD60x18 spot,
        UD60x18 strike,
        UD60x18 timeToMaturity,
        UD60x18 volAnnualized,
        UD60x18 riskFreeRate
    ) internal pure returns (SD59x18 d1, SD59x18 d2) {
        UD60x18 timeScaledRiskFreeRate = riskFreeRate * timeToMaturity;
        UD60x18 timeScaledVariance = (volAnnualized.powu(2) / TWO) * timeToMaturity;
        UD60x18 timeScaledStd = volAnnualized * timeToMaturity.sqrt();
        SD59x18 lnSpot = (spot / strike).intoSD59x18().ln();

        d1 =
            (lnSpot + timeScaledVariance.intoSD59x18() + timeScaledRiskFreeRate.intoSD59x18()) /
            timeScaledStd.intoSD59x18();

        d2 = d1 - timeScaledStd.intoSD59x18();
    }

    /// @notice Calculate option delta
    /// @param spot Spot price
    /// @param strike Strike price
    /// @param timeToMaturity Duration of option contract (in years)
    /// @param volAnnualized Annualized volatility
    /// @param isCall whether to price "call" or "put" option
    /// @return price Option delta
    function optionDelta(
        UD60x18 spot,
        UD60x18 strike,
        UD60x18 timeToMaturity,
        UD60x18 volAnnualized,
        UD60x18 riskFreeRate,
        bool isCall
    ) internal pure returns (SD59x18) {
        (SD59x18 d1, ) = d1d2(spot, strike, timeToMaturity, volAnnualized, riskFreeRate);

        if (isCall) {
            return normalCdf(d1);
        } else {
            return -normalCdf(-d1);
        }
    }

    /// @notice Calculate the price of an option using the Black-Scholes model
    /// @dev this implementation assumes zero interest
    /// @param spot Spot price (18 decimals)
    /// @param strike Strike price (18 decimals)
    /// @param timeToMaturity Duration of option contract (in years) (18 decimals)
    /// @param volAnnualized Annualized volatility (18 decimals)
    /// @param riskFreeRate The risk-free rate (18 decimals)
    /// @param isCall whether to price "call" or "put" option
    /// @return price The Black-Scholes option price (18 decimals)
    function blackScholesPrice(
        UD60x18 spot,
        UD60x18 strike,
        UD60x18 timeToMaturity,
        UD60x18 volAnnualized,
        UD60x18 riskFreeRate,
        bool isCall
    ) internal pure returns (UD60x18) {
        SD59x18 _spot = spot.intoSD59x18();
        SD59x18 _strike = strike.intoSD59x18();
        if (volAnnualized == ZERO) revert OptionMath__NonPositiveVol();

        if (timeToMaturity == ZERO) {
            if (isCall) {
                return relu(_spot - _strike);
            }
            return relu(_strike - _spot);
        }

        SD59x18 discountFactor;
        if (riskFreeRate > ZERO) {
            discountFactor = (riskFreeRate * timeToMaturity).intoSD59x18().exp();
        } else {
            discountFactor = iONE;
        }

        (SD59x18 d1, SD59x18 d2) = d1d2(spot, strike, timeToMaturity, volAnnualized, riskFreeRate);
        SD59x18 sign = isCall ? iONE : -iONE;
        SD59x18 a = (_spot / _strike) * normalCdf(d1 * sign);
        SD59x18 b = normalCdf(d2 * sign) / discountFactor;
        SD59x18 scaledPrice = (a - b) * sign;

        if (scaledPrice < SD59x18.wrap(-1e12)) revert OptionMath__Underflow();
        if (scaledPrice >= SD59x18.wrap(-1e12) && scaledPrice <= iZERO) scaledPrice = iZERO;

        return (scaledPrice * _strike).intoUD60x18();
    }

    /// @notice Returns true if the maturity time is 8AM UTC
    /// @param maturity The maturity timestamp of the option
    /// @return True if the maturity time is 8AM UTC, false otherwise
    function is8AMUTC(uint256 maturity) internal pure returns (bool) {
        return maturity % 24 hours == 8 hours;
    }

    /// @notice Returns true if the maturity day is Friday
    /// @param maturity The maturity timestamp of the option
    /// @return True if the maturity day is Friday, false otherwise
    function isFriday(uint256 maturity) internal pure returns (bool) {
        return DateTime.getDayOfWeek(maturity) == DateTime.DOW_FRI;
    }

    /// @notice Returns true if the maturity day is the last Friday of the month
    /// @param maturity The maturity timestamp of the option
    /// @return True if the maturity day is the last Friday of the month, false otherwise
    function isLastFriday(uint256 maturity) internal pure returns (bool) {
        uint256 dayOfMonth = DateTime.getDay(maturity);
        uint256 lastDayOfMonth = DateTime.getDaysInMonth(maturity);
        if (lastDayOfMonth - dayOfMonth >= 7) return false;
        return isFriday(maturity);
    }

    /// @notice Calculates the time to maturity in seconds
    /// @param maturity The maturity timestamp of the option
    /// @return Time to maturity in seconds
    function calculateTimeToMaturity(uint256 maturity) internal view returns (uint256) {
        return maturity - block.timestamp;
    }

    /// @notice Calculates the strike interval for `strike`
    /// @param strike The price to calculate strike interval for (18 decimals)
    /// @return The strike interval (18 decimals)
    function calculateStrikeInterval(UD60x18 strike) internal pure returns (UD60x18) {
        if (strike < MIN_INPUT_PRICE || strike > MAX_INPUT_PRICE)
            revert OptionMath__OutOfBoundsPrice(MIN_INPUT_PRICE, MAX_INPUT_PRICE, strike);

        uint256 _strike = strike.unwrap();
        uint256 exponent = log10Floor(_strike);
        uint256 multiplier = (_strike >= 5 * 10 ** exponent) ? 5 : 1;
        return ud(multiplier * 10 ** (exponent - 1));
    }

    /// @notice Rounds `strike` using the calculated strike interval
    /// @param strike The price to round (18 decimals)
    /// @return The rounded strike price (18 decimals)
    function roundToStrikeInterval(UD60x18 strike) internal pure returns (UD60x18) {
        uint256 _strike = strike.div(ONE).unwrap();
        uint256 interval = calculateStrikeInterval(strike).div(ONE).unwrap();
        uint256 lower = interval * (_strike / interval);
        uint256 upper = interval * ((_strike / interval) + 1);
        return (_strike - lower < upper - _strike) ? ud(lower) : ud(upper);
    }

    /// @notice Calculate the log moneyness of a strike/spot price pair
    /// @param spot The spot price (18 decimals)
    /// @param strike The strike price (18 decimals)
    /// @return The log moneyness of the strike price (18 decimals)
    function logMoneyness(UD60x18 spot, UD60x18 strike) internal pure returns (UD60x18) {
        return (spot / strike).intoSD59x18().ln().abs().intoUD60x18();
    }

    /// @notice Calculate the initialization fee for a pool
    /// @param spot The spot price (18 decimals)
    /// @param strike The strike price (18 decimals)
    /// @param maturity The maturity timestamp of the option
    /// @return The initialization fee (18 decimals)
    function initializationFee(UD60x18 spot, UD60x18 strike, uint256 maturity) internal view returns (UD60x18) {
        UD60x18 moneyness = logMoneyness(spot, strike);
        uint256 timeToMaturity = calculateTimeToMaturity(maturity);
        UD60x18 kBase = moneyness < ATM_MONEYNESS
            ? (ATM_MONEYNESS - moneyness).intoSD59x18().pow(iFOUR).intoUD60x18()
            : moneyness - ATM_MONEYNESS;
        uint256 tBase = timeToMaturity < NEAR_TERM_TTM
            ? 3 * (NEAR_TERM_TTM - timeToMaturity) + NEAR_TERM_TTM
            : timeToMaturity;
        UD60x18 scaledT = (ud(tBase * 1e18) / ud(ONE_YEAR_TTM * 1e18)).sqrt();

        return INITIALIZATION_ALPHA * (kBase + scaledT) * scaledT * FEE_SCALAR;
    }

    /// @notice Converts a number with `inputDecimals`, to a number with given amount of decimals
    /// @param value The value to convert
    /// @param inputDecimals The amount of decimals the input value has
    /// @param targetDecimals The amount of decimals to convert to
    /// @return The converted value
    function scaleDecimals(uint256 value, uint8 inputDecimals, uint8 targetDecimals) internal pure returns (uint256) {
        if (targetDecimals == inputDecimals) return value;
        if (targetDecimals > inputDecimals) return value * (10 ** (targetDecimals - inputDecimals));

        return value / (10 ** (inputDecimals - targetDecimals));
    }

    /// @notice Converts a number with `inputDecimals`, to a number with given amount of decimals
    /// @param value The value to convert
    /// @param inputDecimals The amount of decimals the input value has
    /// @param targetDecimals The amount of decimals to convert to
    /// @return The converted value
    function scaleDecimals(int256 value, uint8 inputDecimals, uint8 targetDecimals) internal pure returns (int256) {
        if (targetDecimals == inputDecimals) return value;
        if (targetDecimals > inputDecimals) return value * int256(10 ** (targetDecimals - inputDecimals));

        return value / int256(10 ** (inputDecimals - targetDecimals));
    }

    /// @notice Performs a naive log10 calculation on `input` returning the floor of the result
    function log10Floor(uint256 input) internal pure returns (uint256 count) {
        while (input >= 10) {
            input /= 10;
            count++;
        }

        return count;
    }
}

// SPDX-License-Identifier: LicenseRef-P3-DUAL
// For terms and conditions regarding commercial use please see https://license.premia.blue
pragma solidity ^0.8.19;

import {OwnableStorage} from "@solidstate/contracts/access/ownable/OwnableStorage.sol";
import {IERC1155} from "@solidstate/contracts/interfaces/IERC1155.sol";
import {IERC165} from "@solidstate/contracts/interfaces/IERC165.sol";
import {ERC165BaseInternal} from "@solidstate/contracts/introspection/ERC165/base/ERC165BaseInternal.sol";
import {Proxy} from "@solidstate/contracts/proxy/Proxy.sol";
import {IERC20Metadata} from "@solidstate/contracts/token/ERC20/metadata/IERC20Metadata.sol";

import {IProxyManager} from "../../proxy/IProxyManager.sol";
import {OptionPSStorage} from "./OptionPSStorage.sol";

contract OptionPSProxy is Proxy, ERC165BaseInternal {
    IProxyManager private immutable MANAGER;

    constructor(IProxyManager manager, address base, address quote, bool isCall) {
        MANAGER = manager;
        OwnableStorage.layout().owner = msg.sender;

        OptionPSStorage.Layout storage l = OptionPSStorage.layout();

        l.isCall = isCall;
        l.baseDecimals = IERC20Metadata(base).decimals();
        l.quoteDecimals = IERC20Metadata(quote).decimals();

        l.base = base;
        l.quote = quote;

        _setSupportsInterface(type(IERC165).interfaceId, true);
        _setSupportsInterface(type(IERC1155).interfaceId, true);
    }

    /// @inheritdoc Proxy
    function _getImplementation() internal view override returns (address) {
        return MANAGER.getManagedProxyImplementation();
    }

    receive() external payable {}
}

// SPDX-License-Identifier: LicenseRef-P3-DUAL
// For terms and conditions regarding commercial use please see https://license.premia.blue
pragma solidity ^0.8.19;

import {UD60x18, ud} from "lib/prb-math/src/UD60x18.sol";
import {IERC20} from "@solidstate/contracts/interfaces/IERC20.sol";
import {SafeCast} from "@solidstate/contracts/utils/SafeCast.sol";
import {SafeERC20} from "@solidstate/contracts/utils/SafeERC20.sol";
import {EnumerableSet} from "@solidstate/contracts/data/EnumerableSet.sol";

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

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

library OptionPSStorage {
    using SafeCast for int256;
    using SafeCast for uint256;
    using SafeERC20 for IERC20;

    bytes32 internal constant STORAGE_SLOT = keccak256("premia.contracts.storage.OptionPS");

    struct Layout {
        bool isCall;
        uint8 baseDecimals;
        uint8 quoteDecimals;
        address base;
        address quote;
        // Total options underwritten for this strike/maturity (Annihilating options decreases this total amount, but exercise does not)
        mapping(UD60x18 strike => mapping(uint64 maturity => UD60x18 amount)) totalUnderwritten;
        // Amount of contracts exercised for this strike/maturity
        mapping(UD60x18 strike => mapping(uint64 maturity => UD60x18 amount)) totalExercised;
        EnumerableSet.UintSet tokenIds;
    }

    function layout() internal pure returns (Layout storage l) {
        bytes32 slot = STORAGE_SLOT;
        assembly {
            l.slot := slot
        }
    }

    /// @notice Calculate ERC1155 token id for given option parameters
    function formatTokenId(
        IOptionPS.TokenType tokenType,
        uint64 maturity,
        UD60x18 strike
    ) internal pure returns (uint256 tokenId) {
        tokenId =
            (uint256(tokenType) << 248) +
            (uint256(maturity) << 128) +
            uint256(int256(fromUD60x18ToInt128(strike)));
    }

    /// @notice Derive option maturity and strike price from ERC1155 token id
    function parseTokenId(
        uint256 tokenId
    ) internal pure returns (IOptionPS.TokenType tokenType, uint64 maturity, int128 strike) {
        assembly {
            tokenType := shr(248, tokenId)
            maturity := shr(128, tokenId)
            strike := tokenId
        }
    }

    function getCollateral(Layout storage l) internal view returns (address) {
        return l.isCall ? l.base : l.quote;
    }

    function getExerciseToken(Layout storage l) internal view returns (address) {
        return l.isCall ? l.quote : l.base;
    }

    /// @notice Adjust decimals of a value with 18 decimals to match the token decimals
    function toTokenDecimals(Layout storage l, UD60x18 value, address token) internal view returns (uint256) {
        uint8 decimals = token == l.base ? l.baseDecimals : l.quoteDecimals;
        return OptionMath.scaleDecimals(value.unwrap(), 18, decimals);
    }

    /// @notice Adjust decimals of a value with token decimals to 18 decimals
    function fromTokenDecimals(Layout storage l, uint256 value, address token) internal view returns (UD60x18) {
        uint8 decimals = token == l.base ? l.baseDecimals : l.quoteDecimals;
        return ud(OptionMath.scaleDecimals(value, decimals, 18));
    }

    /// @notice Converts `UD60x18` to `int128`
    function fromUD60x18ToInt128(UD60x18 u) internal pure returns (int128) {
        return u.unwrap().toInt256().toInt128();
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

library OwnableStorage {
    struct Layout {
        address owner;
    }

    bytes32 internal constant STORAGE_SLOT =
        keccak256('solidstate.contracts.storage.Ownable');

    function layout() internal pure returns (Layout storage l) {
        bytes32 slot = STORAGE_SLOT;
        assembly {
            l.slot := slot
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import { AddressUtils } from '../utils/AddressUtils.sol';
import { IProxy } from './IProxy.sol';

/**
 * @title Base proxy contract
 */
abstract contract Proxy is IProxy {
    using AddressUtils for address;

    /**
     * @notice delegate all calls to implementation contract
     * @dev reverts if implementation address contains no code, for compatibility with metamorphic contracts
     * @dev memory location in use by assembly may be unsafe in other contexts
     */
    fallback() external payable virtual {
        address implementation = _getImplementation();

        if (!implementation.isContract())
            revert Proxy__ImplementationIsNotContract();

        assembly {
            calldatacopy(0, 0, calldatasize())
            let result := delegatecall(
                gas(),
                implementation,
                0,
                calldatasize(),
                0,
                0
            )
            returndatacopy(0, 0, returndatasize())

            switch result
            case 0 {
                revert(0, returndatasize())
            }
            default {
                return(0, returndatasize())
            }
        }
    }

    /**
     * @notice get logic implementation address
     * @return implementation address
     */
    function _getImplementation() internal virtual returns (address);
}