// File: contracts/ABDKTest.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./interfaces/IUARForDollarsCalculator.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./libs/ABDKMathQuad.sol";
import "./DebtCoupon.sol";

contract ABDKTest {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;

    function max() public pure returns (uint256) {
        //   115792089237316195423570985008687907853269984665640564039457584007913129639935

        uint256 maxUInt256 = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff;
        return maxUInt256.fromUInt().toUInt();
    }

    function add(uint256 amount) public pure returns (uint256) {
        uint256 maxUInt256 = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff;
        return maxUInt256.fromUInt().add(amount.fromUInt()).toUInt();
    }
}

// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

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

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

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

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

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

    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

// File: contracts/interfaces/IUARForDollarsCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

/// @title A mechanism for calculating uAR received for a dollar amount burnt
interface IUARForDollarsCalculator {
    function getUARAmount(uint256 dollarsToBurn, uint256 blockHeightDebt)
        external
        view
        returns (uint256);
}

// File: contracts/UbiquityAlgorithmicDollarManager.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/access/AccessControl.sol";
import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "./interfaces/IUbiquityAlgorithmicDollar.sol";
import "./interfaces/ICurveFactory.sol";
import "./interfaces/IMetaPool.sol";

import "./TWAPOracle.sol";

/// @title A central config for the uAD system. Also acts as a central
/// access control manager.
/// @notice For storing constants. For storing variables and allowing them to
/// be changed by the admin (governance)
/// @dev This should be used as a central access control manager which other
/// contracts use to check permissions
contract UbiquityAlgorithmicDollarManager is AccessControl {
    using SafeERC20 for IERC20;

    bytes32 public constant UBQ_MINTER_ROLE = keccak256("UBQ_MINTER_ROLE");
    bytes32 public constant UBQ_BURNER_ROLE = keccak256("UBQ_BURNER_ROLE");

    bytes32 public constant PAUSER_ROLE = keccak256("PAUSER_ROLE");
    bytes32 public constant COUPON_MANAGER_ROLE = keccak256("COUPON_MANAGER");
    bytes32 public constant BONDING_MANAGER_ROLE = keccak256("BONDING_MANAGER");
    bytes32 public constant INCENTIVE_MANAGER_ROLE =
        keccak256("INCENTIVE_MANAGER");
    bytes32 public constant UBQ_TOKEN_MANAGER_ROLE =
        keccak256("UBQ_TOKEN_MANAGER_ROLE");
    address public twapOracleAddress;
    address public debtCouponAddress;
    address public dollarTokenAddress; // uAD
    address public couponCalculatorAddress;
    address public dollarMintingCalculatorAddress;
    address public bondingShareAddress;
    address public bondingContractAddress;
    address public stableSwapMetaPoolAddress;
    address public curve3PoolTokenAddress; // 3CRV
    address public treasuryAddress;
    address public governanceTokenAddress; // uGOV
    address public sushiSwapPoolAddress; // sushi pool uAD-uGOV
    address public masterChefAddress;
    address public formulasAddress;
    address public autoRedeemTokenAddress; // uAR
    address public uarCalculatorAddress; // uAR calculator

    //key = address of couponmanager, value = excessdollardistributor
    mapping(address => address) private _excessDollarDistributors;

    modifier onlyAdmin() {
        require(
            hasRole(DEFAULT_ADMIN_ROLE, msg.sender),
            "uADMGR: Caller is not admin"
        );
        _;
    }

    constructor(address _admin) {
        _setupRole(DEFAULT_ADMIN_ROLE, _admin);
        _setupRole(UBQ_MINTER_ROLE, _admin);
        _setupRole(PAUSER_ROLE, _admin);
        _setupRole(COUPON_MANAGER_ROLE, _admin);
        _setupRole(BONDING_MANAGER_ROLE, _admin);
        _setupRole(INCENTIVE_MANAGER_ROLE, _admin);
        _setupRole(UBQ_TOKEN_MANAGER_ROLE, address(this));
    }

    // TODO Add a generic setter for extra addresses that needs to be linked
    function setTwapOracleAddress(address _twapOracleAddress)
        external
        onlyAdmin
    {
        twapOracleAddress = _twapOracleAddress;
        // to be removed

        TWAPOracle oracle = TWAPOracle(twapOracleAddress);
        oracle.update();
    }

    function setuARTokenAddress(address _uarTokenAddress) external onlyAdmin {
        autoRedeemTokenAddress = _uarTokenAddress;
    }

    function setDebtCouponAddress(address _debtCouponAddress)
        external
        onlyAdmin
    {
        debtCouponAddress = _debtCouponAddress;
    }

    function setIncentiveToUAD(address _account, address _incentiveAddress)
        external
        onlyAdmin
    {
        IUbiquityAlgorithmicDollar(dollarTokenAddress).setIncentiveContract(
            _account,
            _incentiveAddress
        );
    }

    function setDollarTokenAddress(address _dollarTokenAddress)
        external
        onlyAdmin
    {
        dollarTokenAddress = _dollarTokenAddress;
    }

    function setGovernanceTokenAddress(address _governanceTokenAddress)
        external
        onlyAdmin
    {
        governanceTokenAddress = _governanceTokenAddress;
    }

    function setSushiSwapPoolAddress(address _sushiSwapPoolAddress)
        external
        onlyAdmin
    {
        sushiSwapPoolAddress = _sushiSwapPoolAddress;
    }

    function setUARCalculatorAddress(address _uarCalculatorAddress)
        external
        onlyAdmin
    {
        uarCalculatorAddress = _uarCalculatorAddress;
    }

    function setCouponCalculatorAddress(address _couponCalculatorAddress)
        external
        onlyAdmin
    {
        couponCalculatorAddress = _couponCalculatorAddress;
    }

    function setDollarMintingCalculatorAddress(
        address _dollarMintingCalculatorAddress
    ) external onlyAdmin {
        dollarMintingCalculatorAddress = _dollarMintingCalculatorAddress;
    }

    function setExcessDollarsDistributor(
        address debtCouponManagerAddress,
        address excessCouponDistributor
    ) external onlyAdmin {
        _excessDollarDistributors[
            debtCouponManagerAddress
        ] = excessCouponDistributor;
    }

    function setMasterChefAddress(address _masterChefAddress)
        external
        onlyAdmin
    {
        masterChefAddress = _masterChefAddress;
    }

    function setFormulasAddress(address _formulasAddress) external onlyAdmin {
        formulasAddress = _formulasAddress;
    }

    function setBondingShareAddress(address _bondingShareAddress)
        external
        onlyAdmin
    {
        bondingShareAddress = _bondingShareAddress;
    }

    function setStableSwapMetaPoolAddress(address _stableSwapMetaPoolAddress)
        external
        onlyAdmin
    {
        stableSwapMetaPoolAddress = _stableSwapMetaPoolAddress;
    }

    /**
    @notice set the bonding bontract smart contract address
    @dev bonding contract participants deposit  curve LP token
         for a certain duration to earn uGOV and more curve LP token
    @param _bondingContractAddress bonding contract address
     */
    function setBondingContractAddress(address _bondingContractAddress)
        external
        onlyAdmin
    {
        bondingContractAddress = _bondingContractAddress;
    }

    /**
    @notice set the treasury address
    @dev the treasury fund is used to maintain the protocol
    @param _treasuryAddress treasury fund address
     */
    function setTreasuryAddress(address _treasuryAddress) external onlyAdmin {
        treasuryAddress = _treasuryAddress;
    }

    /**
    @notice deploy a new Curve metapools for uAD Token uAD/3Pool
    @dev  From the curve documentation for uncollateralized algorithmic
    stablecoins amplification should be 5-10
    @param _curveFactory MetaPool factory address
    @param _crvBasePool Address of the base pool to use within the new metapool.
    @param _crv3PoolTokenAddress curve 3Pool token Address
    @param _amplificationCoefficient amplification coefficient. The smaller
     it is the closer to a constant product we are.
    @param _fee Trade fee, given as an integer with 1e10 precision.
    */
    function deployStableSwapPool(
        address _curveFactory,
        address _crvBasePool,
        address _crv3PoolTokenAddress,
        uint256 _amplificationCoefficient,
        uint256 _fee
    ) external onlyAdmin {
        // Create new StableSwap meta pool (uAD <-> 3Crv)
        address metaPool = ICurveFactory(_curveFactory).deploy_metapool(
            _crvBasePool,
            ERC20(dollarTokenAddress).name(),
            ERC20(dollarTokenAddress).symbol(),
            dollarTokenAddress,
            _amplificationCoefficient,
            _fee
        );
        stableSwapMetaPoolAddress = metaPool;

        // Approve the newly-deployed meta pool to transfer this contract's funds
        uint256 crv3PoolTokenAmount = IERC20(_crv3PoolTokenAddress).balanceOf(
            address(this)
        );
        uint256 uADTokenAmount = IERC20(dollarTokenAddress).balanceOf(
            address(this)
        );

        // safe approve revert if approve from non-zero to non-zero allowance
        IERC20(_crv3PoolTokenAddress).safeApprove(metaPool, 0);
        IERC20(_crv3PoolTokenAddress).safeApprove(
            metaPool,
            crv3PoolTokenAmount
        );

        IERC20(dollarTokenAddress).safeApprove(metaPool, 0);
        IERC20(dollarTokenAddress).safeApprove(metaPool, uADTokenAmount);

        // coin at index 0 is uAD and index 1 is 3CRV
        require(
            IMetaPool(metaPool).coins(0) == dollarTokenAddress &&
                IMetaPool(metaPool).coins(1) == _crv3PoolTokenAddress,
            "uADMGR: COIN_ORDER_MISMATCH"
        );
        // Add the initial liquidity to the StableSwap meta pool
        uint256[2] memory amounts = [
            IERC20(dollarTokenAddress).balanceOf(address(this)),
            IERC20(_crv3PoolTokenAddress).balanceOf(address(this))
        ];

        // set curve 3Pool address
        curve3PoolTokenAddress = _crv3PoolTokenAddress;
        IMetaPool(metaPool).add_liquidity(amounts, 0, msg.sender);
    }

    function getExcessDollarsDistributor(address _debtCouponManagerAddress)
        external
        view
        returns (address)
    {
        return _excessDollarDistributors[_debtCouponManagerAddress];
    }
}

// File: contracts/libs/ABDKMathQuad.sol



// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math Quad Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
 */
pragma solidity ^0.8.0;

/**
 * Smart contract library of mathematical functions operating with IEEE 754
 * quadruple-precision binary floating-point numbers (quadruple precision
 * numbers).  As long as quadruple precision numbers are 16-bytes long, they are
 * represented by bytes16 type.
 */
library ABDKMathQuad {
    /*
     * 0.
     */
    bytes16 private constant _POSITIVE_ZERO =
        0x00000000000000000000000000000000;

    /*
     * -0.
     */
    bytes16 private constant _NEGATIVE_ZERO =
        0x80000000000000000000000000000000;

    /*
     * +Infinity.
     */
    bytes16 private constant _POSITIVE_INFINITY =
        0x7FFF0000000000000000000000000000;

    /*
     * -Infinity.
     */
    bytes16 private constant _NEGATIVE_INFINITY =
        0xFFFF0000000000000000000000000000;

    /*
     * Canonical NaN value.
     */
    bytes16 private constant NaN = 0x7FFF8000000000000000000000000000;

    /**
     * Convert signed 256-bit integer number into quadruple precision number.
     *
     * @param x signed 256-bit integer number
     * @return quadruple precision number
     */
    function fromInt(int256 x) internal pure returns (bytes16) {
        unchecked {
            if (x == 0) return bytes16(0);
            else {
                // We rely on overflow behavior here
                uint256 result = uint256(x > 0 ? x : -x);

                uint256 msb = mostSignificantBit(result);
                if (msb < 112) result <<= 112 - msb;
                else if (msb > 112) result >>= msb - 112;

                result =
                    (result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                    ((16383 + msb) << 112);
                if (x < 0) result |= 0x80000000000000000000000000000000;

                return bytes16(uint128(result));
            }
        }
    }

    /**
     * Convert quadruple precision number into signed 256-bit integer number
     * rounding towards zero.  Revert on overflow.
     *
     * @param x quadruple precision number
     * @return signed 256-bit integer number
     */
    function toInt(bytes16 x) internal pure returns (int256) {
        unchecked {
            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;

            require(exponent <= 16638); // Overflow
            if (exponent < 16383) return 0; // Underflow

            uint256 result = (uint256(uint128(x)) &
                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                0x10000000000000000000000000000;

            if (exponent < 16495) result >>= 16495 - exponent;
            else if (exponent > 16495) result <<= exponent - 16495;

            if (uint128(x) >= 0x80000000000000000000000000000000) {
                // Negative
                require(
                    result <=
                        0x8000000000000000000000000000000000000000000000000000000000000000
                );
                return -int256(result); // We rely on overflow behavior here
            } else {
                require(
                    result <=
                        0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                );
                return int256(result);
            }
        }
    }

    /**
     * Convert unsigned 256-bit integer number into quadruple precision number.
     *
     * @param x unsigned 256-bit integer number
     * @return quadruple precision number
     */
    function fromUInt(uint256 x) internal pure returns (bytes16) {
        unchecked {
            if (x == 0) return bytes16(0);
            else {
                uint256 result = x;

                uint256 msb = mostSignificantBit(result);
                if (msb < 112) result <<= 112 - msb;
                else if (msb > 112) result >>= msb - 112;

                result =
                    (result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                    ((16383 + msb) << 112);

                return bytes16(uint128(result));
            }
        }
    }

    /**
     * Convert quadruple precision number into unsigned 256-bit integer number
     * rounding towards zero.  Revert on underflow.  Note, that negative floating
     * point numbers in range (-1.0 .. 0.0) may be converted to unsigned integer
     * without error, because they are rounded to zero.
     *
     * @param x quadruple precision number
     * @return unsigned 256-bit integer number
     */
    function toUInt(bytes16 x) internal pure returns (uint256) {
        unchecked {
            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;

            if (exponent < 16383) return 0; // Underflow

            require(uint128(x) < 0x80000000000000000000000000000000); // Negative

            require(exponent <= 16638); // Overflow
            uint256 result = (uint256(uint128(x)) &
                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                0x10000000000000000000000000000;

            if (exponent < 16495) result >>= 16495 - exponent;
            else if (exponent > 16495) result <<= exponent - 16495;

            return result;
        }
    }

    /**
     * Convert signed 128.128 bit fixed point number into quadruple precision
     * number.
     *
     * @param x signed 128.128 bit fixed point number
     * @return quadruple precision number
     */
    function from128x128(int256 x) internal pure returns (bytes16) {
        unchecked {
            if (x == 0) return bytes16(0);
            else {
                // We rely on overflow behavior here
                uint256 result = uint256(x > 0 ? x : -x);

                uint256 msb = mostSignificantBit(result);
                if (msb < 112) result <<= 112 - msb;
                else if (msb > 112) result >>= msb - 112;

                result =
                    (result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                    ((16255 + msb) << 112);
                if (x < 0) result |= 0x80000000000000000000000000000000;

                return bytes16(uint128(result));
            }
        }
    }

    /**
     * Convert quadruple precision number into signed 128.128 bit fixed point
     * number.  Revert on overflow.
     *
     * @param x quadruple precision number
     * @return signed 128.128 bit fixed point number
     */
    function to128x128(bytes16 x) internal pure returns (int256) {
        unchecked {
            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;

            require(exponent <= 16510); // Overflow
            if (exponent < 16255) return 0; // Underflow

            uint256 result = (uint256(uint128(x)) &
                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                0x10000000000000000000000000000;

            if (exponent < 16367) result >>= 16367 - exponent;
            else if (exponent > 16367) result <<= exponent - 16367;

            if (uint128(x) >= 0x80000000000000000000000000000000) {
                // Negative
                require(
                    result <=
                        0x8000000000000000000000000000000000000000000000000000000000000000
                );
                return -int256(result); // We rely on overflow behavior here
            } else {
                require(
                    result <=
                        0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                );
                return int256(result);
            }
        }
    }

    /**
     * Convert signed 64.64 bit fixed point number into quadruple precision
     * number.
     *
     * @param x signed 64.64 bit fixed point number
     * @return quadruple precision number
     */
    function from64x64(int128 x) internal pure returns (bytes16) {
        unchecked {
            if (x == 0) return bytes16(0);
            else {
                // We rely on overflow behavior here
                uint256 result = uint128(x > 0 ? x : -x);

                uint256 msb = mostSignificantBit(result);
                if (msb < 112) result <<= 112 - msb;
                else if (msb > 112) result >>= msb - 112;

                result =
                    (result & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                    ((16319 + msb) << 112);
                if (x < 0) result |= 0x80000000000000000000000000000000;

                return bytes16(uint128(result));
            }
        }
    }

    /**
     * Convert quadruple precision number into signed 64.64 bit fixed point
     * number.  Revert on overflow.
     *
     * @param x quadruple precision number
     * @return signed 64.64 bit fixed point number
     */
    function to64x64(bytes16 x) internal pure returns (int128) {
        unchecked {
            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;

            require(exponent <= 16446); // Overflow
            if (exponent < 16319) return 0; // Underflow

            uint256 result = (uint256(uint128(x)) &
                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF) |
                0x10000000000000000000000000000;

            if (exponent < 16431) result >>= 16431 - exponent;
            else if (exponent > 16431) result <<= exponent - 16431;

            if (uint128(x) >= 0x80000000000000000000000000000000) {
                // Negative
                require(result <= 0x80000000000000000000000000000000);
                return -int128(int256(result)); // We rely on overflow behavior here
            } else {
                require(result <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                return int128(int256(result));
            }
        }
    }

    /**
     * Convert octuple precision number into quadruple precision number.
     *
     * @param x octuple precision number
     * @return quadruple precision number
     */
    function fromOctuple(bytes32 x) internal pure returns (bytes16) {
        unchecked {
            bool negative = x &
                0x8000000000000000000000000000000000000000000000000000000000000000 >
                0;

            uint256 exponent = (uint256(x) >> 236) & 0x7FFFF;
            uint256 significand = uint256(x) &
                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            if (exponent == 0x7FFFF) {
                if (significand > 0) return NaN;
                else return negative ? _NEGATIVE_INFINITY : _POSITIVE_INFINITY;
            }

            if (exponent > 278526)
                return negative ? _NEGATIVE_INFINITY : _POSITIVE_INFINITY;
            else if (exponent < 245649)
                return negative ? _NEGATIVE_ZERO : _POSITIVE_ZERO;
            else if (exponent < 245761) {
                significand =
                    (significand |
                        0x100000000000000000000000000000000000000000000000000000000000) >>
                    (245885 - exponent);
                exponent = 0;
            } else {
                significand >>= 124;
                exponent -= 245760;
            }

            uint128 result = uint128(significand | (exponent << 112));
            if (negative) result |= 0x80000000000000000000000000000000;

            return bytes16(result);
        }
    }

    /**
     * Convert quadruple precision number into octuple precision number.
     *
     * @param x quadruple precision number
     * @return octuple precision number
     */
    function toOctuple(bytes16 x) internal pure returns (bytes32) {
        unchecked {
            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;

            uint256 result = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            if (exponent == 0x7FFF)
                exponent = 0x7FFFF; // Infinity or NaN
            else if (exponent == 0) {
                if (result > 0) {
                    uint256 msb = mostSignificantBit(result);
                    result =
                        (result << (236 - msb)) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    exponent = 245649 + msb;
                }
            } else {
                result <<= 124;
                exponent += 245760;
            }

            result |= exponent << 236;
            if (uint128(x) >= 0x80000000000000000000000000000000)
                result |= 0x8000000000000000000000000000000000000000000000000000000000000000;

            return bytes32(result);
        }
    }

    /**
     * Convert double precision number into quadruple precision number.
     *
     * @param x double precision number
     * @return quadruple precision number
     */
    function fromDouble(bytes8 x) internal pure returns (bytes16) {
        unchecked {
            uint256 exponent = (uint64(x) >> 52) & 0x7FF;

            uint256 result = uint64(x) & 0xFFFFFFFFFFFFF;

            if (exponent == 0x7FF)
                exponent = 0x7FFF; // Infinity or NaN
            else if (exponent == 0) {
                if (result > 0) {
                    uint256 msb = mostSignificantBit(result);
                    result =
                        (result << (112 - msb)) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    exponent = 15309 + msb;
                }
            } else {
                result <<= 60;
                exponent += 15360;
            }

            result |= exponent << 112;
            if (x & 0x8000000000000000 > 0)
                result |= 0x80000000000000000000000000000000;

            return bytes16(uint128(result));
        }
    }

    /**
     * Convert quadruple precision number into double precision number.
     *
     * @param x quadruple precision number
     * @return double precision number
     */
    function toDouble(bytes16 x) internal pure returns (bytes8) {
        unchecked {
            bool negative = uint128(x) >= 0x80000000000000000000000000000000;

            uint256 exponent = (uint128(x) >> 112) & 0x7FFF;
            uint256 significand = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            if (exponent == 0x7FFF) {
                if (significand > 0) return 0x7FF8000000000000;
                // NaN
                else
                    return
                        negative
                            ? bytes8(0xFFF0000000000000) // -Infinity
                            : bytes8(0x7FF0000000000000); // Infinity
            }

            if (exponent > 17406)
                return
                    negative
                        ? bytes8(0xFFF0000000000000) // -Infinity
                        : bytes8(0x7FF0000000000000);
            // Infinity
            else if (exponent < 15309)
                return
                    negative
                        ? bytes8(0x8000000000000000) // -0
                        : bytes8(0x0000000000000000);
            // 0
            else if (exponent < 15361) {
                significand =
                    (significand | 0x10000000000000000000000000000) >>
                    (15421 - exponent);
                exponent = 0;
            } else {
                significand >>= 60;
                exponent -= 15360;
            }

            uint64 result = uint64(significand | (exponent << 52));
            if (negative) result |= 0x8000000000000000;

            return bytes8(result);
        }
    }

    /**
     * Test whether given quadruple precision number is NaN.
     *
     * @param x quadruple precision number
     * @return true if x is NaN, false otherwise
     */
    function isNaN(bytes16 x) internal pure returns (bool) {
        unchecked {
            return
                uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF >
                0x7FFF0000000000000000000000000000;
        }
    }

    /**
     * Test whether given quadruple precision number is positive or negative
     * infinity.
     *
     * @param x quadruple precision number
     * @return true if x is positive or negative infinity, false otherwise
     */
    function isInfinity(bytes16 x) internal pure returns (bool) {
        unchecked {
            return
                uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ==
                0x7FFF0000000000000000000000000000;
        }
    }

    /**
     * Calculate sign of x, i.e. -1 if x is negative, 0 if x if zero, and 1 if x
     * is positive.  Note that sign (-0) is zero.  Revert if x is NaN.
     *
     * @param x quadruple precision number
     * @return sign of x
     */
    function sign(bytes16 x) internal pure returns (int8) {
        unchecked {
            uint128 absoluteX = uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            require(absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN

            if (absoluteX == 0) return 0;
            else if (uint128(x) >= 0x80000000000000000000000000000000)
                return -1;
            else return 1;
        }
    }

    /**
     * Calculate sign (x - y).  Revert if either argument is NaN, or both
     * arguments are infinities of the same sign.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return sign (x - y)
     */
    function cmp(bytes16 x, bytes16 y) internal pure returns (int8) {
        unchecked {
            uint128 absoluteX = uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            require(absoluteX <= 0x7FFF0000000000000000000000000000); // Not NaN

            uint128 absoluteY = uint128(y) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            require(absoluteY <= 0x7FFF0000000000000000000000000000); // Not NaN

            // Not infinities of the same sign
            require(x != y || absoluteX < 0x7FFF0000000000000000000000000000);

            if (x == y) return 0;
            else {
                bool negativeX = uint128(x) >=
                    0x80000000000000000000000000000000;
                bool negativeY = uint128(y) >=
                    0x80000000000000000000000000000000;

                if (negativeX) {
                    if (negativeY) return absoluteX > absoluteY ? -1 : int8(1);
                    else return -1;
                } else {
                    if (negativeY) return 1;
                    else return absoluteX > absoluteY ? int8(1) : -1;
                }
            }
        }
    }

    /**
     * Test whether x equals y.  NaN, infinity, and -infinity are not equal to
     * anything.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return true if x equals to y, false otherwise
     */
    function eq(bytes16 x, bytes16 y) internal pure returns (bool) {
        unchecked {
            if (x == y) {
                return
                    uint128(x) & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF <
                    0x7FFF0000000000000000000000000000;
            } else return false;
        }
    }

    /**
     * Calculate x + y.  Special values behave in the following way:
     *
     * NaN + x = NaN for any x.
     * Infinity + x = Infinity for any finite x.
     * -Infinity + x = -Infinity for any finite x.
     * Infinity + Infinity = Infinity.
     * -Infinity + -Infinity = -Infinity.
     * Infinity + -Infinity = -Infinity + Infinity = NaN.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return quadruple precision number
     */
    function add(bytes16 x, bytes16 y) internal pure returns (bytes16) {
        unchecked {
            uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
            uint256 yExponent = (uint128(y) >> 112) & 0x7FFF;

            if (xExponent == 0x7FFF) {
                if (yExponent == 0x7FFF) {
                    if (x == y) return x;
                    else return NaN;
                } else return x;
            } else if (yExponent == 0x7FFF) return y;
            else {
                bool xSign = uint128(x) >= 0x80000000000000000000000000000000;
                uint256 xSignifier = uint128(x) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (xExponent == 0) xExponent = 1;
                else xSignifier |= 0x10000000000000000000000000000;

                bool ySign = uint128(y) >= 0x80000000000000000000000000000000;
                uint256 ySignifier = uint128(y) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (yExponent == 0) yExponent = 1;
                else ySignifier |= 0x10000000000000000000000000000;

                if (xSignifier == 0)
                    return y == _NEGATIVE_ZERO ? _POSITIVE_ZERO : y;
                else if (ySignifier == 0)
                    return x == _NEGATIVE_ZERO ? _POSITIVE_ZERO : x;
                else {
                    int256 delta = int256(xExponent) - int256(yExponent);

                    if (xSign == ySign) {
                        if (delta > 112) return x;
                        else if (delta > 0) ySignifier >>= uint256(delta);
                        else if (delta < -112) return y;
                        else if (delta < 0) {
                            xSignifier >>= uint256(-delta);
                            xExponent = yExponent;
                        }

                        xSignifier += ySignifier;

                        if (xSignifier >= 0x20000000000000000000000000000) {
                            xSignifier >>= 1;
                            xExponent += 1;
                        }

                        if (xExponent == 0x7FFF)
                            return
                                xSign ? _NEGATIVE_INFINITY : _POSITIVE_INFINITY;
                        else {
                            if (xSignifier < 0x10000000000000000000000000000)
                                xExponent = 0;
                            else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

                            return
                                bytes16(
                                    uint128(
                                        (
                                            xSign
                                                ? 0x80000000000000000000000000000000
                                                : 0
                                        ) |
                                            (xExponent << 112) |
                                            xSignifier
                                    )
                                );
                        }
                    } else {
                        if (delta > 0) {
                            xSignifier <<= 1;
                            xExponent -= 1;
                        } else if (delta < 0) {
                            ySignifier <<= 1;
                            xExponent = yExponent - 1;
                        }

                        if (delta > 112) ySignifier = 1;
                        else if (delta > 1)
                            ySignifier =
                                ((ySignifier - 1) >> uint256(delta - 1)) +
                                1;
                        else if (delta < -112) xSignifier = 1;
                        else if (delta < -1)
                            xSignifier =
                                ((xSignifier - 1) >> uint256(-delta - 1)) +
                                1;

                        if (xSignifier >= ySignifier) xSignifier -= ySignifier;
                        else {
                            xSignifier = ySignifier - xSignifier;
                            xSign = ySign;
                        }

                        if (xSignifier == 0) return _POSITIVE_ZERO;

                        uint256 msb = mostSignificantBit(xSignifier);

                        if (msb == 113) {
                            xSignifier =
                                (xSignifier >> 1) &
                                0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                            xExponent += 1;
                        } else if (msb < 112) {
                            uint256 shift = 112 - msb;
                            if (xExponent > shift) {
                                xSignifier =
                                    (xSignifier << shift) &
                                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                                xExponent -= shift;
                            } else {
                                xSignifier <<= xExponent - 1;
                                xExponent = 0;
                            }
                        } else xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

                        if (xExponent == 0x7FFF)
                            return
                                xSign ? _NEGATIVE_INFINITY : _POSITIVE_INFINITY;
                        else
                            return
                                bytes16(
                                    uint128(
                                        (
                                            xSign
                                                ? 0x80000000000000000000000000000000
                                                : 0
                                        ) |
                                            (xExponent << 112) |
                                            xSignifier
                                    )
                                );
                    }
                }
            }
        }
    }

    /**
     * Calculate x - y.  Special values behave in the following way:
     *
     * NaN - x = NaN for any x.
     * Infinity - x = Infinity for any finite x.
     * -Infinity - x = -Infinity for any finite x.
     * Infinity - -Infinity = Infinity.
     * -Infinity - Infinity = -Infinity.
     * Infinity - Infinity = -Infinity - -Infinity = NaN.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return quadruple precision number
     */
    function sub(bytes16 x, bytes16 y) internal pure returns (bytes16) {
        unchecked {
            return add(x, y ^ 0x80000000000000000000000000000000);
        }
    }

    /**
     * Calculate x * y.  Special values behave in the following way:
     *
     * NaN * x = NaN for any x.
     * Infinity * x = Infinity for any finite positive x.
     * Infinity * x = -Infinity for any finite negative x.
     * -Infinity * x = -Infinity for any finite positive x.
     * -Infinity * x = Infinity for any finite negative x.
     * Infinity * 0 = NaN.
     * -Infinity * 0 = NaN.
     * Infinity * Infinity = Infinity.
     * Infinity * -Infinity = -Infinity.
     * -Infinity * Infinity = -Infinity.
     * -Infinity * -Infinity = Infinity.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return quadruple precision number
     */
    function mul(bytes16 x, bytes16 y) internal pure returns (bytes16) {
        unchecked {
            uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
            uint256 yExponent = (uint128(y) >> 112) & 0x7FFF;

            if (xExponent == 0x7FFF) {
                if (yExponent == 0x7FFF) {
                    if (x == y)
                        return x ^ (y & 0x80000000000000000000000000000000);
                    else if (x ^ y == 0x80000000000000000000000000000000)
                        return x | y;
                    else return NaN;
                } else {
                    if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                    else return x ^ (y & 0x80000000000000000000000000000000);
                }
            } else if (yExponent == 0x7FFF) {
                if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                else return y ^ (x & 0x80000000000000000000000000000000);
            } else {
                uint256 xSignifier = uint128(x) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (xExponent == 0) xExponent = 1;
                else xSignifier |= 0x10000000000000000000000000000;

                uint256 ySignifier = uint128(y) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (yExponent == 0) yExponent = 1;
                else ySignifier |= 0x10000000000000000000000000000;

                xSignifier *= ySignifier;
                if (xSignifier == 0)
                    return
                        (x ^ y) & 0x80000000000000000000000000000000 > 0
                            ? _NEGATIVE_ZERO
                            : _POSITIVE_ZERO;

                xExponent += yExponent;

                uint256 msb = xSignifier >=
                    0x200000000000000000000000000000000000000000000000000000000
                    ? 225
                    : xSignifier >=
                        0x100000000000000000000000000000000000000000000000000000000
                    ? 224
                    : mostSignificantBit(xSignifier);

                if (xExponent + msb < 16496) {
                    // Underflow
                    xExponent = 0;
                    xSignifier = 0;
                } else if (xExponent + msb < 16608) {
                    // Subnormal
                    if (xExponent < 16496) xSignifier >>= 16496 - xExponent;
                    else if (xExponent > 16496)
                        xSignifier <<= xExponent - 16496;
                    xExponent = 0;
                } else if (xExponent + msb > 49373) {
                    xExponent = 0x7FFF;
                    xSignifier = 0;
                } else {
                    if (msb > 112) xSignifier >>= msb - 112;
                    else if (msb < 112) xSignifier <<= 112 - msb;

                    xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

                    xExponent = xExponent + msb - 16607;
                }

                return
                    bytes16(
                        uint128(
                            uint128(
                                (x ^ y) & 0x80000000000000000000000000000000
                            ) |
                                (xExponent << 112) |
                                xSignifier
                        )
                    );
            }
        }
    }

    /**
     * Calculate x / y.  Special values behave in the following way:
     *
     * NaN / x = NaN for any x.
     * x / NaN = NaN for any x.
     * Infinity / x = Infinity for any finite non-negative x.
     * Infinity / x = -Infinity for any finite negative x including -0.
     * -Infinity / x = -Infinity for any finite non-negative x.
     * -Infinity / x = Infinity for any finite negative x including -0.
     * x / Infinity = 0 for any finite non-negative x.
     * x / -Infinity = -0 for any finite non-negative x.
     * x / Infinity = -0 for any finite non-negative x including -0.
     * x / -Infinity = 0 for any finite non-negative x including -0.
     *
     * Infinity / Infinity = NaN.
     * Infinity / -Infinity = -NaN.
     * -Infinity / Infinity = -NaN.
     * -Infinity / -Infinity = NaN.
     *
     * Division by zero behaves in the following way:
     *
     * x / 0 = Infinity for any finite positive x.
     * x / -0 = -Infinity for any finite positive x.
     * x / 0 = -Infinity for any finite negative x.
     * x / -0 = Infinity for any finite negative x.
     * 0 / 0 = NaN.
     * 0 / -0 = NaN.
     * -0 / 0 = NaN.
     * -0 / -0 = NaN.
     *
     * @param x quadruple precision number
     * @param y quadruple precision number
     * @return quadruple precision number
     */
    function div(bytes16 x, bytes16 y) internal pure returns (bytes16) {
        unchecked {
            uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
            uint256 yExponent = (uint128(y) >> 112) & 0x7FFF;

            if (xExponent == 0x7FFF) {
                if (yExponent == 0x7FFF) return NaN;
                else return x ^ (y & 0x80000000000000000000000000000000);
            } else if (yExponent == 0x7FFF) {
                if (y & 0x0000FFFFFFFFFFFFFFFFFFFFFFFFFFFF != 0) return NaN;
                else
                    return
                        _POSITIVE_ZERO |
                        ((x ^ y) & 0x80000000000000000000000000000000);
            } else if (y & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) {
                if (x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF == 0) return NaN;
                else
                    return
                        _POSITIVE_INFINITY |
                        ((x ^ y) & 0x80000000000000000000000000000000);
            } else {
                uint256 ySignifier = uint128(y) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (yExponent == 0) yExponent = 1;
                else ySignifier |= 0x10000000000000000000000000000;

                uint256 xSignifier = uint128(x) &
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (xExponent == 0) {
                    if (xSignifier != 0) {
                        uint256 shift = 226 - mostSignificantBit(xSignifier);

                        xSignifier <<= shift;

                        xExponent = 1;
                        yExponent += shift - 114;
                    }
                } else {
                    xSignifier =
                        (xSignifier | 0x10000000000000000000000000000) <<
                        114;
                }

                xSignifier = xSignifier / ySignifier;
                if (xSignifier == 0)
                    return
                        (x ^ y) & 0x80000000000000000000000000000000 > 0
                            ? _NEGATIVE_ZERO
                            : _POSITIVE_ZERO;

                assert(xSignifier >= 0x1000000000000000000000000000);

                uint256 msb = xSignifier >= 0x80000000000000000000000000000
                    ? mostSignificantBit(xSignifier)
                    : xSignifier >= 0x40000000000000000000000000000
                    ? 114
                    : xSignifier >= 0x20000000000000000000000000000
                    ? 113
                    : 112;

                if (xExponent + msb > yExponent + 16497) {
                    // Overflow
                    xExponent = 0x7FFF;
                    xSignifier = 0;
                } else if (xExponent + msb + 16380 < yExponent) {
                    // Underflow
                    xExponent = 0;
                    xSignifier = 0;
                } else if (xExponent + msb + 16268 < yExponent) {
                    // Subnormal
                    if (xExponent + 16380 > yExponent)
                        xSignifier <<= xExponent + 16380 - yExponent;
                    else if (xExponent + 16380 < yExponent)
                        xSignifier >>= yExponent - xExponent - 16380;

                    xExponent = 0;
                } else {
                    // Normal
                    if (msb > 112) xSignifier >>= msb - 112;

                    xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

                    xExponent = xExponent + msb + 16269 - yExponent;
                }

                return
                    bytes16(
                        uint128(
                            uint128(
                                (x ^ y) & 0x80000000000000000000000000000000
                            ) |
                                (xExponent << 112) |
                                xSignifier
                        )
                    );
            }
        }
    }

    /**
     * Calculate -x.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function neg(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            return x ^ 0x80000000000000000000000000000000;
        }
    }

    /**
     * Calculate |x|.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function abs(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            return x & 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
        }
    }

    /**
     * Calculate square root of x.  Return NaN on negative x excluding -0.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function sqrt(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            if (uint128(x) > 0x80000000000000000000000000000000) return NaN;
            else {
                uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
                if (xExponent == 0x7FFF) return x;
                else {
                    uint256 xSignifier = uint128(x) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    if (xExponent == 0) xExponent = 1;
                    else xSignifier |= 0x10000000000000000000000000000;

                    if (xSignifier == 0) return _POSITIVE_ZERO;

                    bool oddExponent = xExponent & 0x1 == 0;
                    xExponent = (xExponent + 16383) >> 1;

                    if (oddExponent) {
                        if (xSignifier >= 0x10000000000000000000000000000)
                            xSignifier <<= 113;
                        else {
                            uint256 msb = mostSignificantBit(xSignifier);
                            uint256 shift = (226 - msb) & 0xFE;
                            xSignifier <<= shift;
                            xExponent -= (shift - 112) >> 1;
                        }
                    } else {
                        if (xSignifier >= 0x10000000000000000000000000000)
                            xSignifier <<= 112;
                        else {
                            uint256 msb = mostSignificantBit(xSignifier);
                            uint256 shift = (225 - msb) & 0xFE;
                            xSignifier <<= shift;
                            xExponent -= (shift - 112) >> 1;
                        }
                    }

                    uint256 r = 0x10000000000000000000000000000;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1;
                    r = (r + xSignifier / r) >> 1; // Seven iterations should be enough
                    uint256 r1 = xSignifier / r;
                    if (r1 < r) r = r1;

                    return
                        bytes16(
                            uint128(
                                (xExponent << 112) |
                                    (r & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
                            )
                        );
                }
            }
        }
    }

    /**
     * Calculate binary logarithm of x.  Return NaN on negative x excluding -0.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function log_2(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            if (uint128(x) > 0x80000000000000000000000000000000) return NaN;
            else if (x == 0x3FFF0000000000000000000000000000)
                return _POSITIVE_ZERO;
            else {
                uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
                if (xExponent == 0x7FFF) return x;
                else {
                    uint256 xSignifier = uint128(x) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    if (xExponent == 0) xExponent = 1;
                    else xSignifier |= 0x10000000000000000000000000000;

                    if (xSignifier == 0) return _NEGATIVE_INFINITY;

                    bool resultNegative;
                    uint256 resultExponent = 16495;
                    uint256 resultSignifier;

                    if (xExponent >= 0x3FFF) {
                        resultNegative = false;
                        resultSignifier = xExponent - 0x3FFF;
                        xSignifier <<= 15;
                    } else {
                        resultNegative = true;
                        if (xSignifier >= 0x10000000000000000000000000000) {
                            resultSignifier = 0x3FFE - xExponent;
                            xSignifier <<= 15;
                        } else {
                            uint256 msb = mostSignificantBit(xSignifier);
                            resultSignifier = 16493 - msb;
                            xSignifier <<= 127 - msb;
                        }
                    }

                    if (xSignifier == 0x80000000000000000000000000000000) {
                        if (resultNegative) resultSignifier += 1;
                        uint256 shift = 112 -
                            mostSignificantBit(resultSignifier);
                        resultSignifier <<= shift;
                        resultExponent -= shift;
                    } else {
                        uint256 bb = resultNegative ? 1 : 0;
                        while (
                            resultSignifier < 0x10000000000000000000000000000
                        ) {
                            resultSignifier <<= 1;
                            resultExponent -= 1;

                            xSignifier *= xSignifier;
                            uint256 b = xSignifier >> 255;
                            resultSignifier += b ^ bb;
                            xSignifier >>= 127 + b;
                        }
                    }

                    return
                        bytes16(
                            uint128(
                                (
                                    resultNegative
                                        ? 0x80000000000000000000000000000000
                                        : 0
                                ) |
                                    (resultExponent << 112) |
                                    (resultSignifier &
                                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
                            )
                        );
                }
            }
        }
    }

    /**
     * Calculate natural logarithm of x.  Return NaN on negative x excluding -0.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function ln(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            return mul(log_2(x), 0x3FFE62E42FEFA39EF35793C7673007E5);
        }
    }

    /**
     * Calculate 2^x.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function pow_2(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            bool xNegative = uint128(x) > 0x80000000000000000000000000000000;
            uint256 xExponent = (uint128(x) >> 112) & 0x7FFF;
            uint256 xSignifier = uint128(x) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

            if (xExponent == 0x7FFF && xSignifier != 0) return NaN;
            else if (xExponent > 16397)
                return xNegative ? _POSITIVE_ZERO : _POSITIVE_INFINITY;
            else if (xExponent < 16255)
                return 0x3FFF0000000000000000000000000000;
            else {
                if (xExponent == 0) xExponent = 1;
                else xSignifier |= 0x10000000000000000000000000000;

                if (xExponent > 16367) xSignifier <<= xExponent - 16367;
                else if (xExponent < 16367) xSignifier >>= 16367 - xExponent;

                if (
                    xNegative &&
                    xSignifier > 0x406E00000000000000000000000000000000
                ) return _POSITIVE_ZERO;

                if (
                    !xNegative &&
                    xSignifier > 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                ) return _POSITIVE_INFINITY;

                uint256 resultExponent = xSignifier >> 128;
                xSignifier &= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                if (xNegative && xSignifier != 0) {
                    xSignifier = ~xSignifier;
                    resultExponent += 1;
                }

                uint256 resultSignifier = 0x80000000000000000000000000000000;
                if (xSignifier & 0x80000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x16A09E667F3BCC908B2FB1366EA957D3E) >>
                        128;
                if (xSignifier & 0x40000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1306FE0A31B7152DE8D5A46305C85EDEC) >>
                        128;
                if (xSignifier & 0x20000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1172B83C7D517ADCDF7C8C50EB14A791F) >>
                        128;
                if (xSignifier & 0x10000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10B5586CF9890F6298B92B71842A98363) >>
                        128;
                if (xSignifier & 0x8000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1059B0D31585743AE7C548EB68CA417FD) >>
                        128;
                if (xSignifier & 0x4000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x102C9A3E778060EE6F7CACA4F7A29BDE8) >>
                        128;
                if (xSignifier & 0x2000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10163DA9FB33356D84A66AE336DCDFA3F) >>
                        128;
                if (xSignifier & 0x1000000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100B1AFA5ABCBED6129AB13EC11DC9543) >>
                        128;
                if (xSignifier & 0x800000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10058C86DA1C09EA1FF19D294CF2F679B) >>
                        128;
                if (xSignifier & 0x400000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1002C605E2E8CEC506D21BFC89A23A00F) >>
                        128;
                if (xSignifier & 0x200000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100162F3904051FA128BCA9C55C31E5DF) >>
                        128;
                if (xSignifier & 0x100000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000B175EFFDC76BA38E31671CA939725) >>
                        128;
                if (xSignifier & 0x80000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100058BA01FB9F96D6CACD4B180917C3D) >>
                        128;
                if (xSignifier & 0x40000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10002C5CC37DA9491D0985C348C68E7B3) >>
                        128;
                if (xSignifier & 0x20000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000162E525EE054754457D5995292026) >>
                        128;
                if (xSignifier & 0x10000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000B17255775C040618BF4A4ADE83FC) >>
                        128;
                if (xSignifier & 0x8000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000058B91B5BC9AE2EED81E9B7D4CFAB) >>
                        128;
                if (xSignifier & 0x4000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100002C5C89D5EC6CA4D7C8ACC017B7C9) >>
                        128;
                if (xSignifier & 0x2000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000162E43F4F831060E02D839A9D16D) >>
                        128;
                if (xSignifier & 0x1000000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000B1721BCFC99D9F890EA06911763) >>
                        128;
                if (xSignifier & 0x800000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000058B90CF1E6D97F9CA14DBCC1628) >>
                        128;
                if (xSignifier & 0x400000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000002C5C863B73F016468F6BAC5CA2B) >>
                        128;
                if (xSignifier & 0x200000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000162E430E5A18F6119E3C02282A5) >>
                        128;
                if (xSignifier & 0x100000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000B1721835514B86E6D96EFD1BFE) >>
                        128;
                if (xSignifier & 0x80000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000058B90C0B48C6BE5DF846C5B2EF) >>
                        128;
                if (xSignifier & 0x40000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000002C5C8601CC6B9E94213C72737A) >>
                        128;
                if (xSignifier & 0x20000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000162E42FFF037DF38AA2B219F06) >>
                        128;
                if (xSignifier & 0x10000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000B17217FBA9C739AA5819F44F9) >>
                        128;
                if (xSignifier & 0x8000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000058B90BFCDEE5ACD3C1CEDC823) >>
                        128;
                if (xSignifier & 0x4000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000002C5C85FE31F35A6A30DA1BE50) >>
                        128;
                if (xSignifier & 0x2000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000162E42FF0999CE3541B9FFFCF) >>
                        128;
                if (xSignifier & 0x1000000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000B17217F80F4EF5AADDA45554) >>
                        128;
                if (xSignifier & 0x800000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000058B90BFBF8479BD5A81B51AD) >>
                        128;
                if (xSignifier & 0x400000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000002C5C85FDF84BD62AE30A74CC) >>
                        128;
                if (xSignifier & 0x200000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000162E42FEFB2FED257559BDAA) >>
                        128;
                if (xSignifier & 0x100000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000B17217F7D5A7716BBA4A9AE) >>
                        128;
                if (xSignifier & 0x80000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000058B90BFBE9DDBAC5E109CCE) >>
                        128;
                if (xSignifier & 0x40000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000002C5C85FDF4B15DE6F17EB0D) >>
                        128;
                if (xSignifier & 0x20000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000162E42FEFA494F1478FDE05) >>
                        128;
                if (xSignifier & 0x10000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000B17217F7D20CF927C8E94C) >>
                        128;
                if (xSignifier & 0x8000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000058B90BFBE8F71CB4E4B33D) >>
                        128;
                if (xSignifier & 0x4000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000002C5C85FDF477B662B26945) >>
                        128;
                if (xSignifier & 0x2000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000162E42FEFA3AE53369388C) >>
                        128;
                if (xSignifier & 0x1000000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000B17217F7D1D351A389D40) >>
                        128;
                if (xSignifier & 0x800000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000058B90BFBE8E8B2D3D4EDE) >>
                        128;
                if (xSignifier & 0x400000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000002C5C85FDF4741BEA6E77E) >>
                        128;
                if (xSignifier & 0x200000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000162E42FEFA39FE95583C2) >>
                        128;
                if (xSignifier & 0x100000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000B17217F7D1CFB72B45E1) >>
                        128;
                if (xSignifier & 0x80000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000058B90BFBE8E7CC35C3F0) >>
                        128;
                if (xSignifier & 0x40000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000002C5C85FDF473E242EA38) >>
                        128;
                if (xSignifier & 0x20000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000162E42FEFA39F02B772C) >>
                        128;
                if (xSignifier & 0x10000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000B17217F7D1CF7D83C1A) >>
                        128;
                if (xSignifier & 0x8000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000058B90BFBE8E7BDCBE2E) >>
                        128;
                if (xSignifier & 0x4000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000002C5C85FDF473DEA871F) >>
                        128;
                if (xSignifier & 0x2000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000162E42FEFA39EF44D91) >>
                        128;
                if (xSignifier & 0x1000000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000B17217F7D1CF79E949) >>
                        128;
                if (xSignifier & 0x800000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000058B90BFBE8E7BCE544) >>
                        128;
                if (xSignifier & 0x400000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000002C5C85FDF473DE6ECA) >>
                        128;
                if (xSignifier & 0x200000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000162E42FEFA39EF366F) >>
                        128;
                if (xSignifier & 0x100000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000B17217F7D1CF79AFA) >>
                        128;
                if (xSignifier & 0x80000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000058B90BFBE8E7BCD6D) >>
                        128;
                if (xSignifier & 0x40000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000002C5C85FDF473DE6B2) >>
                        128;
                if (xSignifier & 0x20000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000162E42FEFA39EF358) >>
                        128;
                if (xSignifier & 0x10000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000B17217F7D1CF79AB) >>
                        128;
                if (xSignifier & 0x8000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000058B90BFBE8E7BCD5) >>
                        128;
                if (xSignifier & 0x4000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000002C5C85FDF473DE6A) >>
                        128;
                if (xSignifier & 0x2000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000162E42FEFA39EF34) >>
                        128;
                if (xSignifier & 0x1000000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000B17217F7D1CF799) >>
                        128;
                if (xSignifier & 0x800000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000058B90BFBE8E7BCC) >>
                        128;
                if (xSignifier & 0x400000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000002C5C85FDF473DE5) >>
                        128;
                if (xSignifier & 0x200000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000162E42FEFA39EF2) >>
                        128;
                if (xSignifier & 0x100000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000B17217F7D1CF78) >>
                        128;
                if (xSignifier & 0x80000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000058B90BFBE8E7BB) >>
                        128;
                if (xSignifier & 0x40000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000002C5C85FDF473DD) >>
                        128;
                if (xSignifier & 0x20000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000162E42FEFA39EE) >>
                        128;
                if (xSignifier & 0x10000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000B17217F7D1CF6) >>
                        128;
                if (xSignifier & 0x8000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000058B90BFBE8E7A) >>
                        128;
                if (xSignifier & 0x4000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000002C5C85FDF473C) >>
                        128;
                if (xSignifier & 0x2000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000162E42FEFA39D) >>
                        128;
                if (xSignifier & 0x1000000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000B17217F7D1CE) >>
                        128;
                if (xSignifier & 0x800000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000058B90BFBE8E6) >>
                        128;
                if (xSignifier & 0x400000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000002C5C85FDF472) >>
                        128;
                if (xSignifier & 0x200000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000162E42FEFA38) >>
                        128;
                if (xSignifier & 0x100000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000B17217F7D1B) >>
                        128;
                if (xSignifier & 0x80000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000058B90BFBE8D) >>
                        128;
                if (xSignifier & 0x40000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000002C5C85FDF46) >>
                        128;
                if (xSignifier & 0x20000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000162E42FEFA2) >>
                        128;
                if (xSignifier & 0x10000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000B17217F7D0) >>
                        128;
                if (xSignifier & 0x8000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000058B90BFBE7) >>
                        128;
                if (xSignifier & 0x4000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000002C5C85FDF3) >>
                        128;
                if (xSignifier & 0x2000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000162E42FEF9) >>
                        128;
                if (xSignifier & 0x1000000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000B17217F7C) >>
                        128;
                if (xSignifier & 0x800000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000058B90BFBD) >>
                        128;
                if (xSignifier & 0x400000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000002C5C85FDE) >>
                        128;
                if (xSignifier & 0x200000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000162E42FEE) >>
                        128;
                if (xSignifier & 0x100000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000B17217F6) >>
                        128;
                if (xSignifier & 0x80000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000058B90BFA) >>
                        128;
                if (xSignifier & 0x40000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000002C5C85FC) >>
                        128;
                if (xSignifier & 0x20000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000162E42FD) >>
                        128;
                if (xSignifier & 0x10000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000B17217E) >>
                        128;
                if (xSignifier & 0x8000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000058B90BE) >>
                        128;
                if (xSignifier & 0x4000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000002C5C85E) >>
                        128;
                if (xSignifier & 0x2000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000162E42E) >>
                        128;
                if (xSignifier & 0x1000000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000B17216) >>
                        128;
                if (xSignifier & 0x800000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000058B90A) >>
                        128;
                if (xSignifier & 0x400000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000002C5C84) >>
                        128;
                if (xSignifier & 0x200000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000162E41) >>
                        128;
                if (xSignifier & 0x100000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000000B1720) >>
                        128;
                if (xSignifier & 0x80000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000058B8F) >>
                        128;
                if (xSignifier & 0x40000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000002C5C7) >>
                        128;
                if (xSignifier & 0x20000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000000162E3) >>
                        128;
                if (xSignifier & 0x10000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000000B171) >>
                        128;
                if (xSignifier & 0x8000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000000058B8) >>
                        128;
                if (xSignifier & 0x4000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000002C5B) >>
                        128;
                if (xSignifier & 0x2000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000000162D) >>
                        128;
                if (xSignifier & 0x1000 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000B16) >>
                        128;
                if (xSignifier & 0x800 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000000058A) >>
                        128;
                if (xSignifier & 0x400 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000000002C4) >>
                        128;
                if (xSignifier & 0x200 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000161) >>
                        128;
                if (xSignifier & 0x100 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x1000000000000000000000000000000B0) >>
                        128;
                if (xSignifier & 0x80 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000057) >>
                        128;
                if (xSignifier & 0x40 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000000002B) >>
                        128;
                if (xSignifier & 0x20 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000015) >>
                        128;
                if (xSignifier & 0x10 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x10000000000000000000000000000000A) >>
                        128;
                if (xSignifier & 0x8 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000004) >>
                        128;
                if (xSignifier & 0x4 > 0)
                    resultSignifier =
                        (resultSignifier *
                            0x100000000000000000000000000000001) >>
                        128;

                if (!xNegative) {
                    resultSignifier =
                        (resultSignifier >> 15) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    resultExponent += 0x3FFF;
                } else if (resultExponent <= 0x3FFE) {
                    resultSignifier =
                        (resultSignifier >> 15) &
                        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
                    resultExponent = 0x3FFF - resultExponent;
                } else {
                    resultSignifier =
                        resultSignifier >>
                        (resultExponent - 16367);
                    resultExponent = 0;
                }

                return
                    bytes16(uint128((resultExponent << 112) | resultSignifier));
            }
        }
    }

    /**
     * Calculate e^x.
     *
     * @param x quadruple precision number
     * @return quadruple precision number
     */
    function exp(bytes16 x) internal pure returns (bytes16) {
        unchecked {
            return pow_2(mul(x, 0x3FFF71547652B82FE1777D0FFDA0D23A));
        }
    }

    /**
     * Get index of the most significant non-zero bit in binary representation of
     * x.  Reverts if x is zero.
     *
     * @return index of the most significant non-zero bit in binary representation
     *         of x
     */
    function mostSignificantBit(uint256 x) private pure returns (uint256) {
        unchecked {
            require(x > 0);

            uint256 result = 0;

            if (x >= 0x100000000000000000000000000000000) {
                x >>= 128;
                result += 128;
            }
            if (x >= 0x10000000000000000) {
                x >>= 64;
                result += 64;
            }
            if (x >= 0x100000000) {
                x >>= 32;
                result += 32;
            }
            if (x >= 0x10000) {
                x >>= 16;
                result += 16;
            }
            if (x >= 0x100) {
                x >>= 8;
                result += 8;
            }
            if (x >= 0x10) {
                x >>= 4;
                result += 4;
            }
            if (x >= 0x4) {
                x >>= 2;
                result += 2;
            }
            if (x >= 0x2) result += 1; // No need to shift x anymore

            return result;
        }
    }
}

// File: contracts/DebtCoupon.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./ERC1155Ubiquity.sol";
import "solidity-linked-list/contracts/StructuredLinkedList.sol";
import "./UbiquityAlgorithmicDollarManager.sol";

/// @title A coupon redeemable for dollars with an expiry block number
/// @notice An ERC1155 where the token ID is the expiry block number
/// @dev Implements ERC1155 so receiving contracts must implement IERC1155Receiver
contract DebtCoupon is ERC1155Ubiquity {
    using StructuredLinkedList for StructuredLinkedList.List;

    //not public as if called externally can give inaccurate value. see method
    uint256 private _totalOutstandingDebt;

    //represents tokenSupply of each expiry (since 1155 doesnt have this)
    mapping(uint256 => uint256) private _tokenSupplies;

    //ordered list of coupon expiries
    StructuredLinkedList.List private _sortedBlockNumbers;

    event MintedCoupons(address recipient, uint256 expiryBlock, uint256 amount);

    event BurnedCoupons(
        address couponHolder,
        uint256 expiryBlock,
        uint256 amount
    );

    modifier onlyCouponManager() {
        require(
            manager.hasRole(manager.COUPON_MANAGER_ROLE(), msg.sender),
            "Caller is not a coupon manager"
        );
        _;
    }

    //@dev URI param is if we want to add an off-chain meta data uri associated with this contract
    constructor(address _manager) ERC1155Ubiquity(_manager, "URI") {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        _totalOutstandingDebt = 0;
    }

    /// @notice Mint an amount of coupons expiring at a certain block for a certain recipient
    /// @param amount amount of tokens to mint
    /// @param expiryBlockNumber the expiration block number of the coupons to mint
    function mintCoupons(
        address recipient,
        uint256 amount,
        uint256 expiryBlockNumber
    ) public onlyCouponManager {
        mint(recipient, expiryBlockNumber, amount, "");
        emit MintedCoupons(recipient, expiryBlockNumber, amount);

        //insert new relevant block number if it doesnt exist in our list
        // (linkedlist implementation wont insert if dupe)
        _sortedBlockNumbers.pushBack(expiryBlockNumber);

        //update the total supply for that expiry and total outstanding debt
        _tokenSupplies[expiryBlockNumber] =
            _tokenSupplies[expiryBlockNumber] +
            (amount);
        _totalOutstandingDebt = _totalOutstandingDebt + (amount);
    }

    /// @notice Burn an amount of coupons expiring at a certain block from
    /// a certain holder's balance
    /// @param couponOwner the owner of those coupons
    /// @param amount amount of tokens to burn
    /// @param expiryBlockNumber the expiration block number of the coupons to burn
    function burnCoupons(
        address couponOwner,
        uint256 amount,
        uint256 expiryBlockNumber
    ) public onlyCouponManager {
        require(
            balanceOf(couponOwner, expiryBlockNumber) >= amount,
            "Coupon owner not enough coupons"
        );
        burn(couponOwner, expiryBlockNumber, amount);
        emit BurnedCoupons(couponOwner, expiryBlockNumber, amount);

        //update the total supply for that expiry and total outstanding debt
        _tokenSupplies[expiryBlockNumber] =
            _tokenSupplies[expiryBlockNumber] -
            (amount);
        _totalOutstandingDebt = _totalOutstandingDebt - (amount);
    }

    /// @notice Should be called prior to any state changing functions.
    // Updates debt according to current block number
    function updateTotalDebt() public {
        bool reachedEndOfExpiredKeys = false;
        uint256 currentBlockNumber = _sortedBlockNumbers.popFront();

        //if list is empty, currentBlockNumber will be 0
        while (!reachedEndOfExpiredKeys && currentBlockNumber != 0) {
            if (currentBlockNumber > block.number) {
                //put the key back in since we popped, and end loop
                _sortedBlockNumbers.pushFront(currentBlockNumber);
                reachedEndOfExpiredKeys = true;
            } else {
                //update tally and remove key from blocks and map
                _totalOutstandingDebt =
                    _totalOutstandingDebt -
                    (_tokenSupplies[currentBlockNumber]);
                delete _tokenSupplies[currentBlockNumber];
                _sortedBlockNumbers.remove(currentBlockNumber);
            }
            currentBlockNumber = _sortedBlockNumbers.popFront();
        }
    }

    /// @notice Returns outstanding debt by fetching current tally and removing any expired debt
    function getTotalOutstandingDebt() public view returns (uint256) {
        uint256 outstandingDebt = _totalOutstandingDebt;
        bool reachedEndOfExpiredKeys = false;
        (, uint256 currentBlockNumber) = _sortedBlockNumbers.getNextNode(0);

        while (!reachedEndOfExpiredKeys && currentBlockNumber != 0) {
            if (currentBlockNumber > block.number) {
                reachedEndOfExpiredKeys = true;
            } else {
                outstandingDebt =
                    outstandingDebt -
                    (_tokenSupplies[currentBlockNumber]);
            }
            (, currentBlockNumber) = _sortedBlockNumbers.getNextNode(
                currentBlockNumber
            );
        }

        return outstandingDebt;
    }
}

// File: @openzeppelin/contracts/access/AccessControl.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../utils/Context.sol";
import "../utils/Strings.sol";
import "../utils/introspection/ERC165.sol";

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControl {
    function hasRole(bytes32 role, address account) external view returns (bool);

    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    function grantRole(bytes32 role, address account) external;

    function revokeRole(bytes32 role, address account) external;

    function renounceRole(bytes32 role, address account) external;
}

/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it.
 */
abstract contract AccessControl is Context, IAccessControl, ERC165 {
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{20}) is missing role (0x[0-9a-f]{32})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role, _msgSender());
        _;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IAccessControl).interfaceId || super.supportsInterface(interfaceId);
    }

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{20}) is missing role (0x[0-9a-f]{32})$/
     */
    function _checkRole(bytes32 role, address account) internal view {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        Strings.toHexString(uint160(account), 20),
                        " is missing role ",
                        Strings.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        emit RoleAdminChanged(role, getRoleAdmin(role), adminRole);
        _roles[role].adminRole = adminRole;
    }

    function _grantRole(bytes32 role, address account) private {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    function _revokeRole(bytes32 role, address account) private {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }
}

// File: @openzeppelin/contracts/token/ERC20/ERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

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

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

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

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

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

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5,05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

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

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

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

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

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);

        uint256 currentAllowance = _allowances[sender][_msgSender()];
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        unchecked {
            _approve(sender, _msgSender(), currentAllowance - amount);
        }

        return true;
    }

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

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

        return true;
    }

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

        _beforeTokenTransfer(sender, recipient, amount);

        uint256 senderBalance = _balances[sender];
        require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[sender] = senderBalance - amount;
        }
        _balances[recipient] += amount;

        emit Transfer(sender, recipient, amount);

        _afterTokenTransfer(sender, recipient, amount);
    }

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

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

        _totalSupply += amount;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);

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

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

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

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
        }
        _totalSupply -= amount;

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

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

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

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

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

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

// File: @openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

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

    function safeIncreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(
        IERC20 token,
        address spender,
        uint256 value
    ) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

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

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

// File: contracts/interfaces/IUbiquityAlgorithmicDollar.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "./IERC20Ubiquity.sol";

/// @title UAD stablecoin interface
/// @author Ubiquity Algorithmic Dollar
interface IUbiquityAlgorithmicDollar is IERC20Ubiquity {
    event IncentiveContractUpdate(
        address indexed _incentivized,
        address indexed _incentiveContract
    );

    function setIncentiveContract(address account, address incentive) external;

    function incentiveContract(address account) external view returns (address);
}

// File: contracts/interfaces/ICurveFactory.sol



// SPDX-License-Identifier: MIT
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

interface ICurveFactory {
    event BasePoolAdded(address base_pool, address implementat);
    event MetaPoolDeployed(
        address coin,
        address base_pool,
        uint256 A,
        uint256 fee,
        address deployer
    );

    function find_pool_for_coins(address _from, address _to)
        external
        view
        returns (address);

    function find_pool_for_coins(
        address _from,
        address _to,
        uint256 i
    ) external view returns (address);

    function get_n_coins(address _pool)
        external
        view
        returns (uint256, uint256);

    function get_coins(address _pool) external view returns (address[2] memory);

    function get_underlying_coins(address _pool)
        external
        view
        returns (address[8] memory);

    function get_decimals(address _pool)
        external
        view
        returns (uint256[2] memory);

    function get_underlying_decimals(address _pool)
        external
        view
        returns (uint256[8] memory);

    function get_rates(address _pool) external view returns (uint256[2] memory);

    function get_balances(address _pool)
        external
        view
        returns (uint256[2] memory);

    function get_underlying_balances(address _pool)
        external
        view
        returns (uint256[8] memory);

    function get_A(address _pool) external view returns (uint256);

    function get_fees(address _pool) external view returns (uint256, uint256);

    function get_admin_balances(address _pool)
        external
        view
        returns (uint256[2] memory);

    function get_coin_indices(
        address _pool,
        address _from,
        address _to
    )
        external
        view
        returns (
            int128,
            int128,
            bool
        );

    function add_base_pool(
        address _base_pool,
        address _metapool_implementation,
        address _fee_receiver
    ) external;

    function deploy_metapool(
        address _base_pool,
        string memory _name,
        string memory _symbol,
        address _coin,
        uint256 _A,
        uint256 _fee
    ) external returns (address);

    function commit_transfer_ownership(address addr) external;

    function accept_transfer_ownership() external;

    function set_fee_receiver(address _base_pool, address _fee_receiver)
        external;

    function convert_fees() external returns (bool);

    function admin() external view returns (address);

    function future_admin() external view returns (address);

    function pool_list(uint256 arg0) external view returns (address);

    function pool_count() external view returns (uint256);

    function base_pool_list(uint256 arg0) external view returns (address);

    function base_pool_count() external view returns (uint256);

    function fee_receiver(address arg0) external view returns (address);
}

// File: contracts/interfaces/IMetaPool.sol



// SPDX-License-Identifier: UNLICENSED
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

interface IMetaPool {
    event Transfer(
        address indexed sender,
        address indexed receiver,
        uint256 value
    );
    event Approval(
        address indexed owner,
        address indexed spender,
        uint256 value
    );
    event TokenExchange(
        address indexed buyer,
        int128 sold_id,
        uint256 tokens_sold,
        int128 bought_id,
        uint256 tokens_bought
    );
    event TokenExchangeUnderlying(
        address indexed buyer,
        int128 sold_id,
        uint256 tokens_sold,
        int128 bought_id,
        uint256 tokens_bought
    );
    event AddLiquidity(
        address indexed provider,
        uint256[2] token_amounts,
        uint256[2] fees,
        uint256 invariant,
        uint256 token_supply
    );
    event RemoveLiquidity(
        address indexed provider,
        uint256[2] token_amounts,
        uint256[2] fees,
        uint256 token_supply
    );
    event RemoveLiquidityOne(
        address indexed provider,
        uint256 token_amount,
        uint256 coin_amount,
        uint256 token_supply
    );
    event RemoveLiquidityImbalance(
        address indexed provider,
        uint256[2] token_amounts,
        uint256[2] fees,
        uint256 invariant,
        uint256 token_supply
    );
    event CommitNewAdmin(uint256 indexed deadline, address indexed admin);
    event NewAdmin(address indexed admin);
    event CommitNewFee(
        uint256 indexed deadline,
        uint256 fee,
        uint256 admin_fee
    );
    event NewFee(uint256 fee, uint256 admin_fee);
    event RampA(
        uint256 old_A,
        uint256 new_A,
        uint256 initial_time,
        uint256 future_time
    );
    event StopRampA(uint256 A, uint256 t);

    function initialize(
        string memory _name,
        string memory _symbol,
        address _coin,
        uint256 _decimals,
        uint256 _A,
        uint256 _fee,
        address _admin
    ) external;

    function decimals() external view returns (uint256);

    function transfer(address _to, uint256 _value) external returns (bool);

    function transferFrom(
        address _from,
        address _to,
        uint256 _value
    ) external returns (bool);

    function approve(address _spender, uint256 _value) external returns (bool);

    function get_previous_balances() external view returns (uint256[2] memory);

    function get_balances() external view returns (uint256[2] memory);

    function get_twap_balances(
        uint256[2] memory _first_balances,
        uint256[2] memory _last_balances,
        uint256 _time_elapsed
    ) external view returns (uint256[2] memory);

    function get_price_cumulative_last()
        external
        view
        returns (uint256[2] memory);

    function admin_fee() external view returns (uint256);

    function A() external view returns (uint256);

    function A_precise() external view returns (uint256);

    function get_virtual_price() external view returns (uint256);

    function calc_token_amount(uint256[2] memory _amounts, bool _is_deposit)
        external
        view
        returns (uint256);

    function calc_token_amount(
        uint256[2] memory _amounts,
        bool _is_deposit,
        bool _previous
    ) external view returns (uint256);

    function add_liquidity(uint256[2] memory _amounts, uint256 _min_mint_amount)
        external
        returns (uint256);

    function add_liquidity(
        uint256[2] memory _amounts,
        uint256 _min_mint_amount,
        address _receiver
    ) external returns (uint256);

    function get_dy(
        int128 i,
        int128 j,
        uint256 dx
    ) external view returns (uint256);

    function get_dy(
        int128 i,
        int128 j,
        uint256 dx,
        uint256[2] memory _balances
    ) external view returns (uint256);

    function get_dy_underlying(
        int128 i,
        int128 j,
        uint256 dx
    ) external view returns (uint256);

    function get_dy_underlying(
        int128 i,
        int128 j,
        uint256 dx,
        uint256[2] memory _balances
    ) external view returns (uint256);

    function exchange(
        int128 i,
        int128 j,
        uint256 dx,
        uint256 min_dy
    ) external returns (uint256);

    function exchange(
        int128 i,
        int128 j,
        uint256 dx,
        uint256 min_dy,
        address _receiver
    ) external returns (uint256);

    function exchange_underlying(
        int128 i,
        int128 j,
        uint256 dx,
        uint256 min_dy
    ) external returns (uint256);

    function exchange_underlying(
        int128 i,
        int128 j,
        uint256 dx,
        uint256 min_dy,
        address _receiver
    ) external returns (uint256);

    function remove_liquidity(
        uint256 _burn_amount,
        uint256[2] memory _min_amounts
    ) external returns (uint256[2] memory);

    function remove_liquidity(
        uint256 _burn_amount,
        uint256[2] memory _min_amounts,
        address _receiver
    ) external returns (uint256[2] memory);

    function remove_liquidity_imbalance(
        uint256[2] memory _amounts,
        uint256 _max_burn_amount
    ) external returns (uint256);

    function remove_liquidity_imbalance(
        uint256[2] memory _amounts,
        uint256 _max_burn_amount,
        address _receiver
    ) external returns (uint256);

    function calc_withdraw_one_coin(uint256 _burn_amount, int128 i)
        external
        view
        returns (uint256);

    function calc_withdraw_one_coin(
        uint256 _burn_amount,
        int128 i,
        bool _previous
    ) external view returns (uint256);

    function remove_liquidity_one_coin(
        uint256 _burn_amount,
        int128 i,
        uint256 _min_received
    ) external returns (uint256);

    function remove_liquidity_one_coin(
        uint256 _burn_amount,
        int128 i,
        uint256 _min_received,
        address _receiver
    ) external returns (uint256);

    function ramp_A(uint256 _future_A, uint256 _future_time) external;

    function stop_ramp_A() external;

    function admin_balances(uint256 i) external view returns (uint256);

    function withdraw_admin_fees() external;

    function admin() external view returns (address);

    function coins(uint256 arg0) external view returns (address);

    function balances(uint256 arg0) external view returns (uint256);

    function fee() external view returns (uint256);

    function block_timestamp_last() external view returns (uint256);

    function initial_A() external view returns (uint256);

    function future_A() external view returns (uint256);

    function initial_A_time() external view returns (uint256);

    function future_A_time() external view returns (uint256);

    function name() external view returns (string memory);

    function symbol() external view returns (string memory);

    function balanceOf(address arg0) external view returns (uint256);

    function allowance(address arg0, address arg1)
        external
        view
        returns (uint256);

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

// File: contracts/TWAPOracle.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "./interfaces/IMetaPool.sol";

contract TWAPOracle {
    address public immutable pool;
    address public immutable token0;
    address public immutable token1;
    uint256 public price0Average;
    uint256 public price1Average;
    uint256 public pricesBlockTimestampLast;
    uint256[2] public priceCumulativeLast;

    constructor(
        address _pool,
        address _uADtoken0,
        address _curve3CRVtoken1
    ) {
        pool = _pool;
        // coin at index 0 is uAD and index 1 is 3CRV
        require(
            IMetaPool(_pool).coins(0) == _uADtoken0 &&
                IMetaPool(_pool).coins(1) == _curve3CRVtoken1,
            "TWAPOracle: COIN_ORDER_MISMATCH"
        );

        token0 = _uADtoken0;
        token1 = _curve3CRVtoken1;

        uint256 _reserve0 = uint112(IMetaPool(_pool).balances(0));
        uint256 _reserve1 = uint112(IMetaPool(_pool).balances(1));

        // ensure that there's liquidity in the pair
        require(_reserve0 != 0 && _reserve1 != 0, "TWAPOracle: NO_RESERVES");
        // ensure that pair balance is perfect
        require(_reserve0 == _reserve1, "TWAPOracle: PAIR_UNBALANCED");
        priceCumulativeLast = IMetaPool(_pool).get_price_cumulative_last();
        pricesBlockTimestampLast = IMetaPool(_pool).block_timestamp_last();

        price0Average = 1 ether;
        price1Average = 1 ether;
    }

    // calculate average price
    function update() external {
        (
            uint256[2] memory priceCumulative,
            uint256 blockTimestamp
        ) = _currentCumulativePrices();

        if (blockTimestamp - pricesBlockTimestampLast > 0) {
            // get the balances between now and the last price cumulative snapshot
            uint256[2] memory twapBalances = IMetaPool(pool).get_twap_balances(
                priceCumulativeLast,
                priceCumulative,
                blockTimestamp - pricesBlockTimestampLast
            );

            // price to exchange amounIn uAD to 3CRV based on TWAP
            price0Average = IMetaPool(pool).get_dy(0, 1, 1 ether, twapBalances);
            // price to exchange amounIn 3CRV to uAD  based on TWAP
            price1Average = IMetaPool(pool).get_dy(1, 0, 1 ether, twapBalances);
            // we update the priceCumulative
            priceCumulativeLast = priceCumulative;
            pricesBlockTimestampLast = blockTimestamp;
        }
    }

    // note this will always return 0 before update has been called successfully
    // for the first time.
    function consult(address token) external view returns (uint256 amountOut) {
        if (token == token0) {
            // price to exchange 1 uAD to 3CRV based on TWAP
            amountOut = price0Average;
        } else {
            require(token == token1, "TWAPOracle: INVALID_TOKEN");
            // price to exchange 1 3CRV to uAD  based on TWAP
            amountOut = price1Average;
        }
    }

    function _currentCumulativePrices()
        internal
        view
        returns (uint256[2] memory priceCumulative, uint256 blockTimestamp)
    {
        priceCumulative = IMetaPool(pool).get_price_cumulative_last();
        blockTimestamp = IMetaPool(pool).block_timestamp_last();
    }
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

// File: @openzeppelin/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _HEX_SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }
}

// File: @openzeppelin/contracts/utils/introspection/ERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File: @openzeppelin/contracts/utils/introspection/IERC165.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

// File: @openzeppelin/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        assembly {
            size := extcodesize(account)
        }
        return size > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

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

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

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

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

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

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) private pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: contracts/interfaces/IERC20Ubiquity.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

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

/// @title ERC20 Ubiquiti preset interface
/// @author Ubiquity Algorithmic Dollar
interface IERC20Ubiquity is IERC20 {
    // ----------- Events -----------
    event Minting(
        address indexed _to,
        address indexed _minter,
        uint256 _amount
    );

    event Burning(address indexed _burned, uint256 _amount);

    // ----------- State changing api -----------
    function burn(uint256 amount) external;

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    // ----------- Burner only state changing api -----------
    function burnFrom(address account, uint256 amount) external;

    // ----------- Minter only state changing api -----------
    function mint(address account, uint256 amount) external;
}

// File: contracts/ERC1155Ubiquity.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/ERC1155.sol";
import "@openzeppelin/contracts/token/ERC1155/extensions/ERC1155Burnable.sol";
import "@openzeppelin/contracts/token/ERC1155/extensions/ERC1155Pausable.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./utils/SafeAddArray.sol";

/// @title ERC1155 Ubiquity preset
/// @author Ubiquity Algorithmic Dollar
/// @notice ERC1155 with :
/// - ERC1155 minter, burner and pauser
/// - TotatSupply per id
/// - Ubiquity Manager access control
contract ERC1155Ubiquity is ERC1155, ERC1155Burnable, ERC1155Pausable {
    using SafeAddArray for uint256[];
    UbiquityAlgorithmicDollarManager public manager;
    // Mapping from account to operator approvals
    mapping(address => uint256[]) private _holderBalances;
    uint256 private _totalSupply;

    // ----------- Modifiers -----------
    modifier onlyMinter() {
        require(
            manager.hasRole(manager.UBQ_MINTER_ROLE(), msg.sender),
            "Governance token: not minter"
        );
        _;
    }

    modifier onlyBurner() {
        require(
            manager.hasRole(manager.UBQ_BURNER_ROLE(), msg.sender),
            "Governance token: not burner"
        );
        _;
    }

    modifier onlyPauser() {
        require(
            manager.hasRole(manager.PAUSER_ROLE(), msg.sender),
            "Governance token: not pauser"
        );
        _;
    }

    /**
     * @dev constructor
     */
    constructor(address _manager, string memory uri) ERC1155(uri) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    // @dev Creates `amount` new tokens for `to`, of token type `id`.
    function mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public virtual onlyMinter {
        _mint(to, id, amount, data);
        _totalSupply += amount;
        _holderBalances[to].add(id);
    }

    // @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] variant of {mint}.
    function mintBatch(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual onlyMinter whenNotPaused {
        _mintBatch(to, ids, amounts, data);
        for (uint256 i = 0; i < ids.length; ++i) {
            _totalSupply += amounts[i];
        }
        _holderBalances[to].add(ids);
    }

    /**
     * @dev Pauses all token transfers.
     *
     * See {ERC1155Pausable} and {Pausable-_pause}.
     *
     */
    function pause() public virtual onlyPauser {
        _pause();
    }

    /**
     * @dev Unpauses all token transfers.
     *
     * See {ERC1155Pausable} and {Pausable-_unpause}.
     *
     */
    function unpause() public virtual onlyPauser {
        _unpause();
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public override {
        super.safeTransferFrom(from, to, id, amount, data);
        _holderBalances[to].add(id);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual override {
        super.safeBatchTransferFrom(from, to, ids, amounts, data);
        _holderBalances[to].add(ids);
    }

    /**
     * @dev Total amount of tokens in with a given id.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev array of token Id held by the msg.sender.
     */
    function holderTokens(address holder)
        public
        view
        returns (uint256[] memory)
    {
        return _holderBalances[holder];
    }

    function _burn(
        address account,
        uint256 id,
        uint256 amount
    ) internal virtual override whenNotPaused {
        super._burn(account, id, amount);
        _totalSupply -= amount;
    }

    function _burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual override whenNotPaused {
        super._burnBatch(account, ids, amounts);
        for (uint256 i = 0; i < ids.length; ++i) {
            _totalSupply -= amounts[i];
        }
    }

    function _beforeTokenTransfer(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual override(ERC1155, ERC1155Pausable) {
        super._beforeTokenTransfer(operator, from, to, ids, amounts, data);
    }
}

// File: solidity-linked-list/contracts/StructuredLinkedList.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

interface  IStructureInterface {
    function getValue(uint256 _id) external view returns (uint256);
}

/**
 * @title StructuredLinkedList
 * @author Vittorio Minacori (https://github.com/vittominacori)
 * @dev An utility library for using sorted linked list data structures in your Solidity project.
 */
library StructuredLinkedList {

    uint256 private constant _NULL = 0;
    uint256 private constant _HEAD = 0;

    bool private constant _PREV = false;
    bool private constant _NEXT = true;

    struct List {
        uint256 size;
        mapping(uint256 => mapping(bool => uint256)) list;
    }

    /**
     * @dev Checks if the list exists
     * @param self stored linked list from contract
     * @return bool true if list exists, false otherwise
     */
    function listExists(List storage self) internal view returns (bool) {
        // if the head nodes previous or next pointers both point to itself, then there are no items in the list
        if (self.list[_HEAD][_PREV] != _HEAD || self.list[_HEAD][_NEXT] != _HEAD) {
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Checks if the node exists
     * @param self stored linked list from contract
     * @param _node a node to search for
     * @return bool true if node exists, false otherwise
     */
    function nodeExists(List storage self, uint256 _node) internal view returns (bool) {
        if (self.list[_node][_PREV] == _HEAD && self.list[_node][_NEXT] == _HEAD) {
            if (self.list[_HEAD][_NEXT] == _node) {
                return true;
            } else {
                return false;
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Returns the number of elements in the list
     * @param self stored linked list from contract
     * @return uint256
     */
    function sizeOf(List storage self) internal view returns (uint256) {
        return self.size;
    }

    /**
     * @dev Returns the links of a node as a tuple
     * @param self stored linked list from contract
     * @param _node id of the node to get
     * @return bool, uint256, uint256 true if node exists or false otherwise, previous node, next node
     */
    function getNode(List storage self, uint256 _node) internal view returns (bool, uint256, uint256) {
        if (!nodeExists(self, _node)) {
            return (false, 0, 0);
        } else {
            return (true, self.list[_node][_PREV], self.list[_node][_NEXT]);
        }
    }

    /**
     * @dev Returns the link of a node `_node` in direction `_direction`.
     * @param self stored linked list from contract
     * @param _node id of the node to step from
     * @param _direction direction to step in
     * @return bool, uint256 true if node exists or false otherwise, node in _direction
     */
    function getAdjacent(List storage self, uint256 _node, bool _direction) internal view returns (bool, uint256) {
        if (!nodeExists(self, _node)) {
            return (false, 0);
        } else {
            return (true, self.list[_node][_direction]);
        }
    }

    /**
     * @dev Returns the link of a node `_node` in direction `_NEXT`.
     * @param self stored linked list from contract
     * @param _node id of the node to step from
     * @return bool, uint256 true if node exists or false otherwise, next node
     */
    function getNextNode(List storage self, uint256 _node) internal view returns (bool, uint256) {
        return getAdjacent(self, _node, _NEXT);
    }

    /**
     * @dev Returns the link of a node `_node` in direction `_PREV`.
     * @param self stored linked list from contract
     * @param _node id of the node to step from
     * @return bool, uint256 true if node exists or false otherwise, previous node
     */
    function getPreviousNode(List storage self, uint256 _node) internal view returns (bool, uint256) {
        return getAdjacent(self, _node, _PREV);
    }

    /**
     * @dev Can be used before `insert` to build an ordered list.
     * @dev Get the node and then `insertBefore` or `insertAfter` basing on your list order.
     * @dev If you want to order basing on other than `structure.getValue()` override this function
     * @param self stored linked list from contract
     * @param _structure the structure instance
     * @param _value value to seek
     * @return uint256 next node with a value less than _value
     */
    function getSortedSpot(List storage self, address _structure, uint256 _value) internal view returns (uint256) {
        if (sizeOf(self) == 0) {
            return 0;
        }

        uint256 next;
        (, next) = getAdjacent(self, _HEAD, _NEXT);
        while ((next != 0) && ((_value < IStructureInterface(_structure).getValue(next)) != _NEXT)) {
            next = self.list[next][_NEXT];
        }
        return next;
    }

    /**
     * @dev Insert node `_new` beside existing node `_node` in direction `_NEXT`.
     * @param self stored linked list from contract
     * @param _node existing node
     * @param _new  new node to insert
     * @return bool true if success, false otherwise
     */
    function insertAfter(List storage self, uint256 _node, uint256 _new) internal returns (bool) {
        return _insert(self, _node, _new, _NEXT);
    }

    /**
     * @dev Insert node `_new` beside existing node `_node` in direction `_PREV`.
     * @param self stored linked list from contract
     * @param _node existing node
     * @param _new  new node to insert
     * @return bool true if success, false otherwise
     */
    function insertBefore(List storage self, uint256 _node, uint256 _new) internal returns (bool) {
        return _insert(self, _node, _new, _PREV);
    }

    /**
     * @dev Removes an entry from the linked list
     * @param self stored linked list from contract
     * @param _node node to remove from the list
     * @return uint256 the removed node
     */
    function remove(List storage self, uint256 _node) internal returns (uint256) {
        if ((_node == _NULL) || (!nodeExists(self, _node))) {
            return 0;
        }
        _createLink(self, self.list[_node][_PREV], self.list[_node][_NEXT], _NEXT);
        delete self.list[_node][_PREV];
        delete self.list[_node][_NEXT];

        self.size -= 1; // NOT: SafeMath library should be used here to decrement.

        return _node;
    }

    /**
     * @dev Pushes an entry to the head of the linked list
     * @param self stored linked list from contract
     * @param _node new entry to push to the head
     * @return bool true if success, false otherwise
     */
    function pushFront(List storage self, uint256 _node) internal returns (bool) {
        return _push(self, _node, _NEXT);
    }

    /**
     * @dev Pushes an entry to the tail of the linked list
     * @param self stored linked list from contract
     * @param _node new entry to push to the tail
     * @return bool true if success, false otherwise
     */
    function pushBack(List storage self, uint256 _node) internal returns (bool) {
        return _push(self, _node, _PREV);
    }

    /**
     * @dev Pops the first entry from the head of the linked list
     * @param self stored linked list from contract
     * @return uint256 the removed node
     */
    function popFront(List storage self) internal returns (uint256) {
        return _pop(self, _NEXT);
    }

    /**
     * @dev Pops the first entry from the tail of the linked list
     * @param self stored linked list from contract
     * @return uint256 the removed node
     */
    function popBack(List storage self) internal returns (uint256) {
        return _pop(self, _PREV);
    }

    /**
     * @dev Pushes an entry to the head of the linked list
     * @param self stored linked list from contract
     * @param _node new entry to push to the head
     * @param _direction push to the head (_NEXT) or tail (_PREV)
     * @return bool true if success, false otherwise
     */
    function _push(List storage self, uint256 _node, bool _direction) private returns (bool) {
        return _insert(self, _HEAD, _node, _direction);
    }

    /**
     * @dev Pops the first entry from the linked list
     * @param self stored linked list from contract
     * @param _direction pop from the head (_NEXT) or the tail (_PREV)
     * @return uint256 the removed node
     */
    function _pop(List storage self, bool _direction) private returns (uint256) {
        uint256 adj;
        (, adj) = getAdjacent(self, _HEAD, _direction);
        return remove(self, adj);
    }

    /**
     * @dev Insert node `_new` beside existing node `_node` in direction `_direction`.
     * @param self stored linked list from contract
     * @param _node existing node
     * @param _new  new node to insert
     * @param _direction direction to insert node in
     * @return bool true if success, false otherwise
     */
    function _insert(List storage self, uint256 _node, uint256 _new, bool _direction) private returns (bool) {
        if (!nodeExists(self, _new) && nodeExists(self, _node)) {
            uint256 c = self.list[_node][_direction];
            _createLink(self, _node, _new, _direction);
            _createLink(self, _new, c, _direction);

            self.size += 1; // NOT: SafeMath library should be used here to increment.

            return true;
        }

        return false;
    }

    /**
     * @dev Creates a bidirectional link between two nodes on direction `_direction`
     * @param self stored linked list from contract
     * @param _node existing node
     * @param _link node to link to in the _direction
     * @param _direction direction to insert node in
     */
    function _createLink(List storage self, uint256 _node, uint256 _link, bool _direction) private {
        self.list[_link][!_direction] = _node;
        self.list[_node][_direction] = _link;
    }
}

// File: @openzeppelin/contracts/token/ERC1155/ERC1155.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./IERC1155.sol";
import "./IERC1155Receiver.sol";
import "./extensions/IERC1155MetadataURI.sol";
import "../../utils/Address.sol";
import "../../utils/Context.sol";
import "../../utils/introspection/ERC165.sol";

/**
 * @dev Implementation of the basic standard multi-token.
 * See https://eips.ethereum.org/EIPS/eip-1155
 * Originally based on code by Enjin: https://github.com/enjin/erc-1155
 *
 * _Available since v3.1._
 */
contract ERC1155 is Context, ERC165, IERC1155, IERC1155MetadataURI {
    using Address for address;

    // Mapping from token ID to account balances
    mapping(uint256 => mapping(address => uint256)) private _balances;

    // Mapping from account to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    // Used as the URI for all token types by relying on ID substitution, e.g. https://token-cdn-domain/{id}.json
    string private _uri;

    /**
     * @dev See {_setURI}.
     */
    constructor(string memory uri_) {
        _setURI(uri_);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC1155).interfaceId ||
            interfaceId == type(IERC1155MetadataURI).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC1155MetadataURI-uri}.
     *
     * This implementation returns the same URI for *all* token types. It relies
     * on the token type ID substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the EIP].
     *
     * Clients calling this function must replace the `\{id\}` substring with the
     * actual token type ID.
     */
    function uri(uint256) public view virtual override returns (string memory) {
        return _uri;
    }

    /**
     * @dev See {IERC1155-balanceOf}.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function balanceOf(address account, uint256 id) public view virtual override returns (uint256) {
        require(account != address(0), "ERC1155: balance query for the zero address");
        return _balances[id][account];
    }

    /**
     * @dev See {IERC1155-balanceOfBatch}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(address[] memory accounts, uint256[] memory ids)
        public
        view
        virtual
        override
        returns (uint256[] memory)
    {
        require(accounts.length == ids.length, "ERC1155: accounts and ids length mismatch");

        uint256[] memory batchBalances = new uint256[](accounts.length);

        for (uint256 i = 0; i < accounts.length; ++i) {
            batchBalances[i] = balanceOf(accounts[i], ids[i]);
        }

        return batchBalances;
    }

    /**
     * @dev See {IERC1155-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual override {
        require(_msgSender() != operator, "ERC1155: setting approval status for self");

        _operatorApprovals[_msgSender()][operator] = approved;
        emit ApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC1155-isApprovedForAll}.
     */
    function isApprovedForAll(address account, address operator) public view virtual override returns (bool) {
        return _operatorApprovals[account][operator];
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public virtual override {
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );
        _safeTransferFrom(from, to, id, amount, data);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual override {
        require(
            from == _msgSender() || isApprovedForAll(from, _msgSender()),
            "ERC1155: transfer caller is not owner nor approved"
        );
        _safeBatchTransferFrom(from, to, ids, amounts, data);
    }

    /**
     * @dev Transfers `amount` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `from` must have a balance of tokens of type `id` of at least `amount`.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        require(to != address(0), "ERC1155: transfer to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, to, _asSingletonArray(id), _asSingletonArray(amount), data);

        uint256 fromBalance = _balances[id][from];
        require(fromBalance >= amount, "ERC1155: insufficient balance for transfer");
        unchecked {
            _balances[id][from] = fromBalance - amount;
        }
        _balances[id][to] += amount;

        emit TransferSingle(operator, from, to, id, amount);

        _doSafeTransferAcceptanceCheck(operator, from, to, id, amount, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");
        require(to != address(0), "ERC1155: transfer to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, from, to, ids, amounts, data);

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

            uint256 fromBalance = _balances[id][from];
            require(fromBalance >= amount, "ERC1155: insufficient balance for transfer");
            unchecked {
                _balances[id][from] = fromBalance - amount;
            }
            _balances[id][to] += amount;
        }

        emit TransferBatch(operator, from, to, ids, amounts);

        _doSafeBatchTransferAcceptanceCheck(operator, from, to, ids, amounts, data);
    }

    /**
     * @dev Sets a new URI for all token types, by relying on the token type ID
     * substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the EIP].
     *
     * By this mechanism, any occurrence of the `\{id\}` substring in either the
     * URI or any of the amounts in the JSON file at said URI will be replaced by
     * clients with the token type ID.
     *
     * For example, the `https://token-cdn-domain/\{id\}.json` URI would be
     * interpreted by clients as
     * `https://token-cdn-domain/000000000000000000000000000000000000000000000000000000000004cce0.json`
     * for token type ID 0x4cce0.
     *
     * See {uri}.
     *
     * Because these URIs cannot be meaningfully represented by the {URI} event,
     * this function emits no events.
     */
    function _setURI(string memory newuri) internal virtual {
        _uri = newuri;
    }

    /**
     * @dev Creates `amount` tokens of token type `id`, and assigns them to `account`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - If `account` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _mint(
        address account,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) internal virtual {
        require(account != address(0), "ERC1155: mint to the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, address(0), account, _asSingletonArray(id), _asSingletonArray(amount), data);

        _balances[id][account] += amount;
        emit TransferSingle(operator, address(0), account, id, amount);

        _doSafeTransferAcceptanceCheck(operator, address(0), account, id, amount, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_mint}.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _mintBatch(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {
        require(to != address(0), "ERC1155: mint to the zero address");
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, address(0), to, ids, amounts, data);

        for (uint256 i = 0; i < ids.length; i++) {
            _balances[ids[i]][to] += amounts[i];
        }

        emit TransferBatch(operator, address(0), to, ids, amounts);

        _doSafeBatchTransferAcceptanceCheck(operator, address(0), to, ids, amounts, data);
    }

    /**
     * @dev Destroys `amount` tokens of token type `id` from `account`
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens of token type `id`.
     */
    function _burn(
        address account,
        uint256 id,
        uint256 amount
    ) internal virtual {
        require(account != address(0), "ERC1155: burn from the zero address");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, account, address(0), _asSingletonArray(id), _asSingletonArray(amount), "");

        uint256 accountBalance = _balances[id][account];
        require(accountBalance >= amount, "ERC1155: burn amount exceeds balance");
        unchecked {
            _balances[id][account] = accountBalance - amount;
        }

        emit TransferSingle(operator, account, address(0), id, amount);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_burn}.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     */
    function _burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual {
        require(account != address(0), "ERC1155: burn from the zero address");
        require(ids.length == amounts.length, "ERC1155: ids and amounts length mismatch");

        address operator = _msgSender();

        _beforeTokenTransfer(operator, account, address(0), ids, amounts, "");

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

            uint256 accountBalance = _balances[id][account];
            require(accountBalance >= amount, "ERC1155: burn amount exceeds balance");
            unchecked {
                _balances[id][account] = accountBalance - amount;
            }
        }

        emit TransferBatch(operator, account, address(0), ids, amounts);
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting
     * and burning, as well as batched variants.
     *
     * The same hook is called on both single and batched variants. For single
     * transfers, the length of the `id` and `amount` arrays will be 1.
     *
     * Calling conditions (for each `id` and `amount` pair):
     *
     * - When `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * of token type `id` will be  transferred to `to`.
     * - When `from` is zero, `amount` tokens of token type `id` will be minted
     * for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens of token type `id`
     * will be burned.
     * - `from` and `to` are never both zero.
     * - `ids` and `amounts` have the same, non-zero length.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual {}

    function _doSafeTransferAcceptanceCheck(
        address operator,
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) private {
        if (to.isContract()) {
            try IERC1155Receiver(to).onERC1155Received(operator, from, id, amount, data) returns (bytes4 response) {
                if (response != IERC1155Receiver(to).onERC1155Received.selector) {
                    revert("ERC1155: ERC1155Receiver rejected tokens");
                }
            } catch Error(string memory reason) {
                revert(reason);
            } catch {
                revert("ERC1155: transfer to non ERC1155Receiver implementer");
            }
        }
    }

    function _doSafeBatchTransferAcceptanceCheck(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) private {
        if (to.isContract()) {
            try IERC1155Receiver(to).onERC1155BatchReceived(operator, from, ids, amounts, data) returns (
                bytes4 response
            ) {
                if (response != IERC1155Receiver(to).onERC1155BatchReceived.selector) {
                    revert("ERC1155: ERC1155Receiver rejected tokens");
                }
            } catch Error(string memory reason) {
                revert(reason);
            } catch {
                revert("ERC1155: transfer to non ERC1155Receiver implementer");
            }
        }
    }

    function _asSingletonArray(uint256 element) private pure returns (uint256[] memory) {
        uint256[] memory array = new uint256[](1);
        array[0] = element;

        return array;
    }
}

// File: @openzeppelin/contracts/token/ERC1155/extensions/ERC1155Burnable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC1155.sol";

/**
 * @dev Extension of {ERC1155} that allows token holders to destroy both their
 * own tokens and those that they have been approved to use.
 *
 * _Available since v3.1._
 */
abstract contract ERC1155Burnable is ERC1155 {
    function burn(
        address account,
        uint256 id,
        uint256 value
    ) public virtual {
        require(
            account == _msgSender() || isApprovedForAll(account, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );

        _burn(account, id, value);
    }

    function burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory values
    ) public virtual {
        require(
            account == _msgSender() || isApprovedForAll(account, _msgSender()),
            "ERC1155: caller is not owner nor approved"
        );

        _burnBatch(account, ids, values);
    }
}

// File: @openzeppelin/contracts/token/ERC1155/extensions/ERC1155Pausable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC1155.sol";
import "../../../security/Pausable.sol";

/**
 * @dev ERC1155 token with pausable token transfers, minting and burning.
 *
 * Useful for scenarios such as preventing trades until the end of an evaluation
 * period, or having an emergency switch for freezing all token transfers in the
 * event of a large bug.
 *
 * _Available since v3.1._
 */
abstract contract ERC1155Pausable is ERC1155, Pausable {
    /**
     * @dev See {ERC1155-_beforeTokenTransfer}.
     *
     * Requirements:
     *
     * - the contract must not be paused.
     */
    function _beforeTokenTransfer(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual override {
        super._beforeTokenTransfer(operator, from, to, ids, amounts, data);

        require(!paused(), "ERC1155Pausable: token transfer while paused");
    }
}

// File: contracts/utils/SafeAddArray.sol



// SPDX-License-Identifier: MIT

// SPDX-License-Identifier: EUPL V1.2
pragma solidity ^0.8.3;

/**
 * @dev Wrappers over Solidity's array push operations with added check
 *
 */
library SafeAddArray {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     */
    function add(bytes32[] storage array, bytes32 value) internal {
        for (uint256 i; i < array.length; i++) {
            if (array[i] == value) {
                return;
            }
        }
        array.push(value);
    }

    function add(string[] storage array, string memory value) internal {
        bytes32 hashValue = keccak256(bytes(value));
        for (uint256 i; i < array.length; i++) {
            if (keccak256(bytes(array[i])) == hashValue) {
                return;
            }
        }
        array.push(value);
    }

    function add(uint256[] storage array, uint256 value) internal {
        for (uint256 i; i < array.length; i++) {
            if (array[i] == value) {
                return;
            }
        }
        array.push(value);
    }

    function add(uint256[] storage array, uint256[] memory values) internal {
        for (uint256 i; i < values.length; i++) {
            bool exist = false;
            for (uint256 j; j < array.length; j++) {
                if (array[j] == values[i]) {
                    exist = true;
                    break;
                }
            }
            if (!exist) {
                array.push(values[i]);
            }
        }
    }
}

// File: @openzeppelin/contracts/token/ERC1155/IERC1155.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

/**
 * @dev Required interface of an ERC1155 compliant contract, as defined in the
 * https://eips.ethereum.org/EIPS/eip-1155[EIP].
 *
 * _Available since v3.1._
 */
interface IERC1155 is IERC165 {
    /**
     * @dev Emitted when `value` tokens of token type `id` are transferred from `from` to `to` by `operator`.
     */
    event TransferSingle(address indexed operator, address indexed from, address indexed to, uint256 id, uint256 value);

    /**
     * @dev Equivalent to multiple {TransferSingle} events, where `operator`, `from` and `to` are the same for all
     * transfers.
     */
    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] values
    );

    /**
     * @dev Emitted when `account` grants or revokes permission to `operator` to transfer their tokens, according to
     * `approved`.
     */
    event ApprovalForAll(address indexed account, address indexed operator, bool approved);

    /**
     * @dev Emitted when the URI for token type `id` changes to `value`, if it is a non-programmatic URI.
     *
     * If an {URI} event was emitted for `id`, the standard
     * https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[guarantees] that `value` will equal the value
     * returned by {IERC1155MetadataURI-uri}.
     */
    event URI(string value, uint256 indexed id);

    /**
     * @dev Returns the amount of tokens of token type `id` owned by `account`.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function balanceOf(address account, uint256 id) external view returns (uint256);

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {balanceOf}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(address[] calldata accounts, uint256[] calldata ids)
        external
        view
        returns (uint256[] memory);

    /**
     * @dev Grants or revokes permission to `operator` to transfer the caller's tokens, according to `approved`,
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the caller.
     */
    function setApprovalForAll(address operator, bool approved) external;

    /**
     * @dev Returns true if `operator` is approved to transfer ``account``'s tokens.
     *
     * See {setApprovalForAll}.
     */
    function isApprovedForAll(address account, address operator) external view returns (bool);

    /**
     * @dev Transfers `amount` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If the caller is not `from`, it must be have been approved to spend ``from``'s tokens via {setApprovalForAll}.
     * - `from` must have a balance of tokens of type `id` of at least `amount`.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes calldata data
    ) external;

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `ids` and `amounts` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata amounts,
        bytes calldata data
    ) external;
}

// File: @openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

/**
 * @dev _Available since v3.1._
 */
interface IERC1155Receiver is IERC165 {
    /**
        @dev Handles the receipt of a single ERC1155 token type. This function is
        called at the end of a `safeTransferFrom` after the balance has been updated.
        To accept the transfer, this must return
        `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
        (i.e. 0xf23a6e61, or its own function selector).
        @param operator The address which initiated the transfer (i.e. msg.sender)
        @param from The address which previously owned the token
        @param id The ID of the token being transferred
        @param value The amount of tokens being transferred
        @param data Additional data with no specified format
        @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
    */
    function onERC1155Received(
        address operator,
        address from,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external returns (bytes4);

    /**
        @dev Handles the receipt of a multiple ERC1155 token types. This function
        is called at the end of a `safeBatchTransferFrom` after the balances have
        been updated. To accept the transfer(s), this must return
        `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
        (i.e. 0xbc197c81, or its own function selector).
        @param operator The address which initiated the batch transfer (i.e. msg.sender)
        @param from The address which previously owned the token
        @param ids An array containing ids of each token being transferred (order and length must match values array)
        @param values An array containing amounts of each token being transferred (order and length must match ids array)
        @param data Additional data with no specified format
        @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
    */
    function onERC1155BatchReceived(
        address operator,
        address from,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external returns (bytes4);
}

// File: @openzeppelin/contracts/token/ERC1155/extensions/IERC1155MetadataURI.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../IERC1155.sol";

/**
 * @dev Interface of the optional ERC1155MetadataExtension interface, as defined
 * in the https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[EIP].
 *
 * _Available since v3.1._
 */
interface IERC1155MetadataURI is IERC1155 {
    /**
     * @dev Returns the URI for token type `id`.
     *
     * If the `\{id\}` substring is present in the URI, it must be replaced by
     * clients with the actual token type ID.
     */
    function uri(uint256 id) external view returns (string memory);
}

// File: @openzeppelin/contracts/security/Pausable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

    bool private _paused;

    /**
     * @dev Initializes the contract in unpaused state.
     */
    constructor() {
        _paused = false;
    }

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

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

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

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

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

// File: contracts/UARForDollarsCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./interfaces/IUARForDollarsCalculator.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./libs/ABDKMathQuad.sol";
import "./DebtCoupon.sol";

/// @title Uses the following formula: ((1/(1-R)^2) - 1)
contract UARForDollarsCalculator is IUARForDollarsCalculator {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;
    UbiquityAlgorithmicDollarManager public manager;
    uint256 private _coef = 1 ether;

    modifier onlyAdmin() {
        require(
            manager.hasRole(manager.INCENTIVE_MANAGER_ROLE(), msg.sender),
            "UARCalc: not admin"
        );
        _;
    }

    /// @param _manager the address of the manager/config contract so we can fetch variables
    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    /// @notice set the constant for uAR calculation
    /// @param coef new constant for uAR calculation in ETH format
    /// @dev a coef of 1 ether means 1
    function setConstant(uint256 coef) external onlyAdmin {
        _coef = coef;
    }

    /// @notice get the constant for uAR calculation
    function getConstant() external view returns (uint256) {
        return _coef;
    }

    // dollarsToBurn * (blockheight_debt/blockheight_burn) * _coef
    function getUARAmount(uint256 dollarsToBurn, uint256 blockHeightDebt)
        external
        view
        override
        returns (uint256)
    {
        require(
            DebtCoupon(manager.debtCouponAddress()).getTotalOutstandingDebt() <
                IERC20(manager.dollarTokenAddress()).totalSupply(),
            "uAR to Dollar: DEBT_TOO_HIGH"
        );
        bytes16 coef = _coef.fromUInt().div((uint256(1 ether)).fromUInt());
        bytes16 curBlock = uint256(block.number).fromUInt();
        bytes16 multiplier = blockHeightDebt.fromUInt().div(curBlock);
        // x^a = e^(a*lnx(x)) so multiplier^(_coef) = e^(_coef*lnx(multiplier))
        bytes16 op = (coef.mul(multiplier.ln())).exp();
        uint256 res = dollarsToBurn.fromUInt().mul(op).toUInt();
        return res;
    }
}

// File: contracts/UbiquityFormulas.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./libs/ABDKMathQuad.sol";

contract UbiquityFormulas {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;

    /// @dev formula duration multiply
    /// @param _uLP , amount of LP tokens
    /// @param _weeks , mimimun duration of staking period
    /// @param _multiplier , bonding discount multiplier = 0.0001
    /// @return _shares , amount of shares
    /// @notice _shares = (1 + _multiplier * _weeks^3/2) * _uLP
    //          D32 = D^3/2
    //          S = m * D32 * A + A
    function durationMultiply(
        uint256 _uLP,
        uint256 _weeks,
        uint256 _multiplier
    ) public pure returns (uint256 _shares) {
        bytes16 unit = uint256(1 ether).fromUInt();
        bytes16 d = _weeks.fromUInt();
        bytes16 d32 = (d.mul(d).mul(d)).sqrt();
        bytes16 m = _multiplier.fromUInt().div(unit); // 0.0001
        bytes16 a = _uLP.fromUInt();

        _shares = m.mul(d32).mul(a).add(a).toUInt();
    }

    /// @dev formula bonding
    /// @param _shares , amount of shares
    /// @param _currentShareValue , current share value
    /// @param _targetPrice , target uAD price
    /// @return _uBOND , amount of bonding shares
    /// @notice UBOND = _shares / _currentShareValue * _targetPrice
    // newShares = A / V * T
    function bonding(
        uint256 _shares,
        uint256 _currentShareValue,
        uint256 _targetPrice
    ) public pure returns (uint256 _uBOND) {
        bytes16 a = _shares.fromUInt();
        bytes16 v = _currentShareValue.fromUInt();
        bytes16 t = _targetPrice.fromUInt();

        _uBOND = a.div(v).mul(t).toUInt();
    }

    /// @dev formula redeem bonds
    /// @param _uBOND , amount of bonding shares
    /// @param _currentShareValue , current share value
    /// @param _targetPrice , target uAD price
    /// @return _uLP , amount of LP tokens
    /// @notice _uLP = _uBOND * _currentShareValue / _targetPrice
    // _uLP = A * V / T
    function redeemBonds(
        uint256 _uBOND,
        uint256 _currentShareValue,
        uint256 _targetPrice
    ) public pure returns (uint256 _uLP) {
        bytes16 a = _uBOND.fromUInt();
        bytes16 v = _currentShareValue.fromUInt();
        bytes16 t = _targetPrice.fromUInt();

        _uLP = a.mul(v).div(t).toUInt();
    }

    /// @dev formula bond price
    /// @param _totalULP , total LP tokens
    /// @param _totalUBOND , total bond shares
    /// @param _targetPrice ,  target uAD price
    /// @return _priceUBOND , bond share price
    /// @notice
    // IF _totalUBOND = 0  priceBOND = TARGET_PRICE
    // ELSE                priceBOND = totalLP / totalShares * TARGET_PRICE
    // R = T == 0 ? 1 : LP / S
    // P = R * T
    function bondPrice(
        uint256 _totalULP,
        uint256 _totalUBOND,
        uint256 _targetPrice
    ) public pure returns (uint256 _priceUBOND) {
        bytes16 lp = _totalULP.fromUInt();
        bytes16 s = _totalUBOND.fromUInt();
        bytes16 r = _totalUBOND == 0 ? uint256(1).fromUInt() : lp.div(s);
        bytes16 t = _targetPrice.fromUInt();

        _priceUBOND = r.mul(t).toUInt();
    }

    /// @dev formula ugov multiply
    /// @param _multiplier , initial ugov min multiplier
    /// @param _price , current share price
    /// @return _newMultiplier , new ugov min multiplier
    /// @notice new_multiplier = multiplier * ( 1.05 / (1 + abs( 1 - price ) ) )
    // nM = M * C / A
    // A = ( 1 + abs( 1 - P)))
    // 5 >= multiplier >= 0.2
    function ugovMultiply(uint256 _multiplier, uint256 _price)
        public
        pure
        returns (uint256 _newMultiplier)
    {
        bytes16 m = _multiplier.fromUInt();
        bytes16 p = _price.fromUInt();
        bytes16 c = uint256(105 * 1e16).fromUInt(); // 1.05
        bytes16 u = uint256(1e18).fromUInt(); // 1
        bytes16 a = u.add(u.sub(p).abs()); // 1 + abs( 1 - P )

        _newMultiplier = m.mul(c).div(a).toUInt(); // nM = M * C / A

        // 5 >= multiplier >= 0.2
        if (_newMultiplier > 5e18 || _newMultiplier < 2e17)
            _newMultiplier = _multiplier;
    }
}

// File: contracts/ExcessDollarsDistributor.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./interfaces/IERC20Ubiquity.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol";
import "@uniswap/v2-periphery/contracts/interfaces/IUniswapV2Router02.sol";
import "./interfaces/IExcessDollarsDistributor.sol";
import "./interfaces/IMetaPool.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./SushiSwapPool.sol";
import "./libs/ABDKMathQuad.sol";

/// @title An excess dollar distributor which sends dollars to treasury,
/// lp rewards and inflation rewards
contract ExcessDollarsDistributor is IExcessDollarsDistributor {
    using SafeERC20 for IERC20Ubiquity;
    using SafeERC20 for IERC20;
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;
    UbiquityAlgorithmicDollarManager public manager;
    uint256 private immutable _minAmountToDistribute = 100 ether;
    IUniswapV2Router02 private immutable _router =
        IUniswapV2Router02(0xd9e1cE17f2641f24aE83637ab66a2cca9C378B9F); // SushiV2Router02

    /// @param _manager the address of the manager contract so we can fetch variables
    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    function distributeDollars() external override {
        //the excess dollars which were sent to this contract by the coupon manager
        uint256 excessDollars = IERC20Ubiquity(manager.dollarTokenAddress())
            .balanceOf(address(this));
        if (excessDollars > _minAmountToDistribute) {
            address treasuryAddress = manager.treasuryAddress();

            // curve uAD-3CRV liquidity pool
            uint256 tenPercent = excessDollars
                .fromUInt()
                .div(uint256(10).fromUInt())
                .toUInt();
            uint256 fiftyPercent = excessDollars
                .fromUInt()
                .div(uint256(2).fromUInt())
                .toUInt();
            IERC20Ubiquity(manager.dollarTokenAddress()).safeTransfer(
                treasuryAddress,
                fiftyPercent
            );
            // convert uAD to uGOV-UAD LP on sushi and burn them
            _governanceBuyBackLPAndBurn(tenPercent);
            // convert remaining uAD to curve LP tokens
            // and transfer the curve LP tokens to the bonding contract
            _convertToCurveLPAndTransfer(
                excessDollars - fiftyPercent - tenPercent
            );
        }
    }

    // swap half amount to uGOV
    function _swapDollarsForGovernance(bytes16 amountIn)
        internal
        returns (uint256)
    {
        address[] memory path = new address[](2);
        path[0] = manager.dollarTokenAddress();
        path[1] = manager.governanceTokenAddress();
        uint256[] memory amounts = _router.swapExactTokensForTokens(
            amountIn.toUInt(),
            0,
            path,
            address(this),
            block.timestamp + 100
        );

        return amounts[1];
    }

    // buy-back and burn uGOV
    function _governanceBuyBackLPAndBurn(uint256 amount) internal {
        bytes16 amountUAD = (amount.fromUInt()).div(uint256(2).fromUInt());

        // we need to approve sushi router
        IERC20Ubiquity(manager.dollarTokenAddress()).safeApprove(
            address(_router),
            0
        );
        IERC20Ubiquity(manager.dollarTokenAddress()).safeApprove(
            address(_router),
            amount
        );
        uint256 amountUGOV = _swapDollarsForGovernance(amountUAD);

        IERC20Ubiquity(manager.governanceTokenAddress()).safeApprove(
            address(_router),
            0
        );
        IERC20Ubiquity(manager.governanceTokenAddress()).safeApprove(
            address(_router),
            amountUGOV
        );

        // deposit liquidity and transfer to zero address (burn)
        _router.addLiquidity(
            manager.dollarTokenAddress(),
            manager.governanceTokenAddress(),
            amountUAD.toUInt(),
            amountUGOV,
            0,
            0,
            address(0),
            block.timestamp + 100
        );
    }

    // @dev convert to curve LP
    // @param amount to convert to curve LP by swapping to 3CRV
    //        and deposit the 3CRV as liquidity to get uAD-3CRV LP tokens
    //        the LP token are sent to the bonding contract
    function _convertToCurveLPAndTransfer(uint256 amount)
        internal
        returns (uint256)
    {
        // we need to approve  metaPool
        IERC20Ubiquity(manager.dollarTokenAddress()).safeApprove(
            manager.stableSwapMetaPoolAddress(),
            0
        );
        IERC20Ubiquity(manager.dollarTokenAddress()).safeApprove(
            manager.stableSwapMetaPoolAddress(),
            amount
        );

        // swap  amount of uAD => 3CRV
        uint256 amount3CRVReceived = IMetaPool(
            manager.stableSwapMetaPoolAddress()
        ).exchange(0, 1, amount, 0);

        // approve metapool to transfer our 3CRV
        IERC20(manager.curve3PoolTokenAddress()).safeApprove(
            manager.stableSwapMetaPoolAddress(),
            0
        );
        IERC20(manager.curve3PoolTokenAddress()).safeApprove(
            manager.stableSwapMetaPoolAddress(),
            amount3CRVReceived
        );

        // deposit liquidity
        uint256 res = IMetaPool(manager.stableSwapMetaPoolAddress())
            .add_liquidity(
                [0, amount3CRVReceived],
                0,
                manager.bondingContractAddress()
            );
        // update TWAP price
        return res;
    }
}

// File: @uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol



pragma solidity >=0.5.0;

interface IUniswapV2Pair {
    event Approval(address indexed owner, address indexed spender, uint value);
    event Transfer(address indexed from, address indexed to, uint value);

    function name() external pure returns (string memory);
    function symbol() external pure returns (string memory);
    function decimals() external pure returns (uint8);
    function totalSupply() external view returns (uint);
    function balanceOf(address owner) external view returns (uint);
    function allowance(address owner, address spender) external view returns (uint);

    function approve(address spender, uint value) external returns (bool);
    function transfer(address to, uint value) external returns (bool);
    function transferFrom(address from, address to, uint value) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);
    function PERMIT_TYPEHASH() external pure returns (bytes32);
    function nonces(address owner) external view returns (uint);

    function permit(address owner, address spender, uint value, uint deadline, uint8 v, bytes32 r, bytes32 s) external;

    event Mint(address indexed sender, uint amount0, uint amount1);
    event Burn(address indexed sender, uint amount0, uint amount1, address indexed to);
    event Swap(
        address indexed sender,
        uint amount0In,
        uint amount1In,
        uint amount0Out,
        uint amount1Out,
        address indexed to
    );
    event Sync(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint);
    function factory() external view returns (address);
    function token0() external view returns (address);
    function token1() external view returns (address);
    function getReserves() external view returns (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast);
    function price0CumulativeLast() external view returns (uint);
    function price1CumulativeLast() external view returns (uint);
    function kLast() external view returns (uint);

    function mint(address to) external returns (uint liquidity);
    function burn(address to) external returns (uint amount0, uint amount1);
    function swap(uint amount0Out, uint amount1Out, address to, bytes calldata data) external;
    function skim(address to) external;
    function sync() external;

    function initialize(address, address) external;
}

// File: @uniswap/v2-periphery/contracts/interfaces/IUniswapV2Router02.sol



pragma solidity >=0.6.2;

import './IUniswapV2Router01.sol';

interface IUniswapV2Router02 is IUniswapV2Router01 {
    function removeLiquidityETHSupportingFeeOnTransferTokens(
        address token,
        uint liquidity,
        uint amountTokenMin,
        uint amountETHMin,
        address to,
        uint deadline
    ) external returns (uint amountETH);
    function removeLiquidityETHWithPermitSupportingFeeOnTransferTokens(
        address token,
        uint liquidity,
        uint amountTokenMin,
        uint amountETHMin,
        address to,
        uint deadline,
        bool approveMax, uint8 v, bytes32 r, bytes32 s
    ) external returns (uint amountETH);

    function swapExactTokensForTokensSupportingFeeOnTransferTokens(
        uint amountIn,
        uint amountOutMin,
        address[] calldata path,
        address to,
        uint deadline
    ) external;
    function swapExactETHForTokensSupportingFeeOnTransferTokens(
        uint amountOutMin,
        address[] calldata path,
        address to,
        uint deadline
    ) external payable;
    function swapExactTokensForETHSupportingFeeOnTransferTokens(
        uint amountIn,
        uint amountOutMin,
        address[] calldata path,
        address to,
        uint deadline
    ) external;
}

// File: contracts/interfaces/IExcessDollarsDistributor.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol";

/// @title A mechanism for distributing excess dollars to relevant places
interface IExcessDollarsDistributor {
    function distributeDollars() external;
}

// File: contracts/SushiSwapPool.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@uniswap/v2-core/contracts/interfaces/IUniswapV2Factory.sol";
import "@uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol";
import "./UbiquityAlgorithmicDollarManager.sol";

contract SushiSwapPool {
    IUniswapV2Factory public factory =
        IUniswapV2Factory(0xC0AEe478e3658e2610c5F7A4A2E1777cE9e4f2Ac);

    UbiquityAlgorithmicDollarManager public manager;
    IUniswapV2Pair public pair;

    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        require(
            manager.dollarTokenAddress() != address(0),
            "Dollar address not set"
        );
        require(
            manager.governanceTokenAddress() != address(0),
            "uGOV Address not set"
        );
        // check if pair already exist
        address pool = factory.getPair(
            manager.dollarTokenAddress(),
            manager.governanceTokenAddress()
        );
        if (pool == address(0)) {
            pool = factory.createPair(
                manager.dollarTokenAddress(),
                manager.governanceTokenAddress()
            );
        }
        pair = IUniswapV2Pair(pool);
    }
}

// File: @uniswap/v2-periphery/contracts/interfaces/IUniswapV2Router01.sol



pragma solidity >=0.6.2;

interface IUniswapV2Router01 {
    function factory() external pure returns (address);
    function WETH() external pure returns (address);

    function addLiquidity(
        address tokenA,
        address tokenB,
        uint amountADesired,
        uint amountBDesired,
        uint amountAMin,
        uint amountBMin,
        address to,
        uint deadline
    ) external returns (uint amountA, uint amountB, uint liquidity);
    function addLiquidityETH(
        address token,
        uint amountTokenDesired,
        uint amountTokenMin,
        uint amountETHMin,
        address to,
        uint deadline
    ) external payable returns (uint amountToken, uint amountETH, uint liquidity);
    function removeLiquidity(
        address tokenA,
        address tokenB,
        uint liquidity,
        uint amountAMin,
        uint amountBMin,
        address to,
        uint deadline
    ) external returns (uint amountA, uint amountB);
    function removeLiquidityETH(
        address token,
        uint liquidity,
        uint amountTokenMin,
        uint amountETHMin,
        address to,
        uint deadline
    ) external returns (uint amountToken, uint amountETH);
    function removeLiquidityWithPermit(
        address tokenA,
        address tokenB,
        uint liquidity,
        uint amountAMin,
        uint amountBMin,
        address to,
        uint deadline,
        bool approveMax, uint8 v, bytes32 r, bytes32 s
    ) external returns (uint amountA, uint amountB);
    function removeLiquidityETHWithPermit(
        address token,
        uint liquidity,
        uint amountTokenMin,
        uint amountETHMin,
        address to,
        uint deadline,
        bool approveMax, uint8 v, bytes32 r, bytes32 s
    ) external returns (uint amountToken, uint amountETH);
    function swapExactTokensForTokens(
        uint amountIn,
        uint amountOutMin,
        address[] calldata path,
        address to,
        uint deadline
    ) external returns (uint[] memory amounts);
    function swapTokensForExactTokens(
        uint amountOut,
        uint amountInMax,
        address[] calldata path,
        address to,
        uint deadline
    ) external returns (uint[] memory amounts);
    function swapExactETHForTokens(uint amountOutMin, address[] calldata path, address to, uint deadline)
        external
        payable
        returns (uint[] memory amounts);
    function swapTokensForExactETH(uint amountOut, uint amountInMax, address[] calldata path, address to, uint deadline)
        external
        returns (uint[] memory amounts);
    function swapExactTokensForETH(uint amountIn, uint amountOutMin, address[] calldata path, address to, uint deadline)
        external
        returns (uint[] memory amounts);
    function swapETHForExactTokens(uint amountOut, address[] calldata path, address to, uint deadline)
        external
        payable
        returns (uint[] memory amounts);

    function quote(uint amountA, uint reserveA, uint reserveB) external pure returns (uint amountB);
    function getAmountOut(uint amountIn, uint reserveIn, uint reserveOut) external pure returns (uint amountOut);
    function getAmountIn(uint amountOut, uint reserveIn, uint reserveOut) external pure returns (uint amountIn);
    function getAmountsOut(uint amountIn, address[] calldata path) external view returns (uint[] memory amounts);
    function getAmountsIn(uint amountOut, address[] calldata path) external view returns (uint[] memory amounts);
}

// File: @uniswap/v2-core/contracts/interfaces/IUniswapV2Factory.sol



pragma solidity >=0.5.0;

interface IUniswapV2Factory {
    event PairCreated(address indexed token0, address indexed token1, address pair, uint);

    function feeTo() external view returns (address);
    function feeToSetter() external view returns (address);

    function getPair(address tokenA, address tokenB) external view returns (address pair);
    function allPairs(uint) external view returns (address pair);
    function allPairsLength() external view returns (uint);

    function createPair(address tokenA, address tokenB) external returns (address pair);

    function setFeeTo(address) external;
    function setFeeToSetter(address) external;
}

// File: contracts/MasterChefOriginal.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.3;

import "./interfaces/IERC20Ubiquity.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@openzeppelin/contracts/access/Ownable.sol";
import "./UbiquityAlgorithmicDollarManager.sol";

// MasterChef is the master of UBQ. He can make UBQ and he is a fair guy.
//
// Note that it's ownable and the owner wields tremendous power. The ownership
// will be transferred to a governance smart contract once UBQ is sufficiently
// distributed and the community can show to govern itself.
//
// Have fun reading it. Hopefully it's bug-free. God bless.
contract MasterChefOriginal is Ownable {
    using SafeERC20 for IERC20Ubiquity;
    using SafeERC20 for IERC20;
    // Info of each user.
    struct UserInfo {
        uint256 amount; // How many LP tokens the user has provided.
        uint256 rewardDebt; // Reward debt. See explanation below.
        //
        // We do some fancy math here. Basically, any point in time, the amount of UBQs
        // entitled to a user but is pending to be distributed is:
        //
        //   pending reward = (user.amount * pool.accUbqPerShare) - user.rewardDebt
        //
        // Whenever a user deposits or withdraws LP tokens to a pool. Here's what happens:
        //   1. The pool's `accUbqPerShare` (and `lastRewardBlock`) gets updated.
        //   2. User receives the pending reward sent to his/her address.
        //   3. User's `amount` gets updated.
        //   4. User's `rewardDebt` gets updated.
    }
    // Info of each pool.
    struct PoolInfo {
        IERC20 lpToken; // Address of LP token contract.
        // How many allocation points assigned to this pool. UBQ to distribute per block.
        uint256 allocPoint;
        uint256 lastRewardBlock; // Last block number that UBQs distribution occurs.
        uint256 accUbqPerShare; // Accumulated UBQs per share, times 1e12. See below.
    }
    // Ubiquity Manager
    UbiquityAlgorithmicDollarManager public manager;
    // Block number when bonus UBQ period ends.
    uint256 public bonusEndBlock;
    // UBQ tokens created per block.
    uint256 public ubqPerBlock;
    // Bonus muliplier for early ubq makers.
    uint256 public constant BONUS_MULTIPLIER = 10;
    uint256 public uGOVDivider;
    // Info of each pool.
    PoolInfo[] public poolInfo;
    // Info of each user that stakes LP tokens.
    mapping(uint256 => mapping(address => UserInfo)) public userInfo;
    // Total allocation poitns. Must be the sum of all allocation points in all pools.
    uint256 public totalAllocPoint = 0;
    // The block number when UBQ mining starts.
    uint256 public startBlock;
    event Deposit(address indexed user, uint256 indexed pid, uint256 amount);
    event Withdraw(address indexed user, uint256 indexed pid, uint256 amount);
    event EmergencyWithdraw(
        address indexed user,
        uint256 indexed pid,
        uint256 amount
    );

    // ----------- Modifiers -----------
    modifier onlyTokenManager() {
        require(
            manager.hasRole(manager.UBQ_TOKEN_MANAGER_ROLE(), msg.sender),
            "MasterChef: not UBQ manager"
        );
        _;
    }

    constructor(
        UbiquityAlgorithmicDollarManager _manager,
        uint256 _ubqPerBlock,
        uint256 _startBlock,
        uint256 _bonusEndBlock
    ) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        ubqPerBlock = _ubqPerBlock;
        bonusEndBlock = _bonusEndBlock;
        startBlock = _startBlock;
        uGOVDivider = 5; // 100 / 5 = 20% extra minted ugov for treasury
    }

    function setUBQPerBlock(uint256 _ubqPerBlock) external onlyTokenManager {
        ubqPerBlock = _ubqPerBlock;
    }

    // the bigger uGOVDivider is the less extra Ugov will be minted for the treasury
    function setUGOVShareForTreasury(uint256 _uGOVDivider)
        external
        onlyTokenManager
    {
        uGOVDivider = _uGOVDivider;
    }

    function poolLength() external view returns (uint256) {
        return poolInfo.length;
    }

    // View function to see pending UBQs on frontend.
    function pendingUBQ(uint256 _pid, address _user)
        external
        view
        returns (uint256)
    {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][_user];
        uint256 accUbqPerShare = pool.accUbqPerShare;
        uint256 lpSupply = pool.lpToken.balanceOf(address(this));
        if (block.number > pool.lastRewardBlock && lpSupply != 0) {
            uint256 multiplier = getMultiplier(
                pool.lastRewardBlock,
                block.number
            );

            uint256 ubqReward = (multiplier *
                (ubqPerBlock) *
                (pool.allocPoint)) / (totalAllocPoint);
            accUbqPerShare =
                accUbqPerShare +
                ((ubqReward * (1e12)) / (lpSupply));
        }
        return ((user.amount * accUbqPerShare) / 1e12) - user.rewardDebt;
    }

    // Add a new lp to the pool. Can only be called by the owner.
    // XXX DO NOT add the same LP token more than once. Rewards will be messed up if you do.
    function add(
        uint256 _allocPoint,
        IERC20 _lpToken,
        bool _withUpdate
    ) public onlyOwner {
        if (_withUpdate) {
            massUpdatePools();
        }
        uint256 lastRewardBlock = block.number > startBlock
            ? block.number
            : startBlock;
        totalAllocPoint = totalAllocPoint + _allocPoint;
        poolInfo.push(
            PoolInfo({
                lpToken: _lpToken,
                allocPoint: _allocPoint,
                lastRewardBlock: lastRewardBlock,
                accUbqPerShare: 0
            })
        );
    }

    // Update the given pool's UBQ allocation point. Can only be called by the owner.
    function set(
        uint256 _pid,
        uint256 _allocPoint,
        bool _withUpdate
    ) public onlyOwner {
        if (_withUpdate) {
            massUpdatePools();
        }
        totalAllocPoint =
            totalAllocPoint -
            poolInfo[_pid].allocPoint +
            _allocPoint;
        poolInfo[_pid].allocPoint = _allocPoint;
    }

    // Update reward vairables for all pools. Be careful of gas spending!
    function massUpdatePools() public {
        uint256 length = poolInfo.length;
        for (uint256 pid = 0; pid < length; ++pid) {
            updatePool(pid);
        }
    }

    // Update reward variables of the given pool to be up-to-date.
    function updatePool(uint256 _pid) public {
        PoolInfo storage pool = poolInfo[_pid];
        if (block.number <= pool.lastRewardBlock) {
            return;
        }
        uint256 lpSupply = pool.lpToken.balanceOf(address(this));
        if (lpSupply == 0) {
            pool.lastRewardBlock = block.number;
            return;
        }
        uint256 multiplier = getMultiplier(pool.lastRewardBlock, block.number);
        uint256 ubqReward = (multiplier * ubqPerBlock * pool.allocPoint) /
            totalAllocPoint;

        // mint another x% for the treasury
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            manager.treasuryAddress(),
            ubqReward / uGOVDivider
        );
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            address(this),
            ubqReward
        );

        pool.accUbqPerShare =
            pool.accUbqPerShare +
            ((ubqReward * 1e12) / lpSupply);
        pool.lastRewardBlock = block.number;
    }

    // Deposit LP tokens to MasterChef for UBQ allocation.
    function deposit(uint256 _pid, uint256 _amount) public {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        updatePool(_pid);
        if (user.amount > 0) {
            uint256 pending = ((user.amount * pool.accUbqPerShare) / 1e12) -
                user.rewardDebt;
            _safeUGOVTransfer(msg.sender, pending);
        }
        pool.lpToken.safeTransferFrom(
            address(msg.sender),
            address(this),
            _amount
        );
        user.amount = user.amount + _amount;
        user.rewardDebt = (user.amount * pool.accUbqPerShare) / 1e12;
        emit Deposit(msg.sender, _pid, _amount);
    }

    // Withdraw LP tokens from MasterChef.
    function withdraw(uint256 _pid, uint256 _amount) public {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        require(user.amount >= _amount, "withdraw: not good");
        updatePool(_pid);
        uint256 pending = ((user.amount * pool.accUbqPerShare) / 1e12) -
            user.rewardDebt;
        _safeUGOVTransfer(msg.sender, pending);
        user.amount = user.amount - _amount;
        user.rewardDebt = (user.amount * pool.accUbqPerShare) / 1e12;
        pool.lpToken.safeTransfer(address(msg.sender), _amount);
        emit Withdraw(msg.sender, _pid, _amount);
    }

    // Withdraw without caring about rewards. EMERGENCY ONLY.
    function emergencyWithdraw(uint256 _pid) public {
        PoolInfo storage pool = poolInfo[_pid];
        UserInfo storage user = userInfo[_pid][msg.sender];
        pool.lpToken.safeTransfer(address(msg.sender), user.amount);
        emit EmergencyWithdraw(msg.sender, _pid, user.amount);
        user.amount = 0;
        user.rewardDebt = 0;
    }

    // Return reward multiplier over the given _from to _to block.
    function getMultiplier(uint256 _from, uint256 _to)
        public
        view
        returns (uint256)
    {
        if (_to <= bonusEndBlock) {
            return (_to - _from) * BONUS_MULTIPLIER;
        } else if (_from >= bonusEndBlock) {
            return _to - _from;
        } else {
            return
                ((bonusEndBlock - _from) * BONUS_MULTIPLIER) +
                (_to - bonusEndBlock);
        }
    }

    // Safe uGOV transfer function, just in case if rounding
    // error causes pool to not have enough uGOVs.
    function _safeUGOVTransfer(address _to, uint256 _amount) internal {
        IERC20Ubiquity uGOV = IERC20Ubiquity(manager.governanceTokenAddress());
        uint256 uGOVBal = uGOV.balanceOf(address(this));
        if (_amount > uGOVBal) {
            uGOV.safeTransfer(_to, uGOVBal);
        } else {
            uGOV.safeTransfer(_to, _amount);
        }
    }
}

// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../utils/Context.sol";

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

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

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

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

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _setOwner(newOwner);
    }

    function _setOwner(address newOwner) private {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/ERC20Burnable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../../../utils/Context.sol";

/**
 * @dev Extension of {ERC20} that allows token holders to destroy both their own
 * tokens and those that they have an allowance for, in a way that can be
 * recognized off-chain (via event analysis).
 */
abstract contract ERC20Burnable is Context, ERC20 {
    /**
     * @dev Destroys `amount` tokens from the caller.
     *
     * See {ERC20-_burn}.
     */
    function burn(uint256 amount) public virtual {
        _burn(_msgSender(), amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, deducting from the caller's
     * allowance.
     *
     * See {ERC20-_burn} and {ERC20-allowance}.
     *
     * Requirements:
     *
     * - the caller must have allowance for ``accounts``'s tokens of at least
     * `amount`.
     */
    function burnFrom(address account, uint256 amount) public virtual {
        uint256 currentAllowance = allowance(account, _msgSender());
        require(currentAllowance >= amount, "ERC20: burn amount exceeds allowance");
        unchecked {
            _approve(account, _msgSender(), currentAllowance - amount);
        }
        _burn(account, amount);
    }
}

// File: contracts/mocks/MockuADToken.sol



// contracts/GLDToken.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/ERC20.sol";

contract MockuADToken is ERC20 {
    constructor(uint256 initialSupply) ERC20("ubiquityDollar", "uAD") {
        _mint(msg.sender, initialSupply);
    }

    function burn(address account, uint256 amount) public {
        _burn(account, amount);
    }

    function mint(address account, uint256 amount) public {
        _mint(account, amount);
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/ERC20Pausable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../../../security/Pausable.sol";

/**
 * @dev ERC20 token with pausable token transfers, minting and burning.
 *
 * Useful for scenarios such as preventing trades until the end of an evaluation
 * period, or having an emergency switch for freezing all token transfers in the
 * event of a large bug.
 */
abstract contract ERC20Pausable is ERC20, Pausable {
    /**
     * @dev See {ERC20-_beforeTokenTransfer}.
     *
     * Requirements:
     *
     * - the contract must not be paused.
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual override {
        super._beforeTokenTransfer(from, to, amount);

        require(!paused(), "ERC20Pausable: token transfer while paused");
    }
}

// File: contracts/BondingV2.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "@openzeppelin/contracts/security/Pausable.sol";
import "./interfaces/IERC1155Ubiquity.sol";
import "./interfaces/IMetaPool.sol";
import "./interfaces/IUbiquityFormulas.sol";
import "./UbiquityAlgorithmicDollar.sol";
import "./BondingFormulas.sol";
import "./BondingShareV2.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/ISablier.sol";
import "./interfaces/IMasterChefV2.sol";
import "./interfaces/ITWAPOracle.sol";
import "./interfaces/IERC1155Ubiquity.sol";
import "./utils/CollectableDust.sol";

contract BondingV2 is CollectableDust, Pausable {
    using SafeERC20 for IERC20;

    bytes public data = "";
    UbiquityAlgorithmicDollarManager public manager;
    uint256 public constant ONE = uint256(1 ether); // 3Crv has 18 decimals
    uint256 public bondingDiscountMultiplier = uint256(1000000 gwei); // 0.001
    uint256 public blockCountInAWeek = 45361;
    uint256 public accLpRewardPerShare = 0;

    uint256 public lpRewards;
    uint256 public totalLpToMigrate;
    address public bondingFormulasAddress;

    address public migrator; // temporary address to handle migration
    address[] private _toMigrateOriginals;
    uint256[] private _toMigrateLpBalances;
    uint256[] private _toMigrateWeeks;

    // toMigrateId[address] > 0 when address is to migrate, or 0 in all other cases
    mapping(address => uint256) public toMigrateId;
    bool public migrating = false;

    event PriceReset(
        address _tokenWithdrawn,
        uint256 _amountWithdrawn,
        uint256 _amountTransfered
    );

    event Deposit(
        address indexed _user,
        uint256 indexed _id,
        uint256 _lpAmount,
        uint256 _bondingShareAmount,
        uint256 _weeks,
        uint256 _endBlock
    );
    event RemoveLiquidityFromBond(
        address indexed _user,
        uint256 indexed _id,
        uint256 _lpAmount,
        uint256 _lpAmountTransferred,
        uint256 _lprewards,
        uint256 _bondingShareAmount
    );

    event AddLiquidityFromBond(
        address indexed _user,
        uint256 indexed _id,
        uint256 _lpAmount,
        uint256 _bondingShareAmount
    );

    event BondingDiscountMultiplierUpdated(uint256 _bondingDiscountMultiplier);
    event BlockCountInAWeekUpdated(uint256 _blockCountInAWeek);

    event Migrated(
        address indexed _user,
        uint256 indexed _id,
        uint256 _lpsAmount,
        uint256 _sharesAmount,
        uint256 _weeks
    );

    modifier onlyBondingManager() {
        require(
            manager.hasRole(manager.BONDING_MANAGER_ROLE(), msg.sender),
            "not manager"
        );
        _;
    }

    modifier onlyPauser() {
        require(
            manager.hasRole(manager.PAUSER_ROLE(), msg.sender),
            "not pauser"
        );
        _;
    }

    modifier onlyMigrator() {
        require(msg.sender == migrator, "not migrator");
        _;
    }

    modifier whenMigrating() {
        require(migrating, "not in migration");
        _;
    }

    constructor(
        address _manager,
        address _bondingFormulasAddress,
        address[] memory _originals,
        uint256[] memory _lpBalances,
        uint256[] memory _weeks
    ) CollectableDust() Pausable() {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        bondingFormulasAddress = _bondingFormulasAddress;
        migrator = msg.sender;

        uint256 lgt = _originals.length;
        require(lgt > 0, "address array empty");
        require(lgt == _lpBalances.length, "balances array not same length");
        require(lgt == _weeks.length, "weeks array not same length");

        _toMigrateOriginals = _originals;
        _toMigrateLpBalances = _lpBalances;
        _toMigrateWeeks = _weeks;
        for (uint256 i = 0; i < lgt; ++i) {
            toMigrateId[_originals[i]] = i + 1;
            totalLpToMigrate += _lpBalances[i];
        }
    }

    // solhint-disable-next-line no-empty-blocks
    receive() external payable {}

    /// @dev addUserToMigrate add a user to migrate from V1.
    ///      IMPORTANT execute that function BEFORE sending the corresponding LP token
    ///      otherwise they will have extra LP rewards
    /// @param _original address of v1 user
    /// @param _lpBalance LP Balance of v1 user
    /// @param _weeks weeks lockup of v1 user
    /// @notice user will then be able to migrate.
    function addUserToMigrate(
        address _original,
        uint256 _lpBalance,
        uint256 _weeks
    ) external onlyMigrator {
        _toMigrateOriginals.push(_original);
        _toMigrateLpBalances.push(_lpBalance);
        totalLpToMigrate += _lpBalance;
        _toMigrateWeeks.push(_weeks);
        toMigrateId[_original] = _toMigrateOriginals.length;
    }

    function setMigrator(address _migrator) external onlyMigrator {
        migrator = _migrator;
    }

    function setMigrating(bool _migrating) external onlyMigrator {
        migrating = _migrating;
    }

    /// @dev uADPriceReset remove uAD unilateraly from the curve LP share sitting inside
    ///      the bonding contract and send the uAD received to the treasury.
    ///      This will have the immediate effect of pushing the uAD price HIGHER
    /// @param amount of LP token to be removed for uAD
    /// @notice it will remove one coin only from the curve LP share sitting in the bonding contract
    function uADPriceReset(uint256 amount) external onlyBondingManager {
        IMetaPool metaPool = IMetaPool(manager.stableSwapMetaPoolAddress());
        // remove one coin
        uint256 coinWithdrawn = metaPool.remove_liquidity_one_coin(
            amount,
            0,
            0
        );
        ITWAPOracle(manager.twapOracleAddress()).update();
        uint256 toTransfer = IERC20(manager.dollarTokenAddress()).balanceOf(
            address(this)
        );
        IERC20(manager.dollarTokenAddress()).transfer(
            manager.treasuryAddress(),
            toTransfer
        );
        emit PriceReset(
            manager.dollarTokenAddress(),
            coinWithdrawn,
            toTransfer
        );
    }

    /// @dev crvPriceReset remove 3CRV unilateraly from the curve LP share sitting inside
    ///      the bonding contract and send the 3CRV received to the treasury
    ///      This will have the immediate effect of pushing the uAD price LOWER
    /// @param amount of LP token to be removed for 3CRV tokens
    /// @notice it will remove one coin only from the curve LP share sitting in the bonding contract
    function crvPriceReset(uint256 amount) external onlyBondingManager {
        IMetaPool metaPool = IMetaPool(manager.stableSwapMetaPoolAddress());
        // remove one coin
        uint256 coinWithdrawn = metaPool.remove_liquidity_one_coin(
            amount,
            1,
            0
        );
        // update twap
        ITWAPOracle(manager.twapOracleAddress()).update();
        uint256 toTransfer = IERC20(manager.curve3PoolTokenAddress()).balanceOf(
            address(this)
        );
        IERC20(manager.curve3PoolTokenAddress()).transfer(
            manager.treasuryAddress(),
            toTransfer
        );
        emit PriceReset(
            manager.curve3PoolTokenAddress(),
            coinWithdrawn,
            toTransfer
        );
    }

    function setBondingFormulasAddress(address _bondingFormulasAddress)
        external
        onlyBondingManager
    {
        bondingFormulasAddress = _bondingFormulasAddress;
    }

    /// Collectable Dust
    function addProtocolToken(address _token)
        external
        override
        onlyBondingManager
    {
        _addProtocolToken(_token);
    }

    function removeProtocolToken(address _token)
        external
        override
        onlyBondingManager
    {
        _removeProtocolToken(_token);
    }

    function sendDust(
        address _to,
        address _token,
        uint256 _amount
    ) external override onlyBondingManager {
        _sendDust(_to, _token, _amount);
    }

    function setBondingDiscountMultiplier(uint256 _bondingDiscountMultiplier)
        external
        onlyBondingManager
    {
        bondingDiscountMultiplier = _bondingDiscountMultiplier;
        emit BondingDiscountMultiplierUpdated(_bondingDiscountMultiplier);
    }

    function setBlockCountInAWeek(uint256 _blockCountInAWeek)
        external
        onlyBondingManager
    {
        blockCountInAWeek = _blockCountInAWeek;
        emit BlockCountInAWeekUpdated(_blockCountInAWeek);
    }

    /// @dev deposit uAD-3CRV LP tokens for a duration to receive bonding shares
    /// @param _lpsAmount of LP token to send
    /// @param _weeks during lp token will be held
    /// @notice weeks act as a multiplier for the amount of bonding shares to be received
    function deposit(uint256 _lpsAmount, uint256 _weeks)
        external
        whenNotPaused
        returns (uint256 _id)
    {
        require(
            1 <= _weeks && _weeks <= 208,
            "Bonding: duration must be between 1 and 208 weeks"
        );
        ITWAPOracle(manager.twapOracleAddress()).update();

        // update the accumulated lp rewards per shares
        _updateLpPerShare();
        // transfer lp token to the bonding contract
        IERC20(manager.stableSwapMetaPoolAddress()).safeTransferFrom(
            msg.sender,
            address(this),
            _lpsAmount
        );

        // calculate the amount of share based on the amount of lp deposited and the duration
        uint256 _sharesAmount = IUbiquityFormulas(manager.formulasAddress())
            .durationMultiply(_lpsAmount, _weeks, bondingDiscountMultiplier);
        // calculate end locking period block number
        uint256 _endBlock = block.number + _weeks * blockCountInAWeek;
        _id = _mint(msg.sender, _lpsAmount, _sharesAmount, _endBlock);

        // set masterchef for uGOV rewards
        IMasterChefV2(manager.masterChefAddress()).deposit(
            msg.sender,
            _sharesAmount,
            _id
        );

        emit Deposit(
            msg.sender,
            _id,
            _lpsAmount,
            _sharesAmount,
            _weeks,
            _endBlock
        );
    }

    /// @dev Add an amount of uAD-3CRV LP tokens
    /// @param _amount of LP token to deposit
    /// @param _id bonding shares id
    /// @param _weeks during lp token will be held
    /// @notice bonding shares are ERC1155 (aka NFT) because they have an expiration date
    function addLiquidity(
        uint256 _amount,
        uint256 _id,
        uint256 _weeks
    ) external whenNotPaused {
        (
            uint256[2] memory bs,
            BondingShareV2.Bond memory bond
        ) = _checkForLiquidity(_id);

        // calculate pending LP rewards
        uint256 sharesToRemove = bs[0];
        _updateLpPerShare();
        uint256 pendingLpReward = lpRewardForShares(
            sharesToRemove,
            bond.lpRewardDebt
        );

        // add an extra step to be able to decrease rewards if locking end is near
        pendingLpReward = BondingFormulas(this.bondingFormulasAddress())
            .lpRewardsAddLiquidityNormalization(bond, bs, pendingLpReward);
        // add these LP Rewards to the deposited amount of LP token
        bond.lpAmount += pendingLpReward;
        lpRewards -= pendingLpReward;
        IERC20(manager.stableSwapMetaPoolAddress()).safeTransferFrom(
            msg.sender,
            address(this),
            _amount
        );
        bond.lpAmount += _amount;

        // redeem all shares
        IMasterChefV2(manager.masterChefAddress()).withdraw(
            msg.sender,
            sharesToRemove,
            _id
        );

        // calculate the amount of share based on the new amount of lp deposited and the duration
        uint256 _sharesAmount = IUbiquityFormulas(manager.formulasAddress())
            .durationMultiply(bond.lpAmount, _weeks, bondingDiscountMultiplier);

        // deposit new shares
        IMasterChefV2(manager.masterChefAddress()).deposit(
            msg.sender,
            _sharesAmount,
            _id
        );
        // calculate end locking period block number
        // 1 week = 45361 blocks = 2371753*7/366
        // n = (block + duration * 45361)
        bond.endBlock = block.number + _weeks * blockCountInAWeek;

        // should be done after masterchef withdraw
        _updateLpPerShare();
        bond.lpRewardDebt =
            (IMasterChefV2(manager.masterChefAddress()).getBondingShareInfo(
                _id
            )[0] * accLpRewardPerShare) /
            1e12;

        BondingShareV2(manager.bondingShareAddress()).updateBond(
            _id,
            bond.lpAmount,
            bond.lpRewardDebt,
            bond.endBlock
        );
        emit AddLiquidityFromBond(
            msg.sender,
            _id,
            bond.lpAmount,
            _sharesAmount
        );
    }

    /// @dev Remove an amount of uAD-3CRV LP tokens
    /// @param _amount of LP token deposited when _id was created to be withdrawn
    /// @param _id bonding shares id
    /// @notice bonding shares are ERC1155 (aka NFT) because they have an expiration date
    function removeLiquidity(uint256 _amount, uint256 _id)
        external
        whenNotPaused
    {
        (
            uint256[2] memory bs,
            BondingShareV2.Bond memory bond
        ) = _checkForLiquidity(_id);
        require(bond.lpAmount >= _amount, "Bonding: amount too big");
        // we should decrease the UBQ rewards proportionally to the LP removed
        // sharesToRemove = (bonding shares * _amount )  / bond.lpAmount ;
        uint256 sharesToRemove = BondingFormulas(this.bondingFormulasAddress())
            .sharesForLP(bond, bs, _amount);

        //get all its pending LP Rewards
        _updateLpPerShare();
        uint256 pendingLpReward = lpRewardForShares(bs[0], bond.lpRewardDebt);
        // update bonding shares
        // bond.shares = bond.shares - sharesToRemove;
        // get masterchef for uGOV rewards To ensure correct computation
        // it needs to be done BEFORE updating the bonding share
        IMasterChefV2(manager.masterChefAddress()).withdraw(
            msg.sender,
            sharesToRemove,
            _id
        );

        // redeem of the extra LP
        // bonding lp balance - BondingShareV2.totalLP
        IERC20 metapool = IERC20(manager.stableSwapMetaPoolAddress());

        // add an extra step to be able to decrease rewards if locking end is near
        pendingLpReward = BondingFormulas(this.bondingFormulasAddress())
            .lpRewardsRemoveLiquidityNormalization(bond, bs, pendingLpReward);

        uint256 correctedAmount = BondingFormulas(this.bondingFormulasAddress())
            .correctedAmountToWithdraw(
                BondingShareV2(manager.bondingShareAddress()).totalLP(),
                metapool.balanceOf(address(this)) - lpRewards,
                _amount
            );

        lpRewards -= pendingLpReward;
        bond.lpAmount -= _amount;

        // bond.lpRewardDebt = (bonding shares * accLpRewardPerShare) /  1e18;
        // user.amount.mul(pool.accSushiPerShare).div(1e12);
        // should be done after masterchef withdraw
        bond.lpRewardDebt =
            (IMasterChefV2(manager.masterChefAddress()).getBondingShareInfo(
                _id
            )[0] * accLpRewardPerShare) /
            1e12;

        BondingShareV2(manager.bondingShareAddress()).updateBond(
            _id,
            bond.lpAmount,
            bond.lpRewardDebt,
            bond.endBlock
        );

        // lastly redeem lp tokens
        metapool.safeTransfer(msg.sender, correctedAmount + pendingLpReward);
        emit RemoveLiquidityFromBond(
            msg.sender,
            _id,
            _amount,
            correctedAmount,
            pendingLpReward,
            sharesToRemove
        );
    }

    // View function to see pending lpRewards on frontend.
    function pendingLpRewards(uint256 _id) external view returns (uint256) {
        BondingShareV2 bonding = BondingShareV2(manager.bondingShareAddress());
        BondingShareV2.Bond memory bond = bonding.getBond(_id);
        uint256[2] memory bs = IMasterChefV2(manager.masterChefAddress())
            .getBondingShareInfo(_id);

        uint256 lpBalance = IERC20(manager.stableSwapMetaPoolAddress())
            .balanceOf(address(this));
        // the excess LP is the current balance minus the total deposited LP
        if (lpBalance >= (bonding.totalLP() + totalLpToMigrate)) {
            uint256 currentLpRewards = lpBalance -
                (bonding.totalLP() + totalLpToMigrate);
            uint256 curAccLpRewardPerShare = accLpRewardPerShare;
            // if new rewards we should calculate the new curAccLpRewardPerShare
            if (currentLpRewards > lpRewards) {
                uint256 newLpRewards = currentLpRewards - lpRewards;
                curAccLpRewardPerShare =
                    accLpRewardPerShare +
                    ((newLpRewards * 1e12) /
                        IMasterChefV2(manager.masterChefAddress())
                            .totalShares());
            }
            // we multiply the shares amount by the accumulated lpRewards per share
            // and remove the lp Reward Debt
            return
                (bs[0] * (curAccLpRewardPerShare)) /
                (1e12) -
                (bond.lpRewardDebt);
        }
        return 0;
    }

    function pause() public virtual onlyPauser {
        _pause();
    }

    function unpause() public virtual onlyPauser {
        _unpause();
    }

    /// @dev migrate let a user migrate from V1
    /// @notice user will then be able to migrate
    function migrate() public whenMigrating returns (uint256 _id) {
        _id = toMigrateId[msg.sender];
        require(_id > 0, "not v1 address");

        _migrate(
            _toMigrateOriginals[_id - 1],
            _toMigrateLpBalances[_id - 1],
            _toMigrateWeeks[_id - 1]
        );
    }

    /// @dev return the amount of Lp token rewards an amount of shares entitled
    /// @param amount of bonding shares
    /// @param lpRewardDebt lp rewards that has already been distributed
    function lpRewardForShares(uint256 amount, uint256 lpRewardDebt)
        public
        view
        returns (uint256 pendingLpReward)
    {
        if (accLpRewardPerShare > 0) {
            pendingLpReward =
                (amount * accLpRewardPerShare) /
                1e12 -
                (lpRewardDebt);
        }
    }

    function currentShareValue() public view returns (uint256 priceShare) {
        uint256 totalShares = IMasterChefV2(manager.masterChefAddress())
            .totalShares();
        // priceShare = totalLP / totalShares
        priceShare = IUbiquityFormulas(manager.formulasAddress()).bondPrice(
            BondingShareV2(manager.bondingShareAddress()).totalLP(),
            totalShares,
            ONE
        );
    }

    /// @dev migrate let a user migrate from V1
    /// @notice user will then be able to migrate
    function _migrate(
        address user,
        uint256 _lpsAmount,
        uint256 _weeks
    ) internal returns (uint256 _id) {
        require(toMigrateId[user] > 0, "not v1 address");
        require(_lpsAmount > 0, "LP amount is zero");
        require(
            1 <= _weeks && _weeks <= 208,
            "Duration must be between 1 and 208 weeks"
        );

        // unregister address
        toMigrateId[user] = 0;

        // calculate the amount of share based on the amount of lp deposited and the duration
        uint256 _sharesAmount = IUbiquityFormulas(manager.formulasAddress())
            .durationMultiply(_lpsAmount, _weeks, bondingDiscountMultiplier);

        // update the accumulated lp rewards per shares
        _updateLpPerShare();
        // calculate end locking period block number
        uint256 endBlock = block.number + _weeks * blockCountInAWeek;
        _id = _mint(user, _lpsAmount, _sharesAmount, endBlock);
        // reduce the total LP to migrate after the minting
        // to keep the _updateLpPerShare calculation consistent
        totalLpToMigrate -= _lpsAmount;
        // set masterchef for uGOV rewards
        IMasterChefV2(manager.masterChefAddress()).deposit(
            user,
            _sharesAmount,
            _id
        );

        emit Migrated(user, _id, _lpsAmount, _sharesAmount, _weeks);
    }

    /// @dev update the accumulated excess LP per share
    function _updateLpPerShare() internal {
        BondingShareV2 bond = BondingShareV2(manager.bondingShareAddress());
        uint256 lpBalance = IERC20(manager.stableSwapMetaPoolAddress())
            .balanceOf(address(this));
        // the excess LP is the current balance
        // minus the total deposited LP + LP that needs to be migrated
        uint256 totalShares = IMasterChefV2(manager.masterChefAddress())
            .totalShares();
        if (
            lpBalance >= (bond.totalLP() + totalLpToMigrate) && totalShares > 0
        ) {
            uint256 currentLpRewards = lpBalance -
                (bond.totalLP() + totalLpToMigrate);

            // is there new LP rewards to be distributed ?
            if (currentLpRewards > lpRewards) {
                // we calculate the new accumulated LP rewards per share
                accLpRewardPerShare =
                    accLpRewardPerShare +
                    (((currentLpRewards - lpRewards) * 1e12) / totalShares);

                // update the bonding contract lpRewards
                lpRewards = currentLpRewards;
            }
        }
    }

    function _mint(
        address to,
        uint256 lpAmount,
        uint256 shares,
        uint256 endBlock
    ) internal returns (uint256) {
        uint256 _currentShareValue = currentShareValue();
        require(
            _currentShareValue != 0,
            "Bonding: share value should not be null"
        );
        // set the lp rewards debts so that this bonding share only get lp rewards from this day
        uint256 lpRewardDebt = (shares * accLpRewardPerShare) / 1e12;
        return
            BondingShareV2(manager.bondingShareAddress()).mint(
                to,
                lpAmount,
                lpRewardDebt,
                endBlock
            );
    }

    function _checkForLiquidity(uint256 _id)
        internal
        returns (uint256[2] memory bs, BondingShareV2.Bond memory bond)
    {
        require(
            IERC1155Ubiquity(manager.bondingShareAddress()).balanceOf(
                msg.sender,
                _id
            ) == 1,
            "Bonding: caller is not owner"
        );
        BondingShareV2 bonding = BondingShareV2(manager.bondingShareAddress());
        bond = bonding.getBond(_id);
        require(
            block.number > bond.endBlock,
            "Bonding: Redeem not allowed before bonding time"
        );

        ITWAPOracle(manager.twapOracleAddress()).update();
        bs = IMasterChefV2(manager.masterChefAddress()).getBondingShareInfo(
            _id
        );
    }
}

// File: contracts/interfaces/IERC1155Ubiquity.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155.sol";

/// @title ERC1155 Ubiquiti preset interface
/// @author Ubiquity Algorithmic Dollar
interface IERC1155Ubiquity is IERC1155 {
    function mint(
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) external;

    function mintBatch(
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) external;

    function burn(
        address account,
        uint256 id,
        uint256 value
    ) external;

    function burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory values
    ) external;

    function pause() external;

    function unpause() external;

    function totalSupply() external view returns (uint256);

    function exists(uint256 id) external view returns (bool);

    function holderTokens() external view returns (uint256[] memory);
}

// File: contracts/interfaces/IUbiquityFormulas.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

interface IUbiquityFormulas {
    function durationMultiply(
        uint256 _uLP,
        uint256 _weeks,
        uint256 _multiplier
    ) external pure returns (uint256 _shares);

    function bonding(
        uint256 _shares,
        uint256 _currentShareValue,
        uint256 _targetPrice
    ) external pure returns (uint256 _uBOND);

    function redeemBonds(
        uint256 _uBOND,
        uint256 _currentShareValue,
        uint256 _targetPrice
    ) external pure returns (uint256 _uLP);

    function bondPrice(
        uint256 _totalULP,
        uint256 _totalUBOND,
        uint256 _targetPrice
    ) external pure returns (uint256 _priceUBOND);

    function ugovMultiply(uint256 _multiplier, uint256 _price)
        external
        pure
        returns (uint256 _newMultiplier);
}

// File: contracts/UbiquityAlgorithmicDollar.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./interfaces/IIncentive.sol";
import "./ERC20Ubiquity.sol";

contract UbiquityAlgorithmicDollar is ERC20Ubiquity {
    /// @notice get associated incentive contract, 0 address if N/A
    mapping(address => address) public incentiveContract;

    event IncentiveContractUpdate(
        address indexed _incentivized,
        address indexed _incentiveContract
    );

    constructor(address _manager)
        ERC20Ubiquity(_manager, "Ubiquity Algorithmic Dollar", "uAD")
    {} // solhint-disable-line no-empty-blocks

    /// @param account the account to incentivize
    /// @param incentive the associated incentive contract
    /// @notice only UAD manager can set Incentive contract
    function setIncentiveContract(address account, address incentive) external {
        require(
            ERC20Ubiquity.manager.hasRole(
                ERC20Ubiquity.manager.UBQ_TOKEN_MANAGER_ROLE(),
                msg.sender
            ),
            "Dollar: must have admin role"
        );

        incentiveContract[account] = incentive;
        emit IncentiveContractUpdate(account, incentive);
    }

    function _checkAndApplyIncentives(
        address sender,
        address recipient,
        uint256 amount
    ) internal {
        // incentive on sender
        address senderIncentive = incentiveContract[sender];
        if (senderIncentive != address(0)) {
            IIncentive(senderIncentive).incentivize(
                sender,
                recipient,
                msg.sender,
                amount
            );
        }

        // incentive on recipient
        address recipientIncentive = incentiveContract[recipient];
        if (recipientIncentive != address(0)) {
            IIncentive(recipientIncentive).incentivize(
                sender,
                recipient,
                msg.sender,
                amount
            );
        }

        // incentive on operator
        address operatorIncentive = incentiveContract[msg.sender];
        if (
            msg.sender != sender &&
            msg.sender != recipient &&
            operatorIncentive != address(0)
        ) {
            IIncentive(operatorIncentive).incentivize(
                sender,
                recipient,
                msg.sender,
                amount
            );
        }

        // all incentive, if active applies to every transfer
        address allIncentive = incentiveContract[address(0)];
        if (allIncentive != address(0)) {
            IIncentive(allIncentive).incentivize(
                sender,
                recipient,
                msg.sender,
                amount
            );
        }
    }

    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal override {
        super._transfer(sender, recipient, amount);
        _checkAndApplyIncentives(sender, recipient, amount);
    }
}

// File: contracts/BondingFormulas.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./BondingShareV2.sol";
import "./libs/ABDKMathQuad.sol";

import "./interfaces/IMasterChefV2.sol";

contract BondingFormulas {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;

    uint256 public constant ONE = uint256(1 ether); //   18 decimals

    /// @dev formula UBQ Rights corresponding to a bonding shares LP amount
    /// @param _bond , bonding share
    /// @param _amount , amount of LP tokens
    /// @notice shares = (bond.shares * _amount )  / bond.lpAmount ;
    function sharesForLP(
        BondingShareV2.Bond memory _bond,
        uint256[2] memory _shareInfo,
        uint256 _amount
    ) public pure returns (uint256 _uLP) {
        bytes16 a = _shareInfo[0].fromUInt(); // shares amount
        bytes16 v = _amount.fromUInt();
        bytes16 t = _bond.lpAmount.fromUInt();

        _uLP = a.mul(v).div(t).toUInt();
    }

    /// @dev formula may add a decreasing rewards if locking end is near when removing liquidity
    /// @param _bond , bonding share
    /// @param _amount , amount of LP tokens
    /// @notice rewards = _amount;
    // solhint-disable-block  no-unused-vars
    /* solhint-disable no-unused-vars */
    function lpRewardsRemoveLiquidityNormalization(
        BondingShareV2.Bond memory _bond,
        uint256[2] memory _shareInfo,
        uint256 _amount
    ) public pure returns (uint256) {
        return _amount;
    }

    /* solhint-enable no-unused-vars */
    /// @dev formula may add a decreasing rewards if locking end is near when adding liquidity
    /// @param _bond , bonding share
    /// @param _amount , amount of LP tokens
    /// @notice rewards = _amount;
    // solhint-disable-block  no-unused-vars
    /* solhint-disable no-unused-vars */
    function lpRewardsAddLiquidityNormalization(
        BondingShareV2.Bond memory _bond,
        uint256[2] memory _shareInfo,
        uint256 _amount
    ) public pure returns (uint256) {
        return _amount;
    }

    /* solhint-enable no-unused-vars */

    /// @dev formula to calculate the corrected amount to withdraw based on the proportion of
    ///      lp deposited against actual LP token on thge bonding contract
    /// @param _totalLpDeposited , Total amount of LP deposited by users
    /// @param _bondingLpBalance , actual bonding contract LP tokens balance minus lp rewards
    /// @param _amount , amount of LP tokens
    /// @notice corrected_amount = amount * ( bondingLpBalance / totalLpDeposited)
    ///         if there is more or the same amount of LP than deposited then do nothing
    function correctedAmountToWithdraw(
        uint256 _totalLpDeposited,
        uint256 _bondingLpBalance,
        uint256 _amount
    ) public pure returns (uint256) {
        if (_bondingLpBalance < _totalLpDeposited && _bondingLpBalance > 0) {
            // if there is less LP token inside the bonding contract that what have been deposited
            // we have to reduce proportionnaly the lp amount to withdraw
            return
                _amount
                    .fromUInt()
                    .mul(_bondingLpBalance.fromUInt())
                    .div(_totalLpDeposited.fromUInt())
                    .toUInt();
        }
        return _amount;
    }
}

// File: contracts/BondingShareV2.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/ERC1155.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC1155/extensions/ERC1155Burnable.sol";
import "@openzeppelin/contracts/token/ERC1155/extensions/ERC1155Pausable.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./utils/SafeAddArray.sol";

contract BondingShareV2 is ERC1155, ERC1155Burnable, ERC1155Pausable {
    using SafeAddArray for uint256[];
    struct Bond {
        // address of the minter
        address minter;
        // lp amount deposited by the user
        uint256 lpFirstDeposited;
        uint256 creationBlock;
        // lp that were already there when created
        uint256 lpRewardDebt;
        uint256 endBlock;
        // lp remaining for a user
        uint256 lpAmount;
    }

    UbiquityAlgorithmicDollarManager public manager;
    // Mapping from account to operator approvals
    mapping(address => uint256[]) private _holderBalances;
    mapping(uint256 => Bond) private _bonds;
    uint256 private _totalLP;
    uint256 private _totalSupply;

    // ----------- Modifiers -----------
    modifier onlyMinter() {
        require(
            manager.hasRole(manager.UBQ_MINTER_ROLE(), msg.sender),
            "Governance token: not minter"
        );
        _;
    }

    modifier onlyBurner() {
        require(
            manager.hasRole(manager.UBQ_BURNER_ROLE(), msg.sender),
            "Governance token: not burner"
        );
        _;
    }

    modifier onlyPauser() {
        require(
            manager.hasRole(manager.PAUSER_ROLE(), msg.sender),
            "Governance token: not pauser"
        );
        _;
    }

    /**
     * @dev constructor
     */
    constructor(address _manager, string memory uri) ERC1155(uri) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    /// @dev update bond LP amount , LP rewards debt and end block.
    /// @param _bondId bonding share id
    /// @param _lpAmount amount of LP token deposited
    /// @param _lpRewardDebt amount of excess LP token inside the bonding contract
    /// @param _endBlock end locking period block number
    function updateBond(
        uint256 _bondId,
        uint256 _lpAmount,
        uint256 _lpRewardDebt,
        uint256 _endBlock
    ) external onlyMinter whenNotPaused {
        Bond storage bond = _bonds[_bondId];
        uint256 curLpAmount = bond.lpAmount;
        if (curLpAmount > _lpAmount) {
            // we are removing LP
            _totalLP -= curLpAmount - _lpAmount;
        } else {
            // we are adding LP
            _totalLP += _lpAmount - curLpAmount;
        }
        bond.lpAmount = _lpAmount;
        bond.lpRewardDebt = _lpRewardDebt;
        bond.endBlock = _endBlock;
    }

    // @dev Creates `amount` new tokens for `to`, of token type `id`.
    /// @param to owner address
    /// @param lpDeposited amount of LP token deposited
    /// @param lpRewardDebt amount of excess LP token inside the bonding contract
    /// @param endBlock block number when the locking period ends
    function mint(
        address to,
        uint256 lpDeposited,
        uint256 lpRewardDebt,
        uint256 endBlock
    ) public virtual onlyMinter whenNotPaused returns (uint256 id) {
        id = _totalSupply + 1;
        _mint(to, id, 1, bytes(""));
        _totalSupply += 1;
        _holderBalances[to].add(id);
        Bond storage _bond = _bonds[id];
        _bond.minter = to;
        _bond.lpFirstDeposited = lpDeposited;
        _bond.lpAmount = lpDeposited;
        _bond.lpRewardDebt = lpRewardDebt;
        _bond.creationBlock = block.number;
        _bond.endBlock = endBlock;
        _totalLP += lpDeposited;
    }

    /**
     * @dev Pauses all token transfers.
     *
     * See {ERC1155Pausable} and {Pausable-_pause}.
     *
     */
    function pause() public virtual onlyPauser {
        _pause();
    }

    /**
     * @dev Unpauses all token transfers.
     *
     * See {ERC1155Pausable} and {Pausable-_unpause}.
     *
     */
    function unpause() public virtual onlyPauser {
        _unpause();
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 amount,
        bytes memory data
    ) public override whenNotPaused {
        super.safeTransferFrom(from, to, id, amount, data);
        _holderBalances[to].add(id);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) public virtual override whenNotPaused {
        super.safeBatchTransferFrom(from, to, ids, amounts, data);
        _holderBalances[to].add(ids);
    }

    /**
     * @dev Total amount of tokens  .
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev Total amount of LP tokens deposited.
     */
    function totalLP() public view virtual returns (uint256) {
        return _totalLP;
    }

    /**
     * @dev return bond details.
     */
    function getBond(uint256 id) public view returns (Bond memory) {
        return _bonds[id];
    }

    /**
     * @dev array of token Id held by the msg.sender.
     */
    function holderTokens(address holder)
        public
        view
        returns (uint256[] memory)
    {
        return _holderBalances[holder];
    }

    function _burn(
        address account,
        uint256 id,
        uint256 amount
    ) internal virtual override whenNotPaused {
        require(amount == 1, "amount <> 1");
        super._burn(account, id, 1);
        Bond storage _bond = _bonds[id];
        require(_bond.lpAmount == 0, "LP <> 0");
        _totalSupply -= 1;
    }

    function _burnBatch(
        address account,
        uint256[] memory ids,
        uint256[] memory amounts
    ) internal virtual override whenNotPaused {
        super._burnBatch(account, ids, amounts);
        for (uint256 i = 0; i < ids.length; ++i) {
            _totalSupply -= amounts[i];
        }
    }

    function _beforeTokenTransfer(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory amounts,
        bytes memory data
    ) internal virtual override(ERC1155, ERC1155Pausable) {
        super._beforeTokenTransfer(operator, from, to, ids, amounts, data);
    }
}

// File: contracts/interfaces/ISablier.sol



// SPDX-License-Identifier: MIT
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

interface ISablier {
    event CreateCompoundingStream(
        uint256 indexed streamId,
        uint256 exchangeRate,
        uint256 senderSharePercentage,
        uint256 recipientSharePercentage
    );
    event PayInterest(
        uint256 indexed streamId,
        uint256 senderInterest,
        uint256 recipientInterest,
        uint256 sablierInterest
    );
    event TakeEarnings(address indexed tokenAddress, uint256 indexed amount);
    event UpdateFee(uint256 indexed fee);
    event Paused(address account);
    event Unpaused(address account);
    event PauserAdded(address indexed account);
    event PauserRemoved(address indexed account);
    event OwnershipTransferred(
        address indexed previousOwner,
        address indexed newOwner
    );
    event CreateStream(
        uint256 indexed streamId,
        address indexed sender,
        address indexed recipient,
        uint256 deposit,
        address tokenAddress,
        uint256 startTime,
        uint256 stopTime
    );
    event WithdrawFromStream(
        uint256 indexed streamId,
        address indexed recipient,
        uint256 amount
    );
    event CancelStream(
        uint256 indexed streamId,
        address indexed sender,
        address indexed recipient,
        uint256 senderBalance,
        uint256 recipientBalance
    );

    function unpause() external;

    function cancelStream(uint256 streamId) external returns (bool);

    function withdrawFromStream(uint256 streamId, uint256 amount)
        external
        returns (bool);

    function initialize() external;

    function createCompoundingStream(
        address recipient,
        uint256 deposit,
        address tokenAddress,
        uint256 startTime,
        uint256 stopTime,
        uint256 senderSharePercentage,
        uint256 recipientSharePercentage
    ) external returns (uint256);

    function addPauser(address account) external;

    function pause() external;

    function interestOf(uint256 streamId, uint256 amount)
        external
        returns (
            uint256 senderInterest,
            uint256 recipientInterest,
            uint256 sablierInterest
        );

    function updateFee(uint256 feePercentage) external;

    function takeEarnings(address tokenAddress, uint256 amount) external;

    function initialize(address sender) external;

    function createStream(
        address recipient,
        uint256 deposit,
        address tokenAddress,
        uint256 startTime,
        uint256 stopTime
    ) external returns (uint256);

    function transferOwnership(address newOwner) external;

    function getEarnings(address tokenAddress) external view returns (uint256);

    function nextStreamId() external view returns (uint256);

    function getCompoundingStream(uint256 streamId)
        external
        view
        returns (
            address sender,
            address recipient,
            uint256 deposit,
            address tokenAddress,
            uint256 startTime,
            uint256 stopTime,
            uint256 remainingBalance,
            uint256 ratePerSecond,
            uint256 exchangeRateInitial,
            uint256 senderSharePercentage,
            uint256 recipientSharePercentage
        );

    function balanceOf(uint256 streamId, address who)
        external
        view
        returns (uint256 balance);

    function isPauser(address account) external view returns (bool);

    function paused() external view returns (bool);

    function getStream(uint256 streamId)
        external
        view
        returns (
            address sender,
            address recipient,
            uint256 deposit,
            address tokenAddress,
            uint256 startTime,
            uint256 stopTime,
            uint256 remainingBalance,
            uint256 ratePerSecond
        );

    function owner() external view returns (address);

    function isOwner() external view returns (bool);

    function isCompoundingStream(uint256 streamId) external view returns (bool);

    function deltaOf(uint256 streamId) external view returns (uint256 delta);

    function cTokenManager() external view returns (address);

    function fee() external view returns (uint256 mantissa);
}

// File: contracts/interfaces/IMasterChefV2.sol



// SPDX-License-Identifier: UNLICENSED
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

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

import "../MasterChefV2.sol";

interface IMasterChefV2 {
    struct BondingShareInfo {
        uint256 amount; // How many LP tokens the user has provided.
        uint256 rewardDebt; // Reward debt. See explanation below.
    }
    struct PoolInfo {
        uint256 lastRewardBlock; // Last block number that SUSHI distribution occurs.
        uint256 accuGOVPerShare; // Accumulated SUSHI per share, times 1e12. See below.
    }

    event Deposit(address indexed user, uint256 amount, uint256 bondingShareID);
    event Withdraw(
        address indexed user,
        uint256 amount,
        uint256 bondingShareID
    );

    function deposit(
        address sender,
        uint256 amount,
        uint256 bondingShareID
    ) external;

    // Withdraw LP tokens from MasterChef.
    function withdraw(
        address sender,
        uint256 amount,
        uint256 bondingShareID
    ) external;

    // Info about a bondinh share
    function getBondingShareInfo(uint256 _id)
        external
        view
        returns (uint256[2] memory);

    // Total amount of shares
    function totalShares() external view returns (uint256);

    // View function to see pending SUSHIs on frontend.
    function pendingUGOV(address _user) external view returns (uint256);
}

// THIS FILE WAS AUTOGENERATED FROM THE FOLLOWING ABI JSON:

// File: contracts/interfaces/ITWAPOracle.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

interface ITWAPOracle {
    function update() external;

    function consult(address token) external view returns (uint256 amountOut);
}

// File: contracts/utils/CollectableDust.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/utils/Address.sol";
import "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "../interfaces/utils/ICollectableDust.sol";

abstract contract CollectableDust is ICollectableDust {
    using SafeERC20 for IERC20;
    using EnumerableSet for EnumerableSet.AddressSet;

    address public constant ETH_ADDRESS =
        0xEeeeeEeeeEeEeeEeEeEeeEEEeeeeEeeeeeeeEEeE;
    EnumerableSet.AddressSet internal _protocolTokens;

    // solhint-disable-next-line no-empty-blocks
    constructor() {}

    function _addProtocolToken(address _token) internal {
        require(
            !_protocolTokens.contains(_token),
            "collectable-dust::token-is-part-of-the-protocol"
        );
        _protocolTokens.add(_token);
        emit ProtocolTokenAdded(_token);
    }

    function _removeProtocolToken(address _token) internal {
        require(
            _protocolTokens.contains(_token),
            "collectable-dust::token-not-part-of-the-protocol"
        );
        _protocolTokens.remove(_token);
        emit ProtocolTokenRemoved(_token);
    }

    function _sendDust(
        address _to,
        address _token,
        uint256 _amount
    ) internal {
        require(
            _to != address(0),
            "collectable-dust::cant-send-dust-to-zero-address"
        );
        require(
            !_protocolTokens.contains(_token),
            "collectable-dust::token-is-part-of-the-protocol"
        );
        if (_token == ETH_ADDRESS) {
            payable(_to).transfer(_amount);
        } else {
            IERC20(_token).safeTransfer(_to, _amount);
        }
        emit DustSent(_to, _token, _amount);
    }
}

// File: contracts/interfaces/IIncentive.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

/// @title incentive contract interface
/// @notice Called by uAD token contract when transferring with an incentivized address
/// @dev should be appointed as a Minter or Burner as needed
interface IIncentive {
    /// @notice apply incentives on transfer
    /// @param sender the sender address of uAD
    /// @param receiver the receiver address of uAD
    /// @param operator the operator (msg.sender) of the transfer
    /// @param amount the amount of uAD transferred
    function incentivize(
        address sender,
        address receiver,
        address operator,
        uint256 amount
    ) external;
}

// File: contracts/ERC20Ubiquity.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/ERC20Burnable.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/ERC20Pausable.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/IERC20Ubiquity.sol";

/// @title ERC20 Ubiquity preset
/// @author Ubiquity Algorithmic Dollar
/// @notice ERC20 with :
/// - ERC20 minter, burner and pauser
/// - draft-ERC20 permit
/// - Ubiquity Manager access control
contract ERC20Ubiquity is IERC20Ubiquity, ERC20, ERC20Burnable, ERC20Pausable {
    UbiquityAlgorithmicDollarManager public manager;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 public DOMAIN_SEPARATOR;
    // keccak256("Permit(address owner,address spender,
    //                   uint256 value,uint256 nonce,uint256 deadline)");
    bytes32 public constant PERMIT_TYPEHASH =
        0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;
    mapping(address => uint256) public nonces;
    string private _tokenName;
    string private _symbol;

    // ----------- Modifiers -----------
    modifier onlyMinter() {
        require(
            manager.hasRole(manager.UBQ_MINTER_ROLE(), msg.sender),
            "Governance token: not minter"
        );
        _;
    }

    modifier onlyBurner() {
        require(
            manager.hasRole(manager.UBQ_BURNER_ROLE(), msg.sender),
            "Governance token: not burner"
        );
        _;
    }

    modifier onlyPauser() {
        require(
            manager.hasRole(manager.PAUSER_ROLE(), msg.sender),
            "Governance token: not pauser"
        );
        _;
    }

    modifier onlyAdmin() {
        require(
            manager.hasRole(manager.DEFAULT_ADMIN_ROLE(), msg.sender),
            "ERC20: deployer must be manager admin"
        );
        _;
    }

    constructor(
        address _manager,
        string memory name_,
        string memory symbol_
    ) ERC20(name_, symbol_) {
        _tokenName = name_;
        _symbol = symbol_;
        manager = UbiquityAlgorithmicDollarManager(_manager);
        // sender must be UbiquityAlgorithmicDollarManager roleAdmin
        // because he will get the admin, minter and pauser role on uAD and we want to
        // manage all permissions through the manager
        require(
            manager.hasRole(manager.DEFAULT_ADMIN_ROLE(), msg.sender),
            "ERC20: deployer must be manager admin"
        );
        uint256 chainId;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            chainId := chainid()
        }

        DOMAIN_SEPARATOR = keccak256(
            abi.encode(
                keccak256(
                    // solhint-disable-next-line max-line-length
                    "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
                ),
                keccak256(bytes(name())),
                keccak256(bytes("1")),
                chainId,
                address(this)
            )
        );
    }

    /// @notice setSymbol update token symbol
    /// @param newSymbol new token symbol
    function setSymbol(string memory newSymbol) external onlyAdmin {
        _symbol = newSymbol;
    }

    /// @notice setName update token name
    /// @param newName new token name
    function setName(string memory newName) external onlyAdmin {
        _tokenName = newName;
    }

    /// @notice permit spending of uAD. owner has signed a message allowing
    ///         spender to transfer up to amount uAD
    /// @param owner the uAD holder
    /// @param spender the approved operator
    /// @param value the amount approved
    /// @param deadline the deadline after which the approval is no longer valid
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external override {
        // solhint-disable-next-line not-rely-on-time
        require(deadline >= block.timestamp, "Dollar: EXPIRED");
        bytes32 digest = keccak256(
            abi.encodePacked(
                "\x19\x01",
                DOMAIN_SEPARATOR,
                keccak256(
                    abi.encode(
                        PERMIT_TYPEHASH,
                        owner,
                        spender,
                        value,
                        nonces[owner]++,
                        deadline
                    )
                )
            )
        );
        address recoveredAddress = ecrecover(digest, v, r, s);
        require(
            recoveredAddress != address(0) && recoveredAddress == owner,
            "Dollar: INVALID_SIGNATURE"
        );
        _approve(owner, spender, value);
    }

    /// @notice burn UAD tokens from caller
    /// @param amount the amount to burn
    function burn(uint256 amount)
        public
        override(ERC20Burnable, IERC20Ubiquity)
        whenNotPaused
    {
        super.burn(amount);
        emit Burning(msg.sender, amount);
    }

    /// @notice burn uAD tokens from specified account
    /// @param account the account to burn from
    /// @param amount the amount to burn
    function burnFrom(address account, uint256 amount)
        public
        override(ERC20Burnable, IERC20Ubiquity)
        onlyBurner
        whenNotPaused // to suppress ? if BURNER_ROLE should do it even paused ?
    {
        _burn(account, amount);
        emit Burning(account, amount);
    }

    // @dev Creates `amount` new tokens for `to`.
    function mint(address to, uint256 amount)
        public
        override
        onlyMinter
        whenNotPaused
    {
        _mint(to, amount);
        emit Minting(to, msg.sender, amount);
    }

    // @dev Pauses all token transfers.
    function pause() public onlyPauser {
        _pause();
    }

    // @dev Unpauses all token transfers.
    function unpause() public onlyPauser {
        _unpause();
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view override(ERC20) returns (string memory) {
        return _tokenName;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view override(ERC20) returns (string memory) {
        return _symbol;
    }

    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual override(ERC20, ERC20Pausable) {
        super._beforeTokenTransfer(from, to, amount);
    }

    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal virtual override whenNotPaused {
        super._transfer(sender, recipient, amount);
    }
}

// File: contracts/MasterChefV2.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.3;

import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "./interfaces/IERC20Ubiquity.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/ITWAPOracle.sol";
import "./BondingShareV2.sol";
import "./interfaces/IUbiquityFormulas.sol";

import "./interfaces/IERC1155Ubiquity.sol";

contract MasterChefV2 {
    using SafeERC20 for IERC20Ubiquity;
    using SafeERC20 for IERC20;

    // Info of each user.
    struct BondingShareInfo {
        uint256 amount; // bonding rights.
        uint256 rewardDebt; // Reward debt. See explanation below.
        //
        // We do some fancy math here. Basically, any point in time, the amount of uGOVs
        // entitled to a user but is pending to be distributed is:
        //
        //   pending reward = (user.amount * pool.accuGOVPerShare) - user.rewardDebt
        //
        // Whenever a user deposits or withdraws LP tokens to a pool. Here's what happens:
        //   1. The pool's `accuGOVPerShare` (and `lastRewardBlock`) gets updated.
        //   2. User receives the pending reward sent to his/her address.
        //   3. User's `amount` gets updated.
        //   4. User's `rewardDebt` gets updated.
    }
    // Info of each pool.
    struct PoolInfo {
        uint256 lastRewardBlock; // Last block number that uGOVs distribution occurs.
        uint256 accuGOVPerShare; // Accumulated uGOVs per share, times 1e12. See below.
    }

    uint256 private _totalShares;

    // Ubiquity Manager
    UbiquityAlgorithmicDollarManager public manager;

    // uGOV tokens created per block.
    uint256 public uGOVPerBlock = 1e18;
    // Bonus muliplier for early uGOV makers.
    uint256 public uGOVmultiplier = 1e18;
    uint256 public minPriceDiffToUpdateMultiplier = 1000000000000000;
    uint256 public lastPrice = 1 ether;
    uint256 public uGOVDivider;
    // Info of each pool.
    PoolInfo public pool;
    // Info of each user that stakes LP tokens.
    mapping(uint256 => BondingShareInfo) private _bsInfo;

    event Deposit(
        address indexed user,
        uint256 amount,
        uint256 indexed bondingShareId
    );

    event Withdraw(
        address indexed user,
        uint256 amount,
        uint256 indexed bondingShareId
    );

    // ----------- Modifiers -----------
    modifier onlyTokenManager() {
        require(
            manager.hasRole(manager.UBQ_TOKEN_MANAGER_ROLE(), msg.sender),
            "MasterChef: not UBQ manager"
        );
        _;
    }
    modifier onlyBondingContract() {
        require(
            msg.sender == manager.bondingContractAddress(),
            "MasterChef: not Bonding Contract"
        );
        _;
    }

    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        pool.lastRewardBlock = block.number;
        pool.accuGOVPerShare = 0; // uint256(1e12);
        uGOVDivider = 5; // 100 / 5 = 20% extra minted ugov for treasury
        _updateUGOVMultiplier();
    }

    function setUGOVPerBlock(uint256 _uGOVPerBlock) external onlyTokenManager {
        uGOVPerBlock = _uGOVPerBlock;
    }

    // the bigger uGOVDivider is the less extra Ugov will be minted for the treasury
    function setUGOVShareForTreasury(uint256 _uGOVDivider)
        external
        onlyTokenManager
    {
        uGOVDivider = _uGOVDivider;
    }

    function setMinPriceDiffToUpdateMultiplier(
        uint256 _minPriceDiffToUpdateMultiplier
    ) external onlyTokenManager {
        minPriceDiffToUpdateMultiplier = _minPriceDiffToUpdateMultiplier;
    }

    // Deposit LP tokens to MasterChef for uGOV allocation.
    function deposit(
        address to,
        uint256 _amount,
        uint256 _bondingShareID
    ) external onlyBondingContract {
        BondingShareInfo storage bs = _bsInfo[_bondingShareID];
        _updatePool();
        if (bs.amount > 0) {
            uint256 pending = ((bs.amount * pool.accuGOVPerShare) / 1e12) -
                bs.rewardDebt;
            _safeUGOVTransfer(to, pending);
        }
        bs.amount += _amount;
        bs.rewardDebt = (bs.amount * pool.accuGOVPerShare) / 1e12;
        _totalShares += _amount;
        emit Deposit(to, _amount, _bondingShareID);
    }

    // Withdraw LP tokens from MasterChef.
    function withdraw(
        address to,
        uint256 _amount,
        uint256 _bondingShareID
    ) external onlyBondingContract {
        BondingShareInfo storage bs = _bsInfo[_bondingShareID];
        require(bs.amount >= _amount, "MC: amount too high");
        _updatePool();
        uint256 pending = ((bs.amount * pool.accuGOVPerShare) / 1e12) -
            bs.rewardDebt;
        // send UGOV to Bonding Share holder

        _safeUGOVTransfer(to, pending);
        bs.amount -= _amount;
        bs.rewardDebt = (bs.amount * pool.accuGOVPerShare) / 1e12;
        _totalShares -= _amount;
        emit Withdraw(to, _amount, _bondingShareID);
    }

    /// @dev get pending uGOV rewards from MasterChef.
    /// @return amount of pending rewards transfered to msg.sender
    /// @notice only send pending rewards
    function getRewards(uint256 bondingShareID) external returns (uint256) {
        require(
            IERC1155Ubiquity(manager.bondingShareAddress()).balanceOf(
                msg.sender,
                bondingShareID
            ) == 1,
            "MS: caller is not owner"
        );

        // calculate user reward
        BondingShareInfo storage user = _bsInfo[bondingShareID];
        _updatePool();
        uint256 pending = ((user.amount * pool.accuGOVPerShare) / 1e12) -
            user.rewardDebt;
        _safeUGOVTransfer(msg.sender, pending);
        user.rewardDebt = (user.amount * pool.accuGOVPerShare) / 1e12;
        return pending;
    }

    // View function to see pending uGOVs on frontend.
    function pendingUGOV(uint256 bondingShareID)
        external
        view
        returns (uint256)
    {
        BondingShareInfo storage user = _bsInfo[bondingShareID];
        uint256 accuGOVPerShare = pool.accuGOVPerShare;
        uint256 lpSupply = IERC1155Ubiquity(manager.bondingShareAddress())
            .totalSupply();

        if (block.number > pool.lastRewardBlock && lpSupply != 0) {
            uint256 multiplier = _getMultiplier();

            uint256 uGOVReward = (multiplier * uGOVPerBlock) / 1e18;
            accuGOVPerShare =
                accuGOVPerShare +
                ((uGOVReward * 1e12) / lpSupply);
        }

        return (user.amount * accuGOVPerShare) / 1e12 - user.rewardDebt;
    }

    /**
     * @dev get the amount of shares and the reward debt of a bonding share .
     */
    function getBondingShareInfo(uint256 _id)
        external
        view
        returns (uint256[2] memory)
    {
        return [_bsInfo[_id].amount, _bsInfo[_id].rewardDebt];
    }

    /**
     * @dev Total amount of shares .
     */
    function totalShares() external view virtual returns (uint256) {
        return _totalShares;
    }

    // UPDATE uGOV multiplier
    function _updateUGOVMultiplier() internal {
        // (1.05/(1+abs(1-TWAP_PRICE)))
        uint256 currentPrice = _getTwapPrice();

        bool isPriceDiffEnough = false;
        // a minimum price variation is needed to update the multiplier
        if (currentPrice > lastPrice) {
            isPriceDiffEnough =
                currentPrice - lastPrice > minPriceDiffToUpdateMultiplier;
        } else {
            isPriceDiffEnough =
                lastPrice - currentPrice > minPriceDiffToUpdateMultiplier;
        }

        if (isPriceDiffEnough) {
            uGOVmultiplier = IUbiquityFormulas(manager.formulasAddress())
                .ugovMultiply(uGOVmultiplier, currentPrice);
            lastPrice = currentPrice;
        }
    }

    // Update reward variables of the given pool to be up-to-date.
    function _updatePool() internal {
        if (block.number <= pool.lastRewardBlock) {
            return;
        }
        _updateUGOVMultiplier();
        uint256 lpSupply = IERC1155Ubiquity(manager.bondingShareAddress())
            .totalSupply();
        if (lpSupply == 0) {
            pool.lastRewardBlock = block.number;
            return;
        }
        uint256 multiplier = _getMultiplier();
        uint256 uGOVReward = (multiplier * uGOVPerBlock) / 1e18;
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            address(this),
            uGOVReward
        );
        // mint another x% for the treasury
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            manager.treasuryAddress(),
            uGOVReward / uGOVDivider
        );
        pool.accuGOVPerShare =
            pool.accuGOVPerShare +
            ((uGOVReward * 1e12) / lpSupply);
        pool.lastRewardBlock = block.number;
    }

    // Safe uGOV transfer function, just in case if rounding
    // error causes pool to not have enough uGOVs.
    function _safeUGOVTransfer(address _to, uint256 _amount) internal {
        IERC20Ubiquity uGOV = IERC20Ubiquity(manager.governanceTokenAddress());
        uint256 uGOVBal = uGOV.balanceOf(address(this));
        if (_amount > uGOVBal) {
            uGOV.safeTransfer(_to, uGOVBal);
        } else {
            uGOV.safeTransfer(_to, _amount);
        }
    }

    function _getMultiplier() internal view returns (uint256) {
        return (block.number - pool.lastRewardBlock) * uGOVmultiplier;
    }

    function _getTwapPrice() internal view returns (uint256) {
        return
            ITWAPOracle(manager.twapOracleAddress()).consult(
                manager.dollarTokenAddress()
            );
    }
}

// File: @openzeppelin/contracts/utils/structs/EnumerableSet.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            if (lastIndex != toDeleteIndex) {
                bytes32 lastvalue = set._values[lastIndex];

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastvalue;
                // Update the index for the moved value
                set._indexes[lastvalue] = valueIndex; // Replace lastvalue's index to valueIndex
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }
}

// File: contracts/interfaces/utils/ICollectableDust.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

interface ICollectableDust {
    event DustSent(address _to, address token, uint256 amount);
    event ProtocolTokenAdded(address _token);
    event ProtocolTokenRemoved(address _token);

    function addProtocolToken(address _token) external;

    function removeProtocolToken(address _token) external;

    function sendDust(
        address _to,
        address _token,
        uint256 _amount
    ) external;
}

// File: contracts/MasterChef.sol



// SPDX-License-Identifier: MIT
pragma solidity 0.8.3;

import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "./interfaces/IERC20Ubiquity.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/ITWAPOracle.sol";
import "./interfaces/IERC1155Ubiquity.sol";
import "./interfaces/IUbiquityFormulas.sol";

contract MasterChef {
    using SafeERC20 for IERC20Ubiquity;
    using SafeERC20 for IERC20;
    // Info of each user.
    struct UserInfo {
        uint256 amount; // How many uAD-3CRV LP tokens the user has provided.
        uint256 rewardDebt; // Reward debt. See explanation below.
        //
        // We do some fancy math here. Basically, any point in time, the amount of uGOVs
        // entitled to a user but is pending to be distributed is:
        //
        //   pending reward = (user.amount * pool.accuGOVPerShare) - user.rewardDebt
        //
        // Whenever a user deposits or withdraws LP tokens to a pool. Here's what happens:
        //   1. The pool's `accuGOVPerShare` (and `lastRewardBlock`) gets updated.
        //   2. User receives the pending reward sent to his/her address.
        //   3. User's `amount` gets updated.
        //   4. User's `rewardDebt` gets updated.
    }
    // Info of each pool.
    struct PoolInfo {
        uint256 lastRewardBlock; // Last block number that uGOVs distribution occurs.
        uint256 accuGOVPerShare; // Accumulated uGOVs per share, times 1e12. See below.
    }

    // Ubiquity Manager
    UbiquityAlgorithmicDollarManager public manager;

    // uGOV tokens created per block.
    uint256 public uGOVPerBlock = 1e18;
    // Bonus muliplier for early uGOV makers.
    uint256 public uGOVmultiplier = 1e18;
    uint256 public minPriceDiffToUpdateMultiplier = 1000000000000000;
    uint256 public lastPrice = 1 ether;
    // Info of each pool.
    PoolInfo public pool;
    // Info of each user that stakes LP tokens.
    mapping(address => UserInfo) public userInfo;

    event Deposit(address indexed user, uint256 amount);

    event Withdraw(address indexed user, uint256 amount);

    // ----------- Modifiers -----------
    modifier onlyTokenManager() {
        require(
            manager.hasRole(manager.UBQ_TOKEN_MANAGER_ROLE(), msg.sender),
            "MasterChef: not UBQ manager"
        );
        _;
    }
    modifier onlyBondingContract() {
        require(
            msg.sender == manager.bondingContractAddress(),
            "MasterChef: not Bonding Contract"
        );
        _;
    }

    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        pool.lastRewardBlock = block.number;
        pool.accuGOVPerShare = 0; // uint256(1e12);
        _updateUGOVMultiplier();
    }

    function setUGOVPerBlock(uint256 _uGOVPerBlock) external onlyTokenManager {
        uGOVPerBlock = _uGOVPerBlock;
    }

    function setMinPriceDiffToUpdateMultiplier(
        uint256 _minPriceDiffToUpdateMultiplier
    ) external onlyTokenManager {
        minPriceDiffToUpdateMultiplier = _minPriceDiffToUpdateMultiplier;
    }

    // Deposit LP tokens to MasterChef for uGOV allocation.
    function deposit(uint256 _amount, address sender)
        external
        onlyBondingContract
    {
        UserInfo storage user = userInfo[sender];
        _updatePool();
        if (user.amount > 0) {
            uint256 pending = ((user.amount * pool.accuGOVPerShare) / 1e12) -
                user.rewardDebt;
            _safeUGOVTransfer(sender, pending);
        }
        user.amount = user.amount + _amount;
        user.rewardDebt = (user.amount * pool.accuGOVPerShare) / 1e12;
        emit Deposit(sender, _amount);
    }

    // Withdraw LP tokens from MasterChef.
    function withdraw(uint256 _amount, address sender)
        external
        onlyBondingContract
    {
        UserInfo storage user = userInfo[sender];
        require(user.amount >= _amount, "MC: amount too high");
        _updatePool();
        uint256 pending = ((user.amount * pool.accuGOVPerShare) / 1e12) -
            user.rewardDebt;
        _safeUGOVTransfer(sender, pending);
        user.amount = user.amount - _amount;
        user.rewardDebt = (user.amount * pool.accuGOVPerShare) / 1e12;
        emit Withdraw(sender, _amount);
    }

    /// @dev get pending uGOV rewards from MasterChef.
    /// @return amount of pending rewards transfered to msg.sender
    /// @notice only send pending rewards
    function getRewards() external returns (uint256) {
        UserInfo storage user = userInfo[msg.sender];
        _updatePool();
        uint256 pending = ((user.amount * pool.accuGOVPerShare) / 1e12) -
            user.rewardDebt;
        _safeUGOVTransfer(msg.sender, pending);
        user.rewardDebt = (user.amount * pool.accuGOVPerShare) / 1e12;
        return pending;
    }

    // View function to see pending uGOVs on frontend.
    function pendingUGOV(address _user) external view returns (uint256) {
        UserInfo storage user = userInfo[_user];
        uint256 accuGOVPerShare = pool.accuGOVPerShare;
        uint256 lpSupply = IERC1155Ubiquity(manager.bondingShareAddress())
            .totalSupply();

        if (block.number > pool.lastRewardBlock && lpSupply != 0) {
            uint256 multiplier = _getMultiplier();

            uint256 uGOVReward = (multiplier * uGOVPerBlock) / 1e18;
            accuGOVPerShare =
                accuGOVPerShare +
                ((uGOVReward * 1e12) / lpSupply);
        }

        return (user.amount * accuGOVPerShare) / 1e12 - user.rewardDebt;
    }

    // UPDATE uGOV multiplier
    function _updateUGOVMultiplier() internal {
        // (1.05/(1+abs(1-TWAP_PRICE)))
        uint256 currentPrice = _getTwapPrice();

        bool isPriceDiffEnough = false;
        // a minimum price variation is needed to update the multiplier
        if (currentPrice > lastPrice) {
            isPriceDiffEnough =
                currentPrice - lastPrice > minPriceDiffToUpdateMultiplier;
        } else {
            isPriceDiffEnough =
                lastPrice - currentPrice > minPriceDiffToUpdateMultiplier;
        }

        if (isPriceDiffEnough) {
            uGOVmultiplier = IUbiquityFormulas(manager.formulasAddress())
                .ugovMultiply(uGOVmultiplier, currentPrice);
            lastPrice = currentPrice;
        }
    }

    // Update reward variables of the given pool to be up-to-date.
    function _updatePool() internal {
        if (block.number <= pool.lastRewardBlock) {
            return;
        }
        _updateUGOVMultiplier();
        uint256 lpSupply = IERC1155Ubiquity(manager.bondingShareAddress())
            .totalSupply();
        if (lpSupply == 0) {
            pool.lastRewardBlock = block.number;
            return;
        }
        uint256 multiplier = _getMultiplier();
        uint256 uGOVReward = (multiplier * uGOVPerBlock) / 1e18;
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            address(this),
            uGOVReward
        );
        // mint another 20% for the treasury
        IERC20Ubiquity(manager.governanceTokenAddress()).mint(
            manager.treasuryAddress(),
            uGOVReward / 5
        );
        pool.accuGOVPerShare =
            pool.accuGOVPerShare +
            ((uGOVReward * 1e12) / lpSupply);
        pool.lastRewardBlock = block.number;
    }

    // Safe uGOV transfer function, just in case if rounding
    // error causes pool to not have enough uGOVs.
    function _safeUGOVTransfer(address _to, uint256 _amount) internal {
        IERC20Ubiquity uGOV = IERC20Ubiquity(manager.governanceTokenAddress());
        uint256 uGOVBal = uGOV.balanceOf(address(this));
        if (_amount > uGOVBal) {
            uGOV.safeTransfer(_to, uGOVBal);
        } else {
            uGOV.safeTransfer(_to, _amount);
        }
    }

    function _getMultiplier() internal view returns (uint256) {
        return (block.number - pool.lastRewardBlock) * uGOVmultiplier;
    }

    function _getTwapPrice() internal view returns (uint256) {
        return
            ITWAPOracle(manager.twapOracleAddress()).consult(
                manager.dollarTokenAddress()
            );
    }
}

// File: contracts/interfaces/IDebtCoupon.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155.sol";

/// @title A debt coupon which corresponds to a IDebtRedemption contract
interface IDebtCoupon is IERC1155 {
    function updateTotalDebt() external;

    function burnCoupons(
        address couponOwner,
        uint256 amount,
        uint256 expiryBlockNumber
    ) external;

    function mintCoupons(
        address recipient,
        uint256 amount,
        uint256 expiryBlockNumber
    ) external;

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

// File: contracts/mocks/MockDebtCoupon.sol



// contracts/GLDToken.sol
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/ERC1155.sol";

contract MockDebtCoupon is ERC1155 {
    uint256 private _totalOutstandingDebt;

    //@dev URI param is if we want to add an off-chain meta data uri associated with this contract
    constructor(uint256 totalDebt) ERC1155("URI") {
        _totalOutstandingDebt = totalDebt;
    }

    function getTotalOutstandingDebt() public view returns (uint256) {
        return _totalOutstandingDebt;
    }
}

// File: contracts/BondingShare.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./ERC1155Ubiquity.sol";

contract BondingShare is ERC1155Ubiquity {
    // solhint-disable-next-line no-empty-blocks
    constructor(address _manager) ERC1155Ubiquity(_manager, "URI") {}
}

// File: contracts/interfaces/ISushiMasterChef.sol



// SPDX-License-Identifier: UNLICENSED
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

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

interface ISushiMasterChef {
    struct UserInfo {
        uint256 amount; // How many LP tokens the user has provided.
        uint256 rewardDebt; // Reward debt. See explanation below.
    }
    struct PoolInfo {
        IERC20 lpToken; // Address of LP token contract.
        uint256 allocPoint; // How many allocation points assigned to this pool.
        uint256 lastRewardBlock; // Last block number that SUSHI distribution occurs.
        uint256 accSushiPerShare; // Accumulated SUSHI per share, times 1e12. See below.
    }
    event Deposit(address indexed user, uint256 indexed pid, uint256 amount);
    event Withdraw(address indexed user, uint256 indexed pid, uint256 amount);
    event EmergencyWithdraw(
        address indexed user,
        uint256 indexed pid,
        uint256 amount
    );

    function deposit(uint256 _pid, uint256 _amount) external;

    // Withdraw LP tokens from MasterChef.
    function withdraw(uint256 _pid, uint256 _amount) external;

    // Update reward vairables for all pools. Be careful of gas spending!
    function massUpdatePools() external;

    // Update reward variables of the given pool to be up-to-date.
    function updatePool(uint256 _pid) external;

    // Add a new lp to the pool. Can only be called by the owner.
    // XXX DO NOT add the same LP token more than once. Rewards will be messed up if you do.
    function add(
        uint256 _allocPoint,
        IERC20 _lpToken,
        bool _withUpdate
    ) external;

    // Update the given pool's SUSHI allocation point. Can only be called by the owner.
    function set(
        uint256 _pid,
        uint256 _allocPoint,
        bool _withUpdate
    ) external;

    // Returns the address of the current owner.
    function owner() external view returns (address);

    // Info of each pool.
    function userInfo(uint256 pid, address user)
        external
        view
        returns (ISushiMasterChef.UserInfo memory);

    // SUSHI tokens created per block.
    function sushiPerBlock() external view returns (uint256);

    // Info of each pool.
    function poolInfo(uint256 pid)
        external
        view
        returns (ISushiMasterChef.PoolInfo memory);

    // Total allocation poitns. Must be the sum of all allocation points in all pools.
    function totalAllocPoint() external view returns (uint256);

    function poolLength() external view returns (uint256);

    // View function to see pending SUSHIs on frontend.
    function pendingSushi(uint256 _pid, address _user)
        external
        view
        returns (uint256);
}

// THIS FILE WAS AUTOGENERATED FROM THE FOLLOWING ABI JSON:

// File: contracts/DollarMintingCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/IDollarMintingCalculator.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./TWAPOracle.sol";
import "./libs/ABDKMathQuad.sol";

/// @title A mock coupon calculator that always returns a constant
contract DollarMintingCalculator is IDollarMintingCalculator {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;

    bytes16 private immutable _one = (uint256(1 ether)).fromUInt();
    UbiquityAlgorithmicDollarManager public manager;

    /// @param _manager the address of the manager contract so we can fetch variables
    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    /// @notice returns (TWAP_PRICE  -1) * UAD_Total_Supply
    function getDollarsToMint() external view override returns (uint256) {
        TWAPOracle oracle = TWAPOracle(manager.twapOracleAddress());
        uint256 twapPrice = oracle.consult(manager.dollarTokenAddress());
        require(twapPrice > 1, "DollarMintingCalculator: not > 1");
        return
            twapPrice
                .fromUInt()
                .sub(_one)
                .mul(
                    (
                        IERC20(manager.dollarTokenAddress())
                            .totalSupply()
                            .fromUInt()
                            .div(_one)
                    )
                )
                .toUInt();
    }
}

// File: contracts/interfaces/IDollarMintingCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol";

/// @title A mechanism for calculating dollars to be minted
interface IDollarMintingCalculator {
    function getDollarsToMint() external view returns (uint256);
}

// File: contracts/DebtCouponManager.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/utils/introspection/ERC165.sol";
import "./interfaces/IDebtRedemption.sol";
import "./interfaces/IUARForDollarsCalculator.sol";
import "./interfaces/ICouponsForDollarsCalculator.sol";
import "./interfaces/IDollarMintingCalculator.sol";
import "./interfaces/IExcessDollarsDistributor.sol";
import "./TWAPOracle.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "./UbiquityAlgorithmicDollar.sol";
import "./UbiquityAutoRedeem.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./DebtCoupon.sol";

/// @title A basic debt issuing and redemption mechanism for coupon holders
/// @notice Allows users to burn their uAD in exchange for coupons
/// redeemable in the future
/// @notice Allows users to redeem individual debt coupons or batch redeem
/// coupons on a first-come first-serve basis
contract DebtCouponManager is ERC165, IERC1155Receiver {
    using SafeERC20 for IERC20Ubiquity;
    UbiquityAlgorithmicDollarManager public manager;

    //the amount of dollars we minted this cycle, so we can calculate delta.
    // should be reset to 0 when cycle ends
    uint256 public dollarsMintedThisCycle;
    bool public debtCycle;
    uint256 public blockHeightDebt;
    uint256 public couponLengthBlocks;
    uint256 public expiredCouponConvertionRate = 2;
    event ExpiredCouponConvertionRateChanged(
        uint256 newRate,
        uint256 previousRate
    );

    event CouponLengthChanged(
        uint256 newCouponLengthBlocks,
        uint256 previousCouponLengthBlocks
    );

    modifier onlyCouponManager() {
        require(
            manager.hasRole(manager.COUPON_MANAGER_ROLE(), msg.sender),
            "Caller is not a coupon manager"
        );
        _;
    }

    /// @param _manager the address of the manager contract so we can fetch variables
    /// @param _couponLengthBlocks how many blocks coupons last. can't be changed
    /// once set (unless migrated)
    constructor(address _manager, uint256 _couponLengthBlocks) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        couponLengthBlocks = _couponLengthBlocks;
    }

    function setExpiredCouponConvertionRate(uint256 rate)
        external
        onlyCouponManager
    {
        emit ExpiredCouponConvertionRateChanged(
            rate,
            expiredCouponConvertionRate
        );
        expiredCouponConvertionRate = rate;
    }

    function setCouponLength(uint256 _couponLengthBlocks)
        external
        onlyCouponManager
    {
        emit CouponLengthChanged(_couponLengthBlocks, couponLengthBlocks);
        couponLengthBlocks = _couponLengthBlocks;
    }

    /// @dev called when a user wants to burn UAD for debt coupon.
    ///      should only be called when oracle is below a dollar
    /// @param amount the amount of dollars to exchange for coupons
    function exchangeDollarsForDebtCoupons(uint256 amount)
        external
        returns (uint256)
    {
        uint256 twapPrice = _getTwapPrice();

        require(twapPrice < 1 ether, "Price must be below 1 to mint coupons");

        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());
        debtCoupon.updateTotalDebt();

        //we are in a down cycle so reset the cycle counter
        // and set the blockHeight Debt
        if (!debtCycle) {
            debtCycle = true;
            blockHeightDebt = block.number;
            dollarsMintedThisCycle = 0;
        }

        ICouponsForDollarsCalculator couponCalculator = ICouponsForDollarsCalculator(
                manager.couponCalculatorAddress()
            );
        uint256 couponsToMint = couponCalculator.getCouponAmount(amount);

        // we burn user's dollars.
        UbiquityAlgorithmicDollar(manager.dollarTokenAddress()).burnFrom(
            msg.sender,
            amount
        );

        uint256 expiryBlockNumber = block.number + (couponLengthBlocks);
        debtCoupon.mintCoupons(msg.sender, couponsToMint, expiryBlockNumber);

        //give the caller the block number of the minted nft
        return expiryBlockNumber;
    }

    /// @dev called when a user wants to burn UAD for uAR.
    ///      should only be called when oracle is below a dollar
    /// @param amount the amount of dollars to exchange for uAR
    /// @return amount of auto redeem tokens minted
    function exchangeDollarsForUAR(uint256 amount) external returns (uint256) {
        uint256 twapPrice = _getTwapPrice();

        require(twapPrice < 1 ether, "Price must be below 1 to mint uAR");

        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());
        debtCoupon.updateTotalDebt();

        //we are in a down cycle so reset the cycle counter
        // and set the blockHeight Debt
        if (!debtCycle) {
            debtCycle = true;
            blockHeightDebt = block.number;
            dollarsMintedThisCycle = 0;
        }

        IUARForDollarsCalculator uarCalculator = IUARForDollarsCalculator(
            manager.uarCalculatorAddress()
        );
        uint256 uarToMint = uarCalculator.getUARAmount(amount, blockHeightDebt);

        // we burn user's dollars.
        UbiquityAlgorithmicDollar(manager.dollarTokenAddress()).burnFrom(
            msg.sender,
            amount
        );
        // mint uAR
        UbiquityAutoRedeem autoRedeemToken = UbiquityAutoRedeem(
            manager.autoRedeemTokenAddress()
        );
        autoRedeemToken.mint(msg.sender, uarToMint);

        //give minted uAR amount
        return uarToMint;
    }

    /// @dev uses the current coupons for dollars calculation to get coupons for dollars
    /// @param amount the amount of dollars to exchange for coupons
    function getCouponsReturnedForDollars(uint256 amount)
        external
        view
        returns (uint256)
    {
        ICouponsForDollarsCalculator couponCalculator = ICouponsForDollarsCalculator(
                manager.couponCalculatorAddress()
            );
        return couponCalculator.getCouponAmount(amount);
    }

    /// @dev uses the current uAR for dollars calculation to get uAR for dollars
    /// @param amount the amount of dollars to exchange for uAR
    function getUARReturnedForDollars(uint256 amount)
        external
        view
        returns (uint256)
    {
        IUARForDollarsCalculator uarCalculator = IUARForDollarsCalculator(
            manager.uarCalculatorAddress()
        );
        return uarCalculator.getUARAmount(amount, blockHeightDebt);
    }

    /// @dev should be called by this contract only when getting coupons to be burnt
    function onERC1155Received(
        address operator,
        address,
        uint256,
        uint256,
        bytes calldata
    ) external view override returns (bytes4) {
        if (manager.hasRole(manager.COUPON_MANAGER_ROLE(), operator)) {
            //allow the transfer since it originated from this contract
            return
                bytes4(
                    keccak256(
                        "onERC1155Received(address,address,uint256,uint256,bytes)"
                    )
                );
        } else {
            //reject the transfer
            return "";
        }
    }

    /// @dev this method is never called by the contract so if called,
    /// it was called by someone else -> revert.
    function onERC1155BatchReceived(
        address,
        address,
        uint256[] calldata,
        uint256[] calldata,
        bytes calldata
    ) external pure override returns (bytes4) {
        //reject the transfer
        return "";
    }

    /// @dev let debt holder burn expired coupons for UGOV. Doesn't make TWAP > 1 check.
    /// @param id the timestamp of the coupon
    /// @param amount the amount of coupons to redeem
    /// @return uGovAmount amount of UGOV tokens minted to debt holder
    function burnExpiredCouponsForUGOV(uint256 id, uint256 amount)
        public
        returns (uint256 uGovAmount)
    {
        // Check whether debt coupon hasn't expired --> Burn debt coupons.
        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());

        require(id <= block.number, "Coupon has not expired");
        require(
            debtCoupon.balanceOf(msg.sender, id) >= amount,
            "User not enough coupons"
        );

        debtCoupon.burnCoupons(msg.sender, amount, id);

        // Mint UGOV tokens to this contract. Transfer UGOV tokens to msg.sender i.e. debt holder
        IERC20Ubiquity uGOVToken = IERC20Ubiquity(
            manager.governanceTokenAddress()
        );
        uGovAmount = amount / expiredCouponConvertionRate;
        uGOVToken.mint(msg.sender, uGovAmount);
    }

    // TODO should we leave it ?
    /// @dev Lets debt holder burn coupons for auto redemption. Doesn't make TWAP > 1 check.
    /// @param id the timestamp of the coupon
    /// @param amount the amount of coupons to redeem
    /// @return amount of auto redeem pool tokens (i.e. LP tokens) minted to debt holder
    function burnCouponsForAutoRedemption(uint256 id, uint256 amount)
        public
        returns (uint256)
    {
        // Check whether debt coupon hasn't expired --> Burn debt coupons.
        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());

        require(id > block.timestamp, "Coupon has expired");
        require(
            debtCoupon.balanceOf(msg.sender, id) >= amount,
            "User not enough coupons"
        );

        debtCoupon.burnCoupons(msg.sender, amount, id);

        // Mint LP tokens to this contract. Transfer LP tokens to msg.sender i.e. debt holder
        UbiquityAutoRedeem autoRedeemToken = UbiquityAutoRedeem(
            manager.autoRedeemTokenAddress()
        );
        autoRedeemToken.mint(address(this), amount);
        autoRedeemToken.transfer(msg.sender, amount);

        return autoRedeemToken.balanceOf(msg.sender);
    }

    /// @dev Exchange auto redeem pool token for uAD tokens.
    /// @param amount Amount of uAR tokens to burn in exchange for uAD tokens.
    /// @return amount of unredeemed uAR
    function burnAutoRedeemTokensForDollars(uint256 amount)
        public
        returns (uint256)
    {
        uint256 twapPrice = _getTwapPrice();
        require(twapPrice > 1 ether, "Price must be above 1 to auto redeem");
        if (debtCycle) {
            debtCycle = false;
        }
        UbiquityAutoRedeem autoRedeemToken = UbiquityAutoRedeem(
            manager.autoRedeemTokenAddress()
        );
        require(
            autoRedeemToken.balanceOf(msg.sender) >= amount,
            "User doesn't have enough auto redeem pool tokens."
        );

        UbiquityAlgorithmicDollar uAD = UbiquityAlgorithmicDollar(
            manager.dollarTokenAddress()
        );
        uint256 maxRedeemableUAR = uAD.balanceOf(address(this));

        if (maxRedeemableUAR <= 0) {
            mintClaimableDollars();
            maxRedeemableUAR = uAD.balanceOf(address(this));
        }

        uint256 uarToRedeem = amount;
        if (amount > maxRedeemableUAR) {
            uarToRedeem = maxRedeemableUAR;
        }
        autoRedeemToken.burnFrom(msg.sender, uarToRedeem);
        uAD.transfer(msg.sender, uarToRedeem);

        return amount - uarToRedeem;
    }

    /// @param id the block number of the coupon
    /// @param amount the amount of coupons to redeem
    /// @return amount of unredeemed coupons
    function redeemCoupons(uint256 id, uint256 amount)
        public
        returns (uint256)
    {
        uint256 twapPrice = _getTwapPrice();

        require(twapPrice > 1 ether, "Price must be above 1 to redeem coupons");
        if (debtCycle) {
            debtCycle = false;
        }
        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());

        require(id > block.number, "Coupon has expired");
        require(
            debtCoupon.balanceOf(msg.sender, id) >= amount,
            "User not enough coupons"
        );

        mintClaimableDollars();
        UbiquityAlgorithmicDollar uAD = UbiquityAlgorithmicDollar(
            manager.dollarTokenAddress()
        );
        UbiquityAutoRedeem autoRedeemToken = UbiquityAutoRedeem(
            manager.autoRedeemTokenAddress()
        );
        // uAR have a priority on uDEBT coupon holder
        require(
            autoRedeemToken.totalSupply() <= uAD.balanceOf(address(this)),
            "There aren't enough uAD to redeem currently"
        );
        uint256 maxRedeemableCoupons = uAD.balanceOf(address(this)) -
            autoRedeemToken.totalSupply();
        uint256 couponsToRedeem = amount;

        if (amount > maxRedeemableCoupons) {
            couponsToRedeem = maxRedeemableCoupons;
        }
        require(
            uAD.balanceOf(address(this)) > 0,
            "There aren't any uAD to redeem currently"
        );

        // debtCouponManager must be an operator to transfer on behalf of msg.sender
        debtCoupon.burnCoupons(msg.sender, couponsToRedeem, id);
        uAD.transfer(msg.sender, couponsToRedeem);

        return amount - (couponsToRedeem);
    }

    function mintClaimableDollars() public {
        DebtCoupon debtCoupon = DebtCoupon(manager.debtCouponAddress());
        debtCoupon.updateTotalDebt();

        // uint256 twapPrice = _getTwapPrice(); //unused variable. Why here?
        uint256 totalMintableDollars = IDollarMintingCalculator(
            manager.dollarMintingCalculatorAddress()
        ).getDollarsToMint();
        uint256 dollarsToMint = totalMintableDollars - (dollarsMintedThisCycle);
        //update the dollars for this cycle
        dollarsMintedThisCycle = totalMintableDollars;

        UbiquityAlgorithmicDollar uAD = UbiquityAlgorithmicDollar(
            manager.dollarTokenAddress()
        );
        // uAD  dollars should  be minted to address(this)
        uAD.mint(address(this), dollarsToMint);
        UbiquityAutoRedeem autoRedeemToken = UbiquityAutoRedeem(
            manager.autoRedeemTokenAddress()
        );

        uint256 currentRedeemableBalance = uAD.balanceOf(address(this));
        uint256 totalOutstandingDebt = debtCoupon.getTotalOutstandingDebt() +
            autoRedeemToken.totalSupply();

        if (currentRedeemableBalance > totalOutstandingDebt) {
            uint256 excessDollars = currentRedeemableBalance -
                (totalOutstandingDebt);

            IExcessDollarsDistributor dollarsDistributor = IExcessDollarsDistributor(
                    manager.getExcessDollarsDistributor(address(this))
                );
            //transfer excess dollars to the distributor and tell it to distribute
            uAD.transfer(
                manager.getExcessDollarsDistributor(address(this)),
                excessDollars
            );
            dollarsDistributor.distributeDollars();
        }
    }

    function _getTwapPrice() internal returns (uint256) {
        TWAPOracle(manager.twapOracleAddress()).update();
        return
            TWAPOracle(manager.twapOracleAddress()).consult(
                manager.dollarTokenAddress()
            );
    }
}

// File: contracts/interfaces/IDebtRedemption.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol";

/// @title A debt redemption mechanism for coupon holders
/// @notice Allows users to redeem individual debt coupons or batch redeem coupons
/// @dev Implements IERC1155Receiver so that it can deal with redemptions
interface IDebtCouponManager is IERC1155Receiver {
    function redeemCoupons(
        address from,
        uint256 id,
        uint256 amount
    ) external;

    function exchangeDollarsForDebtCoupons(uint256 amount) external;
}

// File: contracts/interfaces/ICouponsForDollarsCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC1155/IERC1155Receiver.sol";

/// @title A mechanism for calculating coupons received for a dollar amount burnt
interface ICouponsForDollarsCalculator {
    function getCouponAmount(uint256 dollarsToBurn)
        external
        view
        returns (uint256);
}

// File: contracts/UbiquityAutoRedeem.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "./ERC20Ubiquity.sol";

contract UbiquityAutoRedeem is ERC20Ubiquity {
    constructor(address _manager)
        ERC20Ubiquity(_manager, "Ubiquity Auto Redeem", "uAR")
    {} // solhint-disable-line no-empty-blocks

    /// @notice raise capital in form of uAR (only redeemable when uAD > 1$)
    /// @param amount the amount to be minted
    /// @dev you should be minter to call that function
    function raiseCapital(uint256 amount) external {
        address treasuryAddress = manager.treasuryAddress();
        mint(treasuryAddress, amount);
    }
}

// File: contracts/UbiquityGovernance.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "./ERC20Ubiquity.sol";

contract UbiquityGovernance is ERC20Ubiquity {
    constructor(address _manager) ERC20Ubiquity(_manager, "Ubiquity", "UBQ") {} // solhint-disable-line no-empty-blocks, max-line-length
}

// File: contracts/interfaces/IUbiquityGovernance.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.8.3;

import "./IERC20Ubiquity.sol";

/// @title uGOV governance token interface
/// @author Ubiquity Algorithmic Dollar
// solhint-disable-next-line no-empty-blocks
interface IUbiquityGovernance is IERC20Ubiquity {

}

// File: contracts/CurveUADIncentive.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/IUbiquityGovernance.sol";
import "./interfaces/IIncentive.sol";
import "./TWAPOracle.sol";
import "./UbiquityAlgorithmicDollar.sol";
import "./libs/ABDKMathQuad.sol";

/// @title Uniswap trading incentive contract
/// @author uAD Protocol
/// @dev incentives
contract CurveUADIncentive is IIncentive {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;
    UbiquityAlgorithmicDollarManager public manager;
    bool public isSellPenaltyOn = true;
    bool public isBuyIncentiveOn = true;
    bytes16 private immutable _one = (uint256(1 ether)).fromUInt();
    mapping(address => bool) private _exempt;
    event ExemptAddressUpdate(address indexed _account, bool _isExempt);
    modifier onlyAdmin() {
        require(
            manager.hasRole(manager.INCENTIVE_MANAGER_ROLE(), msg.sender),
            "CurveIncentive: not admin"
        );
        _;
    }
    modifier onlyUAD() {
        require(
            msg.sender == manager.dollarTokenAddress(),
            "CurveIncentive: Caller is not uAD"
        );
        _;
    }

    /// @notice CurveIncentive constructor
    /// @param _manager uAD Manager
    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    function incentivize(
        address sender,
        address receiver,
        address,
        uint256 amountIn
    ) external override onlyUAD {
        require(sender != receiver, "CurveIncentive: cannot send self");

        if (sender == manager.stableSwapMetaPoolAddress()) {
            _incentivizeBuy(receiver, amountIn);
        }

        if (receiver == manager.stableSwapMetaPoolAddress()) {
            _incentivizeSell(sender, amountIn);
        }
    }

    /// @notice set an address to be exempted from Uniswap trading incentives
    /// @param account the address to update
    /// @param isExempt a flag for whether to exempt or unexempt
    function setExemptAddress(address account, bool isExempt)
        external
        onlyAdmin
    {
        _exempt[account] = isExempt;
        emit ExemptAddressUpdate(account, isExempt);
    }

    /// @notice switch the sell penalty
    function switchSellPenalty() external onlyAdmin {
        isSellPenaltyOn = !isSellPenaltyOn;
    }

    /// @notice switch the buy incentive
    function switchBuyIncentive() external onlyAdmin {
        isBuyIncentiveOn = !isBuyIncentiveOn;
    }

    /// @notice returns true if account is marked as exempt
    function isExemptAddress(address account) public view returns (bool) {
        return _exempt[account];
    }

    function _incentivizeBuy(address target, uint256 amountIn) internal {
        _updateOracle();

        if (isExemptAddress(target) || !isBuyIncentiveOn) {
            return;
        }

        uint256 incentive = _getPercentDeviationFromUnderPeg(amountIn);
        /* swapping 3CRV (or underlying) for uAD (aka buying uAD) will mint x% of uGOV.
             Where x = (1- TWAP_Price) * amountIn.
            E.g. uAD = 0.8, you buy 1000 uAD, you get (1-0.8)*1000 = 200 uGOV */

        if (incentive != 0) {
            // this means CurveIncentive should be a minter of UGOV
            IUbiquityGovernance(manager.governanceTokenAddress()).mint(
                target,
                incentive
            );
        }
    }

    /// @notice returns the percentage of deviation from the peg multiplied by amount
    //          when uAD is <1$
    function _getPercentDeviationFromUnderPeg(uint256 amount)
        internal
        returns (uint256)
    {
        _updateOracle();
        uint256 curPrice = _getTWAPPrice();
        if (curPrice >= 1 ether) {
            return 0;
        }

        uint256 res = _one
            .sub(curPrice.fromUInt())
            .mul((amount.fromUInt().div(_one)))
            .toUInt();
        // returns (1- TWAP_Price) * amount.
        return res;
    }

    function _incentivizeSell(address target, uint256 amount) internal {
        _updateOracle();
        if (isExemptAddress(target) || !isSellPenaltyOn) {
            return;
        }

        /*
        WARNING
        From curve doc :Tokens that take a fee upon a successful transfer may cause the curve pool
        to break or act in unexpected ways.
        fei does it differently because they can make sure only one contract has the ability to sell
        uAD and they control the whole liquidity pool on uniswap.
        here to avoid problem with the curve pool we execute the transfer as specified and then we
        take the penalty so if penalty + amount > balance then we revert
        swapping uAD for 3CRV (or underlying) (aka selling uAD) will burn x% of uAD
        Where x = (1- TWAP_Price) *100.
        */

        uint256 penalty = _getPercentDeviationFromUnderPeg(amount);
        if (penalty != 0) {
            require(penalty < amount, "Dollar: burn exceeds trade size");

            require(
                UbiquityAlgorithmicDollar(manager.dollarTokenAddress())
                    .balanceOf(target) >= penalty + amount,
                "Dollar: balance too low to get penalized"
            );
            UbiquityAlgorithmicDollar(manager.dollarTokenAddress()).burnFrom(
                target,
                penalty
            ); // burn from the recipient
        }
    }

    function _updateOracle() internal {
        TWAPOracle(manager.twapOracleAddress()).update();
    }

    function _getTWAPPrice() internal view returns (uint256) {
        return
            TWAPOracle(manager.twapOracleAddress()).consult(
                manager.dollarTokenAddress()
            );
    }
}

// File: contracts/Bonding.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import "./interfaces/IERC1155Ubiquity.sol";
import "./interfaces/IMetaPool.sol";
import "./interfaces/IUbiquityFormulas.sol";
import "./UbiquityAlgorithmicDollar.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./interfaces/ISablier.sol";
import "./interfaces/IMasterChef.sol";
import "./interfaces/ITWAPOracle.sol";
import "./interfaces/IERC1155Ubiquity.sol";
import "./utils/CollectableDust.sol";

contract Bonding is CollectableDust {
    using SafeERC20 for IERC20;

    bytes public data = "";
    UbiquityAlgorithmicDollarManager public manager;

    uint256 public constant ONE = uint256(1 ether); // 3Crv has 18 decimals
    ISablier public sablier;
    uint256 public bondingDiscountMultiplier = uint256(1000000 gwei); // 0.001
    uint256 public redeemStreamTime = 86400; // 1 day in seconds
    uint256 public blockCountInAWeek = 45361;
    uint256 public blockRonding = 100;
    uint256 public uGOVPerBlock = 1;

    event MaxBondingPriceUpdated(uint256 _maxBondingPrice);
    event SablierUpdated(address _sablier);
    event BondingDiscountMultiplierUpdated(uint256 _bondingDiscountMultiplier);
    event RedeemStreamTimeUpdated(uint256 _redeemStreamTime);
    event BlockRondingUpdated(uint256 _blockRonding);
    event BlockCountInAWeekUpdated(uint256 _blockCountInAWeek);
    event UGOVPerBlockUpdated(uint256 _uGOVPerBlock);

    modifier onlyBondingManager() {
        require(
            manager.hasRole(manager.BONDING_MANAGER_ROLE(), msg.sender),
            "Caller is not a bonding manager"
        );
        _;
    }

    constructor(address _manager, address _sablier) CollectableDust() {
        manager = UbiquityAlgorithmicDollarManager(_manager);
        sablier = ISablier(_sablier);
    }

    // solhint-disable-next-line no-empty-blocks
    receive() external payable {}

    /// @dev uADPriceReset remove uAD unilateraly from the curve LP share sitting inside
    ///      the bonding contract and send the uAD received to the treasury.
    ///      This will have the immediate effect of pushing the uAD price HIGHER
    /// @param amount of LP token to be removed for uAD
    /// @notice it will remove one coin only from the curve LP share sitting in the bonding contract
    function uADPriceReset(uint256 amount) external onlyBondingManager {
        IMetaPool metaPool = IMetaPool(manager.stableSwapMetaPoolAddress());
        // safe approve
        IERC20(manager.stableSwapMetaPoolAddress()).safeApprove(
            address(this),
            amount
        );
        // remove one coin
        uint256 expected = (metaPool.calc_withdraw_one_coin(amount, 0) * 99) /
            100;
        // update twap
        metaPool.remove_liquidity_one_coin(amount, 0, expected);
        ITWAPOracle(manager.twapOracleAddress()).update();
        IERC20(manager.dollarTokenAddress()).safeTransfer(
            manager.treasuryAddress(),
            IERC20(manager.dollarTokenAddress()).balanceOf(address(this))
        );
    }

    /// @dev crvPriceReset remove 3CRV unilateraly from the curve LP share sitting inside
    ///      the bonding contract and send the 3CRV received to the treasury
    ///      This will have the immediate effect of pushing the uAD price LOWER
    /// @param amount of LP token to be removed for 3CRV tokens
    /// @notice it will remove one coin only from the curve LP share sitting in the bonding contract
    function crvPriceReset(uint256 amount) external onlyBondingManager {
        IMetaPool metaPool = IMetaPool(manager.stableSwapMetaPoolAddress());
        // safe approve
        IERC20(manager.stableSwapMetaPoolAddress()).safeApprove(
            address(this),
            amount
        );
        // remove one coin
        uint256 expected = (metaPool.calc_withdraw_one_coin(amount, 1) * 99) /
            100;
        // update twap
        metaPool.remove_liquidity_one_coin(amount, 1, expected);
        ITWAPOracle(manager.twapOracleAddress()).update();
        IERC20(manager.curve3PoolTokenAddress()).safeTransfer(
            manager.treasuryAddress(),
            IERC20(manager.curve3PoolTokenAddress()).balanceOf(address(this))
        );
    }

    /// Collectable Dust
    function addProtocolToken(address _token)
        external
        override
        onlyBondingManager
    {
        _addProtocolToken(_token);
    }

    function removeProtocolToken(address _token)
        external
        override
        onlyBondingManager
    {
        _removeProtocolToken(_token);
    }

    function sendDust(
        address _to,
        address _token,
        uint256 _amount
    ) external override onlyBondingManager {
        _sendDust(_to, _token, _amount);
    }

    function setSablier(address _sablier) external onlyBondingManager {
        sablier = ISablier(_sablier);
        emit SablierUpdated(_sablier);
    }

    function setBondingDiscountMultiplier(uint256 _bondingDiscountMultiplier)
        external
        onlyBondingManager
    {
        bondingDiscountMultiplier = _bondingDiscountMultiplier;
        emit BondingDiscountMultiplierUpdated(_bondingDiscountMultiplier);
    }

    function setRedeemStreamTime(uint256 _redeemStreamTime)
        external
        onlyBondingManager
    {
        redeemStreamTime = _redeemStreamTime;
        emit RedeemStreamTimeUpdated(_redeemStreamTime);
    }

    function setBlockRonding(uint256 _blockRonding)
        external
        onlyBondingManager
    {
        blockRonding = _blockRonding;
        emit BlockRondingUpdated(_blockRonding);
    }

    function setBlockCountInAWeek(uint256 _blockCountInAWeek)
        external
        onlyBondingManager
    {
        blockCountInAWeek = _blockCountInAWeek;
        emit BlockCountInAWeekUpdated(_blockCountInAWeek);
    }

    function setUGOVPerBlock(uint256 _uGOVPerBlock)
        external
        onlyBondingManager
    {
        uGOVPerBlock = _uGOVPerBlock;
        emit UGOVPerBlockUpdated(_uGOVPerBlock);
    }

    /// @dev deposit uAD-3CRV LP tokens for a duration to receive bonding shares
    /// @param _lpsAmount of LP token to send
    /// @param _weeks during lp token will be held
    /// @notice weeks act as a multiplier for the amount of bonding shares to be received
    function deposit(uint256 _lpsAmount, uint256 _weeks)
        public
        returns (uint256 _id)
    {
        require(
            1 <= _weeks && _weeks <= 208,
            "Bonding: duration must be between 1 and 208 weeks"
        );
        _updateOracle();

        IERC20(manager.stableSwapMetaPoolAddress()).safeTransferFrom(
            msg.sender,
            address(this),
            _lpsAmount
        );

        uint256 _sharesAmount = IUbiquityFormulas(manager.formulasAddress())
            .durationMultiply(_lpsAmount, _weeks, bondingDiscountMultiplier);

        // 1 week = 45361 blocks = 2371753*7/366
        // n = (block + duration * 45361)
        // id = n - n % blockRonding
        // blockRonding = 100 => 2 ending zeros
        uint256 n = block.number + _weeks * blockCountInAWeek;
        _id = n - (n % blockRonding);
        _mint(_sharesAmount, _id);
        // set masterchef for uGOV rewards
        IMasterChef(manager.masterChefAddress()).deposit(
            _sharesAmount,
            msg.sender
        );
    }

    /// @dev withdraw an amount of uAD-3CRV LP tokens
    /// @param _sharesAmount of bonding shares of type _id to be withdrawn
    /// @param _id bonding shares id
    /// @notice bonding shares are ERC1155 (aka NFT) because they have an expiration date
    function withdraw(uint256 _sharesAmount, uint256 _id) public {
        require(
            block.number > _id,
            "Bonding: Redeem not allowed before bonding time"
        );

        require(
            IERC1155Ubiquity(manager.bondingShareAddress()).balanceOf(
                msg.sender,
                _id
            ) >= _sharesAmount,
            "Bonding: caller does not have enough shares"
        );

        _updateOracle();
        // get masterchef for uGOV rewards To ensure correct computation
        // it needs to be done BEFORE burning the shares
        IMasterChef(manager.masterChefAddress()).withdraw(
            _sharesAmount,
            msg.sender
        );

        uint256 _currentShareValue = currentShareValue();

        IERC1155Ubiquity(manager.bondingShareAddress()).burn(
            msg.sender,
            _id,
            _sharesAmount
        );

        // if (redeemStreamTime == 0) {
        IERC20(manager.stableSwapMetaPoolAddress()).safeTransfer(
            msg.sender,
            IUbiquityFormulas(manager.formulasAddress()).redeemBonds(
                _sharesAmount,
                _currentShareValue,
                ONE
            )
        );
    }

    function currentShareValue() public view returns (uint256 priceShare) {
        uint256 totalLP = IERC20(manager.stableSwapMetaPoolAddress()).balanceOf(
            address(this)
        );

        uint256 totalShares = IERC1155Ubiquity(manager.bondingShareAddress())
            .totalSupply();

        priceShare = IUbiquityFormulas(manager.formulasAddress()).bondPrice(
            totalLP,
            totalShares,
            ONE
        );
    }

    function currentTokenPrice() public view returns (uint256) {
        return
            ITWAPOracle(manager.twapOracleAddress()).consult(
                manager.dollarTokenAddress()
            );
    }

    function _mint(uint256 _sharesAmount, uint256 _id) internal {
        uint256 _currentShareValue = currentShareValue();
        require(
            _currentShareValue != 0,
            "Bonding: share value should not be null"
        );

        IERC1155Ubiquity(manager.bondingShareAddress()).mint(
            msg.sender,
            _id,
            _sharesAmount,
            data
        );
    }

    function _updateOracle() internal {
        ITWAPOracle(manager.twapOracleAddress()).update();
    }
}

// File: contracts/interfaces/IMasterChef.sol



// SPDX-License-Identifier: UNLICENSED
// !! THIS FILE WAS AUTOGENERATED BY abi-to-sol. SEE BELOW FOR SOURCE. !!
pragma solidity ^0.8.3;

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

interface IMasterChef {
    struct UserInfo {
        uint256 amount; // How many LP tokens the user has provided.
        uint256 rewardDebt; // Reward debt. See explanation below.
    }
    struct PoolInfo {
        uint256 lastRewardBlock; // Last block number that SUSHI distribution occurs.
        uint256 accuGOVPerShare; // Accumulated SUSHI per share, times 1e12. See below.
    }

    event Deposit(address indexed user, uint256 amount);
    event Withdraw(address indexed user, uint256 amount);

    function deposit(uint256 _amount, address sender) external;

    // Withdraw LP tokens from MasterChef.
    function withdraw(uint256 _amount, address sender) external;

    // View function to see pending SUSHIs on frontend.
    function pendingUGOV(address _user) external view returns (uint256);
}

// THIS FILE WAS AUTOGENERATED FROM THE FOLLOWING ABI JSON:

// File: contracts/CouponsForDollarsCalculator.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.3;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./interfaces/ICouponsForDollarsCalculator.sol";
import "./UbiquityAlgorithmicDollarManager.sol";
import "./libs/ABDKMathQuad.sol";
import "./DebtCoupon.sol";

/// @title Uses the following formula: ((1/(1-R)^2) - 1)
contract CouponsForDollarsCalculator is ICouponsForDollarsCalculator {
    using ABDKMathQuad for uint256;
    using ABDKMathQuad for bytes16;
    UbiquityAlgorithmicDollarManager public manager;

    /*   using ABDKMath64x64 for uint256;
    using ABDKMath64x64 for int128;*/

    /// @param _manager the address of the manager/config contract so we can fetch variables
    constructor(address _manager) {
        manager = UbiquityAlgorithmicDollarManager(_manager);
    }

    function getCouponAmount(uint256 dollarsToBurn)
        external
        view
        override
        returns (uint256)
    {
        require(
            DebtCoupon(manager.debtCouponAddress()).getTotalOutstandingDebt() <
                IERC20(manager.dollarTokenAddress()).totalSupply(),
            "Coupon to dollar: DEBT_TOO_HIGH"
        );
        bytes16 one = uint256(1).fromUInt();
        bytes16 totalDebt = DebtCoupon(manager.debtCouponAddress())
            .getTotalOutstandingDebt()
            .fromUInt();
        bytes16 r = totalDebt.div(
            IERC20(manager.dollarTokenAddress()).totalSupply().fromUInt()
        );

        bytes16 oneMinusRAllSquared = (one.sub(r)).mul(one.sub(r));

        bytes16 res = one.div(oneMinusRAllSquared);

        return res.mul(dollarsToBurn.fromUInt()).toUInt();
    }
}