// File: contracts/Hypervisor.sol



// SPDX-License-Identifier: BUSL-1.1

pragma solidity 0.7.6;

import "@openzeppelin/contracts/math/Math.sol";
import "@openzeppelin/contracts/math/SafeMath.sol";
import "@openzeppelin/contracts/math/SignedSafeMath.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/SafeERC20.sol";
import "@openzeppelin/contracts/drafts/ERC20Permit.sol";
import "@openzeppelin/contracts/utils/ReentrancyGuard.sol";

import "./algebra/interfaces/callback/IAlgebraMintCallback.sol";
import "./algebra/interfaces/IAlgebraPool.sol";
import "./algebra/libraries/TickMath.sol";
import "@uniswap/v3-core/contracts/libraries/FullMath.sol";
import "@uniswap/v3-periphery/contracts/libraries/LiquidityAmounts.sol";

/// @title Hypervisor 1.3.1
/// @notice A Uniswap V2-like interface with fungible liquidity to Quickswap
/// which allows for arbitrary liquidity provision: one-sided, lop-sided, and balanced
contract Hypervisor is IAlgebraMintCallback, ERC20Permit, ReentrancyGuard {
    using SafeERC20 for IERC20;
    using SafeMath for uint256;
    using SignedSafeMath for int256;

    IAlgebraPool public pool;
    IERC20 public token0;
    IERC20 public token1;
    uint8 public fee = 5;
    int24 public tickSpacing;

    int24 public baseLower;
    int24 public baseUpper;
    int24 public limitLower;
    int24 public limitUpper;

    address public owner;
    uint256 public deposit0Max;
    uint256 public deposit1Max;
    uint256 public maxTotalSupply;
    address public whitelistedAddress;
    address public feeRecipient;
    bool public directDeposit; /// enter uni on deposit (avoid if client uses public rpc)

    uint256 public constant PRECISION = 1e36;

    bool mintCalled;

   event Deposit(
        address indexed sender,
        address indexed to,
        uint256 shares,
        uint256 amount0,
        uint256 amount1
    );

    event Withdraw(
        address indexed sender,
        address indexed to,
        uint256 shares,
        uint256 amount0,
        uint256 amount1
    );

    event Rebalance(
        int24 tick,
        uint256 totalAmount0,
        uint256 totalAmount1,
        uint256 feeAmount0,
        uint256 feeAmount1,
        uint256 totalSupply
    );

    event ZeroBurn(uint8 fee, uint256 fees0, uint256 fees1);
    event SetFee(uint8 newFee);


    /// @param _pool Uniswap V3 pool for which liquidity is managed
    /// @param _owner Owner of the Hypervisor
    constructor(
        address _pool,
        address _owner,
        string memory name,
        string memory symbol
    ) ERC20Permit(name) ERC20(name, symbol) {
        require(_pool != address(0));
        require(_owner != address(0));
        pool = IAlgebraPool(_pool);
        token0 = IERC20(pool.token0());
        token1 = IERC20(pool.token1());
        require(address(token0) != address(0));
        require(address(token1) != address(0));
        tickSpacing = pool.tickSpacing();

        owner = _owner;

        maxTotalSupply = 0; /// no cap
        deposit0Max = uint256(-1);
        deposit1Max = uint256(-1);
    }

    /// @notice Deposit tokens
    /// @param deposit0 Amount of token0 transfered from sender to Hypervisor
    /// @param deposit1 Amount of token1 transfered from sender to Hypervisor
    /// @param to Address to which liquidity tokens are minted
    /// @param from Address from which asset tokens are transferred
    /// @param inMin min spend for directDeposit is true 
    /// @return shares Quantity of liquidity tokens minted as a result of deposit
    function deposit(
        uint256 deposit0,
        uint256 deposit1,
        address to,
        address from,
        uint256[4] memory inMin
    ) nonReentrant external returns (uint256 shares) {
        require(deposit0 > 0 || deposit1 > 0);
        require(deposit0 <= deposit0Max && deposit1 <= deposit1Max);
        require(to != address(0) && to != address(this), "to");
        require(msg.sender == whitelistedAddress, "WHE");

        /// update fees
        zeroBurn();

        uint160 sqrtPrice = TickMath.getSqrtRatioAtTick(currentTick());
        uint256 price = FullMath.mulDiv(uint256(sqrtPrice).mul(uint256(sqrtPrice)), PRECISION, 2**(96 * 2));

        (uint256 pool0, uint256 pool1) = getTotalAmounts();

        shares = deposit1.add(deposit0.mul(price).div(PRECISION));

        if (deposit0 > 0) {
          token0.safeTransferFrom(from, address(this), deposit0);
        }
        if (deposit1 > 0) {
          token1.safeTransferFrom(from, address(this), deposit1);
        }

        uint256 total = totalSupply();
        if (total != 0) {
          uint256 pool0PricedInToken1 = pool0.mul(price).div(PRECISION);
          shares = shares.mul(total).div(pool0PricedInToken1.add(pool1));
          if (directDeposit) {
            uint128 liquidity = _liquidityForAmounts(
              baseLower,
              baseUpper, 
              token0.balanceOf(address(this)),
              token1.balanceOf(address(this))
            );
            _mintLiquidity(baseLower, baseUpper, liquidity, address(this), inMin[0], inMin[1]);
            liquidity = _liquidityForAmounts(
              limitLower,
              limitUpper, 
              token0.balanceOf(address(this)),
              token1.balanceOf(address(this))
            );
            _mintLiquidity(limitLower, limitUpper, liquidity, address(this), inMin[2], inMin[3]);
          }
        }
        _mint(to, shares);
        emit Deposit(from, to, shares, deposit0, deposit1);
        /// Check total supply cap not exceeded. A value of 0 means no limit.
        require(maxTotalSupply == 0 || total <= maxTotalSupply, "max");
    }

    function _zeroBurn(int24 tickLower, int24 tickUpper) internal returns(uint128 liquidity) {
      /// update fees for inclusion
      (liquidity, ,) = _position(tickLower, tickUpper);
      if(liquidity > 0) {
        pool.burn(tickLower, tickUpper, 0);
        (uint256 owed0, uint256 owed1) = pool.collect(address(this), tickLower, tickUpper, type(uint128).max, type(uint128).max);
        emit ZeroBurn(fee, owed0, owed1);
        if (owed0.div(fee) > 0 && token0.balanceOf(address(this)) > 0) token0.safeTransfer(feeRecipient, owed0.div(fee));
        if (owed1.div(fee) > 0 && token1.balanceOf(address(this)) > 0) token1.safeTransfer(feeRecipient, owed1.div(fee));
      }      
    }

    /// @notice Update fees of the positions
    /// @return baseLiquidity Fee of base position
    /// @return limitLiquidity Fee of limit position
    function zeroBurn() internal returns(uint128 baseLiquidity, uint128 limitLiquidity) {
      baseLiquidity = _zeroBurn(baseLower, baseUpper);
      limitLiquidity = _zeroBurn(limitLower, limitUpper); 
    }

    /// @notice Pull liquidity tokens from liquidity and receive the tokens
    /// @param shares Number of liquidity tokens to pull from liquidity
    /// @param tickLower lower tick
    /// @param tickUpper upper tick
    /// @param amountMin min outs 
    /// @return amount0 amount of token0 received from base position
    /// @return amount1 amount of token1 received from base position
    function pullLiquidity(
        int24 tickLower,
        int24 tickUpper,
        uint128 shares,
        uint256[2] memory amountMin
    ) external onlyOwner returns (uint256 amount0, uint256 amount1) {
        _zeroBurn(tickLower, tickUpper);
        (amount0, amount1) = _burnLiquidity(
          tickLower,
          tickUpper,
          _liquidityForShares(tickLower, tickUpper, shares),
          address(this),
          false,
          amountMin[0],
          amountMin[1]
        );
    }

    /// @param shares Number of liquidity tokens to redeem as pool assets
    /// @param to Address to which redeemed pool assets are sent
    /// @param from Address from which liquidity tokens are sent
    /// @param minAmounts min amount0,1 returned for shares of liq 
    /// @return amount0 Amount of token0 redeemed by the submitted liquidity tokens
    /// @return amount1 Amount of token1 redeemed by the submitted liquidity tokens
    function withdraw(
        uint256 shares,
        address to,
        address from,
        uint256[4] memory minAmounts
    ) nonReentrant external returns (uint256 amount0, uint256 amount1) {
        require(shares > 0, "shares");
        require(to != address(0), "to");

        /// update fees
        zeroBurn();

        /// Withdraw liquidity from Uniswap pool
        (uint256 base0, uint256 base1) = _burnLiquidity(
            baseLower,
            baseUpper,
            _liquidityForShares(baseLower, baseUpper, shares),
            to,
            false,
            minAmounts[0],
            minAmounts[1]
        );
        (uint256 limit0, uint256 limit1) = _burnLiquidity(
            limitLower,
            limitUpper,
            _liquidityForShares(limitLower, limitUpper, shares),
            to,
            false,
            minAmounts[2],
            minAmounts[3]
        );

        // Push tokens proportional to unused balances
        uint256 unusedAmount0 = token0.balanceOf(address(this)).mul(shares).div(totalSupply());
        uint256 unusedAmount1 = token1.balanceOf(address(this)).mul(shares).div(totalSupply());
        if (unusedAmount0 > 0) token0.safeTransfer(to, unusedAmount0);
        if (unusedAmount1 > 0) token1.safeTransfer(to, unusedAmount1);

        amount0 = base0.add(limit0).add(unusedAmount0);
        amount1 = base1.add(limit1).add(unusedAmount1);

        require( from == msg.sender, "own");
        _burn(from, shares);

        emit Withdraw(from, to, shares, amount0, amount1);
    }

    /// @param _baseLower The lower tick of the base position
    /// @param _baseUpper The upper tick of the base position
    /// @param _limitLower The lower tick of the limit position
    /// @param _limitUpper The upper tick of the limit position
    /// @param  inMin min spend 
    /// @param  outMin min amount0,1 returned for shares of liq 
    /// @param _feeRecipient Address of recipient of 10% of earned fees since last rebalance
    function rebalance(
        int24 _baseLower,
        int24 _baseUpper,
        int24 _limitLower,
        int24 _limitUpper,
        address _feeRecipient,
        uint256[4] memory inMin, 
        uint256[4] memory outMin
    ) nonReentrant external onlyOwner {
        require(
            _baseLower < _baseUpper &&
                _baseLower % tickSpacing == 0 &&
                _baseUpper % tickSpacing == 0
        );
        require(
            _limitLower < _limitUpper &&
                _limitLower % tickSpacing == 0 &&
                _limitUpper % tickSpacing == 0
        );
        require(
          _limitUpper != _baseUpper ||
          _limitLower != _baseLower
        );
        require(_feeRecipient != address(0));
        feeRecipient = _feeRecipient;

        /// update fees
        zeroBurn();

        /// Withdraw all liquidity and collect all fees from Uniswap pool
        (uint128 baseLiquidity, uint256 feesLimit0, uint256 feesLimit1) = _position(baseLower, baseUpper);
        (uint128 limitLiquidity, uint256 feesBase0, uint256 feesBase1) = _position(limitLower, limitUpper);

        _burnLiquidity(baseLower, baseUpper, baseLiquidity, address(this), true, outMin[0], outMin[1]);
        _burnLiquidity(limitLower, limitUpper, limitLiquidity, address(this), true, outMin[2], outMin[3]);

        emit Rebalance(
            currentTick(),
            token0.balanceOf(address(this)),
            token1.balanceOf(address(this)),
            feesBase0.add(feesLimit0),
            feesBase1.add(feesLimit1),
            totalSupply()
        );

        baseLower = _baseLower;
        baseUpper = _baseUpper;
        baseLiquidity = _liquidityForAmounts(
          baseLower,
          baseUpper, 
          token0.balanceOf(address(this)),
          token1.balanceOf(address(this))
        );
        _mintLiquidity(baseLower, baseUpper, baseLiquidity, address(this), inMin[0], inMin[1]);

        limitLower = _limitLower;
        limitUpper = _limitUpper;
        limitLiquidity = _liquidityForAmounts(
          limitLower,
          limitUpper, 
          token0.balanceOf(address(this)),
          token1.balanceOf(address(this))
        );
        _mintLiquidity(limitLower, limitUpper, limitLiquidity, address(this), inMin[2], inMin[3]);
    }

    /// @notice Compound pending fees
    /// @param inMin min spend 
    /// @return baseToken0Owed Pending fees of base token0
    /// @return baseToken1Owed Pending fees of base token1
    /// @return limitToken0Owed Pending fees of limit token0
    /// @return limitToken1Owed Pending fees of limit token1
    function compound(uint256[4] memory inMin) external onlyOwner returns (
        uint128 baseToken0Owed,
        uint128 baseToken1Owed,
        uint128 limitToken0Owed,
        uint128 limitToken1Owed 
    ) {
        // update fees for compounding
        zeroBurn();

        uint128 liquidity = _liquidityForAmounts(
          baseLower,
          baseUpper, 
          token0.balanceOf(address(this)),
          token1.balanceOf(address(this))
        );
        _mintLiquidity(baseLower, baseUpper, liquidity, address(this), inMin[0], inMin[1]);

        liquidity = _liquidityForAmounts(
          limitLower,
          limitUpper, 
          token0.balanceOf(address(this)),
          token1.balanceOf(address(this))
        );
        _mintLiquidity(limitLower, limitUpper, liquidity, address(this), inMin[2], inMin[3]);
    }

    /// @notice Add Liquidity
    function addLiquidity(
        int24 tickLower,
        int24 tickUpper,
        uint256 amount0,
        uint256 amount1,
        uint256[2] memory inMin
    ) public onlyOwner {        
        _zeroBurn(tickLower, tickUpper);
        uint128 liquidity = _liquidityForAmounts(tickLower, tickUpper, amount0, amount1);
        _mintLiquidity(tickLower, tickUpper, liquidity, address(this), inMin[0], inMin[1]);
    }

    /// @notice Adds the liquidity for the given position
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param liquidity The amount of liquidity to mint
    /// @param payer Payer Data
    /// @param amount0Min Minimum amount of token0 that should be paid
    /// @param amount1Min Minimum amount of token1 that should be paid
    function _mintLiquidity(
        int24 tickLower,
        int24 tickUpper,
        uint128 liquidity,
        address payer,
        uint256 amount0Min,
        uint256 amount1Min
    ) internal {
        if (liquidity > 0) {
            mintCalled = true;
            (uint256 amount0, uint256 amount1, ) = pool.mint(
                address(this),
                address(this),
                tickLower,
                tickUpper,
                liquidity,
                abi.encode(payer)
            );
            require(amount0 >= amount0Min && amount1 >= amount1Min, 'PSC');
        }
    }

    /// @notice Burn liquidity from the sender and collect tokens owed for the liquidity
    /// @param tickLower The lower tick of the position for which to burn liquidity
    /// @param tickUpper The upper tick of the position for which to burn liquidity
    /// @param liquidity The amount of liquidity to burn
    /// @param to The address which should receive the fees collected
    /// @param collectAll If true, collect all tokens owed in the pool, else collect the owed tokens of the burn
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function _burnLiquidity(
        int24 tickLower,
        int24 tickUpper,
        uint128 liquidity,
        address to,
        bool collectAll,
        uint256 amount0Min,
        uint256 amount1Min
    ) internal returns (uint256 amount0, uint256 amount1) {
        if (liquidity > 0) {
            /// Burn liquidity
            (uint256 owed0, uint256 owed1) = pool.burn(tickLower, tickUpper, liquidity);
            require(owed0 >= amount0Min && owed1 >= amount1Min, "PSC");

            // Collect amount owed
            uint128 collect0 = collectAll ? type(uint128).max : _uint128Safe(owed0);
            uint128 collect1 = collectAll ? type(uint128).max : _uint128Safe(owed1);
            if (collect0 > 0 || collect1 > 0) {
                (amount0, amount1) = pool.collect(to, tickLower, tickUpper, collect0, collect1);
            }
        }
    }

    /// @notice Get the liquidity amount for given liquidity tokens
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param shares Shares of position
    /// @return The amount of liquidity toekn for shares
    function _liquidityForShares(
        int24 tickLower,
        int24 tickUpper,
        uint256 shares
    ) internal view returns (uint128) {
        (uint128 position, , ) = _position(tickLower, tickUpper);
        return _uint128Safe(uint256(position).mul(shares).div(totalSupply()));
    }

    /// @notice Get the info of the given position
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @return liquidity The amount of liquidity of the position
    /// @return tokensOwed0 Amount of token0 owed
    /// @return tokensOwed1 Amount of token1 owed
    function _position(int24 tickLower, int24 tickUpper)
        internal
        view
        returns (
            uint128 liquidity,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        )
    {
      bytes32 positionKey;
      address This = address(this);
      assembly {
        positionKey := or(shl(24, or(shl(24, This), and(tickLower, 0xFFFFFF))), and(tickUpper, 0xFFFFFF))
      }
        (liquidity, , , , tokensOwed0, tokensOwed1) = pool.positions(positionKey);
    }

    /// @notice Callback function of uniswapV3Pool mint
    function algebraMintCallback(
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external override {
        require(msg.sender == address(pool));
        require(mintCalled == true);
        mintCalled = false;

        if (amount0 > 0) token0.safeTransfer(msg.sender, amount0);
        if (amount1 > 0) token1.safeTransfer(msg.sender, amount1);
    }

    /// @return total0 Quantity of token0 in both positions and unused in the Hypervisor
    /// @return total1 Quantity of token1 in both positions and unused in the Hypervisor
    function getTotalAmounts() public view returns (uint256 total0, uint256 total1) {
        (, uint256 base0, uint256 base1) = getBasePosition();
        (, uint256 limit0, uint256 limit1) = getLimitPosition();
        total0 = token0.balanceOf(address(this)).add(base0).add(limit0);
        total1 = token1.balanceOf(address(this)).add(base1).add(limit1);
    }

    /// @return liquidity Amount of total liquidity in the base position
    /// @return amount0 Estimated amount of token0 that could be collected by
    /// burning the base position
    /// @return amount1 Estimated amount of token1 that could be collected by
    /// burning the base position
    function getBasePosition()
        public
        view
        returns (
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        )
    {
        (uint128 positionLiquidity, uint128 tokensOwed0, uint128 tokensOwed1) = _position(
            baseLower,
            baseUpper
        );
        (amount0, amount1) = _amountsForLiquidity(baseLower, baseUpper, positionLiquidity);
        amount0 = amount0.add(uint256(tokensOwed0));
        amount1 = amount1.add(uint256(tokensOwed1));
        liquidity = positionLiquidity;
    }

    /// @return liquidity Amount of total liquidity in the limit position
    /// @return amount0 Estimated amount of token0 that could be collected by
    /// burning the limit position
    /// @return amount1 Estimated amount of token1 that could be collected by
    /// burning the limit position
    function getLimitPosition()
        public
        view
        returns (
            uint128 liquidity,
            uint256 amount0,
            uint256 amount1
        )
    {
        (uint128 positionLiquidity, uint128 tokensOwed0, uint128 tokensOwed1) = _position(
            limitLower,
            limitUpper
        );
        (amount0, amount1) = _amountsForLiquidity(limitLower, limitUpper, positionLiquidity);
        amount0 = amount0.add(uint256(tokensOwed0));
        amount1 = amount1.add(uint256(tokensOwed1));
        liquidity = positionLiquidity;
    }

    /// @notice Get the amounts of the given numbers of liquidity tokens
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param liquidity The amount of liquidity tokens
    /// @return Amount of token0 and token1
    function _amountsForLiquidity(
        int24 tickLower,
        int24 tickUpper,
        uint128 liquidity
    ) internal view returns (uint256, uint256) {
        (uint160 sqrtRatioX96, , , , , , ) = pool.globalState();
        return
            LiquidityAmounts.getAmountsForLiquidity(
                sqrtRatioX96,
                TickMath.getSqrtRatioAtTick(tickLower),
                TickMath.getSqrtRatioAtTick(tickUpper),
                liquidity
            );
    }

    /// @notice Get the liquidity amount of the given numbers of token0 and token1
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount0 The amount of token0
    /// @param amount0 The amount of token1
    /// @return Amount of liquidity tokens
    function _liquidityForAmounts(
        int24 tickLower,
        int24 tickUpper,
        uint256 amount0,
        uint256 amount1
    ) internal view returns (uint128) {
        (uint160 sqrtRatioX96, , , , , , ) = pool.globalState();
        return
            LiquidityAmounts.getLiquidityForAmounts(
                sqrtRatioX96,
                TickMath.getSqrtRatioAtTick(tickLower),
                TickMath.getSqrtRatioAtTick(tickUpper),
                amount0,
                amount1
            );
    }

    /// @return tick Uniswap pool's current price tick
    function currentTick() public view returns (int24 tick) {
        (, tick, , , , , ) = pool.globalState();
    }

    function _uint128Safe(uint256 x) internal pure returns (uint128) {
        assert(x <= type(uint128).max);
        return uint128(x);
    }

    /// @param _address Array of addresses to be appended
    function setWhitelist(address _address) external onlyOwner {
        whitelistedAddress = _address;
    }

    /// @notice Remove Whitelisted
    function removeWhitelisted() external onlyOwner {
        whitelistedAddress = address(0);
    }

    /// @notice set fee 
    function setFee(uint8 newFee) external onlyOwner {
        fee = newFee;
        emit SetFee(fee);
    }

    /// @notice Toggle Direct Deposit
    function toggleDirectDeposit() external onlyOwner {
        directDeposit = !directDeposit;
    }

    function transferOwnership(address newOwner) external onlyOwner {
        require(newOwner != address(0));
        owner = newOwner;
    }

    modifier onlyOwner {
        require(msg.sender == owner, "only owner");
        _;
    }
}

// File: @openzeppelin/contracts/math/Math.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }

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

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

// File: @openzeppelin/contracts/math/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        uint256 c = a + b;
        if (c < a) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the substraction of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b > a) return (false, 0);
        return (true, a - b);
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an overflow flag.
     *
     * _Available since v3.4._
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) return (true, 0);
        uint256 c = a * b;
        if (c / a != b) return (false, 0);
        return (true, c);
    }

    /**
     * @dev Returns the division of two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a / b);
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
     *
     * _Available since v3.4._
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
        if (b == 0) return (false, 0);
        return (true, a % b);
    }

    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "SafeMath: subtraction overflow");
        return a - b;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) return 0;
        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");
        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: division by zero");
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b > 0, "SafeMath: modulo by zero");
        return a % b;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {trySub}.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        return a - b;
    }

    /**
     * @dev Returns the integer division of two unsigned integers, reverting with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryDiv}.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a / b;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * reverting with custom message when dividing by zero.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryMod}.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        return a % b;
    }
}

// File: @openzeppelin/contracts/math/SignedSafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @title SignedSafeMath
 * @dev Signed math operations with safety checks that revert on error.
 */
library SignedSafeMath {
    int256 constant private _INT256_MIN = -2**255;

    /**
     * @dev Returns the multiplication of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(int256 a, int256 b) internal pure returns (int256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        require(!(a == -1 && b == _INT256_MIN), "SignedSafeMath: multiplication overflow");

        int256 c = a * b;
        require(c / a == b, "SignedSafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two signed integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(int256 a, int256 b) internal pure returns (int256) {
        require(b != 0, "SignedSafeMath: division by zero");
        require(!(b == -1 && a == _INT256_MIN), "SignedSafeMath: division overflow");

        int256 c = a / b;

        return c;
    }

    /**
     * @dev Returns the subtraction of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a - b;
        require((b >= 0 && c <= a) || (b < 0 && c > a), "SignedSafeMath: subtraction overflow");

        return c;
    }

    /**
     * @dev Returns the addition of two signed integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a + b;
        require((b >= 0 && c >= a) || (b < 0 && c < a), "SignedSafeMath: addition overflow");

        return c;
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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: @openzeppelin/contracts/token/ERC20/SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "./IERC20.sol";
import "../../math/SafeMath.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 SafeMath for uint256;
    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'
        // solhint-disable-next-line max-line-length
        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).add(value);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).sub(value, "SafeERC20: decreased allowance below zero");
        _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
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: @openzeppelin/contracts/drafts/ERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.5 <0.8.0;

import "../token/ERC20/ERC20.sol";
import "./IERC20Permit.sol";
import "../cryptography/ECDSA.sol";
import "../utils/Counters.sol";
import "./EIP712.sol";

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping (address => Counters.Counter) private _nonces;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private immutable _PERMIT_TYPEHASH = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) internal EIP712(name, "1") {
    }

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public virtual override {
        // solhint-disable-next-line not-rely-on-time
        require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

        bytes32 structHash = keccak256(
            abi.encode(
                _PERMIT_TYPEHASH,
                owner,
                spender,
                value,
                _nonces[owner].current(),
                deadline
            )
        );

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "ERC20Permit: invalid signature");

        _nonces[owner].increment();
        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor () internal {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

        _;

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

// File: contracts/algebra/interfaces/callback/IAlgebraMintCallback.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Callback for IAlgebraPoolActions#mint
/// @notice Any contract that calls IAlgebraPoolActions#mint must implement this interface
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
interface IAlgebraMintCallback {
  /// @notice Called to `msg.sender` after minting liquidity to a position from IAlgebraPool#mint.
  /// @dev In the implementation you must pay the pool tokens owed for the minted liquidity.
  /// The caller of this method must be checked to be a AlgebraPool deployed by the canonical AlgebraFactory.
  /// @param amount0Owed The amount of token0 due to the pool for the minted liquidity
  /// @param amount1Owed The amount of token1 due to the pool for the minted liquidity
  /// @param data Any data passed through by the caller via the IAlgebraPoolActions#mint call
  function algebraMintCallback(
    uint256 amount0Owed,
    uint256 amount1Owed,
    bytes calldata data
  ) external;
}

// File: contracts/algebra/interfaces/IAlgebraPool.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import './pool/IAlgebraPoolImmutables.sol';
import './pool/IAlgebraPoolState.sol';
import './pool/IAlgebraPoolDerivedState.sol';
import './pool/IAlgebraPoolActions.sol';
import './pool/IAlgebraPoolPermissionedActions.sol';
import './pool/IAlgebraPoolEvents.sol';

/**
 * @title The interface for a Algebra Pool
 * @dev The pool interface is broken up into many smaller pieces.
 * Credit to Uniswap Labs under GPL-2.0-or-later license:
 * https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
 */
interface IAlgebraPool is
  IAlgebraPoolImmutables,
  IAlgebraPoolState,
  IAlgebraPoolDerivedState,
  IAlgebraPoolActions,
  IAlgebraPoolPermissionedActions,
  IAlgebraPoolEvents
{
  // used only for combining interfaces
}

// File: contracts/algebra/libraries/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries
library TickMath {
  /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
  int24 internal constant MIN_TICK = -887272;
  /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
  int24 internal constant MAX_TICK = -MIN_TICK;

  /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
  uint160 internal constant MIN_SQRT_RATIO = 4295128739;
  /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
  uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

  /// @notice Calculates sqrt(1.0001^tick) * 2^96
  /// @dev Throws if |tick| > max tick
  /// @param tick The input tick for the above formula
  /// @return price A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
  /// at the given tick
  function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 price) {
    // get abs value
    int24 mask = tick >> (24 - 1);
    uint256 absTick = uint256((tick ^ mask) - mask);
    require(absTick <= uint256(MAX_TICK), 'T');

    uint256 ratio = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
    if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
    if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
    if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
    if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
    if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
    if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
    if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
    if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
    if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
    if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
    if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
    if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
    if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
    if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
    if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
    if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
    if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
    if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
    if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;

    if (tick > 0) ratio = type(uint256).max / ratio;

    // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
    // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
    // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
    price = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
  }

  /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
  /// @dev Throws in case price < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
  /// ever return.
  /// @param price The sqrt ratio for which to compute the tick as a Q64.96
  /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
  function getTickAtSqrtRatio(uint160 price) internal pure returns (int24 tick) {
    // second inequality must be < because the price can never reach the price at the max tick
    require(price >= MIN_SQRT_RATIO && price < MAX_SQRT_RATIO, 'R');
    uint256 ratio = uint256(price) << 32;

    uint256 r = ratio;
    uint256 msb = 0;

    assembly {
      let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(5, gt(r, 0xFFFFFFFF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(4, gt(r, 0xFFFF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(3, gt(r, 0xFF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(2, gt(r, 0xF))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := shl(1, gt(r, 0x3))
      msb := or(msb, f)
      r := shr(f, r)
    }
    assembly {
      let f := gt(r, 0x1)
      msb := or(msb, f)
    }

    if (msb >= 128) r = ratio >> (msb - 127);
    else r = ratio << (127 - msb);

    int256 log_2 = (int256(msb) - 128) << 64;

    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(63, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(62, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(61, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(60, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(59, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(58, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(57, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(56, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(55, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(54, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(53, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(52, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(51, f))
      r := shr(f, r)
    }
    assembly {
      r := shr(127, mul(r, r))
      let f := shr(128, r)
      log_2 := or(log_2, shl(50, f))
    }

    int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

    int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
    int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);

    tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= price ? tickHi : tickLow;
  }
}

// File: @uniswap/v3-core/contracts/libraries/FullMath.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.4.0;

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 512-bit multiply [prod1 prod0] = a * b
        // Compute the product mod 2**256 and mod 2**256 - 1
        // then use the Chinese Remainder Theorem to reconstruct
        // the 512 bit result. The result is stored in two 256
        // variables such that product = prod1 * 2**256 + prod0
        uint256 prod0; // Least significant 256 bits of the product
        uint256 prod1; // Most significant 256 bits of the product
        assembly {
            let mm := mulmod(a, b, not(0))
            prod0 := mul(a, b)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        // Handle non-overflow cases, 256 by 256 division
        if (prod1 == 0) {
            require(denominator > 0);
            assembly {
                result := div(prod0, denominator)
            }
            return result;
        }

        // Make sure the result is less than 2**256.
        // Also prevents denominator == 0
        require(denominator > prod1);

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

        // Make division exact by subtracting the remainder from [prod1 prod0]
        // Compute remainder using mulmod
        uint256 remainder;
        assembly {
            remainder := mulmod(a, b, denominator)
        }
        // Subtract 256 bit number from 512 bit number
        assembly {
            prod1 := sub(prod1, gt(remainder, prod0))
            prod0 := sub(prod0, remainder)
        }

        // Factor powers of two out of denominator
        // Compute largest power of two divisor of denominator.
        // Always >= 1.
        uint256 twos = -denominator & denominator;
        // Divide denominator by power of two
        assembly {
            denominator := div(denominator, twos)
        }

        // Divide [prod1 prod0] by the factors of two
        assembly {
            prod0 := div(prod0, twos)
        }
        // Shift in bits from prod1 into prod0. For this we need
        // to flip `twos` such that it is 2**256 / twos.
        // If twos is zero, then it becomes one
        assembly {
            twos := add(div(sub(0, twos), twos), 1)
        }
        prod0 |= prod1 * twos;

        // Invert denominator mod 2**256
        // Now that denominator is an odd number, it has an inverse
        // modulo 2**256 such that denominator * inv = 1 mod 2**256.
        // Compute the inverse by starting with a seed that is correct
        // correct for four bits. That is, denominator * inv = 1 mod 2**4
        uint256 inv = (3 * denominator) ^ 2;
        // Now use Newton-Raphson iteration to improve the precision.
        // Thanks to Hensel's lifting lemma, this also works in modular
        // arithmetic, doubling the correct bits in each step.
        inv *= 2 - denominator * inv; // inverse mod 2**8
        inv *= 2 - denominator * inv; // inverse mod 2**16
        inv *= 2 - denominator * inv; // inverse mod 2**32
        inv *= 2 - denominator * inv; // inverse mod 2**64
        inv *= 2 - denominator * inv; // inverse mod 2**128
        inv *= 2 - denominator * inv; // inverse mod 2**256

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

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        result = mulDiv(a, b, denominator);
        if (mulmod(a, b, denominator) > 0) {
            require(result < type(uint256).max);
            result++;
        }
    }
}

// File: @uniswap/v3-periphery/contracts/libraries/LiquidityAmounts.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import '@uniswap/v3-core/contracts/libraries/FullMath.sol';
import '@uniswap/v3-core/contracts/libraries/FixedPoint96.sol';

/// @title Liquidity amount functions
/// @notice Provides functions for computing liquidity amounts from token amounts and prices
library LiquidityAmounts {
    /// @notice Downcasts uint256 to uint128
    /// @param x The uint258 to be downcasted
    /// @return y The passed value, downcasted to uint128
    function toUint128(uint256 x) private pure returns (uint128 y) {
        require((y = uint128(x)) == x);
    }

    /// @notice Computes the amount of liquidity received for a given amount of token0 and price range
    /// @dev Calculates amount0 * (sqrt(upper) * sqrt(lower)) / (sqrt(upper) - sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount0 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount0(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        uint256 intermediate = FullMath.mulDiv(sqrtRatioAX96, sqrtRatioBX96, FixedPoint96.Q96);
        return toUint128(FullMath.mulDiv(amount0, intermediate, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the amount of liquidity received for a given amount of token1 and price range
    /// @dev Calculates amount1 / (sqrt(upper) - sqrt(lower)).
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount1 The amount1 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount1(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        return toUint128(FullMath.mulDiv(amount1, FixedPoint96.Q96, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the maximum amount of liquidity received for a given amount of token0, token1, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount of token0 being sent in
    /// @param amount1 The amount of token1 being sent in
    /// @return liquidity The maximum amount of liquidity received
    function getLiquidityForAmounts(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            liquidity = getLiquidityForAmount0(sqrtRatioAX96, sqrtRatioBX96, amount0);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            uint128 liquidity0 = getLiquidityForAmount0(sqrtRatioX96, sqrtRatioBX96, amount0);
            uint128 liquidity1 = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioX96, amount1);

            liquidity = liquidity0 < liquidity1 ? liquidity0 : liquidity1;
        } else {
            liquidity = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioBX96, amount1);
        }
    }

    /// @notice Computes the amount of token0 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    function getAmount0ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return
            FullMath.mulDiv(
                uint256(liquidity) << FixedPoint96.RESOLUTION,
                sqrtRatioBX96 - sqrtRatioAX96,
                sqrtRatioBX96
            ) / sqrtRatioAX96;
    }

    /// @notice Computes the amount of token1 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount1 The amount of token1
    function getAmount1ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
    }

    /// @notice Computes the token0 and token1 value for a given amount of liquidity, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    /// @return amount1 The amount of token1
    function getAmountsForLiquidity(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0, uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioX96, sqrtRatioBX96, liquidity);
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioX96, liquidity);
        } else {
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        }
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.2 <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;
        // solhint-disable-next-line no-inline-assembly
        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");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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");

        // solhint-disable-next-line avoid-low-level-calls
        (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

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../../utils/Context.sol";
import "./IERC20.sol";
import "../../math/SafeMath.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 {
    using SafeMath for uint256;

    mapping (address => uint256) private _balances;

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

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;
    uint8 private _decimals;

    /**
     * @dev Sets the values for {name} and {symbol}, initializes {decimals} with
     * a default value of 18.
     *
     * To select a different value for {decimals}, use {_setupDecimals}.
     *
     * All three of these values are immutable: they can only be set once during
     * construction.
     */
    constructor (string memory name_, string memory symbol_) public {
        _name = name_;
        _symbol = symbol_;
        _decimals = 18;
    }

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

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual 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 {_setupDecimals} is
     * called.
     *
     * 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 returns (uint8) {
        return _decimals;
    }

    /**
     * @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);
        _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance"));
        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].add(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) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].sub(subtractedValue, "ERC20: decreased allowance below zero"));
        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is 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);

        _balances[sender] = _balances[sender].sub(amount, "ERC20: transfer amount exceeds balance");
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(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:
     *
     * - `to` 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 = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(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);

        _balances[account] = _balances[account].sub(amount, "ERC20: burn amount exceeds balance");
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(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 Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal virtual {
        _decimals = decimals_;
    }

    /**
     * @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 to 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 { }
}

// File: @openzeppelin/contracts/drafts/IERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

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

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

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

// File: @openzeppelin/contracts/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        // Check the signature length
        if (signature.length != 65) {
            revert("ECDSA: invalid signature length");
        }

        // Divide the signature in r, s and v variables
        bytes32 r;
        bytes32 s;
        uint8 v;

        // ecrecover takes the signature parameters, and the only way to get them
        // currently is to use assembly.
        // solhint-disable-next-line no-inline-assembly
        assembly {
            r := mload(add(signature, 0x20))
            s := mload(add(signature, 0x40))
            v := byte(0, mload(add(signature, 0x60)))
        }

        return recover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover-bytes32-bytes-} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (281): 0 < s < secp256k1n ÷ 2 + 1, and for v in (282): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        require(uint256(s) <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, "ECDSA: invalid signature 's' value");
        require(v == 27 || v == 28, "ECDSA: invalid signature 'v' value");

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        require(signer != address(0), "ECDSA: invalid signature");

        return signer;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * replicates the behavior of the
     * https://github.com/ethereum/wiki/wiki/JSON-RPC#eth_sign[`eth_sign`]
     * JSON-RPC method.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

import "../math/SafeMath.sol";

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 * Since it is not possible to overflow a 256 bit integer with increments of one, `increment` can skip the {SafeMath}
 * overflow check, thereby saving gas. This does assume however correct usage, in that the underlying `_value` is never
 * directly accessed.
 */
library Counters {
    using SafeMath for uint256;

    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        // The {SafeMath} overflow check can be skipped here, see the comment at the top
        counter._value += 1;
    }

    function decrement(Counter storage counter) internal {
        counter._value = counter._value.sub(1);
    }
}

// File: @openzeppelin/contracts/drafts/EIP712.sol



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;
    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) internal {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = _getChainId();
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view virtual returns (bytes32) {
        if (_getChainId() == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(bytes32 typeHash, bytes32 name, bytes32 version) private view returns (bytes32) {
        return keccak256(
            abi.encode(
                typeHash,
                name,
                version,
                _getChainId(),
                address(this)
            )
        );
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", _domainSeparatorV4(), structHash));
    }

    function _getChainId() private view returns (uint256 chainId) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        // solhint-disable-next-line no-inline-assembly
        assembly {
            chainId := chainid()
        }
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity >=0.6.0 <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 GSN 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 payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolImmutables.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import '../IDataStorageOperator.sol';

/// @title Pool state that never changes
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
interface IAlgebraPoolImmutables {
  /**
   * @notice The contract that stores all the timepoints and can perform actions with them
   * @return The operator address
   */
  function dataStorageOperator() external view returns (address);

  /**
   * @notice The contract that deployed the pool, which must adhere to the IAlgebraFactory interface
   * @return The contract address
   */
  function factory() external view returns (address);

  /**
   * @notice The first of the two tokens of the pool, sorted by address
   * @return The token contract address
   */
  function token0() external view returns (address);

  /**
   * @notice The second of the two tokens of the pool, sorted by address
   * @return The token contract address
   */
  function token1() external view returns (address);

  /**
   * @notice The pool tick spacing
   * @dev Ticks can only be used at multiples of this value
   * e.g.: a tickSpacing of 60 means ticks can be initialized every 60th tick, i.e., ..., -120, -60, 0, 60, 120, ...
   * This value is an int24 to avoid casting even though it is always positive.
   * @return The tick spacing
   */
  function tickSpacing() external view returns (int24);

  /**
   * @notice The maximum amount of position liquidity that can use any tick in the range
   * @dev This parameter is enforced per tick to prevent liquidity from overflowing a uint128 at any point, and
   * also prevents out-of-range liquidity from being used to prevent adding in-range liquidity to a pool
   * @return The max amount of liquidity per tick
   */
  function maxLiquidityPerTick() external view returns (uint128);
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that can change
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
interface IAlgebraPoolState {
  /**
   * @notice The globalState structure in the pool stores many values but requires only one slot
   * and is exposed as a single method to save gas when accessed externally.
   * @return price The current price of the pool as a sqrt(token1/token0) Q64.96 value;
   * Returns tick The current tick of the pool, i.e. according to the last tick transition that was run;
   * Returns This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(price) if the price is on a tick
   * boundary;
   * Returns fee The last pool fee value in hundredths of a bip, i.e. 1e-6;
   * Returns timepointIndex The index of the last written timepoint;
   * Returns communityFeeToken0 The community fee percentage of the swap fee in thousandths (1e-3) for token0;
   * Returns communityFeeToken1 The community fee percentage of the swap fee in thousandths (1e-3) for token1;
   * Returns unlocked Whether the pool is currently locked to reentrancy;
   */
  function globalState()
    external
    view
    returns (
      uint160 price,
      int24 tick,
      uint16 fee,
      uint16 timepointIndex,
      uint8 communityFeeToken0,
      uint8 communityFeeToken1,
      bool unlocked
    );

  /**
   * @notice The fee growth as a Q128.128 fees of token0 collected per unit of liquidity for the entire life of the pool
   * @dev This value can overflow the uint256
   */
  function totalFeeGrowth0Token() external view returns (uint256);

  /**
   * @notice The fee growth as a Q128.128 fees of token1 collected per unit of liquidity for the entire life of the pool
   * @dev This value can overflow the uint256
   */
  function totalFeeGrowth1Token() external view returns (uint256);

  /**
   * @notice The currently in range liquidity available to the pool
   * @dev This value has no relationship to the total liquidity across all ticks.
   * Returned value cannot exceed type(uint128).max
   */
  function liquidity() external view returns (uint128);

  /**
   * @notice Look up information about a specific tick in the pool
   * @dev This is a public structure, so the `return` natspec tags are omitted.
   * @param tick The tick to look up
   * @return liquidityTotal the total amount of position liquidity that uses the pool either as tick lower or
   * tick upper;
   * Returns liquidityDelta how much liquidity changes when the pool price crosses the tick;
   * Returns outerFeeGrowth0Token the fee growth on the other side of the tick from the current tick in token0;
   * Returns outerFeeGrowth1Token the fee growth on the other side of the tick from the current tick in token1;
   * Returns outerTickCumulative the cumulative tick value on the other side of the tick from the current tick;
   * Returns outerSecondsPerLiquidity the seconds spent per liquidity on the other side of the tick from the current tick;
   * Returns outerSecondsSpent the seconds spent on the other side of the tick from the current tick;
   * Returns initialized Set to true if the tick is initialized, i.e. liquidityTotal is greater than 0
   * otherwise equal to false. Outside values can only be used if the tick is initialized.
   * In addition, these values are only relative and must be used only in comparison to previous snapshots for
   * a specific position.
   */
  function ticks(int24 tick)
    external
    view
    returns (
      uint128 liquidityTotal,
      int128 liquidityDelta,
      uint256 outerFeeGrowth0Token,
      uint256 outerFeeGrowth1Token,
      int56 outerTickCumulative,
      uint160 outerSecondsPerLiquidity,
      uint32 outerSecondsSpent,
      bool initialized
    );

  /** @notice Returns 256 packed tick initialized boolean values. See TickTable for more information */
  function tickTable(int16 wordPosition) external view returns (uint256);

  /**
   * @notice Returns the information about a position by the position's key
   * @dev This is a public mapping of structures, so the `return` natspec tags are omitted.
   * @param key The position's key is a hash of a preimage composed by the owner, bottomTick and topTick
   * @return liquidityAmount The amount of liquidity in the position;
   * Returns lastLiquidityAddTimestamp Timestamp of last adding of liquidity;
   * Returns innerFeeGrowth0Token Fee growth of token0 inside the tick range as of the last mint/burn/poke;
   * Returns innerFeeGrowth1Token Fee growth of token1 inside the tick range as of the last mint/burn/poke;
   * Returns fees0 The computed amount of token0 owed to the position as of the last mint/burn/poke;
   * Returns fees1 The computed amount of token1 owed to the position as of the last mint/burn/poke
   */
  function positions(bytes32 key)
    external
    view
    returns (
      uint128 liquidityAmount,
      uint32 lastLiquidityAddTimestamp,
      uint256 innerFeeGrowth0Token,
      uint256 innerFeeGrowth1Token,
      uint128 fees0,
      uint128 fees1
    );

  /**
   * @notice Returns data about a specific timepoint index
   * @param index The element of the timepoints array to fetch
   * @dev You most likely want to use #getTimepoints() instead of this method to get an timepoint as of some amount of time
   * ago, rather than at a specific index in the array.
   * This is a public mapping of structures, so the `return` natspec tags are omitted.
   * @return initialized whether the timepoint has been initialized and the values are safe to use;
   * Returns blockTimestamp The timestamp of the timepoint;
   * Returns tickCumulative the tick multiplied by seconds elapsed for the life of the pool as of the timepoint timestamp;
   * Returns secondsPerLiquidityCumulative the seconds per in range liquidity for the life of the pool as of the timepoint timestamp;
   * Returns volatilityCumulative Cumulative standard deviation for the life of the pool as of the timepoint timestamp;
   * Returns averageTick Time-weighted average tick;
   * Returns volumePerLiquidityCumulative Cumulative swap volume per liquidity for the life of the pool as of the timepoint timestamp;
   */
  function timepoints(uint256 index)
    external
    view
    returns (
      bool initialized,
      uint32 blockTimestamp,
      int56 tickCumulative,
      uint160 secondsPerLiquidityCumulative,
      uint88 volatilityCumulative,
      int24 averageTick,
      uint144 volumePerLiquidityCumulative
    );

  /**
   * @notice Returns the information about active incentive
   * @dev if there is no active incentive at the moment, virtualPool,endTimestamp,startTimestamp would be equal to 0
   * @return virtualPool The address of a virtual pool associated with the current active incentive
   */
  function activeIncentive() external view returns (address virtualPool);

  /**
   * @notice Returns the lock time for added liquidity
   */
  function liquidityCooldown() external view returns (uint32 cooldownInSeconds);
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolDerivedState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/**
 * @title Pool state that is not stored
 * @notice Contains view functions to provide information about the pool that is computed rather than stored on the
 * blockchain. The functions here may have variable gas costs.
 * @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
 * https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
 */
interface IAlgebraPoolDerivedState {
  /**
   * @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
   * @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
   * the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
   * you must call it with secondsAgos = [3600, 0].
   * @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
   * log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
   * @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
   * @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
   * @return secondsPerLiquidityCumulatives Cumulative seconds per liquidity-in-range value as of each `secondsAgos`
   * from the current block timestamp
   * @return volatilityCumulatives Cumulative standard deviation as of each `secondsAgos`
   * @return volumePerAvgLiquiditys Cumulative swap volume per liquidity as of each `secondsAgos`
   */
  function getTimepoints(uint32[] calldata secondsAgos)
    external
    view
    returns (
      int56[] memory tickCumulatives,
      uint160[] memory secondsPerLiquidityCumulatives,
      uint112[] memory volatilityCumulatives,
      uint256[] memory volumePerAvgLiquiditys
    );

  /**
   * @notice Returns a snapshot of the tick cumulative, seconds per liquidity and seconds inside a tick range
   * @dev Snapshots must only be compared to other snapshots, taken over a period for which a position existed.
   * I.e., snapshots cannot be compared if a position is not held for the entire period between when the first
   * snapshot is taken and the second snapshot is taken.
   * @param bottomTick The lower tick of the range
   * @param topTick The upper tick of the range
   * @return innerTickCumulative The snapshot of the tick accumulator for the range
   * @return innerSecondsSpentPerLiquidity The snapshot of seconds per liquidity for the range
   * @return innerSecondsSpent The snapshot of the number of seconds during which the price was in this range
   */
  function getInnerCumulatives(int24 bottomTick, int24 topTick)
    external
    view
    returns (
      int56 innerTickCumulative,
      uint160 innerSecondsSpentPerLiquidity,
      uint32 innerSecondsSpent
    );
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissionless pool actions
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
interface IAlgebraPoolActions {
  /**
   * @notice Sets the initial price for the pool
   * @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value
   * @param price the initial sqrt price of the pool as a Q64.96
   */
  function initialize(uint160 price) external;

  /**
   * @notice Adds liquidity for the given recipient/bottomTick/topTick position
   * @dev The caller of this method receives a callback in the form of IAlgebraMintCallback# AlgebraMintCallback
   * in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
   * on bottomTick, topTick, the amount of liquidity, and the current price.
   * @param sender The address which will receive potential surplus of paid tokens
   * @param recipient The address for which the liquidity will be created
   * @param bottomTick The lower tick of the position in which to add liquidity
   * @param topTick The upper tick of the position in which to add liquidity
   * @param amount The desired amount of liquidity to mint
   * @param data Any data that should be passed through to the callback
   * @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
   * @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
   * @return liquidityActual The actual minted amount of liquidity
   */
  function mint(
    address sender,
    address recipient,
    int24 bottomTick,
    int24 topTick,
    uint128 amount,
    bytes calldata data
  )
    external
    returns (
      uint256 amount0,
      uint256 amount1,
      uint128 liquidityActual
    );

  /**
   * @notice Collects tokens owed to a position
   * @dev Does not recompute fees earned, which must be done either via mint or burn of any amount of liquidity.
   * Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
   * amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
   * actual tokens owed, e.g. type(uint128).max. Tokens owed may be from accumulated swap fees or burned liquidity.
   * @param recipient The address which should receive the fees collected
   * @param bottomTick The lower tick of the position for which to collect fees
   * @param topTick The upper tick of the position for which to collect fees
   * @param amount0Requested How much token0 should be withdrawn from the fees owed
   * @param amount1Requested How much token1 should be withdrawn from the fees owed
   * @return amount0 The amount of fees collected in token0
   * @return amount1 The amount of fees collected in token1
   */
  function collect(
    address recipient,
    int24 bottomTick,
    int24 topTick,
    uint128 amount0Requested,
    uint128 amount1Requested
  ) external returns (uint128 amount0, uint128 amount1);

  /**
   * @notice Burn liquidity from the sender and account tokens owed for the liquidity to the position
   * @dev Can be used to trigger a recalculation of fees owed to a position by calling with an amount of 0
   * @dev Fees must be collected separately via a call to #collect
   * @param bottomTick The lower tick of the position for which to burn liquidity
   * @param topTick The upper tick of the position for which to burn liquidity
   * @param amount How much liquidity to burn
   * @return amount0 The amount of token0 sent to the recipient
   * @return amount1 The amount of token1 sent to the recipient
   */
  function burn(
    int24 bottomTick,
    int24 topTick,
    uint128 amount
  ) external returns (uint256 amount0, uint256 amount1);

  /**
   * @notice Swap token0 for token1, or token1 for token0
   * @dev The caller of this method receives a callback in the form of IAlgebraSwapCallback# AlgebraSwapCallback
   * @param recipient The address to receive the output of the swap
   * @param zeroToOne The direction of the swap, true for token0 to token1, false for token1 to token0
   * @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
   * @param limitSqrtPrice The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
   * value after the swap. If one for zero, the price cannot be greater than this value after the swap
   * @param data Any data to be passed through to the callback. If using the Router it should contain
   * SwapRouter#SwapCallbackData
   * @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
   * @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
   */
  function swap(
    address recipient,
    bool zeroToOne,
    int256 amountSpecified,
    uint160 limitSqrtPrice,
    bytes calldata data
  ) external returns (int256 amount0, int256 amount1);

  /**
   * @notice Swap token0 for token1, or token1 for token0 (tokens that have fee on transfer)
   * @dev The caller of this method receives a callback in the form of I AlgebraSwapCallback# AlgebraSwapCallback
   * @param sender The address called this function (Comes from the Router)
   * @param recipient The address to receive the output of the swap
   * @param zeroToOne The direction of the swap, true for token0 to token1, false for token1 to token0
   * @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
   * @param limitSqrtPrice The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
   * value after the swap. If one for zero, the price cannot be greater than this value after the swap
   * @param data Any data to be passed through to the callback. If using the Router it should contain
   * SwapRouter#SwapCallbackData
   * @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
   * @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
   */
  function swapSupportingFeeOnInputTokens(
    address sender,
    address recipient,
    bool zeroToOne,
    int256 amountSpecified,
    uint160 limitSqrtPrice,
    bytes calldata data
  ) external returns (int256 amount0, int256 amount1);

  /**
   * @notice Receive token0 and/or token1 and pay it back, plus a fee, in the callback
   * @dev The caller of this method receives a callback in the form of IAlgebraFlashCallback# AlgebraFlashCallback
   * @dev All excess tokens paid in the callback are distributed to liquidity providers as an additional fee. So this method can be used
   * to donate underlying tokens to currently in-range liquidity providers by calling with 0 amount{0,1} and sending
   * the donation amount(s) from the callback
   * @param recipient The address which will receive the token0 and token1 amounts
   * @param amount0 The amount of token0 to send
   * @param amount1 The amount of token1 to send
   * @param data Any data to be passed through to the callback
   */
  function flash(
    address recipient,
    uint256 amount0,
    uint256 amount1,
    bytes calldata data
  ) external;
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolPermissionedActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/**
 * @title Permissioned pool actions
 * @notice Contains pool methods that may only be called by the factory owner or tokenomics
 * @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
 * https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
 */
interface IAlgebraPoolPermissionedActions {
  /**
   * @notice Set the community's % share of the fees. Cannot exceed 25% (250)
   * @param communityFee0 new community fee percent for token0 of the pool in thousandths (1e-3)
   * @param communityFee1 new community fee percent for token1 of the pool in thousandths (1e-3)
   */
  function setCommunityFee(uint8 communityFee0, uint8 communityFee1) external;

  /**
   * @notice Sets an active incentive
   * @param virtualPoolAddress The address of a virtual pool associated with the incentive
   */
  function setIncentive(address virtualPoolAddress) external;

  /**
   * @notice Sets new lock time for added liquidity
   * @param newLiquidityCooldown The time in seconds
   */
  function setLiquidityCooldown(uint32 newLiquidityCooldown) external;
}

// File: contracts/algebra/interfaces/pool/IAlgebraPoolEvents.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Events emitted by a pool
/// @dev Credit to Uniswap Labs under GPL-2.0-or-later license:
/// https://github.com/Uniswap/v3-core/tree/main/contracts/interfaces
interface IAlgebraPoolEvents {
  /**
   * @notice Emitted exactly once by a pool when #initialize is first called on the pool
   * @dev Mint/Burn/Swap cannot be emitted by the pool before Initialize
   * @param price The initial sqrt price of the pool, as a Q64.96
   * @param tick The initial tick of the pool, i.e. log base 1.0001 of the starting price of the pool
   */
  event Initialize(uint160 price, int24 tick);

  /**
   * @notice Emitted when liquidity is minted for a given position
   * @param sender The address that minted the liquidity
   * @param owner The owner of the position and recipient of any minted liquidity
   * @param bottomTick The lower tick of the position
   * @param topTick The upper tick of the position
   * @param liquidityAmount The amount of liquidity minted to the position range
   * @param amount0 How much token0 was required for the minted liquidity
   * @param amount1 How much token1 was required for the minted liquidity
   */
  event Mint(
    address sender,
    address indexed owner,
    int24 indexed bottomTick,
    int24 indexed topTick,
    uint128 liquidityAmount,
    uint256 amount0,
    uint256 amount1
  );

  /**
   * @notice Emitted when fees are collected by the owner of a position
   * @dev Collect events may be emitted with zero amount0 and amount1 when the caller chooses not to collect fees
   * @param owner The owner of the position for which fees are collected
   * @param recipient The address that received fees
   * @param bottomTick The lower tick of the position
   * @param topTick The upper tick of the position
   * @param amount0 The amount of token0 fees collected
   * @param amount1 The amount of token1 fees collected
   */
  event Collect(address indexed owner, address recipient, int24 indexed bottomTick, int24 indexed topTick, uint128 amount0, uint128 amount1);

  /**
   * @notice Emitted when a position's liquidity is removed
   * @dev Does not withdraw any fees earned by the liquidity position, which must be withdrawn via #collect
   * @param owner The owner of the position for which liquidity is removed
   * @param bottomTick The lower tick of the position
   * @param topTick The upper tick of the position
   * @param liquidityAmount The amount of liquidity to remove
   * @param amount0 The amount of token0 withdrawn
   * @param amount1 The amount of token1 withdrawn
   */
  event Burn(address indexed owner, int24 indexed bottomTick, int24 indexed topTick, uint128 liquidityAmount, uint256 amount0, uint256 amount1);

  /**
   * @notice Emitted by the pool for any swaps between token0 and token1
   * @param sender The address that initiated the swap call, and that received the callback
   * @param recipient The address that received the output of the swap
   * @param amount0 The delta of the token0 balance of the pool
   * @param amount1 The delta of the token1 balance of the pool
   * @param price The sqrt(price) of the pool after the swap, as a Q64.96
   * @param liquidity The liquidity of the pool after the swap
   * @param tick The log base 1.0001 of price of the pool after the swap
   */
  event Swap(address indexed sender, address indexed recipient, int256 amount0, int256 amount1, uint160 price, uint128 liquidity, int24 tick);

  /**
   * @notice Emitted by the pool for any flashes of token0/token1
   * @param sender The address that initiated the swap call, and that received the callback
   * @param recipient The address that received the tokens from flash
   * @param amount0 The amount of token0 that was flashed
   * @param amount1 The amount of token1 that was flashed
   * @param paid0 The amount of token0 paid for the flash, which can exceed the amount0 plus the fee
   * @param paid1 The amount of token1 paid for the flash, which can exceed the amount1 plus the fee
   */
  event Flash(address indexed sender, address indexed recipient, uint256 amount0, uint256 amount1, uint256 paid0, uint256 paid1);

  /**
   * @notice Emitted when the community fee is changed by the pool
   * @param communityFee0New The updated value of the token0 community fee percent
   * @param communityFee1New The updated value of the token1 community fee percent
   */
  event CommunityFee(uint8 communityFee0New, uint8 communityFee1New);

  /**
   * @notice Emitted when new activeIncentive is set
   * @param virtualPoolAddress The address of a virtual pool associated with the current active incentive
   */
  event Incentive(address indexed virtualPoolAddress);

  /**
   * @notice Emitted when the fee changes
   * @param fee The value of the token fee
   */
  event Fee(uint16 fee);

  /**
   * @notice Emitted when the LiquidityCooldown changes
   * @param liquidityCooldown The value of locktime for added liquidity
   */
  event LiquidityCooldown(uint32 liquidityCooldown);
}

// File: contracts/algebra/interfaces/IDataStorageOperator.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;
pragma abicoder v2;

import '../libraries/AdaptiveFee.sol';

interface IDataStorageOperator {
  event FeeConfiguration(AdaptiveFee.Configuration feeConfig);

  /**
   * @notice Returns data belonging to a certain timepoint
   * @param index The index of timepoint in the array
   * @dev There is more convenient function to fetch a timepoint: observe(). Which requires not an index but seconds
   * @return initialized Whether the timepoint has been initialized and the values are safe to use,
   * blockTimestamp The timestamp of the observation,
   * tickCumulative The tick multiplied by seconds elapsed for the life of the pool as of the timepoint timestamp,
   * secondsPerLiquidityCumulative The seconds per in range liquidity for the life of the pool as of the timepoint timestamp,
   * volatilityCumulative Cumulative standard deviation for the life of the pool as of the timepoint timestamp,
   * averageTick Time-weighted average tick,
   * volumePerLiquidityCumulative Cumulative swap volume per liquidity for the life of the pool as of the timepoint timestamp
   */
  function timepoints(uint256 index)
    external
    view
    returns (
      bool initialized,
      uint32 blockTimestamp,
      int56 tickCumulative,
      uint160 secondsPerLiquidityCumulative,
      uint88 volatilityCumulative,
      int24 averageTick,
      uint144 volumePerLiquidityCumulative
    );

  /// @notice Initialize the dataStorage array by writing the first slot. Called once for the lifecycle of the timepoints array
  /// @param time The time of the dataStorage initialization, via block.timestamp truncated to uint32
  /// @param tick Initial tick
  function initialize(uint32 time, int24 tick) external;

  /// @dev Reverts if an timepoint at or before the desired timepoint timestamp does not exist.
  /// 0 may be passed as `secondsAgo' to return the current cumulative values.
  /// If called with a timestamp falling between two timepoints, returns the counterfactual accumulator values
  /// at exactly the timestamp between the two timepoints.
  /// @param time The current block timestamp
  /// @param secondsAgo The amount of time to look back, in seconds, at which point to return an timepoint
  /// @param tick The current tick
  /// @param index The index of the timepoint that was most recently written to the timepoints array
  /// @param liquidity The current in-range pool liquidity
  /// @return tickCumulative The cumulative tick since the pool was first initialized, as of `secondsAgo`
  /// @return secondsPerLiquidityCumulative The cumulative seconds / max(1, liquidity) since the pool was first initialized, as of `secondsAgo`
  /// @return volatilityCumulative The cumulative volatility value since the pool was first initialized, as of `secondsAgo`
  /// @return volumePerAvgLiquidity The cumulative volume per liquidity value since the pool was first initialized, as of `secondsAgo`
  function getSingleTimepoint(
    uint32 time,
    uint32 secondsAgo,
    int24 tick,
    uint16 index,
    uint128 liquidity
  )
    external
    view
    returns (
      int56 tickCumulative,
      uint160 secondsPerLiquidityCumulative,
      uint112 volatilityCumulative,
      uint256 volumePerAvgLiquidity
    );

  /// @notice Returns the accumulator values as of each time seconds ago from the given time in the array of `secondsAgos`
  /// @dev Reverts if `secondsAgos` > oldest timepoint
  /// @param time The current block.timestamp
  /// @param secondsAgos Each amount of time to look back, in seconds, at which point to return an timepoint
  /// @param tick The current tick
  /// @param index The index of the timepoint that was most recently written to the timepoints array
  /// @param liquidity The current in-range pool liquidity
  /// @return tickCumulatives The cumulative tick since the pool was first initialized, as of each `secondsAgo`
  /// @return secondsPerLiquidityCumulatives The cumulative seconds / max(1, liquidity) since the pool was first initialized, as of each `secondsAgo`
  /// @return volatilityCumulatives The cumulative volatility values since the pool was first initialized, as of each `secondsAgo`
  /// @return volumePerAvgLiquiditys The cumulative volume per liquidity values since the pool was first initialized, as of each `secondsAgo`
  function getTimepoints(
    uint32 time,
    uint32[] memory secondsAgos,
    int24 tick,
    uint16 index,
    uint128 liquidity
  )
    external
    view
    returns (
      int56[] memory tickCumulatives,
      uint160[] memory secondsPerLiquidityCumulatives,
      uint112[] memory volatilityCumulatives,
      uint256[] memory volumePerAvgLiquiditys
    );

  /// @notice Returns average volatility in the range from time-WINDOW to time
  /// @param time The current block.timestamp
  /// @param tick The current tick
  /// @param index The index of the timepoint that was most recently written to the timepoints array
  /// @param liquidity The current in-range pool liquidity
  /// @return TWVolatilityAverage The average volatility in the recent range
  /// @return TWVolumePerLiqAverage The average volume per liquidity in the recent range
  function getAverages(
    uint32 time,
    int24 tick,
    uint16 index,
    uint128 liquidity
  ) external view returns (uint112 TWVolatilityAverage, uint256 TWVolumePerLiqAverage);

  /// @notice Writes an dataStorage timepoint to the array
  /// @dev Writable at most once per block. Index represents the most recently written element. index must be tracked externally.
  /// @param index The index of the timepoint that was most recently written to the timepoints array
  /// @param blockTimestamp The timestamp of the new timepoint
  /// @param tick The active tick at the time of the new timepoint
  /// @param liquidity The total in-range liquidity at the time of the new timepoint
  /// @param volumePerLiquidity The gmean(volumes)/liquidity at the time of the new timepoint
  /// @return indexUpdated The new index of the most recently written element in the dataStorage array
  function write(
    uint16 index,
    uint32 blockTimestamp,
    int24 tick,
    uint128 liquidity,
    uint128 volumePerLiquidity
  ) external returns (uint16 indexUpdated);

  /// @notice Changes fee configuration for the pool
  function changeFeeConfiguration(AdaptiveFee.Configuration calldata feeConfig) external;

  /// @notice Calculates gmean(volume/liquidity) for block
  /// @param liquidity The current in-range pool liquidity
  /// @param amount0 Total amount of swapped token0
  /// @param amount1 Total amount of swapped token1
  /// @return volumePerLiquidity gmean(volume/liquidity) capped by 100000 << 64
  function calculateVolumePerLiquidity(
    uint128 liquidity,
    int256 amount0,
    int256 amount1
  ) external pure returns (uint128 volumePerLiquidity);

  /// @return windowLength Length of window used to calculate averages
  function window() external view returns (uint32 windowLength);

  /// @notice Calculates fee based on combination of sigmoids
  /// @param time The current block.timestamp
  /// @param tick The current tick
  /// @param index The index of the timepoint that was most recently written to the timepoints array
  /// @param liquidity The current in-range pool liquidity
  /// @return fee The fee in hundredths of a bip, i.e. 1e-6
  function getFee(
    uint32 time,
    int24 tick,
    uint16 index,
    uint128 liquidity
  ) external view returns (uint16 fee);
}

// File: contracts/algebra/libraries/AdaptiveFee.sol



// SPDX-License-Identifier: BUSL-1.1
pragma solidity =0.7.6;

import './Constants.sol';

/// @title AdaptiveFee
/// @notice Calculates fee based on combination of sigmoids
library AdaptiveFee {
  // alpha1 + alpha2 + baseFee must be <= type(uint16).max
  struct Configuration {
    uint16 alpha1; // max value of the first sigmoid
    uint16 alpha2; // max value of the second sigmoid
    uint32 beta1; // shift along the x-axis for the first sigmoid
    uint32 beta2; // shift along the x-axis for the second sigmoid
    uint16 gamma1; // horizontal stretch factor for the first sigmoid
    uint16 gamma2; // horizontal stretch factor for the second sigmoid
    uint32 volumeBeta; // shift along the x-axis for the outer volume-sigmoid
    uint16 volumeGamma; // horizontal stretch factor the outer volume-sigmoid
    uint16 baseFee; // minimum possible fee
  }

  /// @notice Calculates fee based on formula:
  /// baseFee + sigmoidVolume(sigmoid1(volatility, volumePerLiquidity) + sigmoid2(volatility, volumePerLiquidity))
  /// maximum value capped by baseFee + alpha1 + alpha2
  function getFee(
    uint88 volatility,
    uint256 volumePerLiquidity,
    Configuration memory config
  ) internal pure returns (uint16 fee) {
    uint256 sumOfSigmoids = sigmoid(volatility, config.gamma1, config.alpha1, config.beta1) +
      sigmoid(volatility, config.gamma2, config.alpha2, config.beta2);

    if (sumOfSigmoids > type(uint16).max) {
      // should be impossible, just in case
      sumOfSigmoids = type(uint16).max;
    }

    return uint16(config.baseFee + sigmoid(volumePerLiquidity, config.volumeGamma, uint16(sumOfSigmoids), config.volumeBeta)); // safe since alpha1 + alpha2 + baseFee _must_ be <= type(uint16).max
  }

  /// @notice calculates α / (1 + e^( (β-x) / γ))
  /// that is a sigmoid with a maximum value of α, x-shifted by β, and stretched by γ
  /// @dev returns uint256 for fuzzy testing. Guaranteed that the result is not greater than alpha
  function sigmoid(
    uint256 x,
    uint16 g,
    uint16 alpha,
    uint256 beta
  ) internal pure returns (uint256 res) {
    if (x > beta) {
      x = x - beta;
      if (x >= 6 * uint256(g)) return alpha; // so x < 19 bits
      uint256 g8 = uint256(g)**8; // < 128 bits (8*16)
      uint256 ex = exp(x, g, g8); // < 155 bits
      res = (alpha * ex) / (g8 + ex); // in worst case: (16 + 155 bits) / 155 bits
      // so res <= alpha
    } else {
      x = beta - x;
      if (x >= 6 * uint256(g)) return 0; // so x < 19 bits
      uint256 g8 = uint256(g)**8; // < 128 bits (8*16)
      uint256 ex = g8 + exp(x, g, g8); // < 156 bits
      res = (alpha * g8) / ex; // in worst case: (16 + 128 bits) / 156 bits
      // g8 <= ex, so res <= alpha
    }
  }

  /// @notice calculates e^(x/g) * g^8 in a series, since (around zero):
  /// e^x = 1 + x + x^2/2 + ... + x^n/n! + ...
  /// e^(x/g) = 1 + x/g + x^2/(2*g^2) + ... + x^(n)/(g^n * n!) + ...
  function exp(
    uint256 x,
    uint16 g,
    uint256 gHighestDegree
  ) internal pure returns (uint256 res) {
    // calculating:
    // g**8 + x * g**7 + (x**2 * g**6) / 2 + (x**3 * g**5) / 6 + (x**4 * g**4) / 24 + (x**5 * g**3) / 120 + (x**6 * g^2) / 720 + x**7 * g / 5040 + x**8 / 40320

    // x**8 < 152 bits (19*8) and g**8 < 128 bits (8*16)
    // so each summand < 152 bits and res < 155 bits
    uint256 xLowestDegree = x;
    res = gHighestDegree; // g**8

    gHighestDegree /= g; // g**7
    res += xLowestDegree * gHighestDegree;

    gHighestDegree /= g; // g**6
    xLowestDegree *= x; // x**2
    res += (xLowestDegree * gHighestDegree) / 2;

    gHighestDegree /= g; // g**5
    xLowestDegree *= x; // x**3
    res += (xLowestDegree * gHighestDegree) / 6;

    gHighestDegree /= g; // g**4
    xLowestDegree *= x; // x**4
    res += (xLowestDegree * gHighestDegree) / 24;

    gHighestDegree /= g; // g**3
    xLowestDegree *= x; // x**5
    res += (xLowestDegree * gHighestDegree) / 120;

    gHighestDegree /= g; // g**2
    xLowestDegree *= x; // x**6
    res += (xLowestDegree * gHighestDegree) / 720;

    xLowestDegree *= x; // x**7
    res += (xLowestDegree * g) / 5040 + (xLowestDegree * x) / (40320);
  }
}

// File: contracts/algebra/libraries/Constants.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

library Constants {
  uint8 internal constant RESOLUTION = 96;
  uint256 internal constant Q96 = 0x1000000000000000000000000;
  uint256 internal constant Q128 = 0x100000000000000000000000000000000;
  // fee value in hundredths of a bip, i.e. 1e-6
  uint16 internal constant BASE_FEE = 100;
  int24 internal constant TICK_SPACING = 60;

  // max(uint128) / ( (MAX_TICK - MIN_TICK) / TICK_SPACING )
  uint128 internal constant MAX_LIQUIDITY_PER_TICK = 11505743598341114571880798222544994;

  uint32 internal constant MAX_LIQUIDITY_COOLDOWN = 1 days;
  uint8 internal constant MAX_COMMUNITY_FEE = 250;
  uint256 internal constant COMMUNITY_FEE_DENOMINATOR = 1000;
}

// File: @uniswap/v3-core/contracts/libraries/FixedPoint96.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.4.0;

/// @title FixedPoint96
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
/// @dev Used in SqrtPriceMath.sol
library FixedPoint96 {
    uint8 internal constant RESOLUTION = 96;
    uint256 internal constant Q96 = 0x1000000000000000000000000;
}