pragma solidity 0.6.7;



/// @title Pool state that never changes

/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values

interface IUniswapV3PoolImmutables {

    /// @notice The contract that deployed the pool, which must adhere to the IUniswapV3Factory 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's fee in hundredths of a bip, i.e. 1e-6

    /// @return The fee

    function fee() external view returns (uint24);



    /// @notice The pool tick spacing

    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive

    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...

    /// 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);

}



/// @title Pool state that can change

/// @notice These methods compose the pool's state, and can change with any frequency including multiple times

/// per transaction

interface IUniswapV3PoolState {

    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas

    /// when accessed externally.

    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value

    /// tick The current tick of the pool, i.e. according to the last tick transition that was run.

    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick

    /// boundary.

    /// observationIndex The index of the last oracle observation that was written,

    /// observationCardinality The current maximum number of observations stored in the pool,

    /// observationCardinalityNext The next maximum number of observations, to be updated when the observation.

    /// feeProtocol The protocol fee for both tokens of the pool.

    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0

    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.

    /// unlocked Whether the pool is currently locked to reentrancy

    function slot0()

        external

        view

        returns (

            uint160 sqrtPriceX96,

            int24 tick,

            uint16 observationIndex,

            uint16 observationCardinality,

            uint16 observationCardinalityNext,

            uint8 feeProtocol,

            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 feeGrowthGlobal0X128() 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 feeGrowthGlobal1X128() external view returns (uint256);



    /// @notice The amounts of token0 and token1 that are owed to the protocol

    /// @dev Protocol fees will never exceed uint128 max in either token

    function protocolFees() external view returns (uint128 token0, uint128 token1);



    /// @notice The currently in range liquidity available to the pool

    /// @dev This value has no relationship to the total liquidity across all ticks

    function liquidity() external view returns (uint128);



    /// @notice Look up information about a specific tick in the pool

    /// @param tick The tick to look up

    /// @return liquidityGross the total amount of position liquidity that uses the pool either as tick lower or

    /// tick upper,

    /// liquidityNet how much liquidity changes when the pool price crosses the tick,

    /// feeGrowthOutside0X128 the fee growth on the other side of the tick from the current tick in token0,

    /// feeGrowthOutside1X128 the fee growth on the other side of the tick from the current tick in token1,

    /// feeGrowthOutsideX128 values can only be used if the tick is initialized,

    /// i.e. if liquidityGross is greater than 0. In addition, these values are only relative and are used to

    /// compute snapshots.

    function ticks(int24 tick)

        external

        view

        returns (

            uint128 liquidityGross,

            int128 liquidityNet,

            uint256 feeGrowthOutside0X128,

            uint256 feeGrowthOutside1X128

        );



    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information

    function tickBitmap(int16 wordPosition) external view returns (uint256);



    /// @notice Returns 8 packed tick seconds outside values. See SecondsOutside for more information

    function secondsOutside(int24 wordPosition) external view returns (uint256);



    /// @notice Returns the information about a position by the position's key

    /// @param key The position's key is a hash of a preimage composed by the owner, tickLower and tickUpper

    /// @return _liquidity The amount of liquidity in the position,

    /// Returns feeGrowthInside0LastX128 fee growth of token0 inside the tick range as of the last mint/burn/poke,

    /// Returns feeGrowthInside1LastX128 fee growth of token1 inside the tick range as of the last mint/burn/poke,

    /// Returns tokensOwed0 the computed amount of token0 owed to the position as of the last mint/burn/poke,

    /// Returns tokensOwed1 the computed amount of token1 owed to the position as of the last mint/burn/poke

    function positions(bytes32 key)

        external

        view

        returns (

            uint128 _liquidity,

            uint256 feeGrowthInside0LastX128,

            uint256 feeGrowthInside1LastX128,

            uint128 tokensOwed0,

            uint128 tokensOwed1

        );



    /// @notice Returns data about a specific observation index

    /// @param index The element of the observations array to fetch

    /// @dev You most likely want to use #observe() instead of this method to get an observation as of some amount of time

    /// ago, rather than at a specific index in the array.

    /// @return blockTimestamp The timestamp of the observation,

    /// Returns tickCumulative the current tick multiplied by seconds elapsed for the life of the pool as of the

    /// observation,

    /// Returns liquidityCumulative the current liquidity multiplied by seconds elapsed for the life of the pool as of

    /// the observation,

    /// Returns initialized whether the observation has been initialized and the values are safe to use

    function observations(uint256 index)

        external

        view

        returns (

            uint32 blockTimestamp,

            int56 tickCumulative,

            uint160 liquidityCumulative,

            bool initialized

        );

}



/// @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.

interface IUniswapV3PoolDerivedState {

    /// @notice Returns a relative timestamp value representing how long, in seconds, the pool has spent between

    /// tickLower and tickUpper

    /// @dev This timestamp is strictly relative. To get a useful elapsed time (i.e., duration) value, the value returned

    /// by this method should be checkpointed externally after a position is minted, and again before a position is

    /// burned. Thus the external contract must control the lifecycle of the position.

    /// @param tickLower The lower tick of the range for which to get the seconds inside

    /// @param tickUpper The upper tick of the range for which to get the seconds inside

    /// @return A relative timestamp for how long the pool spent in the tick range

    function secondsInside(int24 tickLower, int24 tickUpper) external view returns (uint32);



    /// @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 liquidityCumulatives Cumulative liquidity-in-range value as of each `secondsAgos` from the current block

    /// timestamp

    function observe(uint32[] calldata secondsAgos)

        external

        view

        returns (int56[] memory tickCumulatives, uint160[] memory liquidityCumulatives);

}



/// @title Permissionless pool actions

/// @notice Contains pool methods that can be called by anyone

interface IUniswapV3PoolActions {

  /// @notice Sets the initial price for the pool

  /// @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value

  /// @param sqrtPriceX96 the initial sqrt price of the pool as a Q64.96

  function initialize(uint160 sqrtPriceX96) external;



  /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position

  /// @dev The caller of this method receives a callback in the form of IUniswapV3MintCallback#uniswapV3MintCallback

  /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends

  /// on tickLower, tickUpper, the amount of liquidity, and the current price.

  /// @param recipient The address for which the liquidity will be created

  /// @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 amount The 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

  function mint(

    address recipient,

    int24 tickLower,

    int24 tickUpper,

    uint128 amount,

    bytes calldata data

  ) external returns (uint256 amount0, uint256 amount1);



  /// @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. (0 - uint128(1)). Tokens owed may be from accumulated swap fees or burned liquidity.

  /// @param recipient The address which should receive the fees collected

  /// @param tickLower The lower tick of the position for which to collect fees

  /// @param tickUpper 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 tickLower,

    int24 tickUpper,

    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 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 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 tickLower,

    int24 tickUpper,

    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 IUniswapV3SwapCallback#uniswapV3SwapCallback

  /// @param recipient The address to receive the output of the swap

  /// @param zeroForOne 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 sqrtPriceLimitX96 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

  /// @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 zeroForOne,

    int256 amountSpecified,

    uint160 sqrtPriceLimitX96,

    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 IUniswapV3FlashCallback#uniswapV3FlashCallback

  /// @dev Can be used to donate underlying tokens pro-rata 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;



  /// @notice Increase the maximum number of price and liquidity observations that this pool will store

  /// @dev This method is no-op if the pool already has an observationCardinalityNext greater than or equal to

  /// the input observationCardinalityNext.

  /// @param observationCardinalityNext The desired minimum number of observations for the pool to store

  function increaseObservationCardinalityNext(uint16 observationCardinalityNext) external;

}



/// @title Permissioned pool actions

/// @notice Contains pool methods that may only be called by the factory owner

interface IUniswapV3PoolOwnerActions {

    /// @notice Set the denominator of the protocol's % share of the fees

    /// @param feeProtocol0 new protocol fee for token0 of the pool

    /// @param feeProtocol1 new protocol fee for token1 of the pool

    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external;



    /// @notice Collect the protocol fee accrued to the pool

    /// @param recipient The address to which collected protocol fees should be sent

    /// @param amount0Requested The maximum amount of token0 to send, can be 0 to collect fees in only token1

    /// @param amount1Requested The maximum amount of token1 to send, can be 0 to collect fees in only token0

    /// @return amount0 The protocol fee collected in token0

    /// @return amount1 The protocol fee collected in token1

    function collectProtocol(

        address recipient,

        uint128 amount0Requested,

        uint128 amount1Requested

    ) external returns (uint128 amount0, uint128 amount1);

}



/// @title Events emitted by a pool

/// @notice Contains all events emitted by the pool

interface IUniswapV3PoolEvents {

    /// @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 sqrtPriceX96 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 sqrtPriceX96, 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 tickLower The lower tick of the position

    /// @param tickUpper The upper tick of the position

    /// @param amount 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 tickLower,

        int24 indexed tickUpper,

        uint128 amount,

        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 tickLower The lower tick of the position

    /// @param tickUpper 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 tickLower,

        int24 indexed tickUpper,

        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 tickLower The lower tick of the position

    /// @param tickUpper The upper tick of the position

    /// @param amount 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 tickLower,

        int24 indexed tickUpper,

        uint128 amount,

        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 sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96

    /// @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 sqrtPriceX96,

        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 by the pool for increases to the number of observations that can be stored

    /// @dev observationCardinalityNext is not the observation cardinality until an observation is written at the index

    /// just before a mint/swap/burn.

    /// @param observationCardinalityNextOld The previous value of the next observation cardinality

    /// @param observationCardinalityNextNew The updated value of the next observation cardinality

    event IncreaseObservationCardinalityNext(

        uint16 observationCardinalityNextOld,

        uint16 observationCardinalityNextNew

    );



    /// @notice Emitted when the protocol fee is changed by the pool

    /// @param feeProtocol0Old The previous value of the token0 protocol fee

    /// @param feeProtocol1Old The previous value of the token1 protocol fee

    /// @param feeProtocol0New The updated value of the token0 protocol fee

    /// @param feeProtocol1New The updated value of the token1 protocol fee

    event SetFeeProtocol(uint8 feeProtocol0Old, uint8 feeProtocol1Old, uint8 feeProtocol0New, uint8 feeProtocol1New);



    /// @notice Emitted when the collected protocol fees are withdrawn by the factory owner

    /// @param sender The address that collects the protocol fees

    /// @param recipient The address that receives the collected protocol fees

    /// @param amount0 The amount of token0 protocol fees that is withdrawn

    /// @param amount0 The amount of token1 protocol fees that is withdrawn

    event CollectProtocol(address indexed sender, address indexed recipient, uint128 amount0, uint128 amount1);

}



/// @title The interface for a Uniswap V3 Pool

/// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform

/// to the ERC20 specification

/// @dev The pool interface is broken up into many smaller pieces

interface IUniswapV3Pool is

    IUniswapV3PoolImmutables,

    IUniswapV3PoolState,

    IUniswapV3PoolDerivedState,

    IUniswapV3PoolActions,

    IUniswapV3PoolOwnerActions,

    IUniswapV3PoolEvents

{



}



/// @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 < (0 - uint256(1)));

      result++;

    }

  }

}



/// @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

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 sqrtPriceX96 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 sqrtPriceX96) {

    uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));

    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 = (0 - uint256(1)) / 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

    sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));

  }



  /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio

  /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may

  /// ever return.

  /// @param sqrtPriceX96 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 sqrtPriceX96) internal pure returns (int24 tick) {

    // second inequality must be < because the price can never reach the price at the max tick

    require(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO, "R");

    uint256 ratio = uint256(sqrtPriceX96) << 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) <= sqrtPriceX96 ? tickHi : tickLow;

  }

}



/// @title Optimized overflow and underflow safe math operations

/// @notice Contains methods for doing math operations that revert on overflow or underflow for minimal gas cost

library LowGasSafeMath {

  /// @notice Returns x + y, reverts if sum overflows uint256

  /// @param x The augend

  /// @param y The addend

  /// @return z The sum of x and y

  function add(uint256 x, uint256 y) internal pure returns (uint256 z) {

    require((z = x + y) >= x);

  }



  /// @notice Returns x - y, reverts if underflows

  /// @param x The minuend

  /// @param y The subtrahend

  /// @return z The difference of x and y

  function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {

    require((z = x - y) <= x);

  }



  /// @notice Returns x * y, reverts if overflows

  /// @param x The multiplicand

  /// @param y The multiplier

  /// @return z The product of x and y

  function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {

    require(x == 0 || (z = x * y) / x == y);

  }



  /// @notice Returns x + y, reverts if overflows or underflows

  /// @param x The augend

  /// @param y The addend

  /// @return z The sum of x and y

  function add(int256 x, int256 y) internal pure returns (int256 z) {

    require((z = x + y) >= x == (y >= 0));

  }



  /// @notice Returns x - y, reverts if overflows or underflows

  /// @param x The minuend

  /// @param y The subtrahend

  /// @return z The difference of x and y

  function sub(int256 x, int256 y) internal pure returns (int256 z) {

    require((z = x - y) <= x == (y >= 0));

  }

}



/// @title Provides functions for deriving a pool address from the factory, tokens, and the fee

library PoolAddress {

    bytes32 internal constant POOL_INIT_CODE_HASH = 0xe34f199b19b2b4f47f68442619d555527d244f78a3297ea89325f843f87b8b54;



    /// @notice The identifying key of the pool

    struct PoolKey {

        address token0;

        address token1;

        uint24 fee;

    }



    /// @notice Returns PoolKey: the ordered tokens with the matched fee levels

    /// @param tokenA The first token of a pool, unsorted

    /// @param tokenB The second token of a pool, unsorted

    /// @param fee The fee level of the pool

    /// @return Poolkey The pool details with ordered token0 and token1 assignments

    function getPoolKey(

        address tokenA,

        address tokenB,

        uint24 fee

    ) internal pure returns (PoolKey memory) {

        if (tokenA > tokenB) (tokenA, tokenB) = (tokenB, tokenA);

        return PoolKey({token0: tokenA, token1: tokenB, fee: fee});

    }



    /// @notice Deterministically computes the pool address given the factory and PoolKey

    /// @param factory The Uniswap V3 factory contract address

    /// @param key The PoolKey

    /// @return pool The contract address of the V3 pool

    function computeAddress(address factory, PoolKey memory key) internal pure returns (address pool) {

        require(key.token0 < key.token1);

        pool = address(

            uint256(

                keccak256(

                    abi.encodePacked(

                        hex'ff',

                        factory,

                        keccak256(abi.encode(key.token0, key.token1, key.fee)),

                        POOL_INIT_CODE_HASH

                    )

                )

            )

        );

    }

}



/// @title Oracle library

/// @notice Provides functions to integrate with V3 pool oracle

library OracleLibrary {

    /// @notice Fetches time-weighted average tick using Uniswap V3 oracle

    /// @param pool Address of Uniswap V3 pool that we want to observe

    /// @param period Number of seconds in the past to start calculating time-weighted average

    /// @return timeWeightedAverageTick The time-weighted average tick from (block.timestamp - period) to block.timestamp

    function consult(address pool, uint32 period) internal view returns (int24 timeWeightedAverageTick) {

        require(period != 0, 'BP');



        uint32[] memory secondAgos = new uint32[](2);

        secondAgos[0] = period;

        secondAgos[1] = 0;



        (int56[] memory tickCumulatives, ) = IUniswapV3Pool(pool).observe(secondAgos);

        int56 tickCumulativesDelta = tickCumulatives[1] - tickCumulatives[0];



        timeWeightedAverageTick = int24(tickCumulativesDelta / period);



        // Always round to negative infinity

        if (tickCumulativesDelta < 0 && (tickCumulativesDelta % period != 0)) timeWeightedAverageTick--;

    }



    /// @notice Given a tick and a token amount, calculates the amount of token received in exchange

    /// @param tick Tick value used to calculate the quote

    /// @param baseAmount Amount of token to be converted

    /// @param baseToken Address of an ERC20 token contract used as the baseAmount denomination

    /// @param quoteToken Address of an ERC20 token contract used as the quoteAmount denomination

    /// @return quoteAmount Amount of quoteToken received for baseAmount of baseToken

    function getQuoteAtTick(

        int24 tick,

        uint128 baseAmount,

        address baseToken,

        address quoteToken

    ) internal pure returns (uint256 quoteAmount) {

        uint160 sqrtRatioX96 = TickMath.getSqrtRatioAtTick(tick);



        // Calculate quoteAmount with better precision if it doesn't overflow when multiplied by itself

        if (sqrtRatioX96 <= uint128(-1)) {

            uint256 ratioX192 = uint256(sqrtRatioX96) * sqrtRatioX96;

            quoteAmount = baseToken < quoteToken

                ? FullMath.mulDiv(ratioX192, baseAmount, 1 << 192)

                : FullMath.mulDiv(1 << 192, baseAmount, ratioX192);

        } else {

            uint256 ratioX128 = FullMath.mulDiv(sqrtRatioX96, sqrtRatioX96, 1 << 64);

            quoteAmount = baseToken < quoteToken

                ? FullMath.mulDiv(ratioX128, baseAmount, 1 << 128)

                : FullMath.mulDiv(1 << 128, baseAmount, ratioX128);

        }

    }

}



abstract contract TokenLike {

    function balanceOf(address) public view virtual returns (uint256);

}



contract UniswapV3Medianizer {

    // --- Auth ---

    mapping(address => uint) public authorizedAccounts;



    /**

     * @notice Add auth to an account

     * @param account Account to add auth to

     */

    function addAuthorization(address account) external virtual isAuthorized {

        authorizedAccounts[account] = 1;

        emit AddAuthorization(account);

    }



    /**

     * @notice Remove auth from an account

     * @param account Account to remove auth from

     */

    function removeAuthorization(

        address account

    ) external virtual isAuthorized {

        authorizedAccounts[account] = 0;

        emit RemoveAuthorization(account);

    }



    /**

     * @notice Checks whether msg.sender can call an authed function

     **/

    modifier isAuthorized() {

        require(

            authorizedAccounts[msg.sender] == 1,

            "UniswapV3Medianizer/account-not-authorized"

        );

        _;

    }



    // --- Uniswap Vars ---

    // Default amount of targetToken used when calculating the denominationToken output

    uint128 public defaultAmountIn = 1 ether;

    // Minimum liquidity of targetToken to consider a valid result

    uint256 public minimumLiquidity;

    // Token for which the contract calculates the medianPrice for

    address public targetToken;

    // Pair token from the Uniswap pair

    address public denominationToken;

    // The pool to read price data from

    address public uniswapPool;



    // --- General Vars ---

    // The desired amount of time over which the moving average should be computed, e.g. 24 hours

    uint32 public windowSize;

    // Manual flag that can be set by governance and indicates if a result is valid or not

    uint256 public validityFlag;



    // --- Events ---

    event AddAuthorization(address account);

    event RemoveAuthorization(address account);

    event ModifyParameters(bytes32 parameter, address addr);

    event ModifyParameters(bytes32 parameter, uint256 val);



    constructor(

        address uniswapPool_,

        address targetToken_,

        uint32 windowSize_,

        uint256 minimumLiquidity_

    ) public {

        require(

            uniswapPool_ != address(0),

            "UniswapV3Medianizer/null-uniswap-factory"

        );

        require(windowSize_ > 0, "UniswapV3Medianizer/null-window-size");



        authorizedAccounts[msg.sender] = 1;



        uniswapPool = uniswapPool_;

        windowSize = windowSize_;

        minimumLiquidity = minimumLiquidity_;

        validityFlag = 1;

        targetToken = targetToken_;



        address token0 = IUniswapV3Pool(uniswapPool_).token0();

        address token1 = IUniswapV3Pool(uniswapPool_).token1();



        require(

            targetToken_ == token0 || targetToken_ == token1,

            "UniswapV3Medianizer/target-not-from-pool"

        );



        denominationToken = targetToken_ == token0 ? token1 : token0;



        // Emit events

        emit AddAuthorization(msg.sender);

        emit ModifyParameters(bytes32("windowSize"), windowSize_);

    }



    // --- General Utils --

    function either(bool x, bool y) internal pure returns (bool z) {

        assembly {

            z := or(x, y)

        }

    }



    function both(bool x, bool y) private pure returns (bool z) {

        assembly {

            z := and(x, y)

        }

    }



    function toUint128(uint256 value) internal pure returns (uint128) {

        require(value < 2 ** 128, "UniswapV3Medianizer/toUint128_overflow");

        return uint128(value);

    }



    function toUint32(uint256 value) internal pure returns (uint32) {

        require(value < 2 ** 32, "UniswapV3Medianizer/toUint32_overflow");

        return uint32(value);

    }



    // --- Administration ---

    /**

     * @notice Modify uint256 parameters

     * @param parameter Name of the parameter to modify

     * @param data New parameter value

     **/

    function modifyParameters(

        bytes32 parameter,

        uint256 data

    ) external isAuthorized {

        if (parameter == "validityFlag") {

            require(

                either(data == 1, data == 0),

                "UniswapV3Medianizer/invalid-data"

            );

            validityFlag = data;

        } else if (parameter == "defaultAmountIn") {

            require(data > 0, "UniswapV3Medianizer/invalid-default-amount-in");

            defaultAmountIn = toUint128(data);

        } else if (parameter == "windowSize") {

            require(data > 0, "UniswapV3Medianizer/invalid-window-size");

            windowSize = toUint32(data);

        } else if (parameter == "minimumLiquidity") {

            minimumLiquidity = data;

        } else revert("UniswapV3Medianizer/modify-unrecognized-param");

        emit ModifyParameters(parameter, data);

    }



    // --- Getters ---

    /**

     * @notice Returns true if feed is valid

     **/

    function isValid() public view returns (bool) {

        return

            both(

                validityFlag == 1,

                TokenLike(targetToken).balanceOf(address(uniswapPool)) >=

                    minimumLiquidity

            );

    }



    /**

     * @notice Returns medianPrice for windowSize

     **/

    function getTwapPrice() public view returns (uint256) {

        return getTwapPrice(windowSize);

    }



    /**

     * @notice Returns medianPrice for a given period

     * @param period Number of seconds in the past to start calculating time-weighted average

     * @return TWAP

     **/

    function getTwapPrice(uint32 period) public view returns (uint256) {

        int24 timeWeightedAverageTick = consult(

            address(uniswapPool),

            period,

            0

        );

        return

            OracleLibrary.getQuoteAtTick(

                timeWeightedAverageTick,

                defaultAmountIn,

                targetToken,

                denominationToken

            );

    }



    /**

     * @notice Returns medianPrice for a given period

     * @param periodStart Number of seconds in the past to start calculating time-weighted average

     * @param periodEnd Number of seconds in the past to end calculating time-weighted average

     * @return TWAP

     **/

    function getTwapPrice(uint32 periodStart, uint32 periodEnd) public view returns (uint256) {

        int24 timeWeightedAverageTick = consult(

            address(uniswapPool),

            periodStart,

            periodEnd

        );

        return

            OracleLibrary.getQuoteAtTick(

                timeWeightedAverageTick,

                defaultAmountIn,

                targetToken,

                denominationToken

            );

    }    



    /**

     * @notice Fetch the latest medianPrice (for maxWindow) or revert if is is null

     **/

    function read() external view returns (uint256 value) {

        value = getTwapPrice();

        require(

            both(value > 0, isValid()),

            "UniswapV3Medianizer/invalid-price-feed"

        );

    }



    /**

     * @notice Fetch the latest medianPrice and whether it is null or not

     **/

    function getResultWithValidity()

        external

        view

        returns (uint256 value, bool valid)

    {

        value = getTwapPrice();

        valid = both(value > 0, isValid());

    }



    

    /// @notice Fetches time-weighted average tick using Uniswap V3 oracle

    /// @notice Updated from OracleLibrary code to allow for setting an end timestamp to the TWAP

    /// @param pool Address of Uniswap V3 pool that we want to observe

    /// @param periodStartSecondsAgo Number of seconds in the past to start calculating time-weighted average

    /// @param periodEndSecondsAgo Number of seconds in the past to end calculating time-weighted average

    /// @return timeWeightedAverageTick The time-weighted average tick from (block.timestamp - period) to block.timestamp

    function consult(

        address pool,

        uint32 periodStartSecondsAgo,

        uint32 periodEndSecondsAgo

    ) internal view returns (int24 timeWeightedAverageTick) {

        require(periodStartSecondsAgo != 0, "BP");



        uint32 period = periodStartSecondsAgo - periodEndSecondsAgo;



        uint32[] memory secondAgos = new uint32[](2);

        secondAgos[0] = periodStartSecondsAgo;

        secondAgos[1] = periodEndSecondsAgo;



        (int56[] memory tickCumulatives, ) = IUniswapV3Pool(pool).observe(

            secondAgos

        );

        int56 tickCumulativesDelta = tickCumulatives[1] - tickCumulatives[0];



        timeWeightedAverageTick = int24(tickCumulativesDelta / period);



        // Always round to negative infinity

        if (tickCumulativesDelta < 0 && (tickCumulativesDelta % period != 0))

            timeWeightedAverageTick--;

    }

}